Boolean matrix factorization (BMF) has been widely utilized in fields such as recommendation systems, graph learning, text mining, and -omics data analysis. Traditional BMF methods decompose a binary matrix into the Boolean product of two lower-rank Boolean matrices plus homoscedastic random errors. However, real-world binary data typically involves biases arising from heterogeneous row- and column-wise signal distributions. Such biases can lead to suboptimal fitting and unexplainable predictions if not accounted for. In this study, we reconceptualize the binary data generation as the Boolean sum of three components: a binary pattern matrix, a background bias matrix influenced by heterogeneous row or column distributions, and random flipping errors. We introduce a novel Disentangled Representation Learning for Binary matrices (DRLB) method, which employs a dual auto-encoder network to reveal the true patterns. DRLB can be seamlessly integrated with existing BMF techniques to facilitate bias-aware BMF. Our experiments with both synthetic and real-world datasets show that DRLB significantly enhances the precision of traditional BMF methods while offering high scalability. Moreover, the bias matrix detected by DRLB accurately reflects the inherent biases in synthetic data, and the patterns identified in the bias-corrected real-world data exhibit enhanced interpretability.

Matrix low rank approximation is an effective method to reduce or eliminate the statistical redundancy of its components. Compared with the traditional global low rank methods such as singular value decomposition (SVD), local low rank approximation methods are more advantageous to uncover interpretable data structures when clear duality exists between the rows and columns of the matrix. Local low rank approximation is equivalent to low rank submatrix detection. Unfortunately, existing local low rank approximation methods can detect only submatrices of specific mean structure, which may miss a substantial amount of true and interesting patterns. In this work, we develop a novel matrix computational framework called RPSP (Random Probing based submatrix Propagation) that provides an effective solution for the general matrix local low rank representation problem. RPSP detects local low rank patterns that grow from small submatrices of low rank property, which are determined by a random projection approach. RPSP is supported by theories of random projection. Experiments on synthetic data demonstrate that RPSP outperforms all state-of-the-art methods, with the capacity to robustly and correctly identify the low rank matrices when the pattern has a similar mean as the background, background noise is heteroscedastic and multiple patterns present in the data. On real-world datasets, RPSP also demonstrates its effectiveness in identifying interpretable local low rank matrices.

This paper studies the item-to-item recommendation problem in recommender systems from a new perspective of metric learning via implicit feedback. We develop and investigate a personalizable deep metric model that captures both the internal contents of items and how they were interacted with by users. There are two key challenges in learning such model. First, there is no explicit similarity annotation, which deviates from the assumption of most metric learning methods. Second, these approaches do not account for the fact that items are often represented by multiple sources of meta data and different users use different combinations of these sources to form their own notion of similarity. To address these challenges, we develop a new metric representation embedded as kernel parameters of a probabilistic model. This helps express the correlation between items that a user has interacted with, which can be used to predict user interaction with new items. Our approach hinges on the intuition that similar items induce similar interactions from the same user, thus fitting a metric-parameterized model to predict an implicit feedback signal could indirectly guide it towards finding the most suitable metric for each user. To this end, we also analyze how and when the proposed method is effective from a theoretical lens. Its empirical effectiveness is also demonstrated on several real-world datasets.

Sequential recommendation aims to model dynamic user behavior from historical interactions. Self-attentive methods have proven effective at capturing short-term dynamics and long-term preferences. Despite their success, these approaches still struggle to model sparse data, on which they struggle to learn high-quality item representations. We propose to model user dynamics from shopping intents and interacted items simultaneously. The learned intents are coarse-grained and work as prior knowledge for item recommendation. To this end, we present a coarse-to-fine self-attention framework, namely CaFe, which explicitly learns coarse-grained and fine-grained sequential dynamics. Specifically, CaFe first learns intents from coarse-grained sequences which are dense and hence provide high-quality user intent representations. Then, CaFe fuses intent representations into item encoder outputs to obtain improved item representations. Finally, we infer recommended items based on representations of items and corresponding intents. Experiments on sparse datasets show that CaFe outperforms state-of-the-art self-attentive recommenders by 44.03% [email protected] on average.

