CN111913887A - Software behavior prediction method based on beta distribution and Bayesian estimation - Google Patents
Software behavior prediction method based on beta distribution and Bayesian estimation Download PDFInfo
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Abstract
The invention discloses a software behavior prediction method based on beta distribution and Bayesian estimation, which is used for greatly influencing a model by each datum under given behavior training data without converging the model to a fixed value, predicting next binary behavior and achieving good model training and behavior prediction effects. The invention is based on the model prediction technology of probability distribution, Bayesian estimation and hidden Markov models, and completes the functions of model training and prediction under the conditions of small data volume and large model change. The tool uses a hidden Markov model to model and describe the situation, then selects the beta probability distribution, realizes the function of updating the model by single data on the basis of using the Bayesian theory, and realizes the function that the model can be greatly changed according to the actual situation and the prerequisite prior data on the basis that the internal rule accords with the beta distribution by setting the prerequisite prior data. The invention can achieve the effects of obtaining a single data change model by training under given binary behavior training data and predicting the next behavior, and expands the applicable objects of model training software.
Description
Technical Field
The invention relates to the technical field of artificial intelligence, in particular to a software behavior prediction method based on beta distribution and Bayesian estimation.
Background
Currently, most model training software or algorithms are based on a large amount of data, and through processes of multiple iterations, fitting and learning, data convergence is finally achieved, so that a model with a fixed probability is obtained, such as a neural network algorithm, a clustering algorithm, a maximum expectation algorithm and the like. Therefore, there is a lack of such mainstream model training software or algorithm that it cannot be used in situations where the model is changing and does not tend to converge. The situation has two characteristics, firstly, the data amount of a stable and probability-invariant model is small, and even only one model can exist in an extreme case; second, the model, while inherently regular, tracks in the course of changes, varies widely via a single data update. Therefore, in a situation where there is neither a large amount of data nor a model having a property of convergence is clear, it is impossible to obtain a converged and stable model using the existing model training method.
Bayesian estimation typically requires four steps: supposing that the parameters to be estimated are regarded as random variables which accord with a certain prior probability distribution, the prior probability density is converted into the posterior probability density through a Bayes rule by an estimation mode and by observing a sample. Two basic methods of probability density estimation: parameter estimates (parameter methods), which assume that random variables follow a certain distribution according to a general knowledge of the problem, the parameters of the distribution function being estimated by training data, such as ML estimates, Bayesian estimates; nonparametric estimation (nonparametric methods), the probability density is estimated without the model, but only with the training data itself. Bayesian estimation is used in many fields, and for positioning applications, the target to be positioned or tracked is a good estimation of the target from a series of measurements.
In the project, a model prediction technology based on probability distribution, Bayesian estimation and hidden Markov models is used, and the functions of model training and prediction under the conditions of small data volume and large model change are completed. The hidden Markov model is used for modeling and describing the situation, then the beta probability distribution is selected, the function of updating the model by single data is realized on the basis of using the Bayesian theory, and the function that the model can be greatly changed according to the actual situation and the prerequisite prior data on the basis that the rule accords with the beta distribution is realized by setting the prerequisite prior data.
Disclosure of Invention
The invention provides a software behavior prediction method based on beta distribution and Bayesian estimation and realizes a corresponding behavior prediction tool, the tool takes experimental object behavior track data and probability parameters set by experimenters as input, firstly, the experimental object behavior parameters are preprocessed to obtain an experimental object behavior track, then, the experimental object behavior track is used for gradually training a beta distribution, in single training aiming at single binary behavior of the experimental object, firstly, past behaviors are used as priors, integral is carried out to obtain the current probability, then, probability parameters set by the experimenters are added by Bayesian theoretical knowledge to be used as priors, the mode of probability change is changed, and finally, the probability prediction value of a certain behavior next time is obtained.
