CN110390561B - User-financial product selection tendency high-speed prediction method and device based on momentum acceleration random gradient decline - Google Patents

User-financial product selection tendency high-speed prediction method and device based on momentum acceleration random gradient decline Download PDF

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CN110390561B
CN110390561B CN201910598139.3A CN201910598139A CN110390561B CN 110390561 B CN110390561 B CN 110390561B CN 201910598139 A CN201910598139 A CN 201910598139A CN 110390561 B CN110390561 B CN 110390561B
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冯锦刚
秦雯
罗辛
廖殷
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Abstract

The invention discloses a user-financial product selection tendency high-speed prediction method and a device based on momentum acceleration random gradient descent, wherein the prediction method comprises the following steps: collecting user-financial product scoring data and constructing the user-financial product scoring data into a scoring matrix of | M | rows and | N | columns; constructing and initializing a hidden feature matrix, and constructing and solving an objective function; determining the gradient of the decision parameter with the highest updating convergence speed; judging whether the limiting parameters of the prediction model to the gradient meet the conditions or not; judging whether the prediction model reaches convergence; after the prediction model reaches convergence, outputting a hidden feature matrix obtained by training; and using the obtained implicit characteristic matrix for predicting missing values in the scoring matrix. The invention provides a user-financial product selection tendency high-speed prediction result with momentum acceleration and random gradient reduction, provides personalized service for the user, and quickly provides safe, reliable and rigorous financial service for potential users in a family financial e-commerce platform.

Description

User-financial product selection tendency high-speed prediction method and device based on momentum acceleration random gradient decline
Technical Field
The invention relates to the technical field of computer data processing, in particular to a user-financial product selection tendency high-speed prediction method and device based on momentum acceleration random gradient decline.
Background
With the continuous change of computer technology and the active development of social economy, the financial e-commerce platform has deepened into our lives. More and more users select different financial products to invest through the financial e-commerce platform, and generally, after the users purchase the products on the financial platform, the users can correspondingly evaluate the products through investment reports and personal experiences. Thus, a consumer-oriented e-commerce consumption pattern is formed. However, with the increasing maturity of financial platforms and the number of financial products increasing dramatically, users cannot select the most desirable product among numerous financial products. In order to provide accurate personalized services for users, the relationship between the users and the financial products can be represented by a user-financial product scoring matrix, wherein the degree of the user score represents the degree of the acceptance of the products by the users, and the matrix for measuring the relationship between the users and the financial products is a high-dimensional and extremely sparse matrix.
According to the historical scores of the user financial platform statistics, the user can know and analyze the preference rules of the user on financial products, and an effective user-financial product preference prediction model is established on the basis. And the real environment is simulated through the simulation environment of the user scoring the financial products, thereby providing an important scientific basis for the marketing strategy of the financial products.
Prediction methods regarding user-financial product preferences have been implemented, but these methods have significant shortcomings in terms of user-financial product-constructed model training time, prediction accuracy, and other problems, such as: in the model training process, the training time of the model is very high, the prediction precision of the model is low, and safe and reliable high-return financial products cannot be provided for users in time. Due to the particularity of the financial industry, timely provision of high-reward products for users is very important. Therefore, the existing method has great disadvantages in the application of real finance-related e-commerce platforms.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a user-financial product selection tendency high-speed prediction method and device based on momentum acceleration random gradient decline, which can be realized according to the historical scores of users on financial products: (1) high-precision prediction of a user-financial product scoring matrix; (2) high speed prediction of a user-financial product scoring matrix.
To solve the above technical problem, according to a first aspect of the present invention, there is provided a user-financial product election tendency high-speed prediction apparatus based on momentum-accelerated stochastic gradient descent, the apparatus comprising:
a data preprocessing module: collecting data through a financial platform server, processing the data into a data format which can be directly used in model training, and putting the processed data into a storage module;
the data storage module is used for storing data such as temporary variable values, values corresponding to an initialization unit, a hidden feature matrix obtained by final training and the like generated in the high-speed prediction process of the user-financial product selection tendency based on momentum acceleration random gradient decline;
the data initialization module acquires user-financial product data from the storage module and initializes a hidden feature matrix required in model training;
the high-speed convergence direction selection module is used for receiving the initialized hidden feature matrix and determining the high-speed convergence direction in the model training process;
the prediction data generation module is used for predicting the characteristic data at a high speed and storing the obtained characteristic prediction data into a data unit;
and the data output module is used for outputting the finally obtained hidden features of the training and predicting the unknown score by using the obtained hidden features.
Further, the high-speed convergence direction selection module comprises a corresponding initialization data receiving unit and a high-speed convergence direction selection unit, wherein the corresponding initialization data receiving unit is used for receiving initialization data required during model training; the high-speed convergence direction selection unit controls the gradient size by using a gradient self-adaptive control factor and a decay index, the gradient in the direction with the fastest convergence of the current decision parameter is obtained by linear combination of the current gradient and the accumulated gradient, and the gradient control parameter beta and the gradient decay index gamma are kept to be effective values in a (0,1) interval.
Further, the data output module comprises an output hidden feature unit and a prediction unknown scoring unit, and the output hidden feature unit is used for outputting hidden features finally obtained by training; and the unknown prediction scoring unit is used for predicting the hidden features obtained by the unknown scoring according to the output hidden feature unit.
According to the preferred embodiment of the user-financial product selection tendency high-speed prediction device based on momentum acceleration random gradient descent, the data preprocessing module comprises:
the data receiving unit acquires user-financial product related data from a financial platform, a user set on the platform is recorded as M, a commodity set is recorded as N, and a matrix of | M | rows and | N | columns is established as a user-financial product scoring matrix R.
According to the preferred embodiment of the user-financial product selection tendency high-speed prediction device based on momentum acceleration random gradient descent, the data storage module comprises:
and the storage unit is used for storing the received scoring data in a form of a triple. The triplet representation is in the form U ═ m, n, r, where m, n represent the user and financial product, respectively, in the user-financial product relationship matrix, and r represents the score, i.e., the score of user m for financial product n. The feature data of the user and the financial product are stored in a matrix form as two hidden feature matrices B and J, and the two hidden feature matrices have the same feature dimension f.
