CN110781401A - A Top-n Item Recommendation Method Based on Collaborative Autoregressive Flow - Google Patents

Abstract

The invention provides a project recommendation method realized by utilizing Collaborative Autoregressive Flow (CAF), which expands a generation model based on the autoregressive flow to a collaborative filtering technology for modeling implicit feedback. The CAF converts the simple initial density into a more complex density which accords with the real distribution of data through a series of reversible transformations, and mines the items accessed by the user and the potential information in the attribute characteristics of the user and the items, so that the potential representation of the user and the potential representation of the items with more representation capability can be learned, and the items which are most likely to be accessed next time are stably and effectively recommended for the user. In addition, the invention adds a collaborative autoregressive flow to the model to learn the true distribution of the hidden variables, which can reduce the error of the traditional variational model (such as VAE) in the conversation-based recommendation problem.

Description

A Top-n Item Recommendation Method Based on Collaborative Autoregressive Flow

technical field

The invention belongs to the field of neural networks in machine learning, and is a method based on deep learning, which mainly uses autoregressive flow to mine items visited by users and potential information existing in attribute features of users and items, and learn The latent representation of users and items, and on this basis, collaborative filtering (Collaborative Filtering) technology is used to recommend n items that are most likely to be accessed to users.

Background technique

With the rapid development of Internet technology, people's lives are more and more inseparable from the Internet, and a large amount of user project interaction data has emerged. We use the attribute characteristics of these data to study the interaction behavior of users with items, analyze user preferences, and present items to users that they may like but have not visited, so as to promote personalized item recommendation, which can effectively alleviate the Internet The problem of information overload.

Traditional collaborative filtering methods use matrix factorization to predict user preferences by using the user's rating matrix for items. This method does not consider the attribute information of users and items, and can only simply simulate the linear relationship between users and items, but cannot extract the complex relationship between users and items, resulting in poor model recommendation performance. There is also a class of methods that combine traditional Bayesian inference techniques and uncertainty representations to learn complex interactions between users and items with sparse implicit feedback and auxiliary information. Such methods usually need to assume that the posterior distribution of the real data is Gaussian distribution, but real-world data does not necessarily obey this distribution. Therefore, this assumption will make the model inflexible enough to match the true posterior distribution and uncertainty of the recommendation, which can easily lead to recommendation errors.

Based on the above problems, the present invention proposes a method based on deep learning, which uses two variational auto-encoders to model users and items respectively, and encodes the embedding vector representations of users and items to obtain the potential representation process of users and items. The collaborative autoregressive flow is added to the traditional item recommendation method to solve the problems of low recommendation accuracy and low recommendation efficiency caused by the inability to simulate the nonlinear interaction between users and items and the inflexibility of the model.

SUMMARY OF THE INVENTION

The purpose of the present invention is to propose a representation method based on collaborative autoregressive flow in view of the technical deficiencies such as low recommendation accuracy and low recommendation performance in traditional item recommendation methods, which realizes the most likely access to items for users. Accurate and efficient prediction solves the problem of poor recommendation effect of existing models.

The idea of the present invention is to represent the user and the item as an embedding vector according to the user's access to the item, and then use two variational autoencoders (Variational Autoencoder, VAE) to learn the embedding vector of the user and the item, so as to obtain the user and potential representations of items. In addition, in the process of obtaining the potential representation of users and items, the present invention adds the process of variational inference, uses collaborative autoregressive flow to flexibly simulate the nonlinear interaction between users and items, and learns the real distribution of user and item data. To a large extent, the error of directly using the variational autoencoder can be avoided, so as to achieve a better item recommendation effect.

Based on the above inventive idea, the present invention designs a project recommendation method implemented by using collaborative autoregressive flow, which specifically includes the following steps:

S1, data preprocessing: According to the user's historical access items in the original data, the data set is divided into training set, validation set and test set; then an item label matrix R is constructed according to the user access items in the training set; Embed each user and each item in the training set to obtain the user embedding vector matrix U and the item embedding vector matrix V;

和

然后让用户和项目的最终隐含变量表示与其相对应的协同信息相结合得到用户和项目的最终潜在表示矩阵U′和V′，接着将用户和项目的最终潜在表示的矢量积输入到一个分类器中，得到第一损失，再将用户和项目的最终隐含变量表示输入到一个解码器中得到第二损失，将第一损失与第二损失相加生成最后的总损失，然后最小化总损失，即得到所述的项目推荐模型；S2, optimize the model parameters to obtain the optimal item recommendation model: input the user embedding vector matrix U and item embedding vector matrix V into different variational auto-encoders respectively, and introduce a collaborative autoregressive flow in the encoding process, the obtained user and the final latent variable representation matrix of the item

and

Then let the final latent variable representations of users and items be combined with their corresponding collaborative information to obtain the final latent representation matrices U' and V' of users and items, and then input the vector product of the final latent representations of users and items into a classification In the decoder, the first loss is obtained, and the final latent variable representations of users and items are input into a decoder to obtain the second loss, the first loss and the second loss are added to generate the final total loss, and then the total loss is minimized. loss, that is, to obtain the item recommendation model;

S3, recommend items to users: Use the above trained item recommendation model to recommend Top-n items to users.

