Technical Field
[0001] The present specification relates to the technical field of data processing, and in particular to a privacy protection based training sample generation method and device.
Background
[0002] With the development and popularization of the Internet, various Internet-based activities are constantly generating data, and many enterprises, governments, and even individuals have a large amount of user data. Data mining technologies can find valuable knowledge, patterns, rules and other information from a large amount of data and provide auxiliary support for scientific research, business decision-making, process control, etc., thus becoming an important way of data utilization.
[0003] In some application scenarios, the data for mining contains a lot of sensitive information, such as data from the financial industry, data from government departments, and so on. How to protect the sensitive information as privacy in the process of data mining has become an issue of increasing concern.
Summary
[0004] In view of this, the present specification provides a privacy protection based training sample generation method, where original data to be mined includes m original samples, each original sample includes a d-dimensional original vector
x and an output tag value
y, and m and d are natural numbers. The method includes:
generating n d-dimensional transform vectors π, wherein each transform vector π is determined by a sum of yx of a plurality of randomly selected original samples; and
determining the n transform vectors π as training samples of a binary classification model.
[0005] A privacy protection based binary classification model training method provided by the present specification, including:
obtaining n d-dimensional transform vectors π as training samples, wherein each transform vector π is determined by a sum of yx of a plurality of randomly selected original samples, the original sample is one of m samples of the original data, each original sample includes a d-dimensional original vector x and an output tag value y, and m and d are natural numbers; and
training a binary classification model based on the training samples to obtain an outcome model.
[0006] The present specification further provides a privacy protection based training sample generation device, where original data to be mined includes m original samples, each original sample includes a d-dimensional original vector x and an output tag value
y, and m and d are natural numbers. The device includes:
a transform vector generating unit configured to generate n d-dimensional transform vectors π, wherein each transform vector π is determined by a sum of yx of a plurality of randomly selected original samples; and
a training sample generating unit configured to determine the n transform vectors π as training samples of a binary classification model.
[0007] A privacy protection based binary classification model training device provided by the present specification, including:
a training sample obtaining unit configured to obtain n d-dimensional transform vectors π as training samples, wherein each transform vector π is determined by a sum of yx of a plurality of randomly selected original samples, the original sample is one of m samples of the original data, each original sample includes a d-dimensional original vector x and an output tag value y, and m and d are natural numbers; and
a model training unit configured to train a binary classification model based on the training samples to obtain an outcome model.
[0008] A computer device provided by the present specification, including: a memory and a processor, wherein the memory stores a computer program executable by a processor; and when the processor runs the computer program, the steps of the foregoing privacy protection based training sample generation method are executed.
[0009] A computer device provided by the present specification, including: a memory and a processor, wherein the memory stores a computer program executable by a processor; and when the processor runs the computer program, the steps of the foregoing privacy protection based binary classification model training method are executed.
[0010] A computer readable storage medium provided by the present specification, storing a computer program, wherein when the computer program is run by a processor, the steps of the foregoing privacy protection based training sample generation method are executed.
[0011] A computer readable storage medium provided by the present specification, storing a computer program, wherein when the computer program is run by a processor, the steps of the foregoing privacy protection based model training method are executed.
[0012] It may be seen from the above technical solutions that in some embodiments of the present specification, the original vectors
X and the output tag values
y in the m original samples are used, and the sum of a plurality of randomly selected
yx is determined as a transform vector, so that an outcome model obtained through training a binary classification model with n transform vectors is consistent with that obtained through training with original data, without being affected by a random quantity; in addition, since each transform vector is generated from a plurality of original samples and a random quantity, it is extremely difficult to restore the original data from the transform vectors. The embodiments of the present specification can provide good protection for privacy information and further can obtain the mining result consistent with that obtained by using the original data.
Brief Description of the Drawings
[0013]
FIG. 1 is a flowchart of a privacy protection based training sample generation method according to some embodiments of the present specification;
FIG. 2 is a flowchart of a privacy protection based binary classification model training method according to some embodiments of the present specification;
FIG. 3 is a schematic flowchart of a data mining process in an application example of the present specification;
FIG. 4 is a hardware structural diagram of a device running embodiments of the present specification;
FIG. 5 is a logical structural diagram of a privacy protection based training sample generation device according to some embodiments of the present specification; and
FIG. 6 is a logical structural diagram of a privacy protection based model training device according to some embodiments of the present specification.