Boolean matrix factorization (BMF) is a combinatorial problem arising from a wide range of applications including recommendation system, collaborative filtering, and dimensionality reduction. Currently, the noise model of existing BMF methods is often assumed to be homoscedastic; however, in real world data scenarios, the deviations of observed data from their true values are almost surely diverse due to stochastic noises, making each data point not equally suitable for fitting a model. In this case, it is not ideal to treat all data points as equally distributed. Motivated by such observations, we introduce a probabilistic BMF model that recognizes the object- and feature-wise bias distribution respectively, called bias aware BMF (BABF). To the best of our knowledge, BABF is the first approach for Boolean decomposition with consideration of the feature-wise and object-wise bias in binary data. We conducted experiments on datasets with different levels of background noise, bias level, and sizes of the signal patterns, to test the effectiveness of our method in various scenarios. We demonstrated that our model outperforms the state-of-the-art factorization methods in both accuracy and efficiency in recovering the original datasets, and the inferred bias level is highly significantly correlated with true existing bias in both simulated and real world datasets.

In e-commerce websites, multiple related product recommendations are usually organized into “widgets”, each given a name, as a recommendation caption, to describe the products within. These recommendation captions are usually manually crafted and generic in nature, making it difficult to attach meaningful and informative names at scale. As a result, the captions are inadequate in helping customers to better understand the connection between the multiple recommendations and make faster product discovery.

With the increasing demands on e-commerce platforms, numerous user action history is emerging. Those enriched action records are vital to understand users’ interests and intents. Recently, prior works for user behavior prediction mainly focus on the interactions with product-side information. However, the interactions with search queries, which usually act as a bridge between users and products, are still under investigated. In this paper, we explore a new problem named temporal event forecasting, a generalized user behavior prediction task in a unified query product evolutionary graph, to embrace both query and product recommendation in a temporal manner. To fulfill this setting, there involves two challenges: (1) the action data for most users is scarce; (2) user preferences are dynamically evolving and shifting over time. To tackle those issues, we propose a novel Retrieval-Enhanced Temporal Event (RETE) forecasting framework. Unlike existing methods that enhance user representations via roughly absorbing information from connected entities in the whole graph, RETE efficiently and dynamically retrieves relevant entities centrally on each user as high-quality subgraphs, preventing the noise propagation from the densely evolutionary graph structures that incorporate abundant search queries. And meanwhile, RETE autoregressively accumulates retrieval-enhanced user representations from each time step, to capture evolutionary patterns for joint query and product prediction. Empirically, extensive experiments on both the public benchmark and four real-world industrial datasets demonstrate the effectiveness of the proposed RETE method.

Liqiang Xiao, Jun Ma, Xin Luna Dong, Pascual Martínez-Gómez, Nasser Zalmout, Wei Chen, Tong Zhao, Hao He, Yaohui Jin. Proceedings of the 2021 Conference on Empirical Methods in Natural Language Processing. 2021.

In this paper, we propose a Spatial Robust Mixture Regression model to investigate the relationship between a response variable and a set of explanatory variables over the spatial domain, assuming that the relationships may exhibit complex spatially dynamic patterns that cannot be captured by constant regression coefficients. Our method integrates the robust finite mixture Gaussian regression model with spatial constraints, to simultaneously handle the spatial non-stationarity, local homogeneity, and outlier contaminations. Compared with existing spatial regression models, our proposed model assumes the existence a few distinct regression models that are estimated based on observations that exhibit similar response-predictor relationships. As such, the proposed model not only accounts for non-stationarity in the spatial trend, but also clusters observations into a few distinct and homogenous groups. This provides an advantage on interpretation with a few stationary sub-processes identified that capture the predominant relationships between response and predictor variables. Moreover, the proposed method incorporates robust procedures to handle contaminations from both regression outliers and spatial outliers. By doing so, we robustly segment the spatial domain into distinct local regions with similar regression coefficients, and sporadic locations that are purely outliers. Rigorous statistical hypothesis testing procedure has been designed to test the significance of such segmentation. Experimental results on many synthetic and real-world datasets demonstrate the robustness, accuracy, and effectiveness of our proposed method, compared with other robust finite mixture regression, spatial regression and spatial segmentation methods.