In the above-mentioned training method for item recommendation model implemented by collaborative autoregressive flow, the purpose of step S1 is to process the original data set, divide the training set, the verification set and the test set, and then embed all the users and items in the training set, including the following points: step:

S11, divide the data set: according to the user access items in the original data set, randomly select 70% of the items visited by each user as the training set, 20% as the test set, and the remaining 10% as the validation set;

S12, construct the user embedding vector matrix U, the item embedding vector matrix V and the item label matrix R according to the situation of the user accessing the item in the training set, which specifically includes the following steps:

其中M表示用户的数量，N表示项目的数量，u_ij表示用户嵌入向量矩阵中的元素，如果用户u_i访问过项目v_j，则u_ij＝1，否则标记为0，用户嵌入向量矩阵U中的第i行表示用户u_i的嵌入向量u_i；S121, construct a user embedding vector matrix U: represent all users U _s ={u ₁ ,...,u _i ,...,u _M } in the training set as embedding vectors, and initialize a user embedding vector matrix according to the user's preference for items

where M represents the number of users, N represents the number of items, u _ij represents the elements in the user embedding vector matrix, if user _ui has visited item v _j , then u _ij =1, otherwise marked as 0, the user embedding vector matrix U The i-th row in represents the embedding vector _ui of user _ui ;

S122, constructing the item embedding vector moment V: all items in the training set V _s ={v ₁ ,...,v _j ,...,v _N } are represented as embedding vectors, and the item embedding vector matrix is the transpose of the user embedding vector matrix, that is, V= ^UT , the jth row in the item embedding vector matrix V represents the embedding vector v _{j of the item v j ;}

其中r_ij＝u_ij。S123, construct an item label matrix R: construct an item label matrix according to the user access items in the training set

where r _ij = u _ij .

进而得到用户和项目的最终潜在表示矩阵U′和V′。接着构建第一损失和第二损失，最小化两个损失之和，得到最优的项目推荐模型。该步骤具体包括以下分步骤：In the above item recommendation model training method using collaborative autoregressive flow, the purpose of step S2 is to input the user embedded variable matrix U and item embedded variable matrix V obtained in step S1 into two variational variables that have introduced collaborative autoregressive flow. In the autoencoder, the final latent variable representation matrix for users and items is obtained and

Then the final latent representation matrices U' and V' of users and items are obtained. Then construct the first loss and the second loss, minimize the sum of the two losses, and obtain the optimal item recommendation model. This step specifically includes the following sub-steps:

和

初始隐含变量表示都是d维向量；S21, using two variational auto-encoders to encode the user embedding vector _ui and the item embedding vector _vj respectively, and obtain the initial implicit variable representation of the user _ui and the item _vj by encoding

and

The initial hidden variable representations are all d-dimensional vectors;

In this step, an encoder (multi-layer perceptron) is used to encode the embedding vectors expressed as users and items. The calculation process of each layer is as follows:

level one:

Second floor:

...

Layer t:

和

和

均服从高斯分布，其中用户初始隐含变量表示

分布的均值为

方差为

则

对于项目初始隐含变量表示

其均值

方差

通过项目的均值和方差得到

编码器每一层的计算过程中，

表示非线性的激活函数，常见的有sigmoid或tanh，本发明中选取sigmoid作为激活函数，

和

分别表示用户嵌入向量和项目嵌入向量经过第t层神经网络得到的隐藏状态表示，矩阵

和偏差向量

均为用户编码器的训练参数，其中上标t表示这是经过第t层神经网络的参数，而

是求用户初始隐含变量表示

分布时需要学习的参数；矩阵

以及偏差向量

为项目编码器的训练参数，上标t表示这是经过第t层神经网络的参数，

是求项目初始隐含变量表示

分布时需要学习的参数；

和

都是用于随机采样的标准正态分布的变量；In the above formula, t represents the number of layers of the multilayer perceptron, in the present invention t=3, the result of the last layer is passed and Compute initial latent variable representations for users and items separately

and

and

All obey a Gaussian distribution, where the user's initial hidden variable represents

The mean of the distribution is

The variance is

but

The initial implicit variable representation for the project

its mean

variance

Obtained by the mean and variance of the items

During the calculation process of each layer of the encoder,

Represents a nonlinear activation function, the common ones are sigmoid or tanh. In the present invention, sigmoid is selected as the activation function,

and

Represents the hidden state representation obtained by the user embedding vector and the item embedding vector through the t-th layer of neural network, matrix

and the bias vector

are the training parameters of the user encoder, where the superscript t indicates that this is the parameter of the t-th layer of neural network, and

is to find the initial implicit variable representation of the user

Parameters to learn when distributing; matrix

and the bias vector

is the training parameter of the item encoder, the superscript t indicates that this is the parameter of the neural network of the t layer,

is to find the initial implicit variable representation of the project

Parameters that need to be learned when distributing;

and

are standard normally distributed variables used for random sampling;

和项目初始隐含变量表示

输入这K个自回归流中进行可逆变换，学习得到用户和项目的最终隐含变量表示和

使其分布更接近于真实的潜在层数据分布。学习和分布的过程如下(由于用户和项目的最终隐含变量表示的学习过程是一致的，因此我们此处省略下标u_i和v_j，用统一的符号z⁰和z^K去表示初始隐含变量表示和最终隐含变量表示)：S22, define K reversible autoregressive flows, and represent the initial hidden variables of the user obtained in the previous step

and the item initial implicit variable representation

Input these K autoregressive streams for reversible transformation, and learn to obtain the final latent variable representation of users and items and