According to the preferable scheme of the user-financial product selection tendency high-speed prediction device based on momentum acceleration random gradient reduction, the initialization unit user initializes relevant parameters related in the user-financial product selection tendency high-speed prediction process based on momentum acceleration random gradient reduction, and the method specifically comprises the following steps:
initializing two hidden feature matrixes B and J; initializing a characteristic dimension f; initializing a cumulative gradient balance control factor beta; initializing a gradient attenuation index gamma; initializing a convergence termination threshold τ; initializing a maximum training iteration round number L; initializing an iteration round number control variable l in the training process; initializing a regularization factor λ2(ii) a Wherein the characteristic dimensionThe degree f determines the feature space dimension of each hidden feature matrix and is initialized to be a positive integer; two implicit feature matrixes B and J, namely B is an implicit feature matrix of | M | rows and f columns, J is an implicit feature matrix of | N | rows and f columns, and the implicit feature matrixes are initialized by random smaller positive numbers respectively; the maximum training iteration round number L is a variable for controlling the upper limit of the iteration process and is initialized to be a larger positive integer; initializing an iteration round number control variable l to be 0; the convergence termination threshold tau is a parameter for judging whether the iteration process has converged, and is initialized by a minimum positive number; regularization factor lambda2In the extraction iteration process, constants corresponding to the regularization effect of relevant elements of the hidden feature matrix B and J are initialized to be smaller positive numbers. The user-financial product selection tendency high-speed prediction device based on momentum acceleration random gradient decline is used for combining initialized related parameters and constructing high-speed convergence direction selection; the method specifically comprises the following steps:
constructing a target loss function according to a known scoring data set lambda in a user-financial product relation matrix R
Figure BDA0002118282100000041
Is represented as follows:
Figure BDA0002118282100000042
wherein R is(Λ)Representing a set of user known scoring data for a financial product in a user-financial product scoring matrix R; r ism,nThe meaning of the representation is that the entity relationship between the user m and the financial product n is the grade of the user m to the financial product n;
Figure BDA0002118282100000051
representing the scores of the users m to the commodities n in the known score data set lambda; bm′Representing the hidden feature corresponding to the mth user in the user hidden feature matrix B; j is a function ofn′And representing the hidden feature corresponding to the nth commodity in the financial product hidden feature matrix J.
To enhance the generalization performance of the model, it is common toObjective loss function
Figure BDA0002118282100000052
Middle L2Regularization term, using L2And regularization, which restrains the optimization process and prevents the overfitting problem in the optimization process. Thus, adding L to the objective function2After the regularization term, the resulting objective function is:
Figure BDA0002118282100000053
wherein R is(Λ)Representing a set of user known scoring data for a financial product in a user-financial product scoring matrix R; r ism,nThe meaning of the representation is that the entity relation between the user m and the financial product n is the score of the user m and the financial product n;
Figure BDA0002118282100000054
representing the user's m score for the financial product n in a known score data set Λ; bm′Representing the hidden feature corresponding to the mth user in the user hidden feature matrix B; j is a function ofn′And representing the hidden feature corresponding to the nth commodity in the financial product hidden feature matrix J. Lambda [ alpha ]2Regularization parameter, measure L, representing a hidden feature matrix2The limiting effect of the regularization term on the model.
Controlling B and J to satisfy the cumulative error over the set
Figure BDA0002118282100000055
At a minimum, the error is accumulated in the above by using a random gradient descent optimization algorithm with high-speed convergence
Figure BDA0002118282100000056
And training the matrixes B and J to obtain the global optimal solution of the matrixes B and J. In the training process, the selection of the high-speed updating direction of the hidden features of the user and the financial product is carried out, the linear combination of the previous gradient and the current updating gradient is realized according to the gradient balance factor and the exponential decay factor, and the current updating b is calculatedm′And jn′The formula expression of the gradient value corresponding to the fastest convergence speed is as follows:
Figure BDA0002118282100000061
wherein beta is a gradient equilibrium control factor and gamma is a gradient decay index. Parameter k(t)And a parameter v(t)Are respectively a single element bm,kAnd jn,kThe final gradient magnitude at the t-th update, which consists of two parts: kappa(t-1)V and v(t-1)Corresponding to the final gradient and the current gradient accumulation values previously updated by the decision parameter. Parameter k(t-1)And a parameter v(t-1)Are respectively a single element bm,kAnd jn,kThe final gradient magnitude at the t-1 th update is the accumulation of the final gradient at the t-2 th update and the corresponding gradient at the t-1 st update. Wherein b ism,kAnd jn,kAre respectively bm′And jn′The kth element of the vector.
Figure BDA0002118282100000064
And
Figure BDA0002118282100000065
respectively, the current gradient values at the t-th update. The expression is as follows:
Figure BDA0002118282100000062
the user-financial product selection tendency high-speed prediction device based on momentum acceleration random gradient decline is used for generating high-speed prediction data according to the preferred scheme; the method specifically comprises the following steps:
the current update b can be calculated by the high-speed convergence direction selection unitm′And jn′And (3) the corresponding gradient value when the convergence speed is fastest, so that an updating rule of a user-financial product selection tendency high-speed prediction model based on momentum acceleration random gradient decline can be obtained:
in relation to bm,kThe update formula of (2) is as follows:
Figure BDA0002118282100000063
about jn,kThe update formula of (2) is as follows:
Figure BDA0002118282100000071
wherein
Figure BDA0002118282100000075
Representing the user's m score for the financial product n in a known score data set Λ; beta is a gradient balance control factor; gamma is a gradient decay index; parameter k(t)And a parameter v(t)Are respectively a single element bm,kAnd jn,kThe final gradient magnitude at the t-th update, which consists of two parts: k is a radical of(t-1)V and v(t-1)Corresponding to the final gradient and the current gradient accumulation values previously updated by the decision parameter. Parameter k(t-1)And a parameter v(t-1)Are respectively a single element bm,kAnd jn,kThe final gradient magnitude at the t-1 th update is the accumulation of the final gradient at the t-2 th update and the corresponding gradient at the t-1 st update. Wherein b ism,kAnd jn,kAre respectively bm′And jn′The kth element of the vector.
Figure BDA0002118282100000072
And
Figure BDA0002118282100000073
respectively, the current gradient values at the t-th update.
Repeating the training process on lambda until
Figure BDA0002118282100000074
For convergence on lambda, the convergence judgment condition is that the training iteration round number control variable r reaches the maximum trainingNumber of rounds of iteration L, or calculated after the iteration of the round is finished
Figure BDA0002118282100000076
Value and previous round
Figure BDA0002118282100000077
The absolute value of the difference in values is already less than the convergence termination threshold τ.