The invention provides a software behavior prediction method based on beta distribution and Bayesian estimation, which comprises the following steps:
s1, preprocessing software behavior data to obtain a software behavior track;
s2, gradually training the beta distribution by using the software behavior track, wherein the software behavior track can be decomposed into continuous single binary behaviors, and specifically, a beta distribution training algorithm is constructed aiming at the single binary behaviors of the software, namely: :
firstly, establishing a beta probability distribution, wherein the beta probability distribution is a conjugate prior distribution and is characterized in that the posterior distribution and the prior distribution structure of the updated single data are in phaseSimilarly, the difference is only in the parameters. There are two events, a and B, that are mutually exclusive, i.e., a occurrence will result in B not occurring, B occurs will result in a not occurring, and a and B will occur at least one, assuming that what needs to be predicted is the probability of a occurring. Let skIs the probability of occurrence of A at the kth time, rkIs the probability of occurrence of A at the kth time, rkSatisfying the beta probability distribution. Then there are:
p(sk＝1|Sk-1)＝∫p(sk＝1|rk)p(rk|Sk-1)drk
p(sk＝1|Sk-1)＝∫rkp(rk|Sk-1)drk
secondly, through software behavior trajectory training, setting alpha as the probability that the probability of A occurrence remains unchanged, p0Is at initialization time rkAnd finally obtaining the beta probability distribution of single software behavior prediction according to the occurrence probability, namely:
p(rk|Sk-1)＝αp(rk-1|Sk-1)+(1-α)p0(rk)
s3, constructing a prior value optimization model algorithm by taking the single same behavior of the past software as a prior value, namely:
adding prior value information on the well-established beta probability distribution model, and assuming that the probability of the establishment of the prior value is as follows: p (experimental), if the prediction probability before adding the prior value information is p (original), according to the bayesian theory, the following formula holds:
wherein p (experimenter | original) is a probability that the prior information is true under the condition of the predicted probability, namely a probability that a prior value p (original) is true in the corresponding beta distribution;
s4, optimizing the behavior predicted value of the software by selectively using a memory regression optimization algorithm, wherein the specific memory regression optimization processing comprises the following steps:
after adding the prior value information, an optional memory decay optimization is added. The memory degeneration algorithm receives a behavior sequence actionList, and after the memory degeneration processing, returns a Beta distribution list betaMemo DecayList, wherein the length of the list is the same as that of the behavior sequence actionList, and the list represents Beta distribution in a probability prediction function corresponding to each behavior in the actionList.
The one-time memory decay algorithm receives a behavior sequence actionList and then returns a single beta distribution that has undergone memory decay. The essence of the method is that in the process of training by using each behavior in actionList, the more the behavior at the back is, the higher the weight setting is, the more the influence of the behavior on the model is, and the more the behavior at the front is, the lower the weight setting is, which indicates that the influence of the long-term historical information on the current model is reduced. The weight setting is optionally changed, and has two options of discrete and linear, and the distribution shows that the influence of the reinforced recent behaviors on the model is increased linearly with the influence of the behaviors from far to near.
The method provided by the invention has the following advantages:
the software behavior prediction method based on the beta distribution and the Bayesian estimation is based on a single binary behavior update model, and is not a stable model with invariable probability which can be obtained only through training of a large amount of data.
According to the software behavior prediction method based on the beta distribution and the Bayesian estimation, the prior information can be added, so that the prediction probability can be more fit for the actual situation of behavior prediction, namely, the model can not stably change in a small range, but can be greatly changed based on the historical data and the prior information of the model, and more accurate judgment can be made.
According to the software behavior prediction method based on the beta distribution and the Bayesian estimation, a user can choose to add a memory regression model and further choose a memory regression mode in a discrete or linear or exponential mode.
Drawings
FIG. 1 is a flow chart of a method of behavior prediction implementation;
FIG. 2 is a diagram of a beta distribution based behavior prediction architecture;
FIG. 3 is a functional block diagram of a behavior prediction tool.
Detailed Description
The invention is described in detail below with reference to the figures and examples.
