FR3122935A1 - METHOD FOR ESTIMATING A METRIC QUANTITY RELATING TO A DIFFERENCE BETWEEN DATA FROM TWO SERIES OF DATA - Google Patents

Abstract

A method (100) for estimating a metric quantity, implemented by computer, from a first and a second series of data, said method (100) comprising: at least one iteration of a estimation phase (102) of the metric quantity according to the steps: drawing (104) of n data with delivery of the first series of data to obtain a first experimental series, and drawing (104) of m data with delivery of the second series of data to obtain a second experimental series,aligning (106) the first experimental series with the second experimental series, or vice versa,term-to-term comparison (108) between the first experimental series and the second experimental series in order to determine a term-to-term gain,weighting (110) of each gain by a weighting factor,calculation (112) of the metric quantity from the weighted gains. Figure for abstract: FIGURE 1

Description

METHOD FOR ESTIMATING A METRIC QUANTITY RELATING TO A DIFFERENCE BETWEEN DATA FROM TWO SERIES OF DATA

The present invention relates to a method for estimating a metric quantity, implemented by computer, from at least two sets of data. The invention also relates to a computer program and a device implementing such a method.

The field of the invention is that of methods for estimating metric magnitude, implemented by computer, from at least two sets of data. The field of the invention is in particular that of methods for estimating metric magnitude in order to study the reproducibility of the estimation of the metric magnitude from several series of data. The field of the invention is also that of data management.

State of the art

Methods are known for estimating metric quantities from at least two series of data.

• de la sélection de la valeur du seuil d’exclusion car ce choix est souvent fait de manière empirique et de manière purement « arbitraire ». Par conséquent l’estimation ne peut être totalement automatisée et peut manquer d’efficacité.
• de reproductibilité car comme ce seuil dépend de la variation d’une série de données, il n’est pas forcément adéquate pour une autre série de données,
• de précision car ces valeurs extrêmes peuvent être sources d’information et aider dans de futures estimations ou prédictions de la variation de la grandeur métrique sur de nouvelles séries de données. Les exclure conduit souvent à une estimation biaisée et ne permet pas de remonter à leur origine.

For example, a method is known for estimating a mathematical central tendency such as the arithmetic mean, or the median or the mode, from a series of measured data comprising large fluctuations. Often, when one seeks to study the reproducibility of this metric quantity, the direct estimation of this metric quantity from the data series is not representative because the extreme values of the data series, often caused by isolated events, are calculated with the same weight as data having a reproducible value, that is to say current or common to several series of data relating to the same object of study. In this case, it is known to carry out a pre-processing of the data in order to exclude the extreme values from the series of data. However, this method is functional but poses various problems, in particular:

• the selection of the value of the exclusion threshold because this choice is often made empirically and in a purely "arbitrary" manner. Therefore the estimate cannot be fully automated and may lack efficiency.
• reproducibility because as this threshold depends on the variation of a series of data, it is not necessarily adequate for another series of data,
• of precision because these extreme values can be sources of information and help in future estimations or predictions of the variation of the metric quantity on new series of data. Excluding them often leads to a biased estimate and does not make it possible to trace their origin.

An object of the present invention is to remedy at least one of the aforementioned drawbacks.

Another object of the invention is to propose a more automated method for estimating a metric quantity.

Another object of the invention is to propose a method for estimating a more efficient metric quantity.

Another object of the invention is to propose a method for estimating a reproducible metric quantity.

Another object of the invention is to propose a method for estimating a more precise metric quantity.

• au moins une itération d’une phase d’estimation de la grandeur métrique suivant les étapes suivantes :
  • tirage de n données avec remise de la première série initiale pour obtenir une première série de données, dite première série expérimentale, et tirage de m données avec remise de la deuxième série initiale pour obtenir une deuxième série de données, dite deuxième série expérimentale,
  • alignement de la première série expérimentale par rapport à la deuxième série expérimentale, ou inversement,
  • comparaison terme à terme entre la première série expérimentale et la deuxième série expérimentale suite à l’étape d’alignement, afin de déterminer un gain terme à terme,
  • pondération de chaque gain en fonction d’un modèle statistique des valeurs de la première série initiale et d’un modèle statistique des valeurs de la deuxième série initiale,
  • calcul de la grandeur métrique à partir des gains pondérés.

The invention makes it possible to achieve at least one of the aforementioned objects by a method for estimating a metric quantity, implemented by computer, from at least two series of data, respectively called first initial series and second series initial, said method comprising:

• at least one iteration of an estimation phase of the metric quantity according to the following steps:
  • drawing of n data with replacement of the first initial series to obtain a first series of data, called first experimental series, and drawing of m data with replacement of the second initial series to obtain a second series of data, called second experimental series,
  • alignment of the first experimental series with respect to the second experimental series, or vice versa,
  • term-to-term comparison between the first experimental series and the second experimental series following the alignment step, in order to determine a term-to-term gain,
  • weighting of each gain according to a statistical model of the values of the first initial series and a statistical model of the values of the second initial series,
  • calculation of the metric quantity from the weighted gains.

Thus, the method according to the invention makes it possible to estimate a metric quantity from at least two series of data.

According to the method according to the invention, no value is chosen or excluded in an arbitrary manner. Consequently, the method is therefore more automatic, efficient, repeatable and precise.

Indeed, as no extreme value is excluded in the initial and/or experimental series, the process is more precise and repeatable to a multitude of data series that can include different extreme values. Also, no threshold needs to be set arbitrarily based on the variation of the data series. The method according to the invention is therefore more automatic and efficient.

As no extreme value is deleted, the method according to the invention makes it possible to study the variation of the extreme values over several series of data, which makes it possible to find their origin. In addition, the estimated metric quantity is not biased by a threshold used. The process is therefore more precise.

The method according to the invention performs an alignment step which allows it to work with initial and/or experimental series of different sizes. The process adapts to different sizes of data sets. Furthermore, by these processing techniques, no value is arbitrarily excluded.

In particular, the draw step improves the accuracy of the estimate but can be computationally expensive. The greater the number of draws, the more accurate the estimate. Consequently, it is defined in practice according to an objective of precision in relation to a processing cost.

Thus, the method according to the invention makes it possible to improve the processing of the data used in an estimation of a metric quantity, said metric quantity being according to the method according to the invention relating to a difference.

The calculation of the metric quantity may include the calculation of the arithmetic mean on the gains obtained following the comparison step. The calculation of the metric quantity may include a multiplication of an arithmetic mean on the gains calculated following the comparison step by the weighting factor.

In a first variant of the method according to the invention, the number of data drawn at the drawing step can be different for each initial series.

The method according to the invention can estimate the metric quantity from a number N of initial series. For example, the method can be carried out from the first initial series and second initial series then then, in another embodiment, from the first initial series or the second initial series with a third initial series, different from the first and second initial series. This can make it possible to compare metric quantities obtained with several initial series, in particular to look at and study performances. When more than two initial series are used, one initial series, the first or the second initial series, can be used as the reference series. In this case, the reference series can be used in several embodiments of the method according to the invention with a new initial series at each embodiment.