The user-financial product selection tendency high-speed prediction device based on momentum acceleration random gradient decline is characterized by comprising the following steps: the output unit is used for outputting a hidden feature unit and a prediction unknown grading unit for predicting unknown grading; the method specifically comprises the following steps:
output unit outputs target loss function
Figure BDA0002118282100000078
And when the minimum two hidden feature matrixes are reached, the unknown score predicting unit predicts the unknown scores in the user-financial product matrix by using the hidden feature matrixes obtained by the output unit.
According to a second aspect of the present invention, there is provided a method for predicting a user-financial product selection tendency based on a momentum-accelerated stochastic gradient descent, comprising: the method comprises the following steps:
s1: and acquiring user-financial product scoring data through a financial platform server, recording a user set on the financial platform as M and a financial product set as N, and establishing a matrix of | M | rows and | N | columns as a user-financial product scoring matrix R. And sending the data to a user-financial product selection tendency high-speed prediction device based on momentum acceleration random gradient decline.
S2: and initializing a corresponding hidden feature matrix by utilizing the user-financial product scoring data, and constructing a target function by known scoring data and corresponding predicted values.
S3: solving the decision parameters according to the established objective function, and solving the gradient corresponding to the decision parameters to be updated currently in the current round;
s4: determining the gradient of the decision parameter with the highest updating convergence speed;
s5: judging whether the limiting parameters of the gradient of the user-financial product selection tendency high-speed prediction model based on momentum acceleration random gradient decline meet the conditions: if yes, executing step S6, otherwise resetting illegal parameters and executing step S5 again;
s6: judging whether the model reaches convergence according to the convergence condition of the user-financial product selection tendency high-speed prediction model based on momentum acceleration random gradient decline: if convergence is reached, executing step S7, if convergence is not reached, returning to executing step S3;
s7: after the prediction model training reaches convergence, outputting a corresponding hidden feature matrix obtained by the model training;
s8: and predicting missing values in the user-financial product scoring matrix by using the hidden feature matrix obtained by the matrix decomposition method.
According to the preferred embodiment of the present invention, the step S2 includes:
s21, initializing relevant parameters:
initializing two hidden feature matrixes B and J; initializing a characteristic dimension f; initializing a cumulative gradient balance control factor beta; initializing a gradient attenuation index gamma; initializing a maximum training iteration round number L; initializing an iteration round number control variable l and a convergence termination threshold tau in a training process; initializing a regularization factor λ2；
The initialization content is as follows:
the characteristic dimension f determines the characteristic space dimension of the hidden characteristic matrix of the user and the financial product and is initialized to be a positive integer.
The sizes of the two hidden feature matrices B and J are respectively: b is a hidden feature matrix with | M | rows and f columns, J is a hidden feature matrix with | N | rows and f columns, and the two hidden feature matrices are respectively initialized by random small positive numbers.
Initializing the cumulative gradient balance control factor β is initialized to a small positive number.
The initialization gradient decay exponent γ is initialized to a small positive number.
The maximum training iteration round number L is a variable for controlling the upper limit of the iteration process and is initialized to be a larger positive integer.
The iteration round number control variable l is initialized to 0.
The convergence termination threshold τ is a parameter for determining whether the iteration process has converged, and is initialized with a very small positive number.
Regularization factor lambda2In the process of controlling extraction iteration, constants corresponding to regularization effects of relevant elements of the hidden feature matrix B and J are initialized to be small positive numbers.
S22, constructing a target loss function according to the known scoring data set Lambda in the user-financial product relation matrix R
Figure BDA0002118282100000092
Is represented as follows:
Figure BDA0002118282100000091
wherein the Euclidean distance is taken as an optimization target; using L2And regularization, which restrains the optimization process and prevents the overfitting problem in the optimization process.
According to the preferred embodiment of the present invention, the step S3 includes:
s31, according to the objective function, the gradient corresponding to the decision parameter which needs to be updated currently is obtained, and the formula is as follows:
Figure BDA0002118282100000101
according to the preferred embodiment of the present invention, the step S4 includes:
s41, obtaining the gradient corresponding to the current update decision parameter according to the step S3
Figure BDA0002118282100000103
And
Figure BDA0002118282100000104
s42, according to the limit rule of the balance factor and the attenuation index to the gradient, the decision parameter gradient with the highest current updating convergence speed is determined through the linear combination of the accumulated gradient and the current gradient, and the formula is as follows:
Figure BDA0002118282100000102
wherein beta is a gradient equilibrium control factor and gamma is a gradient decay index. Parameter k(t)And a parameter v(t)Are respectively a single element bm,kAnd jn,kThe final gradient magnitude at the t-th update, which consists of two parts: kappa(t-1)V and v(t-1)Corresponding to the final gradient and the current gradient accumulation values previously updated by the decision parameter. Parameter k(t-1)And a parameter v(t-1)Are respectively a single element bm,kAnd jn,kThe final gradient magnitude at the t-1 th update is the accumulation of the final gradient at the t-2 th update and the corresponding gradient at the t-1 st update. Wherein b ism,kAnd jn,kAre respectively bm′And jn′The kth element of the vector.
Figure BDA0002118282100000105
And
Figure BDA0002118282100000106
respectively, the current gradient values at the t-th update.
According to the preferred embodiment of the present invention, the step S6 includes:
s61, updating the user-financial product selection tendency high-speed prediction model based on momentum acceleration random gradient decline:
wherein in respect of bm,kThe update formula of (2) is as follows:
Figure BDA0002118282100000111
wherein with respect to jn,kThe update formula of (2) is as follows:
Figure BDA0002118282100000112
wherein
Figure BDA0002118282100000113
Representing the user's m score for the financial product n in a known score data set Λ; beta is a gradient balance control factor; gamma is a gradient decay index; parameter k(t)And a parameter v(t)Are respectively a single element bm,kAnd jn,kThe final gradient magnitude at the t-th update, which consists of two parts: kappa(t-1)V and v(t-1)Corresponding to the final gradient and the current gradient accumulation values previously updated by the decision parameter. Parameter k(t-1)And a parameter v(t-1)Are respectively a single element bm,kAnd jn,kThe final gradient magnitude at the t-1 th update is the accumulation of the final gradient at the t-2 th update and the corresponding gradient at the t-1 st update. Wherein b ism,kAnd jn,kAre respectively bm′And jn′The kth element of the vector.