Existing recommender systems in the e-commerce domain primarily focus on generating a set of relevant items as recommendations; however, few existing systems utilize underlying item attributes as a key organizing principle in presenting recommendations to users. Mining important attributes of items from customer perspectives and presenting them along with item sets as recommendations can provide users more explainability and help them make better purchase decision. In this work, we generalize the attribute-aware item-set recommendation problem, and develop a new approach to generate sets of items (recommendations) with corresponding important attributes (explanations) that can best justify why the items are recommended to users. In particular, we propose a system that learns important attributes from historical user behavior to derive item set recommendations, so that an organized view of recommendations and their attribute-driven explanations can help users more easily understand how the recommendations relate to their preferences. Our approach is geared towards real world scenarios: we expect a solution to be scalable to billions of items, and be able to learn item and attribute relevance automatically from user behavior without human annotations. To this end, we propose a multi-step learning-based framework called Extract-Expect-Explain (EX3), which is able to adaptively select recommended items and important attributes for users. We experiment on a large-scale real-world benchmark and the results show that our model outperforms state-of-the-art baselines by an 11.35% increase on NDCG with adaptive explainability for item set recommendation.

Boolean matrix has been used to represent digital information in many fields, including bank transaction, crime records, natural language processing, protein-protein interaction, etc. Boolean matrix factorization (BMF) aims to find an approximation of a binary matrix as the Boolean product of two low rank Boolean matrices, which could generate vast amount of information for the patterns of relationships between the features and samples. Inspired by binary matrix permutation theories and geometric segmentation, we developed a fast and efficient BMF approach, called MEBF (Median Expansion for Boolean Factorization). Overall, MEBF adopted a heuristic approach to locate binary patterns presented as submatrices that are dense in 1's. At each iteration, MEBF permutates the rows and columns such that the permutated matrix is approximately Upper Triangular-Like (UTL) with so-called Simultaneous Consecutive-ones Property (SC1P). The largest submatrix dense in 1 would lie on the upper triangular area of the permutated matrix, and its location was determined based on a geometric segmentation of a triangular. We compared MEBF with other state of the art approaches on data scenarios with different density and noise levels. MEBF demonstrated superior performances in lower reconstruction error, and higher computational efficiency, as well as more accurate density patterns than popular methods such as ASSO, PANDA and Message Passing. We demonstrated the application of MEBF on both binary and non-binary data sets, and revealed its further potential in knowledge retrieving and data denoising.

If one customer buys a tennis racket, what are the best 3 complementary products to purchase together? 3 tennis ball packs, 3 headbands, 3 overgrips, or 1 of each respectively? Complementary product recommendation (CPR), aiming at providing product suggestions that are often bought together to serve a joint demand, forms a pivotal component of e-commerce service, however, existing methods are far from optimal. Given one product, how to recommend its complementary products of different types is the key problem we tackle in this work. We first conduct an extensive analysis to correct the inaccurate assumptions adopted by existing work to show that co-purchased products are not always complementary and further propose a new strategy to generate clean distant supervision labels for CPR modeling. Moreover, to bridge in the gap from existing work that CPR does not only need relevance modeling but also requires diversity to fulfill the whole purchase demand, we develop a deep learning framework, P-Companion to explicitly model both relevance and diversity. More specifically, given one product with its product type, P-Companion first uses an encoder-decoder network to predict multiple complementary product types, then a transfer metric learning network is developed to project the embedding of query product to each predicted complementary product type subspace and further learn the complementary relationship based on the distant supervision labels within each subspace. The whole framework can be trained from end-to-end and robust to cold-start products attributed to a novel pretrained product embedding module named Product2Vec, based on graph attention networks. Extensive offline experiments show that P-Companion outperforms state-of-the-art baselines by 7.1% increase on the [email protected] score with well-controlled diversity. Production-wise, we deploy P-Companion to provide online recommendations for over 200M products at Amazon and observe significant gains on product sales and profit.