By way of non-limiting example, the first initial series may be a reference series, that is to say obtained by a known process and the second initial series a test series, that is to say obtained by a process new whose effectiveness, for example, we do not know. Thus, the method according to the invention can make it possible to compare data resulting from different processes (for example different manufacturing processes) in order to compare these processes from all the data available.

Preferably, the steps of the estimation phase and/or the steps and/or the phases of the method according to the invention can be carried out by a separate or similar calculation module. In particular, each module can be a processing unit.

In this document, “data series” means a set of data of the same nature or having a unit between them.

The data series can be grouped in or in the form of a list, an array, preferably in one dimension, or in several dimensions.

Each data series may preferably be a set of data recorded in 2D form. Thus each datum can carry two pieces of information.

By “data” is meant a known quantity. Each datum preferably comprises or consists of a number or figure in integer or decimal format.

The metric quantity is preferably a number or a figure in integer or decimal format.

The data constituting the first and second initial series can comprise a number in integer or decimal format.

By metric quantity, we mean a measurement or a measurable quantity carrying information of interest.

By "draw with replacement" in a series of data, we mean a random experiment in which the datum drawn in the series of data (here initial) is put back in the series of data at each draw before carrying out a new draw in the same data set. The draw of the data is random.

The comparison step can include a term-to-term difference between the experimental series following the alignment step. This step is easy to implement and inexpensive in computation time.

The method according to the invention can use different types of gain in its estimation method. For example, the comparison step may include a term-to-term difference to provide a term-to-term gain or a term-to-term relative gain.

The term-to-term gain can be calculated using the following formula:
with a(i) and b(i) each being a datum of the first (for example a(i)) or second (for example b(i)) experimental series after the alignment step.

The method according to the invention is therefore simple to implement. Also, according to the method according to the invention, the metric quantity is therefore relative to a difference between the first initial series and the second initial series.

Preferably, the comparison step can include the calculation of a relative gain term by term between the experimental series following the alignment step, determined by the following formula:
with a(i) and b(i) each being a datum of the first (for example a(i)) or second, for example b(i)) experimental series after the alignment step.

Such a calculation makes it possible to better take into account the variation of one of the data series, which makes it possible to improve the precision of the method according to the invention.

Preferably, the quotient in the Math 2 formula can be a function of the reference series, which can be, by way of non-limiting example, the first initial series.

The method according to the invention may comprise a step of determining the size of each initial series, before the estimation phase, the number of data drawn with replacement for each initial series, at the drawing step, being a function of the smaller initial series.

Thus, according to the method according to the invention, the number of draws with discount can be a function of the initial series of smaller size.

The number of data drawn with replacement can be equivalent for each initial series (i.e. n = m), even if the method according to the invention works with initial series of different sizes.

Using the same number of draws for each of the initial series saves calculation time, which allows the method according to the invention to be faster.

In a variant, the number of data drawn with replacement (i.e. n and m) for each initial series can be less than or equal to the size of the initial series of smaller size, preferably equal to the size of the initial series of more small size.

When n and m are identical, then the alignment step can include sorting each experimental series according to the same criterion.

Thus, the alignment step can be simple to implement, thus allowing the method according to the invention to be less expensive in terms of calculation time.

In addition, this makes it possible to process the data before the comparison step in order to compare "similar" data, that is to say of the same order of magnitude, of the experimental series. For example, in this way high data from the first experimental series will only be compared with high data from the second experimental series. This therefore makes it possible to avoid increasing the variance of the data obtained following the comparison step.

The criterion may comprise a ranking in ascending or descending order of each experimental series.

Thus, the method according to the invention can classify each initial series according to the same criterion before the comparison step. Arranging in ascending or descending order can be likened to an alignment method. A realization of the alignment step following these steps produces a good quality alignment for a very low calculation time.

• de déformation temporelle dynamique, issu de l’anglais de Dynamic Time Warping (DTW), ou
• de distance de Levenshtein, issu de l’anglais de Levenshtein distance
• recalage élastique, issu de l’anglais Elastic matching, ou
• d’alignement de séquences, issu de l’anglais Sequence alignment, ou
• algorithme de Wagner–Fischer, issu de l’anglais Wagner–Fischer algorithm, ou
• algorithme de Needleman–Wunsch, issu de l’anglais Needleman–Wunsch algorithm, ou
• distance de Fréchet, issu de l’anglais Fréchet distance.

The alignment step can be implemented by other mathematical methods. For example, the alignment method used by the method according to the invention can be of the type:

• dynamic time warping, derived from Dynamic Time Warping (DTW), or
• of Levenshtein distance, from English of Levenshtein distance
• elastic resetting, from English Elastic matching, or
• sequence alignment, from English Sequence alignment, or
• Wagner–Fischer algorithm, from the English Wagner–Fischer algorithm, or
• Needleman–Wunsch algorithm, from the English Needleman–Wunsch algorithm, or
• Fréchet distance, from the English Fréchet distance.

The number of iterations of the estimation phase can be greater than 100 and less than 20000, preferably equal to 10000.

Thus, the estimation method can include a resolution depending on the number of iterations of the estimation phase. The number of iterations of the estimation phase can be modified, for example by a user (i.e. technician) using the method according to the invention according to a compromise between precision of the estimation and calculation time to carry out the estimation.

The higher the number of iterations, the more precise the estimation of the metric quantity. The number of iterations can be decided according to the needs of the estimation process, i.e. if one wishes a very precise estimation with in return a slightly longer implementation time or vice versa obtaining a rapid estimate of the metric quantity but with lower precision compared to a method according to the invention which carried out a greater number of iterations.

Each statistical model can comprise a parametric model or a Gaussian mixture model, said method possibly comprising, before the weighting step, preferably before the estimation phase, a step of modeling each initial series according to the parametric model or the Gaussian mixture model.

Thus, according to the method according to the invention, a model on the initial series is chosen and said chosen model can then be applied to the experimental series during the weighting step.

The modeling step can include a step for calculating at least one parameter, for example calculating the arithmetic mean and the variance of each initial series, the at least one parameter being able to be used in the modeling step .

The method may further comprise, after the modeling step, a step of optimizing the model of each initial series on the corresponding initial series so as to obtain a probable distribution of each datum of the initial series. Thus, according to the process, it is possible to improve the statistical model after the modeling step before obtaining parameters of each statistical model which best correspond to the data of the initial series.

Preferably, the optimization step can include a regression of the model of each initial series on the experimental series.

According to the method according to the invention, the parametric or statistical mixture model can be a function of the variation of the data of each experimental series.

By way of non-limiting example, the chosen parametric model can be a Gaussian or Laplace model, preferably log-normal.

The parametric model chosen or the model by Gaussian mixture can be similar or different for the two initial series.

• de manière empirique, par exemple en fonction de la variation des données de chaque série expérimentale, ou
• de manière automatique, par exemple à partir d’un modèle prédéfini à l’avance. Dans ce cas, le modèle paramétrique peut être mémorisé dans ledit ordinateur mettant en œuvre le procédé.