Make its distribution closer to the true latent layer data distribution. study and The distribution process is as follows (because the learning process represented by the final hidden variables of users and items is the same, we omit the subscripts _ui and v _j here, and use the unified symbols z ⁰ and z ^K to represent the initial hidden variables representation and final implicit variable representation):

是一维概率密度，并且以z^K先前i-1维的概率为条件，d表示的是z^K的维度；In the above formula

is a one-dimensional probability density and is conditioned on the probability of the previous i-1 dimension of z ^K , and d represents the dimension of z ^K ;

The process of finding the final implicit variable representation of users and items includes the following sub-steps:

其分布为p(z^k-1)，计算z^k的d个维度，从而获得z^k的分布p(z^k)，S221, find the target distribution p(z ^k ): in the process of obtaining the final implicit variable representation, we first obtain the d dimensions of z ^k , where k is regarded as passing through the k th flow, the i th in z ^k dimensions are conditioned on the first i-1 dimensions of z ^k-1 , according to

Its distribution is p(z ^k-1 ), and the d dimensions of z ^k are calculated to obtain the distribution p(z ^k ) of z ^k ,

In the above formula, M( ) and S( ) are the neural networks for calculating the mean and variance, respectively. Through S22, we can obtain a target distribution p(z ^k ), since the process of generating the target distribution is based on p(z ^{k- 1} ), the process is very fast for GPU parallelization. This process mainly uses the idea of Inverse Autoregressive Flow (IAF), which is a special neural network that can output all the values of the mean and standard deviation at the same time, which is convenient for μ _{1: i-1} and σ _{1 : sampling of i-1} ;

对于p(z^k-1)密度估计的可逆过程，本发明使用掩模自回归流(Masked Autoregressive Flow,MAF)的思想，评估目标分布 S222, find the target distribution

For the reversible process of p(z ^k-1 ) density estimation, the present invention uses the idea of Masked Autoregressive Flow (MAF) to evaluate the target distribution

In the above formula, M'( ) and S'( ) are special neural networks that use mask autoregressive flow to find the mean and variance, respectively, and act as a reversible calculation process in the model;

但是它们在模拟自回归流的过程中存在不同的偏差，为了利用两个输出分布来稳定训练过程，我们计算两个输出分布之间的KL散度，S223, through steps S221 and S222, two identical target distributions p(z ^k ) and

But they have different biases in the process of simulating autoregressive flow, in order to use the two output distributions to stabilize the training process, we calculate the KL divergence between the two output distributions,

的交叉熵计算方式如下：In the above formula, the two target distributions p(z ^k ) and

The cross entropy is calculated as follows:

的计算过程：Next, entropy is described

The calculation process of:

和

S224, repeating steps S221 to S223 K times to obtain the final implicit variable representation of the user and item

and

和

与用户和项目的协同信息

和结合起来得到用户和项目的最终潜在表示u_i′和v_j′，S23, express the final hidden variables of users and items obtained in S22

and

Collaboration information with users and projects

and Combined to get the final latent representations _ui ' and v _j ' of users and items,

In the above formula, u _c and _vc are obtained from the Gaussian distribution, representing the collaborative information of users and items respectively. With the optimization of the model, these two vectors are also continuously optimized, and finally they can represent users and items well. collaboration information;

S24, continuously repeating steps S21 to S23 until the final latent representations of all users and items are obtained, and connecting the final latent representations of all users and items to obtain the final latent representation matrices U' and V' of users and items;

S25, construct two loss functions L ₁ and L ₂ , add L ₁ and L ₂ together to generate a final total loss L, and minimize this total loss function, complete the training of the model, and obtain the item recommendation model. Among them, L ₁ is the cross-entropy loss function of the predicted item and the label item, and L ₂ is used to make the learned latent variable distribution closer to the real distribution. The reconstruction loss function. This step specifically includes the following sub-steps:

S251, obtain the first loss L ₁ : input the vector product of the final latent representation matrices U′ and V′ of the user and the item obtained in S24 into a classifier composed of a multi-layer perceptron, and output the user access to each item Probability matrix, which is regarded as the user's scoring matrix R' for all items, and then use the item label matrix R obtained from S1 and the predicted scoring matrix R' to calculate the cross entropy loss,

In the above formula, r' _ij represents the probability of user _ui accessing item v _j , L ₁ is taken as the first loss, M is the total number of users, and N is the total number of items;

和

输入到一个可逆的解码器中，构建用户和项目隐含变量的联合分布，让其与输入用户和项目数据的联合分布求相对熵，得到第二损失L₂；(为了表述方便，在第二损失计算公式中，取消用户和项目的下标i和j)S252, obtain the second loss L ₂ : then express the final implicit variables of the user and item obtained in S23

and

Input into a reversible decoder, construct the joint distribution of the hidden variables of users and items, and obtain the relative entropy with the joint distribution of the input user and item data to obtain the second loss L ₂ ; (for convenience of expression, in the second In the loss calculation formula, cancel the subscripts i and j of users and items)

同样的，用项目后验分布q(z_v|v)近似隐含变量z_v的真实分布p(v,z_v)，q(z_v|v)定义为

p(u,z_u)和p(v,z_v)表示用户和项目输入数据的真实分布，z_u、z_v表示协同自回归流模型中的隐含变量，u、v表示模型输入数据，θ、φ分别表示概率分布的参数，上式中