And S62, judging whether the model reaches convergence according to the convergence condition of the user-financial product selection tendency high-speed prediction model based on momentum acceleration random gradient reduction, namely judging whether the current parameter is smaller than the threshold tau when updating. The difference between the current prediction accuracy and the previous prediction accuracy is usually set to be larger than 1 × 10-5And if so, the requirement of updating the parameters is met, otherwise, the model convergence condition is reached.
The method and the device for predicting the user-financial product selection tendency based on momentum acceleration random gradient decline have the advantages that: the invention provides a user-financial product selection tendency high-speed prediction method and device based on momentum acceleration random gradient decline, which are used for analyzing data generated between financial products and users and predicting unknown relationships between the users and the financial products through analysis results. The forecasting strategy is to analyze the internal statistical law of known user-commodity grading data by utilizing a hidden characteristic accelerated analysis idea, so that a user-financial product selection tendency high-speed forecasting result with momentum accelerated random gradient reduction is provided, personalized service is provided for a user, safe, reliable and rigorous financial service is rapidly provided for potential users in a family financial electronic commerce platform, and better wealth distribution and family asset allocation are realized.
Drawings
Fig. 1 is a schematic structural diagram of a user-financial product selection tendency high-speed prediction apparatus based on momentum acceleration random gradient descent.
FIG. 2 is a flow chart illustrating a method for predicting user-financial product selection tendency based on momentum-accelerated stochastic gradient descent.
FIG. 3 is a graph of time comparison of prediction models before and after application of the present invention.
FIG. 4 is a comparison graph of prediction accuracy of prediction models before and after applying the present invention, where RMSE is a measure of prediction error, and the smaller RMSE, the higher the prediction accuracy.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in further detail by way of embodiments with reference to the accompanying drawings. The embodiments described below with reference to the accompanying drawings are illustrative only for the purpose of explaining the present invention, and are not to be construed as limiting the present invention.
Example 1:
referring to fig. 1, fig. 1 shows a user-financial product election tendency high-speed prediction apparatus based on momentum-accelerated stochastic gradient descent according to the present invention, the apparatus comprising:
a data preprocessing module 510 for receiving global user-family financial product scoring data, processing the data into a data format that can be directly used in model training, and putting the processed data into a data storage module 520.
And a data storage module 520, configured to store the preprocessed input data, temporary variables generated in the model prediction process, values corresponding to the initialization unit, and a hidden feature matrix obtained through final training.
And a data initialization module 530, configured to initialize the hidden feature matrix of the model training.
And a high-speed convergence direction selection module 540, configured to receive the initialized hidden feature matrix, and determine a high-speed convergence direction in the model training process.
The high-speed convergence direction selection module 540 includes a unit 541 that receives corresponding initialization data and a high-speed convergence direction selection unit 542.
A unit 541 for receiving corresponding initialization data is configured to receive initialization data required for model training.
The high-speed convergence direction selection unit 542 controls the gradient magnitude using the gradient adaptive control factor and the attenuation index. And obtaining the gradient in the direction with the fastest convergence of the current decision parameter through the linear combination of the current gradient and the accumulated gradient, and keeping the gradient control parameter beta and the gradient attenuation index gamma as effective values in a (0,1) interval.
And a prediction data generation module 550 for predicting the feature data at a high speed and storing the obtained feature prediction data in a data unit.
The prediction data generating module 550 includes a high-speed prediction data generating unit 551, configured to perform linear combination on the updated corresponding gradient and the current gradient in the module 540 before the accumulated decision parameters of different degrees to obtain a final gradient value, and perform an update operation on the decision parameters according to the gradient value.
And the output module 560 is used for outputting the hidden feature matrix finally obtained by the model training, and solving the predicted value of the unknown value in the user-financial product scoring matrix by using the vector inner product in the corresponding hidden feature matrix through a matrix decomposition technology.
In a specific embodiment, the data preprocessing module 510 includes:
the data receiving unit 511 is configured to obtain user-financial product related data from a financial platform, where a user set on the platform is denoted as M, a commodity set is denoted as N, and a matrix of | M | rows and | N | columns is established as a user-financial product scoring matrix R.
In a specific embodiment, the data storage module 520 includes:
the storage unit 521 is configured to store the received scoring data in a triple form. The triplet representation is in the form U ═ U, i, r, where U, i represent the user and financial product, respectively, in the user-financial product relationship matrix, and r represents the score, i.e., the score of the financial product i by the user U. The feature data of the user and the financial product are stored in a matrix form as two hidden feature matrices B and J, and the two hidden feature matrices have the same feature dimension f.
In a specific embodiment, the initialization unit 531 is configured to initialize a hidden feature matrix and related parameters involved in a user-financial product selection tendency high-speed prediction process based on momentum-accelerated random gradient descent; the method specifically comprises the following steps:
initializing two hidden feature matrixes B and J; initializing a characteristic dimension f; initializing a cumulative gradient balance control factor beta; initializing a gradient attenuation index gamma; initializing a convergence termination threshold τ; initializing a maximum training iteration round number L; initializing an iteration round number control variable l in the training process; initializing a regularization factor λ2(ii) a The characteristic dimension f determines the characteristic space dimension of each hidden characteristic matrix and is initialized to be a positive integer; two implicit feature matrixes B and J, namely B is an implicit feature matrix of | M | rows and f columns, J is an implicit feature matrix of | N | rows and f columns, and the implicit feature matrixes are initialized by random smaller positive numbers respectively; the maximum training iteration round number L is a variable for controlling the upper limit of the iteration process and is initialized to be a larger positive integer; initializing an iteration round number control variable l to be 0; the convergence termination threshold tau is a parameter for judging whether the iteration process has converged, and is initialized by a minimum positive number; regularization factor lambda2In the extraction iteration process, constants corresponding to the regularization effect of relevant elements of the hidden feature matrix B and J are initialized to be smaller positive numbers.