The parametric model of each initial series can be chosen:

• empirically, for example according to the variation of the data of each experimental series, or
• automatically, for example from a template predefined in advance. In this case, the parametric model can be stored in said computer implementing the method.

The weighting step can use a weighting factor determined according to the following relationship:
where
and
Where
And
with a(i) and b(i) each being a datum of the first or second experimental series after the alignment step or a datum of the first or second initial series, and
f _A and f _B being statistical models of the values of the first initial series or of the values of the second initial series.

Thus, according to the method according to the invention, the weighting factor is a function of the experimental series. Consequently, the weighting is more precise because it more closely follows the variation of the data of the experimental series.

The Math 4 formula combined with the Math 5 formula are preferred because they give better results, especially in terms of accuracy.

The data a(i) and b(i) can be data from the raw experimental series or data from a model determined from the experimental series, for example after the modeling step.

Thus, the weighting factor depends on the data of the experimental series and the statistical models determined from the initial data, unlike the methods of the state of the art which can choose arbitrary weighting factors. This enhances the accuracy of the estimation process.

• sommation ou multiplication terme à terme entre les données des modèles statistiques de la première et deuxième série après l’étape d’alignement ou entre les données des modèles statistiques de la première et deuxième série initiale (de préférence, entre les modèles paramétriques ou modèles de mélange gaussien obtenus en sortie de l’étape de régression ou en sortie de l’étape de détermination d’un modèle),
• normalisation suite l’étape de sommation, par exemple pour que la somme des données soit égale à 1.

Thus, the weighting factor according to the method according to the invention can be determined from the steps of:

• summation or term-by-term multiplication between the data of the statistical models of the first and second series after the alignment step or between the data of the statistical models of the first and second initial series (preferably, between the parametric models or Gaussian mixture obtained at the output of the regression step or at the output of the step for determining a model),
• normalization following the summation step, for example so that the sum of the data is equal to 1.

In another variant of the method according to the invention, the weighting factor can be equal to a coefficient which can be determined empirically. For example, it can be equal to the average value, or to the median, or to the standard deviation of one of the experimental series, or to an integer or decimal multiplier coefficient determined empirically.

The method according to the invention can, prior to the estimation phase, and preferably after the modeling step, comprise a phase of filtering each initial series by thresholding. The filtering phase may include an assignment, in each initial series, of the average value of the model provided after the modeling step to all the data outside a threshold or an assignment of an average value of a distribution of each initial series to all data outside a threshold.

Thus, the filtering phase makes it possible to replace the erroneous values of each initial series with a more probable value, which may be the average value of the initial series considered. Therefore, no data is discarded. The size of each initial series is therefore preserved.

In particular, such a filtering phase avoids significant biases that could alter or distort the result of the estimation phase.

The average value of the distribution of each initial series can be provided by a representation of each initial series in the form of a distribution, for example after displaying a histogram.

The threshold can be chosen empirically, i.e. according to the variation of the data of each initial series, or automatically, i.e. predefined in advance. In particular, a plausible threshold can be recorded and used for the first time in the method according to the invention. This threshold can then be modified according to the expectations and results obtained with a previous threshold.

The threshold can be determined according to the mathematical expectation, the average value or the maximum value of each model chosen or of each distribution chosen.

The threshold can be similar or equivalent for each initial series.

• d’enregistrement de la grandeur métrique calculée à chaque itération de la phase d’estimation, et
• modélisation d’un modèle paramétrique de la grandeur métrique à partir de l’ensemble des grandeurs métriques enregistrées ou représentation d’une distribution de la grandeur métrique à partir de l’ensemble des grandeurs métriques enregistrées.

The method according to the invention may comprise a step:

• recording of the metric quantity calculated at each iteration of the estimation phase, and
• modeling of a parametric model of the metric quantity from the set of recorded metric quantities or representation of a distribution of the metric quantity from the set of recorded metric quantities.

The step of modeling a parametric model of the metric quantity makes it possible to model the behavior of all the metric quantities recorded. The step of representing the distribution makes it possible to directly visualize the behavior of all the metric quantities recorded. For example, the representation step can comprise a display of the data, for example in the form of a histogram. Thus, the modeling or representation step makes it possible to study the behavior of the metric quantity on all the iterations of the estimation phase.

The metric quantity can be recorded in a database or on a computer storage means, for example in the internal memory of the computer implementing said method.

For each database mentioned in the remainder of the document, the database may be remote, for example recorded on the “Cloud” or on a server connected to the apparatus or device implementing the method according to the invention.

The database can be accessible through a communication network, for example of the Internet type, by a wired or wireless connection of the WIFI, Bluetooth, modem or 3, 4, 5G network type.

The database can be a local or external server or a means of recording said computer (internal memory, internal or external hard drive).

Thus, with the method according to the invention, it is possible to observe the behavior or the variation of the metric quantity over time. The time can be considered, for example, by the number of iterations of the estimation phase or by comparisons with future results obtained by the method according to the invention.

The metric quantity can be saved in a writing file, for example in csv or binary format, in the form of a list or a table.

The distribution can be predefined or depend on the variations of the metric quantity obtained following all the iterations.

The distribution of the metric quantity can be, by way of non-limiting example, a Gaussian law, a Poisson law, a Lorentzian distribution, an exponential distribution, a Maxwell-Boltzmann law, etc.

Preferably, the method can comprise a step of evaluating the metric quantities estimated by a confidence index determined from the parametric model of the metric quantity, or from all the metric quantities recorded following the iterations of the phase d estimation or preferably from the distribution of the metric quantity.

The confidence index can include a confidence interval, a median, an arithmetic mean, or any other tool for judging the level of confidence of the estimated metric quantities, for example a display of the distribution of all the metric quantities recorded.

The level of the confidence interval depends on the objectives of the estimation of the metric quantity. By way of non-limiting examples, the level of the confidence interval may be greater than 50%, or greater than 80%, or greater than or equal to 90%, preferably equal to 95%. Thus, when a metric quantity is judged to be “unlikely”, the method according to the invention can filter or eliminate them.

The method according to the invention may comprise a measurement phase carried out before the estimation phase, said measurement phase comprising a step of measuring the two initial series and a step of recording each initial series on a database capable of communicate with said computer.

Thus, the method according to the invention can be implemented from pre-recorded or recorded initial series.

The measurement step may comprise a measurement of a multitude of data.

The measurement step of the first and second initial series can preferably be carried out at the same time or separated in time.

The step of measuring the two initial series can be carried out over a certain period of time. The time period for the first and second initial series measurement steps may be similar or different.

The time period can be counted in hours, days, months, years, etc. Therefore, the time period of the measurement step can be arbitrary.

The measured data can then be saved to a backup file on a database.

The measuring step can be performed by a measuring means. The measurement means can comprise at least one sensor or a physical sensor or a software sensor. The sensors can be of different types or of the same nature.

Thus, the method according to the invention only works with measured data, that is to say data acquired by any sensor.