和

表示重构损失，

和

为常数项，剩下四项表示自回归流。对第二损失L₂进行优化的过程中，实际上已经完成了对S223中

的最小化，具体的推导过程参照以下论文：【van den Oord,A.,Li,Y.,Babuschkin,I.,Simonyan,K.,Vinyals,O.,Kavukcuoglu,K.,van den Driessche,”Parallel wavenet:Fast high-fidelity speech synthesis”】；The true distribution p(u,z _u ) of the latent variable z _u is approximated by the user posterior distribution q(z _u | _u ), which is defined as

Similarly, the true distribution p(v,z _v ) of the latent variable z _v is approximated by the item posterior distribution q(z _v |v), and q(z _v |v) is defined as

p(u,z _u ) and p(v,z _v ) represent the true distribution of user and item input data, _zu , z _v represent the latent variables in the collaborative autoregressive flow model, u, v represent the model input data, θ and φ represent the parameters of the probability distribution, respectively, in the above formula

and

represents the reconstruction loss,

and

is a constant term, and the remaining four terms represent the autoregressive flow. In the process of optimizing the _second loss L2, the

The minimization of , the specific derivation process refers to the following papers: [van den Oord, A., Li, Y., Babuschkin, I., Simonyan, K., Vinyals, O., Kavukcuoglu, K., van den Driessche, " Parallel wavenet:Fast high-fidelity speech synthesis"];

S253 , add the first loss and the second loss together to generate a final total loss L=L ₁ +L ₂ , and minimize the total loss function to complete the training of the model to obtain the item recommendation model.

In the above-mentioned project recommendation model training method implemented by using collaborative autoregressive flow, the purpose of step S3 is to use the project recommendation model trained by S2 to perform personalized project recommendation for users, including the following steps:

S31, obtain the user rating matrix R' according to the model trained in S2, and then set the rating of the index position of the item visited by the user in the training set to _{0. For example, if the user ui has visited the item v j in} the training set, the rating will be The corresponding element r' _ij in the matrix R' is set to 0, and then each row in the new scoring matrix is sorted according to the score to obtain the matrix R";

S32, according to the scoring matrix R" obtained in S31, select the items with the top n scores in R" as the final recommended result to the user.

The item recommendation method (Collaboration Autoregressive Filtering, CAF) provided by the present invention using the collaborative autoregressive flow extends the flow-based generation model to the collaborative filtering technology for modeling implicit feedback. At the same time, combined with the auxiliary information and collaborative information of users and items, the latent representation of users and items can be better learned, and the true distribution of latent variables can be learned through autoregressive flow, thereby greatly improving the recommendation performance.

The present invention provides an item recommendation method realized by using collaborative autoregressive flow. Compared with the prior art, it has the following beneficial effects:

1. The present invention uses two variational auto-encoders to learn the latent variable representations of users and items respectively, and then uses collaborative filtering technology to recommend items to users. Many traditional methods use the user-item matrix to learn user preferences, and rarely combine users, items, and user-items to make recommendations, which makes the traditional models unable to fully capture the interaction information of user-items.

2. The present invention adds a collaborative autoregressive flow in the model coding process to learn the true distribution of latent variables, reducing the error of traditional variational models (such as VAE) in item recommendation problems; this is because traditional VAE A prior distribution needs to be assumed, and this prior distribution will bring a large error; the regularization flow does not need to assume a prior distribution, so that the learned distribution is closer to the true distribution of the hidden variables.

3. The autoregressive flow in the present invention adopts the reversible autoregressive flow (Inverse Autoregressive Flow, IAF) and the masked autoregressive flow (Masked Autoregressive Flow, MAF), which can effectively promote the efficiency of variational inference and data sampling, and reduce the The gap between a simple distribution of latent variables and actual data with a complex distribution is identified.

Description of drawings

Figure 1 shows the overall structure of the item recommendation model implemented by using collaborative autoregressive flow.

Figure 2 shows the process of variational inference using autoregressive flows.

Figure 3 is a visual graph of the final latent representation of users and items.

在不同数据集上经过K个自回归流的可视化变化过程。Figure 4 shows the initial hidden variables of the project

Visualize the change process through K autoregressive streams on different datasets.

Figure 5 is a schematic diagram of the prediction results of the item recommendation model (CAF) on different datasets with the parameter K in the autoregressive stream; (a) corresponds to MovieLens dataset, (b) corresponds to CiteULike dataset; (c) corresponds to LastFM Data set, K can be understood as the number of reversible functions (or called autoregressive flows).

FIG. 6 is a schematic diagram showing the variation of the prediction results of the item recommendation model (CAF) on different data and with the number of training rounds.

Terminology Explanation

Variational inference: Simply put, variational inference is the need to infer the required distribution p based on existing data; when p is not easy to express and cannot be solved directly, you can try the method of variational inference. That is, look for a distribution q that is easy to express and solve. When the difference between q and p is small, q can be used as an approximate distribution of p to replace p. The whole process uses a Variational Autoencoder (VAE) to derive an Evidence Lower Bound (ELBO) to learn our approximate distribution q by maximizing the evidence lower bound.