In a specific embodiment, the high-speed convergence direction selection unit 542 is configured to combine the initialized relevant parameters and construct a high-speed convergence direction selection; the method specifically comprises the following steps:
constructing a target loss function according to a known scoring data set lambda in a user-financial product relation matrix R
Figure BDA0002118282100000153
Is represented as follows:
Figure BDA0002118282100000151
wherein R is(Λ)Representing a set of user known scoring data for a financial product in a user-financial product scoring matrix R; r ism,nThe meaning of the representation is the entity relation between the user m and the financial product n, namely the score of the user m on the financial product n;
Figure BDA0002118282100000154
representing the user's m score for the financial product n in a known score data set Λ; bm′Representing the hidden feature corresponding to the mth user in the user hidden feature matrix B; j is a function ofn′And representing the hidden feature corresponding to the nth commodity in the financial product hidden feature matrix J.
To enhance the generalization performance of the model, a penalty function is usually applied to the target
Figure BDA0002118282100000155
Adding L2Regularization term, using L2And regularization, which restrains the optimization process and prevents the overfitting problem in the optimization process. Thus, by fitting L into the objective function2After regularization term, the resulting objective function is:
Figure BDA0002118282100000152
wherein R is(Λ)Representing a set of user known scoring data for a financial product in a user-financial product scoring matrix R; lambda [ alpha ]2Representing hidden feature momentsRegularization parameter of array, measure L2The limiting effect of the regularization term on the model.
Controlling B and J to satisfy the cumulative error over the set
Figure BDA0002118282100000163
At a minimum, the error is accumulated in the above by using a random gradient descent optimization algorithm with high-speed convergence
Figure BDA0002118282100000164
And training the matrixes B and J to obtain the global optimal solution of the matrixes B and J. In the training process, the selection of the high-speed updating direction of the hidden features of the user and the financial product is carried out, the linear combination of the previous gradient and the current updating gradient is realized according to the gradient balance factor and the exponential decay factor, and the current updating b is calculatedm′And jn′The formula expression of the gradient value corresponding to the fastest convergence speed is as follows:
Figure BDA0002118282100000161
wherein beta is a gradient equilibrium control factor and gamma is a gradient decay index. Parameter k(t)And a parameter v(t)Are respectively a single element bm,kAnd jn,kThe final gradient magnitude at the t-th update, which consists of two parts: kappa(t-1)V and v(t-1)Corresponding to the final gradient and the current gradient accumulation values previously updated by the decision parameter. Parameter k(t-1)And a parameter v(t-1)Are respectively a single element bm,kAnd jn,kThe final gradient magnitude at the t-1 th update is the accumulation of the final gradient at the t-2 th update and the corresponding gradient at the t-1 st update. Wherein b ism,kAnd jn,kAre respectively bm′And jn′The kth element of the vector.
Figure BDA0002118282100000165
And
Figure BDA0002118282100000166
respectively, the current gradient values at the t-th update. The expression is as follows:
Figure BDA0002118282100000162
in a specific embodiment, the high-speed prediction data generation unit 551 is used for high-speed prediction data generation; the method specifically comprises the following steps:
the current update b can be calculated by the high-speed convergence direction selection unit 551m′And jn′And (3) the corresponding gradient value when the convergence speed is fastest, so that an updating rule of a user-financial product selection tendency high-speed prediction model based on momentum acceleration random gradient decline can be obtained:
in relation to bm,kThe update formula of (2) is as follows:
Figure BDA0002118282100000171
about jn,kThe update formula of (2) is as follows:
Figure BDA0002118282100000172
wherein
Figure BDA0002118282100000173
Representing the user's m score for the financial product n in a known score data set Λ; beta is a gradient balance control factor; gamma is a gradient decay index; parameter k(t)And a parameter v(t)Are respectively a single element bm,kAnd jn,kThe final gradient magnitude at the t-th update, which consists of two parts: kappa(t-1)And upsilon(t-1)Corresponding to the final gradient and the current gradient accumulation values previously updated by the decision parameter. Parameter k(t-1)And a parameter v(t-1)Are respectively a single element bm,kAnd jn,kThe final gradient magnitude at the t-1 updating is the final gradient at the t-2 updating and the t-1 pairShould be accumulated. Wherein b ism,kAnd jn,kAre respectively bm′And jn′The kth element of the vector.
Figure BDA0002118282100000174
And
Figure BDA0002118282100000175
respectively, the current gradient values at the t-th update.
Repeating the training process on lambda until
Figure BDA0002118282100000176
For convergence on the lambda, the convergence judgment condition is that the training iteration round number control variable r reaches the maximum training iteration round number L or is calculated after the iteration of the round is finished
Figure BDA0002118282100000177
Value and previous round
Figure BDA0002118282100000178
The absolute value of the difference in values is already less than the convergence termination threshold τ.
The user-financial product selection tendency high-speed prediction device based on momentum acceleration random gradient decline is characterized by comprising the following steps: the output unit is used for outputting a hidden feature unit and a prediction unknown grading unit for predicting unknown grading; the method specifically comprises the following steps:
output unit outputs target loss function
Figure BDA0002118282100000181
And when the minimum two hidden feature matrixes are reached, the unknown score predicting unit predicts the unknown scores in the user-financial product matrix by using the hidden feature matrixes obtained by the output unit.
The invention is especially used for high-speed prediction of user-financial product selection tendency.
Example 2
Referring to fig. 2, fig. 2 shows a user-financial product election tendency high-speed prediction method based on momentum acceleration random gradient descent, which comprises the following steps:
s1: the server collects user-financial product scoring data, a user set on the platform is recorded as M, a commodity set is recorded as N, and a matrix of M rows and N columns is established as a user-financial product scoring matrix R. And sending the data to a user-financial product selection tendency high-speed prediction device based on momentum acceleration random gradient decline.
S2: and initializing a corresponding hidden feature matrix by utilizing the user-financial product scoring data, and constructing a target function by known scoring data and corresponding predicted values.
S3: solving the objective function according to the established objective function, and solving the gradient corresponding to the decision parameter to be updated currently in the current round;
s4: determining the gradient of the decision parameter with the highest updating convergence speed;
s5: judging whether the limiting parameters of the gradient of the user-financial product selection tendency high-speed prediction model based on momentum acceleration random gradient decline meet the conditions: if yes, go to step S6, otherwise reset the illegal parameters and go to step S5 again.
S6: and judging whether the model reaches convergence according to the convergence condition of the user-financial product selection tendency high-speed prediction model based on momentum acceleration random gradient decline. S6 in fig. 2: selecting a trend high-speed prediction model based on the user-financial product with momentum accelerated random gradient decline, and judging whether the current control parameter condition meets the update condition of the parameters: if the update condition of the parameter is satisfied, returning to step S3; if not, it indicates that the model convergence condition is reached, step S7 is executed.
