The recently proposed Sequential Recommendation Augmentation (SRA) paradigm has shown valuable potential in sequential recommendation, especially for handling long-tail problem via extending short behavior sequences. However, the selfsupervised SRA adopts autoregressive learning with fixed forward or backward direction, which cannot make full use of the contextual correlation information in the training behavior sequences. Due to the direction diference, discrepancy problem exists in the two training stages of SRA, i.e., pretraining and finetuning. In order to overcome the restriction of specific sequential learning direction, we propose to equip SRA with permutation autoregressive learning to extract global contextual correlation information from the behavior sequences in both directions. The adapted SRA method is implemented with two-stream self-attention. Empirical evaluations on multiple sequential recommendation benchmark datasets demonstrate the efectiveness of our proposed model, and the augmented data can significantly reduce the convergence rate.
DL4SR’22: Workshop on Deep Learning for Search and Recommendation, co-located with the 31st ACM International Conference on Information and Knowledge Management (CIKM), October 17-21, 2022, Atlanta, USA $ yuqian81@jd.com (Q. Yu)
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CPWrEooUrckReshdoinpgs IhStpN:/c1e6u1r3-w-0s.o7r3g ACttEribUutRion W4.0oInrtekrnsahtioonpal (PCCroBYce4.0e).dings (CEUR-WS.org) direction. For the inference stage, we try to adopt the
beam search for generating more suitable subsequence
as the augmented data. A latest revision named BiCAT
[
Our contributions can be summarized as following: (a) Global contextual correlation information is explored in Sequential Recommendation Augmentation (SRA). (b) Equipped with Permutation Autoregressive Learning and beam search method, an adapted SRA framework is designed and evaluated. (c) The proposed framework outperforms the state-of-the-art methods for sequential recommendation augmentation without extra information or heuristic rules.
The sequential recommendation task can be regarded as the next-item prediction given the historical behavior recommendation task can be formulated as: sequence. We denote the user set as and the item set as . The interaction behavior of the given user ∈ is denoted as = {1, 2, ..., }. The sequential +1 = arg max (|)
which means finding the next item
+1 with the largest probability given the user behavior sequence .
Recently, a Sequential Recommendation
Augmentation (SRA) paradigm is proposed [
max ( |+1, +2, ..., )
(2) With the pretrained model, pseudo-prior items can be recursively generated for short sequences, in order to eliminate the data sparsity in recommendation and further improve the quality of the whole training set. The pretrained model can be further finetuned for next-item prediction, and the learning objective is the forward autoregressive learning objective: max ( |1, 2, ..., − 1)
We take Transformer as an example backbone for de- an autoregressive way. scribing this learning paradigm. The key component in Transformer, i.e., multi-head self-attention is constructed with linear transformation and the scaled dot-product
Assume that the length of the behavior sequence is ,
we denote the set of all possible permutation of index as
. For example, if = 4, then the original
permutaattention [
(b) Target-stream Attention
For details of SRA paradigm, please refer to [
Now our intention is to help the SRA framework making
use of the global contextual correlation in the
behavior sequences. The idea of “mask and reconstruct” is a
commonly used method for helping the sequence model
to learn from contextual information in arbitrary
position, but the incorporation of [MASK] token in behavior
sequence will bring more severe discrepancy problem
as in BERT [
In order to exploit bidirectional item correlation in bidirectional context, we propose to train the sequence model with diferent permutations of each training sequence in (1) maining the autoregressive learning paradigm. where < stand for the items in x whose index is in <. This new objective calculates the probability of an item conditioned on all possible permutations of items in an autoregressive way, as opposed to just those to the (3) left side or right side of the target item in the existing is ! = 24. For each permutation z in , < stands for indices of all the element before -th element , and is for the current elements. Similar to autoregressive learning, we try to predict given <. In this way, the learning objective is rewritten according to the permutation z instead of the original order of original sequence x as follows.