The embodiment of the present invention provides a behavior prediction method based on a beta distribution and bayesian estimation model training, and in order to make understanding of the present invention more clear to those skilled in the art, a detailed description of the present invention will be described below with reference to specific implementations and accompanying drawings. On the basis of the invention, all other achievements obtained without creative work belong to the protection scope of the invention.
As shown in fig. 2 and 3, a behavior prediction architecture based on beta distribution takes experimental object behavior trajectory data and probability parameters set by experimenters as input, firstly, the experimental object behavior parameters are preprocessed to obtain an experimental object behavior trajectory, then, the experimental object behavior trajectory is used for gradually training one beta distribution, in single training aiming at single binary behavior of the experimental object, firstly, past behavior is used as prior, integral is carried out to obtain current probability, then, Bayesian theory knowledge is used to add probability parameters set by the experimenters as prior, a mode of changing probability is changed, and finally, a probability prediction value of a next behavior is obtained.
As shown in fig. 1, the behavior prediction method based on the model training of the beta distribution and the bayesian estimation includes the following steps:
s1, preprocessing software behavior data to obtain a software behavior track;
s2, gradually training the beta distribution by using the software behavior track, wherein the software behavior track can be decomposed into continuous single binary behaviors, and specifically, a beta distribution training algorithm is constructed aiming at the single binary behaviors of the software, namely: :
firstly, establishing a beta probability distribution, wherein the beta probability distribution is a conjugate prior distribution and is characterized in that the posterior distribution of a single data after being updated is the same as the prior distribution structure, and the difference is only between the posterior distribution and the prior distribution structureAnd (4) parameters. There are two events, a and B, that are mutually exclusive, i.e., a occurrence will result in B not occurring, B occurs will result in a not occurring, and a and B will occur at least one, assuming that what needs to be predicted is the probability of a occurring. Let skIs the probability of occurrence of A at the kth time, rkIs the probability of occurrence of A at the kth time, rkSatisfying the beta probability distribution. Then there are:
p(sk＝1|Sk-1)＝∫p(sk＝1|rk)p(rk|Sk-1)drk
p(sk＝1|Sk-1)＝∫rkp(rk|Sk-1)drk
secondly, through software behavior trajectory training, setting alpha as the probability that the probability of A occurrence remains unchanged, p0Is at initialization time rkAnd finally obtaining the beta probability distribution of single software behavior prediction according to the occurrence probability, namely:
p(rk|Sk-1)＝αp(rk-1|Sk-1)+(1-α)p0(rk)
s3, constructing a prior value optimization model algorithm by taking the single same behavior of the past software as a prior value, namely:
adding prior value information on the well-established beta probability distribution model, and assuming that the probability of the establishment of the prior value is as follows: p (experimental), if the prediction probability before adding the prior value information is p (original), according to the bayesian theory, the following formula holds:
wherein p (experimenter | original) is a probability that the prior information is true under the condition of the predicted probability, namely a probability that a prior value p (original) is true in the corresponding beta distribution;
s4, optimizing the behavior predicted value of the software by selectively using a memory regression optimization algorithm, wherein the specific memory regression optimization processing comprises the following steps:
after adding the prior value information, an optional memory decay optimization is added. The Memory Decay Algorithm (Memory Decay Algorithm) receives a behavior sequence actionList, and after the Memory Decay processing, returns a Beta distribution list betaMemo DecayList, the length of the list is the same as that of the behavior sequence actionList, and the list represents Beta distribution in a probability prediction function corresponding to each behavior in the actionList.
The memory decay algorithm is as follows:
the one-time memory decay algorithm receives a behavior sequence actionList and then returns a single beta distribution that has undergone memory decay. The essence of the method is that in the process of training by using each behavior in actionList, the more the behavior at the back is, the higher the weight setting is, the more the influence of the behavior on the model is, and the more the behavior at the front is, the lower the weight setting is, which indicates that the influence of the long-term historical information on the current model is reduced. The weight setting changes are optional, as shown in fig. 1, there are two options, discrete and linear, and the distribution shows that the influence of the reinforced recent behaviors on the model and the influence of the far-to-near behaviors are increased linearly.