S7: after the prediction model training reaches convergence, outputting a corresponding hidden feature matrix obtained by the model training;
s8: and predicting missing values in the user-financial product scoring matrix by using the hidden feature matrix obtained by the matrix decomposition method.
In a specific embodiment, step S2 initializes the implicit feature matrix of the user and the financial product, and constructs an objective function according to the known score data and the corresponding predicted value, which specifically includes:
s21, initializing relevant parameters:
initializing two hidden feature matrixes B and J; initializing a characteristic dimension f; initializing a cumulative gradient balance control factor beta; initializing a gradient attenuation index gamma; initializing a maximum training iteration round number L; initializing an iteration round number control variable l and a convergence termination threshold tau in a training process; initializing a regularization factor λ2；
The initialization content is as follows:
the characteristic dimension f determines the characteristic space dimension of the hidden characteristic matrix of the user and the financial product and is initialized to be a positive integer; for example, the feature dimension f is initialized to 20.
The sizes of the two hidden feature matrices B and J are respectively: b is a hidden feature matrix of | M | rows and f columns, J is a hidden feature matrix of | N | rows and f columns, and the two hidden feature matrices are respectively initialized by random smaller positive numbers; the two latent feature matrices B and J are initialized, for example, with random positive numbers in the set (0, 0.005).
Initializing the cumulative gradient balance control factor β to a smaller positive number; for example, the cumulative gradient balance control factor β is initialized to a positive number in the set (0, 1).
Initializing a gradient decay exponent gamma to a smaller positive number; for example, the gradient decay exponent γ is initialized to a positive number in the set (0, 1).
The maximum training iteration round number L is a variable for controlling the upper limit of the iteration process and is initialized to be a larger positive integer; for example, the maximum number of training iterations L is initialized to 1000.
The iteration round number control variable l is initialized to 0.
The convergence termination threshold tau is a parameter for judging whether the iteration process has converged, and is initialized by a minimum positive number; for example, the convergence termination threshold τ is initialized to 1 × 10-5。
Regularization factor lambda2In the process of controlling extraction iteration, constants corresponding to regularization effects of relevant elements of the hidden feature matrix B and J are initialized to be smaller positive numbers; for example by a regularization factor λ2Initialized to the set [0.005,0.05 ]]Positive number in (1).
S22, constructing a target loss function according to the known scoring data set Lambda in the user-financial product relation matrix R
Figure BDA0002118282100000203
Is represented as follows:
Figure BDA0002118282100000201
wherein the Euclidean distance is taken as an optimization target; using L2And regularization, which restrains the optimization process and prevents the overfitting problem in the optimization process.
In a specific embodiment, step S3 includes:
s31, according to the objective function, the gradient corresponding to the decision parameter which needs to be updated currently is obtained, and the formula is as follows:
Figure BDA0002118282100000202
in a specific embodiment, step S4 includes:
s41, obtaining the gradient corresponding to the current update decision parameter according to the step S3
Figure BDA0002118282100000204
And
Figure BDA0002118282100000205
s42, according to the limit rule of the balance factor and the attenuation index to the gradient, the decision parameter gradient with the highest current updating convergence speed is determined through the linear combination of the accumulated gradient and the current gradient, and the formula is as follows:
Figure BDA0002118282100000211
wherein beta is a gradient equilibrium control factor and gamma is a gradient decay index. Parameter k(t)And a parameter v(t)Are respectively a single element bm,kAnd jn,kThe final gradient magnitude at the t-th update, which consists of two parts: k is a radical of(t-1)V and v(t-1)Corresponding to the final gradient and the current gradient accumulation values previously updated by the decision parameter. Parameter k(t-1)And a parameter v(t-1)Are respectively a single element bm,kAnd jn,kThe final gradient magnitude at the t-1 th update is the accumulation of the final gradient at the t-2 th update and the corresponding gradient at the t-1 st update. Wherein b ism,kAnd jn,kAre respectively bm′And jn′The kth element of the vector.
Figure BDA0002118282100000213
And
Figure BDA0002118282100000214
respectively, the current gradient values at the t-th update.
In an embodiment, the step S6 of predicting the user-financial product selection tendency includes:
s61, updating the user-financial product selection tendency high-speed prediction model based on momentum acceleration random gradient decline:
wherein in respect of bm,kThe update formula of (2) is as follows:
Figure BDA0002118282100000212
wherein with respect to jn,kThe update formula of (2) is as follows:
Figure BDA0002118282100000221
wherein
Figure BDA0002118282100000222
Representing the user's m score for the financial product n in a known score data set Λ; beta is a gradient balance control factor; gamma is a gradient decay index; parameter k(t)And a parameter v(t)Are respectively a single element bm,kAnd jn,kThe final gradient magnitude at the t-th update, which consists of two parts: k: (t-1)V and v(t-1)Corresponding to the final gradient and the current gradient accumulation values previously updated by the decision parameter. Parameter k(t-1)And a parameter v(t-1)Are respectively a single element bm,kAnd jn,kThe final gradient magnitude at the t-1 th update is the accumulation of the final gradient at the t-2 th update and the corresponding gradient at the t-1 st update. Wherein b ism,kAnd jn,kAre respectively bm′And jn′The kth element of the vector.
And S62, judging whether the model reaches convergence according to the convergence condition of the user-financial product selection tendency high-speed prediction model based on momentum acceleration random gradient reduction, namely judging whether the current parameter is smaller than the threshold tau when updating. The difference between the current prediction accuracy and the previous prediction accuracy is usually set to be larger than 1 × 10-5And if so, the requirement of updating the parameters is met, otherwise, the model convergence condition is reached.
FIG. 3 is a graph illustrating a comparison of execution times for applying a user-financial product election tendency high-speed prediction based on momentum-accelerated stochastic gradient descent and for not applying a user-financial product election tendency high-speed prediction based on momentum-accelerated stochastic gradient descent. As can be seen from FIG. 3, after the technique of the present invention is applied, the model has much less run time for the user-financial product relationship data than if the technique were not applied. Specifically, as can be seen from fig. 3, the time required to use the present invention without the present invention is about 6 times that of the time required to use the present invention after the present invention is applied. Namely, after the technology of the invention is applied, the running time of the model is improved by more than 6 times than the original running time, so that a user can quickly select a product from the heart-of-mind instrument from a plurality of financial products.