max Ez∼ log ( |< ) (4) Algorithm 1 Permutation Autoregressive Learning for SRA 1: Input: A set of behavior sequence {} 2: Output: A sequential recommendation model 3: procedure PAL({}) 4: for each epoch do 5: for each instance in batch do 6: Sample permutations with length . 7: Pretrain with Eqn 4. 8: Save the result pretrained model ℳ0 for generation. 9: Select behavior sequences shorter than . 10: Generate the pseudo-prior items with beam width . 11: for each epoch do 12: for each batch do 13: Finetune ℳ0 with Eqn 3. 14: Save the result finetuned model for sequential recommendation. dataset #user #item #instance avg. length
The first one is the content-stream representation which is exactly the same as the hidden state in the standard self-attention. This corresponding attention is named Content-stream attention: ℎ() ←
Attention( = ℎ(− 1), = ℎ(≤− 1); )
(6) () is the output of the -th block Transformer. where ℎ methods for sequential recommendation augmentation. The second representation is target representation, which It should be emphasised that only the indices, namely contains only the position information of the target in which elements are used for prediction, are changed, order to avoid content information leaking. The Targetwhile the position of each item in the original sequence stream attention is: is rTehtreaianbeodv.e learning objective can help each position ̃ℎ︀() ← Attention( = ̃ℎ︀(− 1), = ℎ(<− 1); ) to learn information from bidirectional context, but it (7) brings a new issue about the position information. In prediction given several known items, the predicted position The content representation ℎ(0) is initialized by the or index is not fixed as in original autoregressive learn- item embedding e( ) which is added with the posiing. So we need to learn the target-aware representation tional encoding as in normal Transformer, and all the which can tell the position that the current predicted item target representation ̃ℎ︀(0) is initialized by an identical located in. Therefore, the ( |< ) is formulated as: trainable vector w. The output ̃ℎ︀ of the last layer Trans ( |< ) = ∑︀* exp[e(* ) h̃︀ (<, )] exp[e( ) h̃︀ (<, )] (5) former is used as h̃︀ (<, ) in Eqn 5 for prediction. In this way, equipped with this two-stream attention, we can force each position in the sequence to learn bidirectional information while maintaining the normal behavwhere h̃︀ (<, ) is the learned target-aware represen- ior order. tation for the item with the -th index.
We propose beam-search for obtain the optimal sequence
as the pseudo-prior items. Instead of recursively predict
As aforementioned, the self-attention module in the se- the next item in a greedy way, Beam Search method
quence model need to be modified for obtaining target- maintains a bufer of candidate subsequences and selects
aware representations. The two-stream attention struc- the best one with the largest joint probability. Beam
ture was used in language modeling to provide target width value is denoted as . More details can be found
position information without leaking the content infor- in [
Specifically, two separated streams of attention vectors are maintained to store content information and position 3.2. PAL Algorithm for SRA information. For each position in the factorization z, Considering the computing complexity of the permutawe keep updating the intermediate vectors ℎ and ̃ℎ︀ , tion autoregressive learning, we need to sample from the representing content stream and target stream respec- set of permutation and predict partial of the sequence. tively. Each stream is learned by a designated attention For each sampled permutation, we train the model via mechanism. The detailed formulations of the two-stream maximizing the probability of last item. The detailed attention structure is described as follows. learning procedure is described in Algorithm 1.
Following the setting in [
We compare our proposed method with the following
methods including the state-of-the-art BiCAT [
We select the Transformer as the backbone to verify our SRA solution. The block number is fixed to 2. The hidden length is selected in {32, 64, 128}. The head number in attention is selected in {2, 4}. The learning rate is fixed at 0.001 since the results are similar with other settings. The dropout rate is fixed to 0.5. The short sequence length threshold is set to 18, and each short sequence is augmented with 15 pseudo-prior items. For the number of sampled permutations ( in Algorithm 1), we select it in {2, 4, 6} with model selection. The epoch number is fixed to 200 which is suficient for all the models to converge. We conduct model selection via grid search. For each behavior sequence, we randomly sample 100 negative items for ranking with the last item, which is the ground-truth. Recall@n, NDCG@n, and Mean Reciprocal Rank (MRR) are employed for as the evaluation metrics, and is selected in {5, 10}.