Detailed Description
[0014] Embodiments of the present specification provide a novel privacy protection based training sample generation method and a novel privacy protection based binary classification model training method. From m d-dimensional original vectors x and output tag values
y (m and d are natural numbers), n (n is a natural number) d-dimensional transform vectors π are randomly generated in such a way that a binary classification model that results in a least loss function based on transform vectors is a model that results in a least loss function based on original vectors and output tag values, and thus an outcome model obtained through training with the transform vectors may be used as the data mining result of the original data.
[0015] Embodiments of the present specification may be run on any computing and storage device, such as a mobile phone, a tablet PC, a PC (Personal Computer), a notebook computer, and a server; and functions in the embodiments of the present specification may also be implemented by mutual cooperation of logical nodes running on two or more devices.
[0016] In some embodiments of the present specification, the original data refers to training samples with output tag values, and the sample capacity is m, which means that m samples are included (the samples of the original data are referred to as original samples), and each original sample includes a d-dimensional original vector
x and an output tag value
y. Let, in an i-th (i is a natural number from 1 to m) original sample, the original vector is
x_{i}, and the output tag value is
y_{i}.
[0017] In some embodiments of the present specification, the flowchart of a privacy protection based training sample generation method is as shown in FIG. 1, and the flowchart of a privacy protection based model training method is as shown in FIG. 2.
[0018] Step 110, n d-dimensional transform vectors
π are generated, wherein each transform vector
π is determined by a sum of
yx of 0 to m randomly selected original samples.
[0019] In m original samples, 0 to m original samples are randomly selected, and
yx of each selected original sample is calculated, and the sum of these
yx is determined as a transform vector
π. The number of original samples selected each time may be fixed or random and is not limited.
[0020] Since each
yx is a d-dimensional vector, the generated transform vector
π is also a d-dimensional vector.
[0021] There are many specific ways to generate the transform vector
π, which is not limited in the embodiments of the present specification, and the following two examples are described for explanation.
[0022] Example 1: In some application scenarios, plus and minus signs are used as the output tag values for binary classification, that is, the value of
y is -v or v (v is a real number). In this case, a transform vector may be generated in the following way:
generating an m-dimensional vector σ, randomly determining -v or v as a value of each dimension of σ, and determining
as a transform vector π, where σ_{i} is the i-th dimension of the vector σ; and
repeating the above process n times to obtain n transform vectors π.
[0023] Since
is either 0 or
y_{i}, the transform vector
π may be a sum of
yx of any 0 to m original samples.
[0024] In Example 1, let a linear model based on original data be:
[0025] In Equation 1,
θ^{T} is a d-dimensional weight vector, and then the loss function of a binary classification algorithm based on the original data is as shown in Equation 2:
[0026] In Equation 2, S = {(
x_{i},
y_{i})|i = 1,2,..., m}.
[0027] Let a linear model based on transform vectors be:
[0028] Then, the loss function of a binary classification algorithm based on transform vectors is as shown in Equation 4:
[0029] In Equation 4,
π_{σ} is a transform vector generated from
σ, and ∑
_{m} = {-
v, +
v}
^{m}.
[0030] The case of
v = 1 is described below as an example to illustrate that there is a
σ-independent linear relationship between
F_{log}(
S, θ) and
which is derived as follows:
Definition:
∀
σ ∈ ∑
_{m}, and a transform vector
π_{σ} may be expressed as:
π_{σ} =
then the following equations are established:
[0031] It may be seen that there is a linear relationship between
F_{log} (5, 0)and
When
U ⊆ ∑
_{m}, the linear relationship between
F_{log}(
S,θ) and
is still established and independent of
σ. Therefore,
θ that results in the least
F_{log}(
S, θ) is
θ that results in the least
that is, Equation 5 is established.
[0032] It may be concluded from the above reasoning process that training a binary classification model with a plurality of transform vectors
π results in the same outcome model as training the binary classification model with original data.
[0033] Example 2: an m-dimensional vector
w is generated, 0 or 1 is randomly determined as a value of each dimension of
w, and
is determined as a transform vector
π, where
w_{i} is the i-th dimension of the vector
w. By repeating the above process n times, n transform vectors
π may be obtained.
[0034] Since
w_{i} is either 0 or 1, the transform vector
π may be a sum of
yx of any 0 to m original samples. The value of
y is not limited in Example 2.