Collaborative filtering (Collaborative Filtering): Simply put, it uses the preferences of a group with similar interests and common experience to recommend information that users are interested in. Individuals respond to the information to a certain extent (such as ratings) through a cooperative mechanism and record it. In order to achieve the purpose of filtering and help others filter information, the response is not necessarily limited to those of special interest, and the record of information of special interest is also very important. Collaborative filtering can be further classified into rating or social filtering. Since then, it has become an important part of e-commerce, that is, recommending a customer's "likely items" based on the customer's previous purchase behavior and the purchase behavior from a customer group with similar purchase behavior, that is, through the community. Personalized information, products and other recommendation services are provided. In addition to recommendations, in recent years, mathematical operations have also been developed to allow the system to automatically calculate the strength of preferences, and then remove the clutter and save the essentials to make the filtered content more basis. It may not be 100% accurate, but due to the addition of a strength rating, this concept is In addition to being used in e-commerce, it can also be used in the field of information retrieval, network personal audio-visual cabinets, personal bookshelves and other fields.

Detailed ways

The present invention will be further described below in conjunction with the accompanying drawings.

Example Item recommendation model training using collaborative autoregressive flow

This example uses three real datasets MovieLens, CiteULike and LastFM (the datasets can be obtained from https://grouplens.org/datasets/movielens/1M/ , http://www.citeulike.org/ , http:// www.lastfm.com/obtain ) as the research object, to give a detailed explanation of the item recommendation model training method provided by the present invention.

As shown in FIG. 1 , the item recommendation model (CAF) implemented by using collaborative autoregressive flow provided by this embodiment is mainly composed of an encoder, an autoregressive flow layer, a decoder, and a classifier. Preprocessing: For the MovieLens dataset, we will keep the data with user ratings for movies from 1 to 5, and delete other data; exclude users who have accessed less than ten articles in the CiteULike dataset; for the LastFM dataset, we keep all The data.

Table 1 Statistics of the dataset

The statistical information of the data set in this embodiment is shown in Table 1. The training set, the verification set and the test set are divided into three experimental data sets. For each user, 70% of the access items are randomly selected as the training set and 10% as the verification set. set, and the remaining 20% is the test set.

Build an item label matrix R according to the user's access to the item, and then embed each user and each item in the input data to obtain the user embedding vector matrix U and the item embedding vector matrix V;

After the training data set is constructed, this embodiment uses the data in the training set to train according to step S2 to obtain three item recommendation models, the verification set is mainly used for parameter adjustment, and the test set is used for the subsequent discussion of the test effect.

和

如附图2所示，为了得到用户和项目最终隐含变量表示

和

将S21中编码器的输出

和

带入到步骤S22中，经过K个可逆自回归流的变换，得到

和然后再根据S23将

和

与服从高斯分布的用户和项目协同信息结合得到用户和项目的最终潜在表示，随着模型的不断更新，用户和项目的潜在表示不断被优化，从而得到用户和项目的最终潜在表示u_i′和v_j′，重复步骤S2直到模型收敛，最终得到所有用户和所有项目的潜在表示U′和V′。As shown in Figure 1, firstly input the user embedding vector matrix U and item embedding vector matrix V into step S2, first obtain the hidden variables of each user and each item according to the multi-layer perceptron network coding in S21

and

As shown in Figure 2, in order to obtain the final implicit variable representation of users and items

and

Convert the output of the encoder in S21

and

Bring it into step S22, after the transformation of K reversible autoregressive flows, get

and Then according to S23,

and

Combined with the user and item collaboration information that obeys the Gaussian distribution, the final latent representation of the user and item is obtained. With the continuous updating of the model, the latent representation of the user and item is continuously optimized, so as to obtain the final latent representation of the user and item _ui ′ and v _j ', repeat step S2 until the model converges, and finally get the latent representations U' and V' of all users and all items.

和

输入到S25的可逆解码器中，构建用户和项目隐含变量的联合分布，根据L₂求第二损失；将第一损失和第二损失联合起来求总损失L，并最小化L，完成对模型的训练，得到所述的项目推荐模型。As shown in the decoder and classifier part in Fig. 1, the vector product of the final latent representation matrices U' and V' of the user and item obtained in S23 is input into the classifier in step S25 to obtain the item label matrix R and the predicted score The matrix R′ calculates the first loss of cross-entropy; then the end-user and item latent variables obtained in S23

and

Input into the reversible decoder of S25, construct the joint distribution of hidden variables of users and items, and obtain the second loss according to L ₂ ; combine the first loss and the second loss to obtain the total loss L, and minimize L to complete the pairing. Model training to obtain the item recommendation model.

Application example

For the test set of the three experimental data sets, the item recommendation model obtained by the training of the embodiment is used to perform item recommendation according to the following steps:

S1', according to the trained model CAF, obtain the user rating matrix R', and then set the value of the index position of the items visited in the user training set in this rating matrix to 0, and sort the newly obtained rating matrix according to the score to get An ordered rating matrix R".

S2', obtain user prediction items, this step adopts the scoring matrix method, and recommends items to each user according to the user scoring matrix R" obtained in step S1', and selects the top n (n=5, 10, 20, 50) as the result of the final recommendation to the user. If there are real label items of the user in the test data among the n items, the prediction is considered correct. In practical applications, n items are recommended to the user each time. If If there are users interested in it, the recommendation is successful. In this way, while the recommended items are obtained, the accuracy and efficiency of the item recommendation can be further improved.

The prediction effect of the above-mentioned item recommendation model (CAF) on the test set is shown in the bold part of Table 2.