The method according to the invention makes it possible to improve the processing of the data measured and used in an estimation of a metric quantity. The method according to the invention therefore allows better management of the measured data, in particular the method according to the invention improves the use of the data measured by the sensors thanks to a better statistical estimation. The method thus makes it possible to produce a better estimate of the metric quantity.

The measurement phase can comprise, in the measurement step, a measurement of k data with k being able to be an even or odd number. Thus, each sensor used in the measurement phase can collect any number of values.

For example, if the method is used for the comparison of two machines, the measurement phase comprises measurements made on a first machine which will consist of the first initial series and measurements made on a second machine which will consist of the second series initial.

Preferably, the initial series are recorded on a database capable of communicating with said computer implementing said method.

In a variant, the method according to the invention may comprise, before the estimation phase, a measurement phase comprising a step of measuring, over a certain time period, a multitude of data, a step of distributing, randomly , in the first and second initial series, data measured over the time period and a step of recording each initial series on a database able to communicate with said computer. This variant may correspond to an A/A type test.

By way of non-limiting example, the measurement phase may include an A/B type test, for example an A/B test used to compare manufacturing processes or used in the medical field to compare at least two drugs. An A/A test can be carried out in a preliminary phase to test the effectiveness of the method according to the invention before the A/B test carried out with the method according to the invention.

Preferably, the calculation of the metric quantity can be an arithmetic mean of the weighted gains. Thus, the metric quantity can be relative to an average difference between two series of data, which makes it possible to compare the processes of the two initial series used. In particular, compared and weighted data can be represented according to one and the same criterion while limiting the errors linked to extreme values.

The metric quantity can give qualitative and quantitative information.

For example, if the first initial series corresponds to a reference series (i.e. from a known and commonly used process) and the second initial series corresponds to a test series (i.e. from an unknown process, in the test phase) , the method makes it possible to measure the effect of the second initial series with respect to the first initial series. The metric quantity may relate to a difference, in particular a difference of the second initial series with respect to the first initial series. Thus, according to the method according to the invention, it is possible to more finely measure the effect of the test (second initial series) compared to the reference (first initial series) in order to decide whether or not to replace the process of reference by the test process, for example in production.

By way of non-limiting example, the test process (i.e. for example, the process represented by the second initial series) can be considered effective if the metric quantity is greater than a reference value, preferably if the metric quantity obtained at each iteration is greater than the reference value. The reference value can be greater than or equal to 0. The higher the metric quantity, the more efficient the test process.

The two initial series can each include data measured, for example the audience of a website or any other means of communication, data on the use of software or mobile applications, frequencies of use such as frequencies use of a website, transactional data, or measurements of physical quantities such as dimension, weight, height, resistance of materials, etc.

In particular, if the measured data relate to physical quantities, the method according to the invention can compare two manufacturing processes, one reference and one test in order to validate or not the test method via the value of the metric quantity. In another variant, the method according to the invention can compare two machines, a reference machine and a test machine, each making it possible to obtain a product.

In this case, the method according to the invention can be a method of comparing the average basket spent by consumers. The sales entity may include a multitude of stores such as e-commerce stores and/or non-e-commerce stores. Initial series data may include different products.

Thus the method according to the invention makes it possible to identify the sales trends of a business or consumer spending in different types of brands, for example e-commerce or not. A consumer's shopping cart may include the purchase of services or products, the products or services may be of the same nature or of different natures such as computer products, household appliances, food, cosmetics, games, clothes, etc. . The confidentiality and anonymity of consumers or buyers are also preserved.

Consequently, the method according to the invention can make it possible to study, in particular to estimate the expenses of a consumer at a merchant, advertiser, retailer, e-commerce sites or any other entity selling objects. By object is meant inert and/or living objects such as animals or robots.

The method according to the invention using at least two series of data can, for example, make it possible to study the difference in money or visit (i.e. view) that the second initial series brings in compared to the first initial series, or vice versa . The goal is to replace the process relating to the first or second initial series.

Initial series can consist of a data set of real and/or integer numbers.

According to another aspect of the invention, there is proposed a computer program which can comprise instructions executable by a data processing device, which when they are executed implement all the steps of the method according to the invention.

The computer program may be in any computer language such as C, C++, JAVA, Python, machine language, etc.

According to another aspect of the invention, a data processing device is proposed comprising means configured to implement all the steps of the method according to the invention.

The device according to the invention confers the same advantages as those listed for the method according to the invention

The data processing device can be a PC, a smartphone, a tablet, a computing unit or any other computing and/or electronic device.

In particular, the data processing device can be an electronic card comprising at least one analog component and/or at least one digital component.

In a particular embodiment, the data processing device can be a processor, a chip, a computer, etc.

• un module d’estimation, appelé premier module d’estimation, configuré pour déterminer une grandeur métrique, de préférence appelée première grandeur métrique, à partir de deux séries de données, dites respectivement première et deuxième série initiale, ledit module d’estimation pouvant comprendre :
  • au moins un module de tirage configuré pour tirer n données de la première série initiale pour obtenir une première série de données, dite première série expérimentale, et tirer m données avec remise de la deuxième série initiale pour obtenir une deuxième série de données, dite deuxième série expérimentale,
  • un module d’alignement configuré pour aligner la première série expérimentale par rapport à la deuxième série expérimentale, ou inversement,
  • un module de comparaison configuré pour comparer terme à terme la première série expérimentale et la deuxième série expérimentale obtenues en sortie du module d’alignement afin de déterminer un gain terme à terme,
  • un module de pondération configuré pour pondérer chaque gain en fonction d’un modèle statistique des valeurs de la première série initiale et d’un modèle statistique des valeurs de la deuxième série initiale,
  • un module de calcul de la grandeur métrique à partir des gains pondérés.

According to one embodiment, the device according to the invention may comprise:

• an estimation module, called first estimation module, configured to determine a metric quantity, preferably called first metric quantity, from two series of data, called respectively first and second initial series, said estimation module possibly comprising :
  • at least one drawing module configured to draw n data from the first initial series to obtain a first series of data, called first experimental series, and to draw m data with replacement from the second initial series to obtain a second series of data, called second experimental series,
  • an alignment module configured to align the first experimental series with respect to the second experimental series, or vice versa,
  • a comparison module configured to compare, term by term, the first experimental series and the second experimental series obtained at the output of the alignment module in order to determine a term-by-term gain,
  • a weighting module configured to weight each gain according to a statistical model of the values of the first initial series and of a statistical model of the values of the second initial series,
  • a module for calculating the metric quantity from the weighted gains.

In a variant, the device according to the invention can comprise two separate drawing modules for each initial series.

The device according to the invention may comprise a measurement module configured to measure the two initial series and record each initial series, for example in a recording file. The initial series can be recorded directly on said device or on a database able to communicate with said device.

The alignment module can be configured to sort each initial series according to the same criterion.

The criterion may comprise a ranking in ascending or descending order of each experimental series.

The device can comprise a modeling module configured to model each initial series according to a parametric model or a Gaussian mixture model.

The modeling module can also be arranged to optimize the model of each initial series on the corresponding initial series so as to provide a probable distribution of each datum of the initial series.

