On Application of B ayesian Parametric and Non-parametric Methods for User Cohorting in Product Search (2020)

Abstract: In this paper, we study the applicability of Bayesian Parametric and Non-parametric methods for user clustering in an E-commerce search setting. To the best of our knowledge, this is the first work that presents a comparative study of various Bayesian clustering methods in the context of product search. Specifically, we cluster users based on their topical patterns from their respective product search queries. To evaluate the quality of the clusters formed, we perform a collaborative query recommendation task. Our findings indicate that simple parametric model like Latent Dirichlet Allocation (LDA) outperforms more sophisticated non-parametric methods like Distance Dependent Chinese Restaurant Process and Dirichlet Process-based clustering in both tasks.

## introduction online retail business has been on an unprecedented growth since last few years, with a market share of 600 billion dollars last year in the united states foot_0 . to cope up with such an epochal growth, product discovery becomes an important aspect for any e-commerce platform. it is an important aspect to help customers navigate an ever increasing inventory of products. product search is an important aspect of e-commerce discovery, where displaying relevant and personalized products in answer to an user query is directly tied to customer satisfaction @xcite . personalizing search results entails mining search behavior logs to represent individual user's search intent. however, due to the large variance in individual user's preference, finding a good representation is often difficult. in the context of web search, search intent mining has been extensively studied @xcite @xcite . however, despite it's apparent importance, personalization in product search is not very well studied. there has been some attempts to model user's search intent based on her past product interactions. qingyao et al. @xcite jointly learn representations of user, query and users' product reviews for personalization. in a follow-up work, qingyao et al. @xcite , learn a 'zero-attention' model for representation learning to account to cold-start problem in new product categories. however, it should be noted that both work attempt to model search interest at the granularity of individual users, which are highly spare in nature. fig. 1 is the distribution of queries across users in the amazon product search dataset @xcite . the distribution is skewed towards left side of the distribution. it shows that query distribution across users is sparse, with very few users have high number of queries and subsequently few interactions as-well. this makes it challenging to model search interests at the granularity of individual users. by modelling each user separately, we are also missing on the chance to capture the heterogeneity in the user's search interests. modelling user's jointly can aid in learning individual user's interest, as-well as aid in handling sparsity through sharing statistical strength within the group. towards this end, we study various bayesian clustering methods to model latent user cohorts by mining user's search query patterns. to the best of our knowledge, this is the first work in the domain of e-commerce search to study the application of bayesian methods for modelling user cohorts. the aim of this paper is to present a comparative study of different bayesian parametric and non-parametric methods in the domain of product search. product search system designers can benifit from this study by making an informed decision when designing e-commerce personalization system. ## related work there has been plenty of work in web search for modelling user cohorts for learning an effective ranking function. previous studies @xcite propose a kmeans clustering of queries and then a learn a ranking function within each sub-group to capture query patterns in each group. however, the focal unit of the previous work is queries, whereas we are interested in modelling user. the closest to our work is by yan et al. @xcite , where they model user cohorts based on click-through rates (ctr) and open directory project (odp) based topics. however, instead of relying on human curated odp based topics, we use probabilistic topic models to identify topics from user's log data and further use it for clustering. towards this end, in this work, we study the problem of user cohorting by clustering user's queries in the probabilistic topic space. specifically, we study application of various probabilistic topic models like latent dirichlet allocation (lda) @xcite , hierarchical dirichlet process (hdp) @xcite , dirichlet process gaussian mixture model (dpgmm) @xcite and the more recent distance dependent chinese restaurant process (ddcrp) @xcite . to the best of our knowledge, this is the first work in product search which studies application of probabilistic topic models for user cohorting. ## user cohorting using probabilistic topic models in this section, we will formally define the problem statement followed by a brief description of the non-parametric ddcrp user clustering method. ## experiments in this section, we will describe the experimental results from our study. ## results we present some preliminary results on the query recommendation task on the two datasets mentioned above. we compare the following methods: from the results, it is clear that lda outperforms more sophisticated non-parameteric methods in terms of precision metric. ## conclusion this paper can serve as a starting point of discussion around the use of bayesian non-parametric models for user cohorting. the prelimary results weigh in favor of simple parametric model like lda, however, we believe that with further investigation, ddcrp method's performance can be improved. more specifically, if we perform clustering in the space of recently proposed neural embedding methods, instead of conventional topic model space, it's performance can be improved. we hope this paper can start that discussion.