Table 2: Item recommendation model results on three datasets

In order to further illustrate the prediction effect of the item recommendation method implemented by the collaborative autoregressive flow provided by the present invention. This application example uses three experimental datasets to train on seven baseline methods (BPR, CDL, CVAE, CVAE-B, MVAE, VAE-AR, CLVAES) to obtain an item recommendation model, and then uses these seven models in the test set to give Users recommend n items that are most likely to be accessed next. The prediction results of these seven models are shown in Table 2. The index R@n indicates the ratio of the number of correctly predicted items to the actual number of items in the test case, that is, the recall rate; P@n indicates that in the test set, the number of correctly predicted items accounted for the number of predicted items The ratio of numbers, that is, the precision rate.

The rest of the methods in the table are described below:

BPR: is a widely used matrix factorization method that utilizes implicit feedback to optimize latent factors via stochastic gradient descent using a pairwise ranking objective function. You can refer to the paper: S.Rendle,C.Freudenthaler,Z.Gantner,and L.Schmidt-Thieme.2009.Bpr:Bayesian personalized ranking from implicitfeedback.In UAI.

CDL: is a joint Bayesian model that learns auxiliary information and extracts latent features by stacking denoising autoencoders and collaborative filtering. You can refer to the paper: P.Wang,J.Guo,Y.Lan,J.Xu,S.Wan,andX.Cheng.2015.Learning hierarchical representation model for nextbasketrecommendation.In SIGIR.

CVAE: is the first collaborative item recommendation method based on variational autoencoder, which incorporates the content information in the item into matrix factorization (combining BPR model to improve CVAE to improve the recommended method of the model is CVAE in Table 2). -B). The CVAE model can refer to the paper: X.Li and J.She.2017.Collaborative variationalautoencoder for recommender systems.In KDD.

MVAE: uses multinomial conditional likelihood as the prior distribution, and it does not contain auxiliary information for recommendation. You can refer to the paper: D.Liang,R.G.Krishnan,M.D.Hoffman,and T.Jebara.2018.Variationalautoencoders for collaborative filtering.In WWW.

VAE-AR: Utilizes a variational autoencoder to model user implicit feedback information and item auxiliary information, and uses an adversarial generative network to extract latent variable representations influenced by auxiliary information. You can refer to the paper: W.Lee,K.Song,and I.-C.Moon.2017.Augmented variational autoencoders for collaborative filtering with auxiliary information.In CIKM.

CLVAE: is a conditional variational autoencoder-based recommendation method that extends CVAE with a hierarchical variational autoencoder structure. You can refer to the paper: W.Lee,K.Song,and I.-C.Moon.2017.Augmentedvariational autoencoders for collaborative filtering with auxiliaryinformation.In CIKM.

It can be seen from the prediction results in Table 2 that the item recommendation method implemented by the collaborative autoregressive flow provided by the present invention has an overall higher prediction accuracy than some existing methods.

In order to explain why the collaborative autoregressive flow can improve the prediction results, the hidden variables provided in this embodiment and the general method are visually compared, as shown in Figure 3. It can be seen from Figure 3 that the clustering effect of the CAF model is better , which is why the prediction effect of CAF is higher than that of other methods.

In order to illustrate that the use of autoregressive flow can approximate the result of the real posterior of the data, this application example provides a visual comparison of the hidden variables of the three data items with different values of the number of autoregressive flows, as shown in Figure 4. In theory, more invertible transformations could approach more complex distributions, but for our model, smaller values were sufficient. On the MovieLens dataset, it can be clearly observed that the most obvious representation is obtained when K = 7, after which the latent variable representation of items is distorted again. On the CiteULike and LastFM datasets, 5 autoregressive stream transformations are sufficient for optimal visualization. This visualization is important because visual representations are inherently more interpretable, and the extent of visualization can be used to guide the training process of autoregressive flow-based recommender systems.

In order to illustrate the influence of the number of autoregressive streams on the prediction results, this application example conducts experiments to study the influence of K (number of autoregressive streams) on the recommendation performance. The results of the recommendation performance (R@10 indicator) are shown in Figure 5. . It can be seen from Figure 5(a) that with the increase of the number of streams in the MovieLens dataset, the prediction accuracy rate increases until K>7 and starts to decline; Figure 5(b)(c) corresponds to CiteULike and LastFM respectively For the data set, when K < 5, the accuracy of the prediction continues to rise, and when K > 5, the accuracy begins to decline. We can see that the results in Figure 5 are consistent with the visualization results in Figure 4, and also illustrate that the more separable the latent variables, the better the recommendation performance of CAF.

In order to illustrate the influence of the number of training rounds on the prediction results, the CAF model in this application example is trained on three data sets for 40 rounds, and then the training sets of the data sets MovieLens, CiteULike and LastFM are used for training according to the method given in the embodiment. And use the trained CAF model to make predictions in the data set in the test set of the three data sets, and recommend the items that are most likely to be accessed in the next time to users. The prediction results are shown in Figure 6. As can be seen from the figure, the best results are obtained when the training epochs are 25 on the MovieLens dataset, while for the CiteULike and LastFM datasets, the best results are obtained after 30 epochs of training.

To sum up, the present invention uses collaborative autoregressive flow to implement item recommendation, and our collaborative autoregressive flow algorithm solves the problem of biased reasoning by using Bayesian inference for probabilistic recommendation and autoregressive flow for flexible posterior approximation, which can effectively It solves the problem that the dataset lacks user item information, and can alleviate the agnostic posterior estimation problem inherent in existing Bayesian recommendation methods. The added autoregressive flow can solve the error in the previous variational inference (such as VAE) process. This enables our model to learn the real distribution of users and items, and at the same time to capture the complex interaction between users and items, which is of great help to improve the prediction accuracy.