[0035] Based on a reasoning process similar to that in Example 1, the same conclusion may be reached that training a binary classification model with a plurality of transform vectors
π will result in the same outcome model as training the binary classification model with original data, and its reasoning process will not be elaborated again.
[0036] At a data provider, Step 120, the n transform vectors
π are determined as training samples of a binary classification model.
[0037] At a data miner, Step 210, n d-dimensional transform vectors
π are obtained as training samples, wherein each transform vector
π is determined by a sum of
yx of a plurality of randomly selected original samples, the original sample is one of m samples of the original data, and each original sample includes a d-dimensional original vector
x and an output tag value
y.
[0038] The data provider outputs the training samples generated in the Step 120 to the data miner. The data miner may obtain the training samples from the data provider in any manner, which is not limited in the embodiments of the present specification.
[0039] At the data miner, Step 220, based on the training samples, the binary classification model is trained to obtain an outcome model.
[0040] After obtaining the training samples, the data miner trains the binary classification model with the training samples. Since the output tag values in the original data are already reflected in the transform vectors
π and the training samples composed of n transform vectors
π have no tag values, an unsupervised learning algorithm may be used for training to obtain an outcome model.
[0041] The binary classification model is not limited in the embodiments of the present specification; for example, a Boosting algorithm, an SGD (Stochastic gradient descent) algorithm, an SVRG (Stochastic variance reduced gradient) algorithm, an Adagrad (Adaptive Gradient) algorithm, etc. may be adopted.
[0042] The manner in which training samples composed of n transform vectors
π are trained by using a specific binary classification model is the same as that in the prior art. Training based on the Boosting algorithm is described below as an example, and other algorithms may be implemented with reference to this example, which will not be elaborated herein.
[0043] Initialization of the Boosting algorithm: let a sample space composed of n transform vectors
π be :
δ^{r} = {
π_{1}, π_{2},···,
π_{n}}; the number T (T is a natural number) of iterations of the Boosting algorithm is preset; an initial value
θ_{0} of a linear model
θ is set to be a d-dimensional 0-vector; an initial value
ω_{1} of an n-dimensional intermediate variable
ω is set in such a way that the value in each dimension is equal to
^{1}/
_{n}; and
π_{∗k} is pre-calculated, where k is every natural number from 1 to d, and
π_{∗k} is the maximum value of n transform vectors
π in the k-th dimension.
[0044] The iteration process of the Boosting algorithm from Round 1 to Round T is as follows:
Let the current round of iteration be t, and for each dimension k of
π, a calculation is performed as follows:
k that results in the maximum |
r_{k}| (the absolute value of
r_{k}) is denoted as
ι(
t), and
r_{t} and
α_{t} are then calculated according to Equation 6 and Equation 7:
[0045] The value of each dimension of the n-dimensional intermediate variable
ω_{(t+1)} for the next round of iteration is then calculated according to Equation 8:
[0046] In Equation 8, j is every natural number from 1 to n.
[0047] At the end of the iteration of the Round T, an outcome model
θ_{T} of the training may be obtained according to Equation 9:
[0048] In Equation 9,
θ_{Tk} is the k-th dimension of the d-dimensional vector
θ_{T}.
[0049] It may be seen that, in the embodiments of the present specification, n d-dimensional transform vectors
π are randomly generated from m d-dimensional original vectors
x and output tag values
y, and each transform vector
π is determined by a sum of a plurality of randomly selected
yx; and binary classification model training is performed by using the n transform vectors
π as training samples to obtain an outcome model consistent with that obtained through training with original data; therefore, it is extremely difficult to restore the original data due to adoption of multiple original samples and introduction of a random quantity during the generation of the transform vectors; moreover, the mining result consistent with that obtained by using the original data is obtained and information distortion is avoided.
[0050] The specific embodiments of the specification are described above. Other embodiments are within the scope of the appended claims. In some cases, the actions or steps recited in the claims may be performed in a different order than the embodiments and still achieve the desired results. In addition, the processes depicted in the figures are not necessarily in a particular order or in a sequential order to achieve the desired results. In some embodiments, multitasking processing and parallel processing are also possible or may be advantageous.
[0051] In an application example of the present specification, the data provider entrusts the data miner to perform data mining for classification rules, and the data miner constructs a data classification rule based on a binary classification linear model. The data provider's original data S = {(
x_{i}, y_{i})|i = 1,2, ..., m}, where
x_{i} ∈
R^{d} (i.e.,
x_{i} is a d-dimensional vector),
y_{i} ∈ {1,-1} (i.e., the value of the output tag value
y_{i} is -1 or 1). Since the data provider's original data contains sensitive information about users, privacy protection is required.