The discrete memory regression model algorithm is shown as follows:
finally, it should be noted that: the above description is only for the purpose of illustrating embodiments of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions of the foregoing embodiments or make equivalent substitutions for some technical features. Any modification, replacement, and improvement, etc., within the spirit and scope of the present invention are within the scope of the present invention.
Claims (3)
1. A software behavior prediction method based on beta distribution and Bayesian estimation is characterized in that:
s1, preprocessing software behavior data to obtain a software behavior track;
s2, gradually training the beta distribution by using the software behavior track, wherein the software behavior track can be decomposed into continuous single binary behaviors, and specifically, a beta distribution training algorithm is constructed aiming at the single binary behaviors of the software, namely:
firstly, establishing a beta probability distribution, and setting two events A and B which are mutually exclusive, namely, A occurrence can lead B not to occur, B occurrence can lead A not to occur, and A and B at least can occur one, and s is setkIs the probability of occurrence of A at the kth time, rkIs the probability of occurrence of A at the kth time, rkSatisfying the beta probability distribution, then there are:
p(sk＝1|Sk-1)＝∫p(sk＝1|rk)p(rk|Sk-1)drk
p(sk＝1|Sk-1)＝∫rkp(rk|Sk-1)drk
secondly, through software behavior trajectory training, setting alpha as the probability that the probability of A occurrence remains unchanged, p0Is at initialization time rkAnd finally obtaining the beta probability distribution of single software behavior prediction according to the occurrence probability, namely:
p(rk|Sk-1)＝αp(rk-1|Sk-1)+(1-α)p0(rk)
s3, constructing a prior value optimization model algorithm by taking the single same behavior of the past software as a prior value, namely:
adding prior value information on the well-established beta probability distribution model, assuming that the probability of the establishment of the prior value is p (experimental), and the prediction probability before adding the prior value information is p (original), and according to the Bayesian theory, the following formula is established:
wherein p (experimenter | original) is a probability that the prior information is true under the condition of the predicted probability, namely a probability that a prior value p (original) is true in the corresponding beta distribution;
then the predicted value of the single binary behavior of the software can be obtained, and further a software behavior prediction sequence is obtained;
s4, optimizing the behavior predicted value of the software by selectively using a memory regression optimization algorithm, wherein the specific memory regression optimization processing comprises the following steps: after adding prior value information, receiving a historical sequence of single software behaviors, and returning a beta distribution list after memory regression processing, wherein the length of the list is the same as that of the historical sequence of the software behaviors, and the beta distribution list represents beta distribution in a probability prediction function corresponding to each software behavior in the historical sequence of the software behaviors.
2. The software behavior prediction method based on beta distribution and bayes estimation according to claim 1, characterized in that: for the historical sequence of individual software behaviors in S4, the weight values are set, the longer the present time is, the lower the weight value is, and the closer the present time is, the higher the weight setting is.
3. The software behavior prediction method based on beta distribution and bayes estimation according to claim 2, characterized in that: there are two options, discrete and linear, for the weight values set for the historical sequence of individual software behaviors in S4.
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| CN113158234A (en) * | 2021-03-29 | 2021-07-23 | 上海雾帜智能科技有限公司 | Method, device, equipment and medium for quantifying occurrence frequency of security event |
| CN113590486A (en) * | 2021-02-23 | 2021-11-02 | 中国人民解放军军事科学院国防科技创新研究院 | Open source software code quality evaluation method based on measurement |
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| CN107679566A (en) * | 2017-09-22 | 2018-02-09 | 西安电子科技大学 | A kind of Bayesian network parameters learning method for merging expert's priori |
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| US20110302031A1 (en) * | 2010-06-07 | 2011-12-08 | Microsoft Corporation | Click modeling for url placements in query response pages |
| CN107358311A (en) * | 2017-06-07 | 2017-11-17 | 西安工业大学 | A kind of Time Series Forecasting Methods |
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