FIG. 4 is a diagram showing the comparison of RMSE, where RMSE is a measure of prediction error, where RMSE is higher in value and lower in prediction accuracy, in the case where user-financial product selection tendency high-speed prediction based on momentum-accelerated random gradient descent is applied and user-financial product selection tendency high-speed prediction based on momentum-accelerated random gradient descent is not applied; the smaller the RMSE value, the higher the prediction accuracy.
As shown in fig. 4, the RMSE after applying the technique of the present invention is more than 3 times lower than that without the technique of the present invention, and the smaller the RMSE value, the higher the prediction accuracy. Namely, the application of the technology of the invention greatly improves the accuracy of the model in the prediction of the financial product selection tendency. In practical application, the financial product which is safe, reliable, has practical guarantee and meets the individual requirements of the user can be better provided for the user.
According to the technical scheme, the user-financial product selection tendency high-speed prediction method based on momentum acceleration random gradient descent is provided, data generated between financial products and users are analyzed based on a momentum acceleration random gradient descent prediction model, and unknown relations between the users and the financial products are predicted through analysis results. The forecasting strategy is to analyze the internal statistical law of known user-commodity grading data by utilizing a hidden characteristic accelerated analysis idea, so that a user-financial product selection tendency high-speed forecasting result with momentum accelerated random gradient reduction is provided, personalized service is provided for a user, safe, reliable and rigorous financial service is rapidly provided for potential users in a family financial electronic commerce platform, and better wealth distribution and family asset allocation are realized.
While embodiments of the invention have been shown and described, it will be understood by those of ordinary skill in the art that: various changes, modifications, substitutions and alterations can be made to the embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.

Claims (8)

1. A user-financial product selection tendency high-speed prediction method based on momentum acceleration random gradient decline is characterized by comprising the following steps:
s1, collecting user-financial product scoring data, and constructing the user-financial product scoring data into a user-financial product scoring matrix R with an M row and an N column, wherein M is a user set, and N is a financial product set;
s2, constructing and initializing a hidden feature matrix, and constructing a target function through known scoring data and a predicted value;
s3, solving the objective function according to the established objective function, and solving the gradient corresponding to the decision parameter to be updated currently in the round;
s4, determining the decision parameter gradient with the fastest current updating convergence speed;
the step S4 includes:
s41, obtaining the gradient corresponding to the current update decision parameter according to the step S3
Figure FDA0003289844270000011
And
Figure FDA0003289844270000012
s42, according to the limit rule of the cumulative gradient balance factor beta and the gradient attenuation index gamma to the gradient, the decision parameter gradient with the highest current updating convergence speed is determined through the linear combination of the cumulative gradient and the current gradient, and the formula is as follows:
Figure FDA0003289844270000013
wherein, κ(t)V and v(t)Are respectively a single element bm,kAnd jn,kFinal gradient magnitude at the t-th update; kappa(t-1)V and v(t-1)Are respectively a single element bm,kAnd jn,kFinal gradient magnitude at t-1 update;
s5, judging whether the limiting parameters of the gradient of the user-financial product selection tendency high-speed prediction model based on momentum acceleration random gradient decline satisfy the conditions: if yes, executing step S6, if not, resetting illegal parameters and executing step S5 again;
s6, judging whether the model is converged according to the convergence condition of the user-financial product selection tendency high-speed prediction model based on momentum acceleration random gradient decline: if convergence is reached, executing step S7, if convergence is not reached, returning to executing step S3;
s7, outputting a hidden feature matrix obtained by model training after the prediction model training reaches convergence;
and S8, using the obtained hidden feature matrix to predict missing values in the user-financial product scoring matrix through a matrix decomposition method.
2. The method for predicting user-financial product election tendency high-speed based on momentum acceleration random gradient descent according to claim 1, wherein the step S2 includes:
s21, initializing relevant parameters:
initializing a characteristic dimension f to be a positive integer;
two latent feature matrices B and J are initialized: the matrix B is a user hidden feature matrix in a | M | row f column, the matrix J is a financial product hidden feature matrix in a | N | row f column, and the two hidden feature matrices are respectively initialized by random smaller positive numbers;
initializing the cumulative gradient balance control factor β to a smaller positive number;
initializing the gradient decay exponent γ to a small positive number;
initializing the maximum training iteration round number L into a larger positive integer;
initializing an iteration round number control variable l to 0;
initializing a convergence termination threshold τ with a very small positive number;
normalizing factor lambda2Is initialized to a small positive number of bits,
s22, constructing an objective function according to the known scoring data set Lambda in the user-financial product relation matrix R
Figure FDA0003289844270000021
For the objective function
Figure FDA0003289844270000022
Using Euclidean distance as optimization target and L2Regularization, and the resulting objective function is represented as follows:
Figure FDA0003289844270000031
wherein R is(Λ)Representing a set of user known scoring data for a financial product in a user-financial product scoring matrix R; bm′Representing the hidden feature corresponding to the mth user in the user hidden feature matrix B; j is a function ofn′Representing the hidden feature corresponding to the nth commodity in the financial product hidden feature matrix J; r ism,nRepresenting the user's m score for financial product n;
Figure FDA0003289844270000032
representing the scores of the users m to the commodities n in the known score data set lambda; lambda [ alpha ]2A regularization factor representing a hidden feature matrix.
3. The method for predicting user-financial product election tendency high-speed based on momentum acceleration random gradient descent according to claim 2, wherein the step S3 includes:
according to the objective function, the gradient corresponding to the decision parameter needing to be updated currently is obtained, and the formula is expressed as follows:
Figure FDA0003289844270000033
wherein, bm,kAnd jn,kAre respectively bm′And jn′The kth element of the vector;
Figure FDA0003289844270000034
and
Figure FDA0003289844270000035
respectively at the time of the t-th updatem,kAnd jn,kThe current gradient value of (a).