[0052] A classification data mining process that can provide privacy protection is as shown in FIG. 3.
[0053] Step 310, m samples of original data are obtained.
[0054] Step 320, n Rados (Rademacher Observations) are calculated by using the original data. Each Rado is a d-dimensional vector, denoted as
π_{σ}, and a transform vector in this application example.
[0055] Each Rado is calculated in the following way: generating a m-dimensional vector
σ, and randomly determining the value of each dimension of
σ as -1 or 1; and determining a Rado corresponding to the
σ, according to Equation 10:
[0056] An example is described below for explanation: assuming that the original data has a total of 5 samples, each original vector x has four dimensions (m=4), and the original data is as shown in Table 1.
Table 1
Sample No. | y | x |
The first dimension | The second dimension | The third dimension | The fourth dimension |
1 |
1 |
1 |
2 |
3 |
4 |
2 |
-1 |
3 |
4 |
5 |
6 |
3 |
-1 |
5 |
6 |
7 |
8 |
4 |
1 |
7 |
8 |
9 |
10 |
5 |
1 |
6 |
9 |
3 |
5 |
[0057] In the case of generation of one Rado, let the random value of the vector
σ be
σ = {-1, 1, - 1, 1, 1}, and then the value of each dimension of
π_{σ} is calculated according to Equation 10:
The first dimension:
The second dimension:
The third dimension:
The fourth dimension:
[0058] It may be concluded that one Rado is {8,11, 5, 7}.
[0059] n vectors
σ are randomly generated, then n Rados are obtained.
[0060] Steps 310 and 320 run on a device or logical node controlled by the data provider. The data provider will generate n Rados as data to be mined and provide them to the data miner.
[0061] Step 330, a binary classification model is trained by a Boosting algorithm with n Rados as training samples to obtain an outcome model.
[0062] The Step 330 runs on a device or logical node controlled by the data provider. The data provider generates a multi-classification rule based on the binary classification linear outcome model obtained from the training and delivers it to the data provider. The manner of transforming multiple binary classification linear outcome models into a multi-classification rule may be implemented by referring to the prior art, which will not be elaborated again.
[0063] Corresponding to the foregoing process implementation, some embodiments of the present specification further provide a privacy protection based training sample generation device and a privacy protection based binary classification model training device. The devices may both be implemented by either software or hardware or by a combination of hardware and software. Taking the software implementation as an example, as a logical apparatus, it is formed in a way that the CPU (Central Process Unit) of a device in which the apparatus is located reads corresponding computer program instructions into a memory for operation. At the hardware level, in addition to the CPU, memory, and storage shown in FIG. 4, the device in which the apparatus is located typically includes other hardware such as a chip for transmitting and receiving wireless signals, and/or other hardware such as a board card for implementing a network communication function.
[0064] FIG. 5 shows a privacy protection based training sample generation device according to some embodiments of the present specification, where original data to be mined includes m original samples, each original sample comprises a d-dimensional original vector x and an output tag value
y, and m and d are natural numbers; and the device comprises: a transform vector generating unit and a training sample generating unit, wherein the transform vector generating unit is configured to generate n d-dimensional transform vectors
π, and each transform vector
π is determined by a sum of
yx of a plurality of randomly selected original samples; and the training sample generating unit is configured to determine the n transform vectors
π as training samples of a binary classification model.
[0065] Optionally, the value of
y is -v or v, and v is a real number; and the transform vector generating unit is specifically configured to: generate an m-dimensional vector
σ, randomly determine -v or v as a value of each dimension of
σ, and determine
as a transform vector
π, where
y_{i} is an output tag value of an i-th original sample,
x_{i} is an original vector of the i-th original sample, and
σ_{i} is the i-th dimension of the vector σ; and repeat the above process n times to obtain n transform vectors
π.
[0066] Optionally, the transform vector generating unit is specifically configured to: generate an m-dimensional vector
w, randomly determine 0 or 1 as a value of each dimension of
w, and determine
as a transform vector
π, where
w_{i} is the i-th dimension of the vector
w, y_{i} is an output tag value of an i-th original sample, and
x_{i} is an original vector of the i-th original sample; and repeat the above process n times to obtain n transform vectors
π.