The device according to the invention may comprise a storage module configured to record the metric quantity calculated by the estimation module. The storage module can also be configured to model the metric quantity from all the recorded metric quantities. In another variant, the modeling module can be configured to represent or display the distribution of the metric quantity from the set of recorded metric quantities.

The device according to the invention can also comprise a precision module configured to determine a confidence interval of the parametric model of the metric quantity.

The device can also comprise a filtering module configured to filter each initial series by thresholding according to a threshold. The filtering module can be included in the modeling module or be separate from the modeling module. Preferably, the filtering module can be configured to assign, in each initial series, the average value of the model provided after the modeling step to all the data outside the threshold or to assign an average value of a distribution of each initial series to all data outside said threshold.

The device according to the invention can also comprise a module for calculating the mean and the variance configured to determine the arithmetic mean and/or the variance of each initial series. The mean/variance calculation module can be separate or included in the modeling and/or filtering module.

Each module can be a means of calculation, such as a processor, a processing unit, an electronic chip, programmed to implement the function assigned to it. Thus the device according to the invention can be arranged to carry out calculations in parallel with a view to carrying out the steps and/or phases of the method according to the invention more quickly.

The device according to the invention may comprise a communication module arranged to retrieve the first and/or the second initial series from a database.

• un moyen d’affichage comprenant une interface utilisateur configurée pour afficher des données, et
• un dispositif selon l’invention pour déterminer la grandeur métrique.

According to another aspect of the invention, equipment is proposed comprising:

• display means comprising a user interface configured to display data, and
• a device according to the invention for determining the metric quantity.

The equipment confers the same advantages as those listed for the method according to the invention.

The data displayed by the display means may comprise the first initial series and/or the second initial series and/or the first experimental series and/or the second experimental series. The data displayed can also comprise the metric quantity measured by the estimation method according to the invention and/or the set of metric quantities measured by all the iterations of the estimation phase or and/or the set of metric quantities measured after the step of determining the mathematical model of the measured quantity. The display means can be a screen, an interface. The display means may or may not be tactile.

The user interface may be a man-machine interface. The user interface may include a display area for displaying data. The user interface can also include an input zone configured to enter commands arranged to be executed by said device according to the invention.

The user interface may include means for controlling said modules. The means for controlling said modules can be a keyboard, for example a tactile or manual keyboard and/or a directional pad and/or a computer mouse. Preferably, the keyboard can be an alphanumeric keyboard.

The interface may include a button arranged to be activated by the user so as to initiate the method according to the invention.

The interface can comprise means for selecting one or more data, for example, from the first initial series and/or the second initial series and/or the first experimental series and/or the second experimental series, and/or the metric quantity measured and/or in all of the metric quantities recorded following all of the iterations of the estimation phase.

The means for selecting data can be a numeric keypad, for example a directional pad of a manual or tactile keyboard, and/or a computer mouse, and/or a tactile cursor moving at the touch of the user on a touchscreen.

• une première partie FIG. 6A, un histogramme des données mesurées dans la phase de mesure du procédé selon l’invention ;

• une deuxième partie FIG. 6B, un histogramme de la première et deuxième séries initiales après une phase de mesure du procédé selon l’invention ;

• une troisième partie FIG. 6C, un histogramme d’un ensemble de grandeurs métriques mesurées suite à plusieurs itérations d’une phase d’estimation selon l’invention.

Other advantages and features of the invention will become apparent on reading the detailed description of implementations and non-limiting embodiments, and of the following appended drawings.
The is a schematic representation of a first non-limiting embodiment of a method according to the invention;
The a schematic representation of a second non-limiting embodiment of a method according to the invention;
The is a schematic representation of a third non-limiting embodiment of a method according to the invention;
The is a schematic representation of a first example of a device according to the invention;
The is a schematic representation of an example of equipment according to the invention.
The , illustrious, in

• a first part FIG. 6A, a histogram of the data measured in the measurement phase of the method according to the invention;

• a second part FIG. 6B, a histogram of the first and second initial series after a measurement phase of the method according to the invention;

• a third part FIG. 6C, a histogram of a set of metric quantities measured following several iterations of an estimation phase according to the invention.

Detailed description of figures

It is understood that the embodiments which will be described below are in no way limiting. In particular, variants of the invention may be imagined comprising only a selection of characteristics described below isolated from the other characteristics described, if this selection of characteristics is sufficient to confer a technical advantage or to differentiate the invention from the prior art. This selection includes at least one preferably functional feature without structural detail, or with only part of the structural detail if only this part is sufficient to confer a technical advantage or to differentiate the invention from the state of the prior art.

In particular, all the variants and all the embodiments described can be combined with each other if nothing prevents this combination from a technical point of view.

In the figures, the elements common to several figures retain the same reference.

The is a schematic representation of a non-limiting embodiment of a method 100 according to the invention.

Method 100 is computer implemented. In particular, the method 100 is a method for estimating a metric quantity M, implemented by computer, from at least two data series, called respectively first initial series A and second initial series B.

The first initial series A and the second initial series B are of different sizes (i.e. they contain a different number of data). By way of non-limiting example, the first initial series A corresponds to a reference series and the second initial series B corresponds to a test series.

The process illustrated in comprises at least one iteration of an estimation phase 102 of the metric quantity M. The estimation phase 102 comprises a step of drawing 104 of n data with replacement of the first initial series A to obtain a first series of data, said first experimental series a, and drawing m data with replacement of the second initial series B to obtain a second series of data, called second experimental series b. Thus, following the drawing step, two new series of data a and b, called experimental, are obtained.

The estimation phase 102 then includes a step 106 of aligning the first experimental series a with the second experimental series b, or vice versa, so that the first initial series A and the second initial series B are of same size.

By way of non-limiting example, the alignment step uses an alignment algorithm, such as the dynamic time warping (DTW) algorithm.

The estimation phase then comprises a step of comparison 108 term by term between the first experimental series a and the second experimental series b following the alignment step 106, in order to determine a gain term by term. The term-to-term gain is preferably a term-to-term relative gain as described by the formula Math. 2, with a(i) being a datum of the first experimental series a and b(i) being a datum of the second experimental series b.

The estimation phase 102 then comprises a step 110 of weighting each gain according to a statistical model f _A of the values of the first initial series A and according to a statistical model f _B of the values of the second initial series B. The weighting step 110 preferably comprises a summation between the data of the statistical models of the first and second experimental series a, b. A normalization step is provided following the summation step. By way of non-limiting example, the weighting factor is calculated according to the formula Math. 3 combined with Math formulas. 4 and Math. 5 or Math formulas. 6 and Math. 7.

Finally, the estimation phase 102 includes a step 112 of calculating the metric quantity M from the weighted gains. Calculation step 112 includes the calculation of the arithmetic mean of the relative gains. The metric quantity M is calculated by multiplying the arithmetic mean of the relative gains by the weighting factor. The metric quantity M relates to an average difference between the first initial series and the second initial series. In this way, the value of the metric quantity M can make it possible to validate the process of the second initial series B (test series).