We performance sequential recommendation on all the 6 datasets with the above mentioned baseline models to demonstrate the efectiveness of PAL. Previous SRA work has shown the advantage of self-attention sequence model for recommendation, so we use the SASRec and BERT4Rec as two baselines without augmentation. The 1http://jmcauley.ucsd.edu/data/amazon/ y t u a e B s e n o h P s t r o p S s l o o T y b a B e c fi O
Model
MRR SASRec 0.3849 0.4863 0.2884 0.3212 0.2870 BERT4Rec 0.4243 0.5371 0.3075 0.3598 0.3021 ASReP 0.4583 0.5743 0.3465 0.4042 0.3540 BiCAT 0.4901 0.5892 0.3704 +6.8% 0.4289 +6.1% 0.3712 +4.8% PAL 0.4934 0.6048 0.3873 +11.7% 0.4400 +8.8% 0.3803 +7.4% PAL++ 0.4936 0.6036 0.3879 +11.9% 0.4415 +9.2% 0.3821 +7.9% performance results are presented in Table 2. All the SRA methods achieve better performance than the others, which verified the efectiveness of augmentation. Compared with the strongest sequential recommendation augmentation baseline BiCAT, the proposed PAL can provide around 2% to 5% improvement on NDCG10, which is significant in these sparse datasets. The beam search method (PAL++) consistently shows efectiveness on all the datasets, and the further performance improvement on the “Tools and Home Improvement” and “Baby” are more significant than other datasets. The explanation for this improvement diference is that the behavior diversity varies in diferent datasets.
Performance improvement on short behavior sequence is critical for an augmentation paradigm. To further analyze the advantages of PAL for short sequence, we reconstruct the test set with all the behavior sequence shorter than 3 and evaluate all the baseline methods and our PAL and PAL++. The results is presented in Figure 3. Improvement on short sequence is a critical for an augmentation paradigm. We can find that the PAL and PAL++ method can significantly outperform the other sequential recommendation augmentation methods on all the datasets. This result illustrate that the proposed learning method can incorporate more contextual correlation information into the short sequence augmentation.
The default backbone model of the SRA methods, i.e., ASReP, BiCAT, PAL, PAL++ in Section 4.3 is the basic Transformer which is the same as in SASRec. All the SRA methods can also be applied to all the Transformer-based SR methods, such as SASRec, BERT4Rec and TiSASRec. For TiSASRec, we ignore the temporal information in the pretraining and sequence generating stages, and assign the smallest timestamp in the original sequence for the generated items. Here we report part of performance (NDCG@5) comparison on “Beauty” dataset in Table 3. According to the results, equipped with SRA methods, the performance of all the backbone models are improved, and the proposed PAL / PAL++ achieve the best results. Please note the TiSASRec is outperformed by SASRec as our current augmentation methods has not incorporated the temporal information, which is a future work for SRA.
Backbone
Base ASReP BiCAT PAL PAL++
0.2884 0.3465 0.3704 0.3873 0.3879
0.3075 0.3562 0.3746 0.3886 0.3886
0.3076 0.3427 0.3625 0.3771 0.3791
One interesting finding is that the pseudo sequence generated by PAL can significantly improve the converge rate of the finetuning stage in sequential recommendation augmentation. We depict the loss value during the ifnetuning stage in Fig 4, where we can observe that the PAL method can converge earlier than ASReP to achieve a stable loss value. Similar results can be found in other datasets. Due to the permutation learning objective, the PAL is of advantage in the generated data and pretrained model, which lead to the improvement of the convergence rate in the final finetuning stage.
(a) Beauty (b) Cell Phones (c) Sports Figure 4: Illustration of Convergence Rate in Finetuning. The x-axis is the epoch, and the y-axis is the loss value. The grey line is for ASReP method, and the blue one is for PAL.