[0067] FIG. 6 shows a privacy protection based binary classification model training device according to some embodiments of the present specification, including a training sample obtaining unit and a model training unit, wherein the training sample obtaining unit is configured to obtain n d-dimensional transform vectors
π as training samples, wherein each transform vector
π is determined by a sum of
yx of a plurality of randomly selected original samples, the original sample is one of m samples of the original data, each original sample includes a d-dimensional original vector
x and an output tag value
y, and m and d are natural numbers; and the model training unit is configured to train a binary classification model based on the training samples to obtain an outcome model.
[0068] Optionally, the binary classification model includes: a Boosting algorithm, an SGD algorithm, an SVRG algorithm, or an Adagrad algorithm.
[0069] Some embodiments of the present specification provide a computer device including a memory and a processor. The memory herein stores a computer program executable by the processor; and when the processor runs the stored computer program, the steps of the privacy protection based training sample generation method in the embodiments of the present specification are executed. For a detailed description of the steps of the privacy protection based training sample generation method, a reference may be made to the previous content, and it will not be elaborated again.
[0070] Some embodiments of the present specification provide a computer device including a memory and a processor. The memory herein stores a computer program executable by the processor; and when the processor runs the stored computer program, the steps of the privacy protection based binary classification model training method in the embodiments of the present specification are executed. For a detailed description of the steps of the privacy protection based binary classification model training method, a reference may be made to the previous content, and it will not be elaborated again.
[0071] Some embodiments of the present specification provide a computer readable storage medium which stores computer programs, and when the computer programs are run by a processor, the steps of the privacy protection based training sample generation method in the embodiments of the present specification are executed. For a detailed description of the steps of the privacy protection based training sample generation method, a reference may be made to the previous content, and it will not be elaborated again.
[0072] Some embodiments of the present specification provide a computer readable storage medium which stores computer programs, and when the computer programs are run by a processor, the steps of the privacy protection based binary classification model training method in the embodiments of the present specification are executed. For a detailed description of the steps of the privacy protection based binary classification model training method, a reference may be made to the previous content, and it will not be elaborated again.
[0073] The embodiments described above are merely preferred embodiments of the present specification and not intended to limit the present application. Any of modifications, equivalent substitutions, improvements and the like made within the spirit and principle of the present application shall be covered in the scope of the present application.
[0074] In a typical configuration, a computing device includes one or more processors (CPUs), input/output interfaces, network interfaces, and a memory.
[0075] The memory may be in a form of a non-permanent memory, a random access memory (RAM), and/or a nonvolatile memory, such as a read-only memory (ROM) or a flash RAM, in computer-readable media. The memory is an example of computer-readable media.
[0076] Computer readable media include both permanent and non-persistent, removable and non-removable media and may store information by any method or technology. The information may be a computer readable instruction, a data structure, a module of a program or other data. Examples of computer storage media include, but are not limited to, a phase change memory (PRAM), a static random access memory (SRAM), a dynamic random access memory (DRAM), other types of random access memory (RAM), a read only memory (ROM), an electrically erasable programmable read-only memory (EEPROM), a flash memory or other memory technologies, a read-only optical disk read-only memory (CD-ROM), a digital versatile disc (DVD) or other optical storages, a magnetic tape cassette, a magnetic disk storage or other magnetic storage devices or any other non-transmission medium for storing information that may be accessed by computing devices. As defined herein, the computer readable media do not include transitory media, such as modulated data signals and carriers.
[0077] It is also to be understood that the term "comprise," "include" or any of other variants thereof is intended to cover non-exclusive inclusions such that a process, method, article, or device that includes a series of elements not only includes those elements but also includes other elements that are not listed explicitly, or also includes inherent elements of this process, method, article, or device. In the absence of more restrictions, an element defined by the sentence "including a/an..." does not preclude additional identical elements existing in the process, method, article or device that includes the element.
[0078] Those skilled in the art should appreciate that embodiments of the present specification may be provided as a method, system, or computer program product. Accordingly, the embodiments of the present specification may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware. Moreover, the embodiments of the present specification may take the form of a computer program product implemented on one or more computer usable storage media (including, but not limited to, disk memories, CD-ROMs and optical memories) comprising computer usable program codes.
1. A privacy protection based training sample generation method, wherein original data to be mined comprises m original samples, each original sample comprises a d-dimensional original vector
x and an output tag value
y, and m and d are natural numbers; and the method comprises:
generating n d-dimensional transform vectors π, each transform vector π being determined by a sum of yx of a plurality of randomly selected original samples; and
determining the n transform vectors π as training samples of a binary classification model.