When the estimation phase 102 is performed, a new iteration of said estimation phase 102 can be performed.

By way of non-limiting example, the method 100 can be configured to perform 10,000 iterations of the estimation phase 102. The number of iterations of the estimation phase 102 can be modified by a user.

By way of non-limiting example, the data of each initial series A, B includes a sales history of different products of an e-commerce brand over the months of November to December. For example, the data of the first initial series can come from a history of product sales on a particular site of a brand, while the data of the second initial series can come from a history of in-store sales of said sign. The estimated metric quantity can therefore be the average difference of the basket spent by a consumer in said store. The value of the metric M can be used to determine which sales process is the most effective and assign a quantitative value to it.

In another variant, the initial series can be data of physical quantities of objects of the same nature. Thus, the data of the first initial series A may correspond to quantities measured on products obtained by a first manufacturing process, called the reference process, while the data of the second initial series B may correspond to quantities measured on products obtained by a second manufacturing process, called the test process. The value of the metric quantity M, relating to the average difference between the data of the second initial series and of the first initial series, can make it possible to validate or not the test manufacturing method. By way of non-limiting example, if the metric quantity M is greater than a reference value, for example greater than 1, the test method is effective.

The is a schematic representation of a non-limiting exemplary embodiment of a method 200 according to the invention.

The process 200 illustrated in includes all the steps of the method 100 illustrated in . Only the differences with the process of the will be described.

The method 200 further comprises a measurement phase 202 carried out before the estimation phase 102, said measurement phase 202 comprising a step of measuring the two initial series A and B.

The data can be measured over a certain period of time, for example over a week.

By way of non-limiting example, the measuring means can be a counting means which for example records, in a recording file, the values spent by a group of consumers over the time period. At the end of the time period, a sales history is recorded on a database connected to the computer implementing the method 200. By way of non-limiting example, the data of the first initial series A can correspond to a sales history on an e-commerce store over a first time period. The data of the second initial series B can correspond to a sales history of the e-commerce store over a second time period, equal to the first time period, but after an advertisement has been broadcast. The comparison step 108 makes it possible to measure a difference between baskets spent by consumers. The weighting step 110 followed by the step 112 of calculating the metric size makes it possible to measure the average difference of the basket spent by consumers following the two sales processes. If the metric M is greater than zero, then this may mean that advertising has improved sales (qualitative information). In addition, it also gives quantitative information on the profit that can be made by the sales process relating to the data of the second initial series B.

In a second non-limiting example, the measuring means can be a sensor or a measuring means, for example a means for measuring the resistance of materials. In this example, two carabiner manufacturing processes are tested. A first method, called reference, in which a first list of components is used and a second method, called test, in which an additional material is added to the list of components of the first method. The purpose of the experiment is to compare the resistance of the carabiners of the reference process with that of the carabiners of the test process. The measuring means is used to measure the resistance of the carabiners of the reference method. These measurements are recorded in the first initial series A. The measuring means is also used to measure the resistance of the carabiners of the test method. These measurements are recorded in the second initial series B. The method 200 is implemented and makes it possible to measure an average resistance difference between the reference and test method. In particular, the comparison step 108 makes it possible to compare the rigidity of the test process with respect to the reference process. The weighting step 110 followed by the step of calculating the metric quantity 112 makes it possible to measure a difference in average resistance of the test process compared to the reference process. Thus, if the metric quantity M is greater than zero, then this may mean that the products of the test process have gained in resistance compared to the product of the reference process. In this way, the method according to the invention can make it possible to validate the test method compared to the reference method because it makes it possible to obtain stronger carabiners. This example is also applicable to the comparison of machines allowing the manufacture of products.

Thus the method according to the invention can make it possible to calculate the average difference between two groups of measurements. In addition, all the compared measurements can be represented according to a single criterion (i.e. the metric quantity M) while limiting the errors linked to extreme values. This metric quantity M gives both quantitative and qualitative information.

In the case of the , the initial series A and B include a number of different data, so they are not of the same size.

The initial first A and second B series are then recorded, during a recording step of the measurement phase 202, on the database capable of communicating with the computer implementing said method 200.

The measurement phase 202 includes, after the measurement step, a step of recording each initial series A and B on a database able to communicate with said computer.

In a non-limiting manner, the method 200 can then comprise a step of retrieving the initial series A and B from said database.

By way of non-limiting example, the initial series A and B are recorded on an external server connected to a network to which the computer has access.

The method comprises a step of determining the size of each initial series A and B before the start of the estimation phase 102. By way of non-limiting example, the step of determining the size of each initial series is carried out after the measurement step of the measurement phase 202 of the initial series A and B, in particular at the time of the recording of the initial series A and B on the database.

By way of non-limiting example, the first initial series A is smaller in size and includes 1000 data.

• l’étape de tirage 104 comprend un tirage de n données pour chaque série initiale A et B, c'est-à-dire un tirage de 1000 données pour chaque série initiale A et B. Deux séries expérimentales a et b de même taille, ici de taille égale à 1000, sont donc obtenues suite à l’étape de tirage 104 ;
• l’étape d’alignement 106 comprend directement un tri de chaque série expérimentale a et b suivant un même critère. A titre d’exemple non limitatif, les séries expérimentales a et b sont rangées par ordre croissant. Dans cet exemple non limitatif, le rangement par ordre croissant est associé à un algorithme d’alignement ;
• l’étape de comparaison 108 comprend une différence terme à terme entre les séries expérimentales a et b suite à l’étape d’alignement 106.

In the case of the process 200 illustrated in , the number of data drawn with replacement is a function of the series of smallest size, i.e. here of the size of the first initial series A. Thus in the method 200 illustrated in , :

• the draw step 104 comprises a draw of n data for each initial series A and B, that is to say a draw of 1000 data for each initial series A and B. Two experimental series a and b of the same size, here of size equal to 1000, are therefore obtained following the draw step 104;
• the alignment step 106 directly comprises a sorting of each experimental series a and b according to the same criterion. By way of non-limiting example, the experimental series a and b are arranged in ascending order. In this non-limiting example, the ranking in ascending order is associated with an alignment algorithm;
• the comparison step 108 includes a term-by-term difference between the experimental series a and b following the alignment step 106.

The process 200 illustrated in is therefore faster and simpler to implement than the method 100 illustrated in .

The is a schematic representation of a non-limiting embodiment of a method 300 according to the invention.

The process 300 illustrated in includes all the steps of the method 200 illustrated in . Only the differences with the process of the will be described.

For each initial series A, B, the statistical model f _A , f _B used in the weighting step 110 can comprise or consist of a parametric model or a Gaussian mixture model.
By way of non-limiting example, the method 300 can comprise, before the weighting step 110, a modeling step 302. The modeling step 302 is preferably carried out after the measurement phase 202 and before the estimation 102. The modeling step 302 can be a modeling of each initial series A, B according to a parametric model or a Gaussian mixture model. The modeling step makes it possible to obtain the statistical models f _A and f _B of each initial series A, B.