Low rank representation of binary matrix is powerful in disentangling sparse individual-attribute associations, and has received wide applications. Existing binary matrix factorization (BMF) or co-clustering (CC) methods often assume i.i.d background noise. However, this assumption could be easily violated in real data, where heterogeneous row- or column-wise probability of binary entries results in disparate element-wise background distribution, and paralyzes the rationality of existing methods. We propose a binary data denoising framework, namely BIND, which optimizes the detection of true patterns by estimating the row- or column-wise mixture distribution of patterns and disparate background, and eliminating the binary attributes that are more likely from the background. BIND is supported by thoroughly derived mathematical property of the row- and column-wise mixture distributions. Our experiment on synthetic and real-world data demonstrated BIND effectively removes background noise and drastically increases the fairness and accuracy of state-of-the arts BMF and CC methods.

Can one build a knowledge graph (KG) for all products in the world? Knowledge graphs have firmly established themselves as valuable sources of information for search and question answering, and it is natural to wonder if a KG can contain information about products offered at online retail sites. There have been several successful examples of generic KGs, but organizing information about products poses many additional challenges, including sparsity and noise of structured data for products, complexity of the domain with millions of product types and thousands of attributes, heterogeneity across large number of categories, as well as large and constantly growing number of products.

Taxonomies have found wide applications in various domains, especially online for item categorization, browsing, and search. Despite the prevalent use of online catalog taxonomies, most of them in practice are maintained by humans, which is labor-intensive and difficult to scale. While taxonomy construction from scratch is considerably studied in the literature, how to effectively enrich existing incomplete taxonomies remains an open yet important research question. Taxonomy enrichment not only requires the robustness to deal with emerging terms but also the consistency between existing taxonomy structure and new term attachment. In this paper, we present a self-supervised end-to-end framework, Octet, for Online Catalog Taxonomy EnrichmenT. Octet leverages heterogeneous information unique to online catalog taxonomies such as user queries, items, and their relations to the taxonomy nodes while requiring no other supervision than the existing taxonomies. We propose to distantly train a sequence labeling model for term extraction and employ graph neural networks (GNNs) to capture the taxonomy structure as well as the query-item-taxonomy interactions for term attachment. Extensive experiments in different online domains demonstrate the superiority of Octet over state-of-the-art methods via both automatic and human evaluations. Notably, Octet enriches an online catalog taxonomy in production to 2 times larger in the open-world evaluation.

Given multiple input signals, how can we infer node importance in a knowledge graph (KG)? Node importance estimation is a crucial and challenging task that can benefit a lot of applications including recommendation, search, and query disambiguation. A key challenge towards this goal is how to effectively use input from different sources. On the one hand, a KG is a rich source of information, with multiple types of nodes and edges. On the other hand, there are external input signals, such as the number of votes or pageviews, which can directly tell us about the importance of entities in a KG. While several methods have been developed to tackle this problem, their use of these external signals has been limited as they are not designed to consider multiple signals simultaneously. In this paper, we develop an end-to-end model MultiImport, which infers latent node importance from multiple, potentially overlapping, input signals. MultiImport is a latent variable model that captures the relation between node importance and input signals, and effectively learns from multiple signals with potential conflicts. Also, MultiImport provides an effective estimator based on attentive graph neural networks. We ran experiments on real-world KGs to show that MultiImport handles several challenges involved with inferring node importance from multiple input signals, and consistently outperforms existing methods, achieving up to 23.7% higher [email protected] than the state-of-the-art method.

Boolean tensor has been broadly utilized in representing high dimensional logical data collected on spatial, temporal and/or other relational domains. Boolean Tensor Decomposition (BTD) factorizes a binary tensor into the Boolean sum of multiple rank-1 tensors, which is an NP-hard problem. Existing BTD methods have been limited by their high computational cost, in applications to large scale or higher order tensors. In this work, we presented a computationally efficient BTD algorithm, namely Geometric Expansion for all-order Tensor Factorization (GETF), that sequentially identifies the rank-1 basis components for a tensor from a geometric perspective. We conducted rigorous theoretical analysis on the validity as well as algorithemic efficiency of GETF in decomposing all-order tensor. Experiments on both synthetic and real-world data demonstrated that GETF has significantly improved performance in reconstruction accuracy, extraction of latent structures and it is an order of magnitude faster than other state-of-the-art methods.