2. The method according to claim 1, wherein the value of
y is -v or v, and v is a real number; and
the generating n d-dimensional transform vectors
π, each transform vector
π being determined by a sum of
yx of a plurality of randomly selected original samples comprises: generating an m-dimensional vector
σ, randomly determining -v or v as a value of each dimension of
σ, and determining
as a transform vector
π, where
y_{i} is an output tag value of an i-th original sample ,
x_{i} is an original vector of the i-th original sample, and
σ_{i} is the i-th dimension of the vector σ; and repeating the above process n times to obtain n transform vectors
π.
3. The method according to claim 1, wherein the generating n d-dimensional transform vectors
π, each transform vector
π being determined by a sum of
yx of a plurality of randomly selected original samples comprises: generating an m-dimensional vector
w, randomly determining 0 or 1 as a value of each dimension of
w, and determining
as a transform vector
π, where
w_{i} is the i-th dimension of the vector
w,
y_{i} is an output tag value of an i-th original sample,
x_{i} is an original vector of the i-th original sample; and repeating the above process n times to obtain n transform vectors
π.
4. A privacy protection based binary classification model training method, comprising:
obtaining n d-dimensional transform vectors π as training samples, wherein each transform vector π is determined by a sum of yx of a plurality of randomly selected original samples, the original sample is one of m samples of the original data, each original sample includes a d-dimensional original vector x and an output tag value y, and m and d are natural numbers; and
training a binary classification model based on the training samples to obtain an outcome model.
5. The method according to claim 4, wherein the binary classification model comprises: a Boosting algorithm, an SGD algorithm, an SVRG algorithm, or an Adagrad algorithm.
6. A privacy protection based training sample generation device, wherein original data to be mined comprises m original samples, each original sample comprises a d-dimensional original vector
x and an output tag value
y, and m and d are natural numbers; and the device comprises:
a transform vector generating unit configured to generate n d-dimensional transform vectors π, wherein each transform vector π is determined by a sum of yx of a plurality of randomly selected original samples; and
a training sample generating unit configured to determine the n transform vectors π as training samples of a binary classification model.
7. The device according to claim 6, wherein the value of
y is -v or v, and v is a real number;
the transform vector generating unit is specifically configured to: generate an m-dimensional vector
σ, randomly determine -v or v as a value of each dimension of
σ, and determine
as a transform vector
π, where
y_{i} is an output tag value of an i-th original sample,
x_{i} is an original vector of the i-th original sample, and
σ_{i} is the i-th dimension of the vector σ; and repeat the above process n times to obtain n transform vectors
π.
8. The device according to claim 6, wherein the transform vector generating unit is specifically configured to: generate an m-dimensional vector
w, randomly determine 0 or 1 as a value of each dimension of
w, and determine
as a transform vector
π, where
w_{i} is the i-th dimension of the vector
w, y_{i} is an output tag value of an i-th original sample, and
x_{i} is an original vector of the i-th original sample; and repeat the above process n times to obtain n transform vectors
π.
9. A privacy protection based binary classification model training device, comprising:
a training sample obtaining unit, configured to obtain n d-dimensional transform vectors π as training samples, wherein each transform vector π is determined by a sum of yx of a plurality of randomly selected original samples, the original sample is one of m samples of original data, each original sample comprises a d-dimensional original vector x and an output tag value y, and m and d are natural numbers; and
a model training unit configured to train a binary classification model based on the training samples to obtain an outcome model.
10. The device according to claim 8, wherein the binary classification model comprises: a Boosting algorithm, an SGD algorithm, an SVRG algorithm, or an Adagrad algorithm.
11. A computer device, comprising: a memory and a processor, wherein the memory stores a computer program executable by the processor; and when the processor runs the computer program, the steps of any of claims 1-3 are executed.
12. A computer device, comprising: a memory and a processor, wherein the memory stores a computer program executable by the processor; and when the processor runs the computer program, the steps of any of claims 4-5 are executed.
13. A computer-readable storage medium storing a computer program thereon, wherein when the computer program is run by a processor, the steps of any of claims 1-3 are executed.
14. A computer-readable storage medium storing a computer program thereon, wherein when the computer program is run by a processor, the steps of any of claims 4-5 are executed.