Optionally, the modeling step 302 can include a step of optimizing the model of each initial series A, B on the initial series A, B so as to obtain a probable distribution of each datum of the initial series A, B.

By way of non-limiting example, the modeling step 302 can be a modeling of a parametric model according to a log-normal law. For this, parameters are calculated on each initial series A and B before the modeling step 302. The parameters can include at least the arithmetic mean and the variance of each initial series A, B. These parameters can be calculated from 'a distribution of a histogram of each initial series A, B. In particular, the parameters such as the mean and the variance can then be optimized so that the model determined is closest to the variation of the data of each initial series A , B.

At each iteration n1, n2, n3 etc. of the estimation phase 102, the method 300 comprises a step of recording 304 of the calculated metric quantity M. The metric quantity M is recorded on a storage means of said computer or the database in which the initial series are recorded.

The process 300 illustrated in comprises, by way of non-limiting example, 10,000 iterations 308 of the estimation phase 102. The number of iterations 308 is chosen according to a speed/accuracy compromise. The greater the number of iterations 308, the more precise the estimation of the metric quantity M, but this can be costly in terms of calculation time.

The metric quantities M measured are thus recorded in a recording file, for example a table or csv document comprising all the metric quantities measured, i.e. here 1000 measurements. From these 1000 measurements of the metric quantity, the method 300 comprises a modeling step 306 of a parametric model of the metric quantity M from all the metric quantities M recorded or a step 306 of representing a distribution of the metric quantity from all the metric quantities M recorded, or from the 1000 measurements of the metric quantity M. The parametric model of the metric quantity M obtained following all the iterations of the method 300 can be a Gaussian law. The step of representing a distribution 306 can comprise the display of a histogram of the 1000 measurements of the metric quantity M. The histogram of the data can follow a Gaussian law.

Each iteration n1, n2, n3 etc. of the method 300 makes it possible to obtain several metric quantities M relating to a difference between the data of each initial series A, B in order to then be able to study the distribution of these metric quantities M.

Optionally, the method 300 can include a filtering phase 310 after the modeling step 302.

The filtering phase 310 is preferably carried out prior to the estimation phase 102 in the form of thresholding. The filtering phase can use the expectation of the parametric or statistical mixture model determined in the modeling step 302. By way of non-limiting example, the thresholding phase 310 comprises, for each initial series A, B, a step assignment, expectation of the parametric model, or Gaussian mixture to all data outside the threshold.

The is a schematic representation of an example of a device 400 according to the invention.

The device 400 is for example a calculation unit 400. The device 400 can be included in a computer.

• un module de tirage 404 configuré pour tirer n données de la première série initiale A pour obtenir la première série de données, dite première série expérimentale a, et tirer m ou n données avec remise de la deuxième série initiale B pour obtenir la deuxième série de données, dite deuxième série expérimentale b. Dans le cas illustré, les première et deuxième séries initiales A, B sont de la même taille. Dans le cas considéré, n données avec remise sont tirées à partir de la deuxième série initiale B.
• un module d’alignement 406 configuré pour aligner la première série expérimentale a par rapport à la deuxième série expérimentale b, ou inversement,
• un module de comparaison 408 configuré pour comparer terme à terme la première série expérimentale a et la deuxième série expérimentale b obtenues en sortie du module d’alignement 406 afin de déterminer un gain terme à terme,
• un module de pondération 410 configuré pour pondérer chaque gain en fonction du modèle statistique f_Ades valeurs de la première série initiale A et du modèle statistique f_Bdes valeurs de la deuxième série initiale B,
• un module de calcul 412 de la grandeur métrique M à partir des gains pondérés.

The device 400 is arranged to implement the method 100 or 200 and comprises an estimation module 402 comprising:

• a drawing module 404 configured to draw n data from the first initial series A to obtain the first series of data, called first experimental series a, and to draw m or n data with replacement from the second initial series B to obtain the second series of data, called the second experimental series b. In the case illustrated, the first and second initial series A, B are the same size. In the case considered, n data with replacement are drawn from the second initial series B.
• an alignment module 406 configured to align the first experimental series a with respect to the second experimental series b, or vice versa,
• a comparison module 408 configured to compare term by term the first experimental series a and the second experimental series b obtained at the output of the alignment module 406 in order to determine a gain term by term,
• a weighting module 410 configured to weight each gain as a function of the statistical model f _A of the values of the first initial series A and of the statistical model f _B of the values of the second initial series B,
• a calculation module 412 of the metric quantity M from the weighted gains.

In , the initial series A, B are pre-recorded on a database. The database can be recorded directly on a storage means of the device 400 or on a "Cloud" or a network connected to said device 400. In particular, said computer comprising the device 400 further comprises a communication module (not shown) to communicate the initial series A, B to said device 400. The communication can be wireless, for example using WIFI, the 3, 4, 5G network.

The metric quantity M is provided at the output of the estimation module 402 at each iteration of the estimation phase 102.

The is a schematic representation of an example of equipment 500 according to the invention. The equipment comprises a device 502. The device 502 comprises all the elements of the device 400 illustrated in . The device 502 is for example a computing unit. Device 502 may be included in a computer. The device 502 is arranged to implement the method 100, 200, 300, 400.

Thus the device 502 therefore provides a metric quantity M at each iteration of the estimation phase 102.

The device 502 further comprises a measurement module 504 configured to implement the measurement phase 202 of the method 200 and/or of the method 300.

The device 502 can comprise a modeling module 506 configured to implement the modeling step 302 illustrated in . The modeling module 506 provides at its output a parametric or Gaussian mixture model f _A , f _B of each initial series A, B. The model f _A , f _B of each initial series A, B is used by the weighting module 410 in the weighting step 110.

Optionally, the device 502 can comprise a filtering module 507 configured to implement the filtering phase 310 of the method 300. The filtering phase 310 being optional, it can be effective if an operator commands the device 502 to perform it. The filtering module 507 can use the model f _A , f _B of each initial series A, B in the filtering phase 310. The device 502 further comprises a storage module 508 configured to implement the recording step 304 of the metric quantity M at each iteration (n1, n2, n3, etc.) of the estimation phase 102 of the method 300. Thus, when the metric quantity is provided by the estimation module 402, said metric quantity M is transmitted to the storage module 508. The storage module 508 can be the computer memory of the device 502, an external storage means such as an external hard disk or the database with which the device 502 can communicate, for example via the communication module of said computer. The database recording the measured value can be on the “Cloud” or an external server connected to said device 502.

All the metric quantities measured can be saved in a backup file in the form of a list or a table.

The device 502 further comprises another modeling module 510 or a representation module 510 of the modeling step 306 or representation 306 of the method 300. Thus, after several iterations (n1, n2, n3, etc.) of the method 100 , 200 or 300, all of the recorded metric quantities M can be transmitted to the modeling 510 or representation module 510 in order to model the behavior of the metric quantity M over all of the iterations 308 of the estimation phase 102 or to display the variation of the metric quantity M, for example in the form of a histogram.