How can we estimate the importance of nodes in a knowledge graph (KG)? A KG is a multi-relational graph that has proven valuable for many tasks including question answering and semantic search. In this paper, we present GENI, a method for tackling the problem of estimating node importance in KGs, which enables several downstream applications such as item recommendation and resource allocation. While a number of approaches have been developed to address this problem for general graphs, they do not fully utilize information available in KGs, or lack flexibility needed to model complex relationship between entities and their importance. To address these limitations, we explore supervised machine learning algorithms. In particular, building upon recent advancement of graph neural networks (GNNs), we develop GENI, a GNN-based method designed to deal with distinctive challenges involved with predicting node importance in KGs. Our method performs an aggregation of importance scores instead of aggregating node embeddings via predicate-aware attention mechanism and flexible centrality adjustment. In our evaluation of GENI and existing methods on predicting node importance in real-world KGs with different characteristics, GENI achieves 5-17% higher [email protected] than the state of the art.

Daily deal websites, such as Groupon and Living-Social, are now becoming increasingly popular current shopping trends worth multi-billion dollars. Understanding customers' purchase behaviors in daily deal websites is important to provide accurate and precise personalized recommendations in order for companies to gain more revenue. However, different from traditional online shopping sites, such as Amazon and Target, in which consumers can evaluate and purchase multiple items at the same time, customer's behaviors in daily deal websites have their unique characteristics and thus pose several challenges for modeling these behaviors: (1) daily deals are not available all the time and customers have to decide whether to purchase today's deal or forgo the opportunity and wait for future deals; (2) daily deals are made sequentially available to the consumers and the future quality of the deals are uncertain. Despite recent advances in user modeling and item recommendation, modeling users' purchase behaviors in daily deal websites is still not well resolved. In this paper, we present a large-scale study of customers' behaviors based on Groupon data with the following contributions: (1) By conducting empirical analysis on customers' complete clickstream data, we first demonstrate that customers are active but prudent for the purchase behaviors, then we show customers have their criteria for the purchase decision and the criteria changes with the waiting time since their last purchase; (2) Based on these observations, we formulate users' behaviors in daily deal websites as the Secretary Problem and propose a structure model based on consumer behavior theories to investigate how individual and deal characteristics would affect the purchase behavior on daily deal website; (3) We model customers' purchase criteria as reservation value and propose the use of copula modeling for reservation value estimation. We demonstrate the performance of the proposed model for purchase behavior modeling and discuss how this model can be used to reveal the behavior mechanism and provide reliable solutions to target the right people at the right time using the product with the right features even in the long run.

Recommender systems are ubiquitous in applications ranging from e-commerce to social media, helping users to navigate a huge selection of items and to meet a variety of special needs and user tastes. Incorporating contextual knowledge into such systems - such as relational information - has proven to be an effective way to improve recommendation accuracy. A popular line of research aims to model relationships between users, through their connections in a social network. In contrast, we aim to model complex relationships between products, using data based on co-purchase and co-browsing behavior. Modeling such networks presents a variety of challenges, in particular because the features that make two items complementary (or likely to be co-purchased) are far more complex than mere similarity. To model these complex relationships we develop a method based on pairwise ranking and embedding learning to build representations of items based on their co-purchasing and co-browsing statistics. We conduct experiments on Amazon product data to demonstrate that modeling such relationships significantly improves accuracy compared to competitive baselines.

Successive point-of-interest (POI) recommendation in location-based social networks (LBSNs) becomes a significant task since it helps users to navigate a number of candidate POIs and provides the best POI recommendations based on users’ most recent check-in knowledge. However, all existing methods for successive POI recommendation only focus on modeling the correlation between POIs based on users’ check-in sequences, but ignore an important fact that successive POI recommendation is a time-subtle recommendation task. In fact, even with the same previous check-in information, users would prefer different successive POIs at different time. To capture the impact of time on successive POI recommendation, in this paper, we propose a spatial-temporal latent ranking (STELLAR) method to explicitly model the interactions among user, POI, and time. In particular, the proposed STELLAR model is built upon a ranking-based pairwise tensor factorization framework with a fine-grained modeling of user-POI, POI-time, and POI-POI interactions for successive POI recommendation. Moreover, we propose a new interval-aware weight utility function to differentiate successive check-ins’ correlations, which breaks the time interval constraint in prior work. Evaluations on two real-world datasets demonstrate that the STELLAR model outperforms state-of-the-art successive POI recommendation model about 20% in Precision@5 and Recall@5.