Those of ordinary skill in the art will appreciate that the embodiments described herein are intended to assist readers in understanding the principles of the present invention, and it should be understood that the scope of protection of the present invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations without departing from the essence of the present invention according to the technical teaching disclosed in the present invention, and these modifications and combinations still fall within the protection scope of the present invention.

Claims (4)

1. a Top-n project recommendation method realized based on collaborative autoregressive flow, is characterized in that comprising the following steps: S1, data preprocessing: According to the user's historical access items in the original data, the data set is divided into training set, validation set and test set; then an item label matrix R is constructed according to the user access items in the training set; Embed each user and each item in the training set to obtain the user embedding vector matrix U and the item embedding vector matrix V; S2, optimize the model parameters to obtain the optimal item recommendation model: input the user embedding vector matrix U and item embedding vector matrix V into different variational auto-encoders respectively, and introduce a collaborative autoregressive flow in the encoding process, the obtained user and the final latent variable representation matrix of the item

and

Then let the final latent variable representations of users and items be combined with their corresponding collaborative information to obtain the final latent representation matrices U' and V' of users and items, and then input the vector product of the final latent representations of users and items into a classification In the decoder, the first loss is obtained, and the final latent variable representations of users and items are input into a decoder to obtain the second loss, the first loss and the second loss are added to generate the final total loss, and then the total loss is minimized. loss, that is, to obtain the item recommendation model; S3, recommend items to users: Use the above trained item recommendation model to recommend Top-n items to users. 2. the Top-n project recommendation method realized based on collaborative autoregressive flow according to claim 1, is characterized in that described step S1 comprises the following sub-steps: S11, divide the data set: according to the user access items in the original data set, randomly select 70% of the items visited by each user as the training set, 20% as the test set, and the remaining 10% as the validation set; S12, construct the user embedding vector matrix U, the item embedding vector matrix V and the item label matrix R according to the situation of the user accessing the item in the training set, which specifically includes the following steps: S121, construct a user embedding vector matrix U: represent all users U _s ={u ₁ ,...,u _i ,...,u _M } in the training set as embedding vectors, and initialize a user embedding vector matrix according to the user's preference for items

where M represents the number of users, N represents the number of items, u _ij represents the elements in the user embedding vector matrix, if user _ui has visited item v _j , then u _ij =1, otherwise marked as 0, the user embedding vector matrix U The i-th row in represents the embedding vector _ui of user _ui ; S122, constructing the item embedding vector moment V: all items in the training set V _s ={v ₁ ,...,v _j ,...,v _N } are represented as embedding vectors, and the item embedding vector matrix is the transpose of the user embedding vector matrix, that is, V= ^UT , the jth row in the item embedding vector matrix V represents the embedding vector v _{j of the item v j ;} S123, construct an item label matrix R: construct an item label matrix according to the user access items in the training set where r _ij = u _ij . 3. the Top-n project recommendation method realized based on collaborative autoregressive flow according to claim 1, is characterized in that described step S2 comprises following substep: S21, using two variational auto-encoders to encode the user embedding vector _ui and the item embedding vector _vj respectively, and obtain the initial implicit variable representation of the user _ui and the item _vj by encoding

and The initial hidden variable representations are all d-dimensional vectors; This step uses an encoder, that is, a multi-layer perceptron, to encode the embedding vectors represented as users and items. The calculation process of each layer is as follows: level one:

Second floor: ... Layer t: In the above formula, t represents the number of layers of the multilayer perceptron, in the present invention t=3, the result of the last layer is passed

and Compute initial latent variable representations for users and items separately

and

and

All obey a Gaussian distribution, where the user's initial hidden variable represents

The mean of the distribution is

The variance is

but

The initial implicit variable representation for the project

its mean

variance Obtained by the mean and variance of the items During the calculation process of each layer of the encoder,

Represents a nonlinear activation function, the common ones are sigmoid or tanh. In the present invention, sigmoid is selected as the activation function,

and

Represents the hidden state representation obtained by the user embedding vector and the item embedding vector through the t-th layer of neural network, matrix and the bias vector

are the training parameters of the user encoder, where the superscript t indicates that this is the parameter of the neural network of the t layer, and

is to find the initial implicit variable representation of the user

Parameters to learn when distributing; matrix

and the bias vector

is the training parameter of the item encoder, the superscript t indicates that this is the parameter of the neural network of the t layer, is to find the initial implicit variable representation of the project

Parameters that need to be learned when distributing; and

are standard normally distributed variables used for random sampling; S22, define K reversible autoregressive flows, and represent the initial hidden variables of the user obtained in the previous step

and the item initial implicit variable representation

Input these K autoregressive streams for reversible transformation, and learn to obtain the final latent variable representation of users and items

and

Make its distribution closer to the true latent layer data distribution. Since the learning process of the final implicit variable representation of the user and the item is the same, we omit the subscripts _ui and v _j here, and use the unified symbols z ⁰ and z ^K to represent the initial implicit variable representation and the final implicit variable representation The variable representation, therefore, learns

and

The distribution process is as follows: In the above formula

is a one-dimensional probability density and is conditioned on the probability of the previous i-1 dimension of z ^K , and d represents the dimension of z ^K ; The process of finding the final implicit variable representation of users and items includes the following sub-steps: S221, find the target distribution p(z ^k ): in the process of obtaining the final implicit variable representation, we first obtain the d dimensions of z ^k , where k is regarded as passing through the k th flow, the i th in z ^k dimensions are conditioned on the first i-1 dimensions of z ^k-1 , according to