4. The method for predicting user-financial product election tendency high-speed based on momentum acceleration random gradient descent according to claim 1, wherein the step S6 includes:
s61, updating b of user-financial product selection tendency high-speed prediction model based on momentum acceleration random gradient declinem,kAnd jn,k：
Wherein in respect of bm,kThe update formula of (2) is as follows:
Figure FDA0003289844270000041
wherein with respect to jn,kThe update formula of (2) is as follows:
Figure FDA0003289844270000042
wherein the content of the first and second substances,
Figure FDA0003289844270000043
representing the user's m score for the financial product n in a known score data set Λ; beta is a cumulative gradient equilibrium control factor; gamma is a gradient decay index; bm,kAnd jn,kAre respectively bm′And jn′The kth element of the vector;
Figure FDA0003289844270000044
and
Figure FDA0003289844270000045
respectively is the current gradient value at the time of the t-th update; kappa(t)V and v(t)Are respectively a single element bm,kAnd jn,kThe final gradient magnitude at the t-th update; kappa(t-1)V and v(t-1)Are respectively a single element bm,kAnd jn,kThe gradient magnitude at the t-1 th update,
s62, judging whether the model is converged according to the convergence condition of the user-financial product selection tendency high-speed prediction model based on momentum acceleration random gradient decline: and judging whether the current parameter is smaller than the threshold tau or not during updating, and if so, reaching the model convergence condition.
5. A user-financial product selection tendency high-speed prediction apparatus based on momentum-accelerated random gradient descent, comprising:
a data preprocessing module configured to collect user-financial product data and process the user-financial product data into a data format that can be directly used in model training;
a data storage module configured to store data in the prediction device;
a data initialization module: the data storage module is configured to acquire user-financial product data and initialize a hidden feature matrix required in model training;
the high-speed convergence direction selection module is configured to receive the initialized hidden feature matrix and determine a high-speed convergence direction in the model training process;
the prediction data generation module is configured to predict the characteristic data at a high speed and store the obtained characteristic prediction data into the data storage module;
the prediction data generation module is configured to perform the steps of:
by the current update b calculatedm′And jn′And obtaining an updating rule of a user-financial product selection tendency high-speed prediction model based on momentum acceleration random gradient decline according to the gradient value corresponding to the fastest convergence speed:
wherein in respect of bm,kThe update formula of (2) is as follows:
Figure FDA0003289844270000051
wherein with respect to jn,kThe update formula of (2) is as follows:
Figure FDA0003289844270000052
wherein the content of the first and second substances,
Figure FDA0003289844270000053
representing the user's m score for the financial product n in a known score data set Λ; beta is a cumulative gradient equilibrium control factor; gamma is a gradient decay index; bm,kAnd jn,kAre respectively bm′And jn′The kth element of the vector;
Figure FDA0003289844270000061
and
Figure FDA0003289844270000062
respectively is the current gradient value at the time of the t-th update; kappa(t)V and v(t)Are respectively a single element bm,kAnd jn,kThe final gradient magnitude at the t-th update; kappa(t-1)V and v(t-1)Are respectively a single element bm,kAnd jn,kThe gradient magnitude at the t-1 th update,
repeating the training process on lambda until
Figure FDA0003289844270000063
For convergence on the lambda, the convergence judgment condition is that the training iteration round number control variable r reaches the maximum training iteration round number L or is calculated after the iteration of the round is finished
Figure FDA0003289844270000064
Value and previous round
Figure FDA0003289844270000065
The absolute value of the difference in values is less than the convergence termination threshold τ;
and the data output module is configured to output the finally obtained hidden features of the training and predict the unknown score by using the obtained hidden features.
6. The user-financial product election tendency high-speed prediction device based on momentum-accelerated random gradient descent according to claim 5,
the data preprocessing module is configured to establish a matrix of | M | rows and | N | columns as a user-financial product scoring matrix R, wherein M is a user set and N is a financial product set.
7. The user-financial product election tendency high-speed prediction device based on momentum-accelerated random gradient descent according to claim 6,
the data initialization module comprises an initialization unit which is configured to initialize relevant parameters involved in a user-financial product selection tendency high-speed prediction process based on momentum acceleration random gradient decline,
the initialization of the relevant parameters involved includes:
initializing a characteristic dimension f to be a positive integer;
two latent feature matrices B and J are initialized: the matrix B is a user hidden feature matrix in a | M | row f column, the matrix J is a financial product hidden feature matrix in a | N | row f column, and the two hidden feature matrices are respectively initialized by random smaller positive numbers;
initializing the cumulative gradient balance control factor β to a smaller positive number;
initializing the gradient decay exponent γ to a small positive number;
initializing the maximum training iteration round number L into a larger positive integer;
initializing an iteration round number control variable l to 0;
initializing a convergence termination threshold τ with a very small positive number;
normalizing factor lambda2Initialised to a small positive number.
8. The user-financial product election tendency high-speed prediction device based on momentum-accelerated random gradient descent according to claim 7,
the high-speed convergence direction selection module comprises a receiving corresponding initialization data unit and a high-speed convergence direction selection unit,
the receiving corresponding initialization data unit is configured to receive initialized relevant parameters;
the high-speed convergence direction selection unit is configured to perform the steps of:
constructing an objective function according to a known scoring data set Lambda in a user-financial product relation matrix R
Figure FDA0003289844270000071
And for the objective function
Figure FDA0003289844270000072
Using Euclidean distance as optimization target and L2Regularization, and the resulting objective function is represented as follows:
Figure FDA0003289844270000073
wherein R is(Λ)Representing a set of user known scoring data for a financial product in a user-financial product scoring matrix R; bm′Representing the hidden feature corresponding to the mth user in the user hidden feature matrix B; j is a function ofn′Representing the hidden feature corresponding to the nth commodity in the financial product hidden feature matrix J; r ism,nRepresenting the user's m score for financial product n;
Figure FDA0003289844270000074
representing the user's m score for the financial product n in a known score data set Λ; lambda [ alpha ]2A regularization factor representing a hidden feature matrix;
random gradient descent optimization algorithm using high speed convergence on the accumulated error
Figure FDA0003289844270000081
Training the matrixes B and J to obtain the global optimal solution of the matrixes B and J;
according to cumulative gradientThe balance factor beta and the gradient attenuation index gamma realize the linear combination of the previous gradient and the current update gradient, and the current update b is calculatedm′And jn′The formula expression of the gradient value corresponding to the fastest convergence speed is as follows:
Figure FDA0003289844270000082
wherein, κ(t)V and v(t)Are respectively a single element bm,kAnd jn,kFinal gradient magnitude at the t-th update; kappa(t-1)V and v(t-1)Are respectively a single element bm,kAnd jn,kFinal gradient magnitude at t-1 update;
Figure FDA0003289844270000083
and
Figure FDA0003289844270000084
the current gradient values are respectively the current gradient values at the t-th updating, and the calculation formula is as follows:
Figure FDA0003289844270000085
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