With the rapid development of information retrieval (IR) systems, online learning to rank (OLR) approaches, which allow retrieval systems to automatically learn best parameters from user interactions, have attracted great research interests in recent years. In OLR, the algorithms usually need to explore some uncertain retrieval results for updating current parameters meanwhile guaranteeing to produce quality retrieval results by exploiting what have already been learned, and the final retrieval results is an interleaved list from both exploratory and exploitative results. However, existing OLR algorithms perform exploration based on either only one stochastic direction or multiple randomly selected stochastic directions, which always involve large variance and uncertainty into the exploration, and may further harm the retrieval quality. Moreover, little historical exploration knowledge is considered when conducting current exploration.

Latent Factor models, which transform both users and items into the same latent feature space, are one of the most successful and ubiquitous models in recommender systems. Most existing models in this paradigm define both users' and items' latent factors to be of the same size and use an inner product to represent a user's "compatibility" with an item. Intuitively, users' factors encode "preferences" while item factors encode "properties", so that the inner product encodes how well an item matches a user's preferences. However, a user's opinion of an item may be more complex, for example each dimension of each user's opinion may depend on a combination of multiple item factors simultaneously. Thus it may be better to view each dimension of a user's preference as a personalized projection of an item's properties so that the preference model can capture complex relationships between items' properties and users' preferences.

The popularity of Online Social Networks (OSNs) has attracted great research interests in different fields. In Economics, researchers use game theory to analyze the mechanism of network formation, which is called Network Formation Game. While in Computer Science, much effort has been done in building machine learning models to predict future or missing links. However, there are few works considering how to combine game theoretic analysis and machine learning models. Therefore, in this paper, we study the problem of Exploiting Game Theoretic Analysis for Link Recommendation in Social Networks. Our goal is to improve link recommendation accuracy via leveraging the power of Network Formation Games into machine learning models. We present two different approaches to solve this problem. First, we propose a three- phase method that straightforwardly combines game theoretic analysis with machine learning models. Second, we develop a unified model, BPRLGT, that incorporates Network Formation Game into a Bayesian ranking framework for link recommendation. Specifically, BPRLGT takes advantage of network topology and we design a game theoretic sampling approach to improve its training process. The experiments are conducted on four real world datasets and the results on all datasets demonstrate that both our proposed three-phase method and the unified ranking model outperform the baseline methods.

Recommending products to users means estimating their preferences for certain items over others. This can be cast either as a problem of estimating the rating that each user will give to each item, or as a problem of estimating users' relative preferences in the form of a ranking. Although collaborative-filtering approaches can be used to identify users who rate and rank products similarly, another source of data that informs us about users' preferences is their set of social connections. Both rating- and ranking-based paradigms are important in real-world recommendation settings, though rankings are especially important in settings where explicit feedback in the form of a numerical rating may not be available. Although many existing works have studied how social connections can be used to build better models for rating prediction, few have used social connections as a means to derive more accurate ranking-based models. Using social connections to better estimate users' rankings of products is the task we consider in this paper. We develop a model, SBPR (Social Bayesian Personalized Ranking), based on the simple observation that users tend to assign higher ranks to items that their friends prefer. We perform experiments on four real-world recommendation data sets, and show that SBPR outperforms alternatives in ranking prediction both in warm- and cold-start settings.

Social information between users has been widely used to improve the traditional Recommender System in many previous works. However, in many websites such as Amazon and eBay, there is no explicit social graph that can be used to improve the recommendation performance. Hence in this work, in order to make it possible to employ social recommendation methods in those non-social information websites, we propose a general framework to construct a homophily-based implicit social network by utilizing both the rating and comments of items given by the users. Our scalable framework can be easily extended to enhance the performance of any recommender systems without social network by replacing the homophily-based implicit social relation definition. We propose four methods to extract and analyze the implicit social links between users, and then conduct the experiments on Amazon dataset. Experimental results show that our proposed methods work better than traditional recommendation methods without social information.