Its distribution is p(z ^k-1 ), and the d dimensions of z ^k are calculated to obtain the distribution p(z ^k ) of z ^k ,

In the above formula, M( ) and S( ) are the neural networks for calculating the mean and variance, respectively. Through S22, we can obtain a target distribution p(z ^k ), since the process of generating the target distribution is based on p(z ^{k- 1} ), the process is very fast for GPU parallelization. This process mainly uses the idea of Inverse Autoregressive Flow (IAF), which is a special neural network that can output all values of mean and standard deviation at the same time, which is convenient for μ _{1: i-1} and σ _{1 : sampling of i-1} ; S222, find the target distribution

For the reversible process of p(z ^k-1 ) density estimation, the present invention uses the idea of Masked Autoregressive Flow (MAF) to evaluate the target distribution

In the above formula, M'( ) and S'( ) are special neural networks that use mask autoregressive flow to find the mean and variance, respectively, and act as a reversible calculation process in the model; S223, through steps S221 and S222, two identical target distributions p(z ^k ) and

But they have different biases in the process of simulating autoregressive flow, in order to use the two output distributions to stabilize the training process, we calculate the KL divergence between the two output distributions,

In the above formula, the two target distributions p(z ^k ) and

The cross entropy is calculated as follows: Next, entropy is described

The calculation process of:

S224, repeating steps S221 to S223 K times to obtain the final implicit variable representation of the user and item

and S23, express the final hidden variables of users and items obtained in S22

and Collaboration information with users and projects and

Combined to get the final latent representations _ui ' and v _j ' of users and items,

In the above formula, u _c and _vc are obtained from the Gaussian distribution, representing the collaborative information of users and items respectively. With the optimization of the model, these two vectors are also continuously optimized, and finally they can represent users and items well. collaboration information; S24, continuously repeating steps S21 to S23 until the final latent representations of all users and items are obtained, and connecting the final latent representations of all users and items to obtain the final latent representation matrices U' and V' of users and items; S25, construct two loss functions L ₁ and L ₂ , add L ₁ and L ₂ together to generate a final total loss L, and minimize this total loss function, complete the training of the model, and obtain the item recommendation model. Among them, L ₁ is the cross-entropy loss function of the predicted item and the label item, and L ₂ is used to make the learned latent variable distribution closer to the real distribution. The reconstruction loss function. This step specifically includes the following sub-steps: S251, obtain the first loss L ₁ : input the vector product of the final latent representation matrices U′ and V′ of the user and the item obtained in S24 into a classifier composed of a multi-layer perceptron, and output the user access to each item Probability matrix, which is regarded as the user's scoring matrix R' for all items, and then use the item label matrix R obtained from S1 and the predicted scoring matrix R' to calculate the cross entropy loss,

In the above formula, r' _ij represents the probability of user _ui accessing item v _j , L ₁ is taken as the first loss, M is the total number of users, and N is the total number of items; S252, obtain the second loss L ₂ : then express the final implicit variables of the user and item obtained in S23 and

Input into a reversible decoder, construct the joint distribution of user and item latent variables, and let it find relative entropy with the joint distribution of input user and item data. For convenience of expression, in the second loss calculation formula, cancel the user and the item data. The subscripts i and j of the items yield the second loss L ₂ :

The true distribution p(u,z _u ) of the latent variable z _u is approximated by the user posterior distribution q(z _u | _u ), which is defined as

Similarly, the true distribution p(v,z _v ) of the latent variable z _v is approximated by the item posterior distribution q(z _v |v), and q(z _v |v) is defined as

p(u,z _u ) and p(v,z _v ) represent the true distribution of user and item input data, _zu , z _v represent the latent variables in the collaborative autoregressive flow model, u, v represent the model input data, θ and φ represent the parameters of the probability distribution, respectively, in the above formula

and

represents the reconstruction loss,

and

is a constant term, and the remaining four terms represent the autoregressive flow. In the process of optimizing the _second loss L2, the The minimization of , the specific derivation process refers to the following papers: [van den Oord, A., Li, Y., Babuschkin, I., Simonyan, K., Vinyals, O., Kavukcuoglu, K., van den Driessche, " Parallel wavenet:Fast high-fidelity speech synthesis"]; S253 , add the first loss and the second loss together to generate a final total loss L=L ₁ +L ₂ , and minimize the total loss function to complete the training of the model to obtain the item recommendation model. 4. the Top-n project recommendation method realized based on collaborative autoregressive flow according to claim 1, is characterized in that described step S3 comprises following sub-steps: S31, obtain the user rating matrix R' according to the model trained in S2, and then set the rating of the index position of the item visited by the user in the training set to _{0. For example, if the user ui has visited the item v j in} the training set, the rating will be The corresponding element r' _ij in the matrix R' is set to 0. Then, sort each row in the new scoring matrix according to the level of scoring to obtain the matrix R"; S32, according to the scoring matrix R" obtained in S31, select the items with the top n scores in R" as the final recommended result to the user.

Images