Each module can be a calculation means, such as a processor, arranged to execute the computer program according to the invention or command lines dedicated to the step or the operation to be carried out of the method 100 or 200.

Although shown separately, at least two of the modules, in particular all of the modules, can be integrated into a single processor.

The device 502 is arranged to execute instructions from a computer program to implement all the steps of the method as described in FIGURES 1, 2, 3.

In a non-limiting way, the computer program can be written in Python.

Equipment 500 further comprises display means 512 comprising a display area and an input area. The input area and the display area can belong to a user interface.

The display means 512 is a screen. The display means 512 can be tactile.

The equipment 500 comprises an alphanumeric keyboard 514 connected to the device 502. The alphanumeric keyboard 514 is arranged to manually enter commands, for example in the input zone of the user interface. The commands can include a display data command, for example to display the initial series as a graph. The alphanumeric keyboard 514 can be tactile by being directly included in the display means 512.

Equipment 500 includes selection means 516 configured to select data, for example to select data from one of the initial series. Selection means 516 may be a computer mouse.

The illustrates several display areas 602 of the user interface displayed on the screen 512 of the equipment 500.

The illustrated in a first part FIG. 6A, an example of a histogram of data measured in the measurement phase 202. The measured data illustrated in FIG. 6A can correspond to the measured data of the first initial series A or to the measured data of the second initial series B.

The histogram of the FIG part. 6A is of the “long tail” type, and includes several extreme values 604 which can bias the estimation of the calculation of an average value in methods of the state of the art. The extreme values of the measured data shown in FIG. 6A are not deleted in processes 100, 200, 300, 400.

The data measured in the measurement phase 202 follow a log-normal law. The estimation phase 102 will be applied to the series of data illustrated in FIG. 6A.

The illustrated in a second part FIG. 6B an example of a histogram of the first initial series A and a histogram of the second initial series B after the measurement phase 202. Thus, two initial series A, B are obtained following the measurement phase 202. In the case illustrated in FIG. 6B, the first initial series A and the second initial series B are of the same size. The first A and second B initial series are obtained following an A/B test.

By way of non-limiting example, the first initial series A and the second initial series B have the same mathematical law, in particular they are represented in the form of a log-normal law.
The distribution of the second initial series B is shifted with respect to the first initial series A.

The illustrated in a fourth part FIG. 6C a histogram of the 1000 metric quantities measured via the 100, 200, 300, 400 method. In particular, the histogram obtained in FIG. 6C is that obtained following the step of representation 306 of the distribution of the metric quantity M. By way of non-limiting example, a 95% confidence interval of the metric quantities M measured has been calculated in order to keep the values most probable of the recorded metric quantities M. The metric quantities M calculated can be in certain iterations negative and for others, majority, positive. When they are positive, this can mean that the test series brings a gain compared to the reference series.

By way of non-limiting example, the histogram of the data in FIG. 6C follows a Gaussian law.

Of course, the invention is not limited to the examples which have just been described. Many modifications can be made to these examples without departing from the scope of the present invention as described.

Claims (15)

Method of estimating (100, 200, 300) a metric quantity for comparing processes or machines, implemented by computer, from at least two series of data, respectively called first initial series of a first process or a first machine, and a second initial series of a second process or a second machine, said process (100, 200, 300, 400) comprising:

• a measurement phase (202) comprising a step of measuring the two initial series and a step of recording each initial series on a database able to communicate with said computer,
• at least one iteration of an estimation phase (102) of the metric quantity according to the following steps:
  • drawing (104) of n data with replacement of the first initial series of the first initial series to obtain a first series of data, called first experimental series, and drawing (104) of m data with replacement of the second initial series to obtain a second series of data, called second experimental series,
  • alignment (106) of the first experimental series with respect to the second experimental series, or vice versa,
  • term-to-term comparison (108) between the first experimental series and the second experimental series following the alignment step, in order to determine a term-to-term gain,
  • weighting (110) of each gain as a function of a statistical model f _A of the values of the first initial series and of a statistical model f _B of the values of the second initial series,
  • calculation (112) of the metric quantity from the weighted gains,
  • comparison of the metric quantity with a reference value.

Method (100, 200, 300) according to the preceding claim, characterized in that the comparison step (108) comprises a term-by-term difference between the experimental series at the output of the alignment step (106). Method (100, 200, 300) according to any one of the preceding claims, characterized in that the comparison step (108) comprises the calculation of a relative gain term by term between the experimental series following the step d alignment (106), determined by the following formula:

with a(i) and b(i) each being a datum of the first or second experimental series after the alignment step (106). Method (100, 200, 300) according to any one of the preceding claims, characterized in that it comprises a step of determining the size of each initial series, before the estimation phase (102), the number of data drawn with replacement for each initial series, in the drawing step (104), being a function of the initial series of smallest size. Method (200, 300) according to any one of the preceding claims, characterized in that, when n and m are identical, then the alignment step (108) comprises a sorting of each experimental series according to the same criterion. Method (100, 200, 300) according to the preceding claim, characterized in that the criterion comprises a ranking in ascending or descending order of each experimental series. Method (100, 200, 300) according to any one of the preceding claims, characterized in that each statistical model f _A , f _B comprises a parametric model or a Gaussian mixture model, the said method comprising, before the step of weighting ( 110), preferably before the estimation phase (102), a step of modeling (306) each initial series according to said parametric model or said Gaussian mixture model. Method (100, 200, 300) according to any one of the preceding claims, characterized in that the weighting step uses a weighting factor determined according to the following relationship:

where

and

Where

and

with a(i) and b(i) each being a datum of the first or second experimental series after the alignment step or a datum of the first or second initial series, and with
f _A and f _B being statistical models of the values of the first initial series A or of the values of the second initial series B. Method (100, 200, 300) according to any one of the preceding claims, characterized in that it comprises, prior to the estimation phase (102), a filtering phase (302) of each initial series by thresholding, including steps of:

• modeling of each initial series according to a parametric model or representation of each initial series in the form of a distribution, and
• assignment, in each initial series, of the expectation of the corresponding model or of the average value of the corresponding distribution to all the data outside a threshold.

Method (100, 200, 300) according to any one of the preceding claims, characterized in that it comprises a step:

• recording (304) of the metric quantity calculated at each iteration of the estimation phase, and
• determining (306) the distribution of the metric quantity from the set of recorded metric quantities.

Method (200, 300) according to any one of the preceding claims, characterized in that it comprises a measurement phase (202) carried out before the estimation phase (102), said measurement phase (202) comprising a step for measuring the two initial series and a step for recording each initial series on a database capable of communicating with said computer. Method (100, 200, 300) according to any one of the preceding claims, characterized in that the calculation of the metric quantity is an arithmetic average of the weighted gains. Method (100, 200, 300) according to any one of the preceding claims, characterized in that the data constituting the first and second initial series comprise a figure in integer or decimal format. A computer program comprising instructions executable by a data processing device (400, 502), which when executed implement the steps of the method according to any preceding claim. Data processing device (400, 502) comprising means configured to implement all the steps of the method (100, 200, 300, 400) according to any one of the preceding claims.