Da Xu

Da Xu, Bo Yang

The use of pretrained embeddings has become widespread in modern e-commerce machine learning (ML) systems. In practice, however, we have encountered several key issues when using pretrained embedding in a real-world production system, many of which cannot be fully explained by current knowledge. Unfortunately, we find that there is a lack of a thorough understanding of how pre-trained embeddings work, especially their intrinsic properties and interactions with downstream tasks. Consequently, it becomes challenging to make interactive and scalable decisions regarding the use of pre-trained embeddings in practice. Our investigation leads to two significant discoveries about using pretrained embeddings in e-commerce applications. Firstly, we find that the design of the pretraining and downstream models, particularly how they encode and decode information via embedding vectors, can have a profound impact. Secondly, we establish a principled perspective of pre-trained embeddings via the lens of kernel analysis, which can be used to evaluate their predictability, interactively and scalably. These findings help to address the practical challenges we faced and offer valuable guidance for successful adoption of pretrained embeddings in real-world production. Our conclusions are backed by solid theoretical reasoning, benchmark experiments, as well as online testings.

Da Xu, Chuanwei Ruan, Evren Korpeoglu et al.

The recent work by Rendle et al. (2020), based on empirical observations, argues that matrix-factorization collaborative filtering (MCF) compares favorably to neural collaborative filtering (NCF), and conjectures the dot product's superiority over the feed-forward neural network as similarity function. In this paper, we address the comparison rigorously by answering the following questions: 1. what is the limiting expressivity of each model; 2. under the practical gradient descent, to which solution does each optimization path converge; 3. how would the models generalize under the inductive and transductive learning setting. Our results highlight the similar expressivity for the overparameterized NCF and MCF as kernelized predictors, and reveal the relation between their optimization paths. We further show their different generalization behaviors, where MCF and NCF experience specific tradeoff and comparison in the transductive and inductive collaborative filtering setting. Lastly, by showing a novel generalization result, we reveal the critical role of correcting exposure bias for model evaluation in the inductive setting. Our results explain some of the previously observed conflicts, and we provide synthetic and real-data experiments to shed further insights to this topic.

Cheng Jie, Da Xu, Zigeng Wang et al.

With the increasing scale of search engine marketing, designing an efficient bidding system is becoming paramount for the success of e-commerce companies. The critical challenges faced by a modern industrial-level bidding system include: 1. the catalog is enormous, and the relevant bidding features are of high sparsity; 2. the large volume of bidding requests induces significant computation burden to both the offline and online serving. Leveraging extraneous user-item information proves essential to mitigate the sparsity issue, for which we exploit the natural language signals from the users' query and the contextual knowledge from the products. In particular, we extract the vector representations of ads via the Transformer model and leverage their geometric relation to building collaborative bidding predictions via clustering. The two-step procedure also significantly reduces the computation stress of bid evaluation and optimization. In this paper, we introduce the end-to-end structure of the bidding system for search engine marketing for Walmart e-commerce, which successfully handles tens of millions of bids each day. We analyze the online and offline performances of our approach and discuss how we find it as a production-efficient solution.

Da Xu, Chuanwei Ruan, Evren Korpeoglu et al.

Product embeddings have been heavily investigated in the past few years, serving as the cornerstone for a broad range of machine learning applications in e-commerce. Despite the empirical success of product embeddings, little is known on how and why they work from the theoretical standpoint. Analogous results from the natural language processing (NLP) often rely on domain-specific properties that are not transferable to the e-commerce setting, and the downstream tasks often focus on different aspects of the embeddings. We take an e-commerce-oriented view of the product embeddings and reveal a complete theoretical view from both the representation learning and the learning theory perspective. We prove that product embeddings trained by the widely-adopted skip-gram negative sampling algorithm and its variants are sufficient dimension reduction regarding a critical product relatedness measure. The generalization performance in the downstream machine learning task is controlled by the alignment between the embeddings and the product relatedness measure. Following the theoretical discoveries, we conduct exploratory experiments that supports our theoretical insights for the product embeddings.

Da Xu, Chuanwei Ruan, Evren Korpeoglu et al.

The feedback data of recommender systems are often subject to what was exposed to the users; however, most learning and evaluation methods do not account for the underlying exposure mechanism. We first show in theory that applying supervised learning to detect user preferences may end up with inconsistent results in the absence of exposure information. The counterfactual propensity-weighting approach from causal inference can account for the exposure mechanism; nevertheless, the partial-observation nature of the feedback data can cause identifiability issues. We propose a principled solution by introducing a minimax empirical risk formulation. We show that the relaxation of the dual problem can be converted to an adversarial game between two recommendation models, where the opponent of the candidate model characterizes the underlying exposure mechanism. We provide learning bounds and conduct extensive simulation studies to illustrate and justify the proposed approach over a broad range of recommendation settings, which shed insights on the various benefits of the proposed approach.

Da Xu, Chuanwei Ruan, Evren Korpeoglu et al.

Inductive representation learning on temporal graphs is an important step toward salable machine learning on real-world dynamic networks. The evolving nature of temporal dynamic graphs requires handling new nodes as well as capturing temporal patterns. The node embeddings, which are now functions of time, should represent both the static node features and the evolving topological structures. Moreover, node and topological features can be temporal as well, whose patterns the node embeddings should also capture. We propose the temporal graph attention (TGAT) layer to efficiently aggregate temporal-topological neighborhood features as well as to learn the time-feature interactions. For TGAT, we use the self-attention mechanism as building block and develop a novel functional time encoding technique based on the classical Bochner's theorem from harmonic analysis. By stacking TGAT layers, the network recognizes the node embeddings as functions of time and is able to inductively infer embeddings for both new and observed nodes as the graph evolves. The proposed approach handles both node classification and link prediction task, and can be naturally extended to include the temporal edge features. We evaluate our method with transductive and inductive tasks under temporal settings with two benchmark and one industrial dataset. Our TGAT model compares favorably to state-of-the-art baselines as well as the previous temporal graph embedding approaches.

Da Xu, Chuanwei Ruan, Sushant Kumar et al.

Sequential modelling with self-attention has achieved cutting edge performances in natural language processing. With advantages in model flexibility, computation complexity and interpretability, self-attention is gradually becoming a key component in event sequence models. However, like most other sequence models, self-attention does not account for the time span between events and thus captures sequential signals rather than temporal patterns. Without relying on recurrent network structures, self-attention recognizes event orderings via positional encoding. To bridge the gap between modelling time-independent and time-dependent event sequence, we introduce a functional feature map that embeds time span into high-dimensional spaces. By constructing the associated translation-invariant time kernel function, we reveal the functional forms of the feature map under classic functional function analysis results, namely Bochner's Theorem and Mercer's Theorem. We propose several models to learn the functional time representation and the interactions with event representation. These methods are evaluated on real-world datasets under various continuous-time event sequence prediction tasks. The experiments reveal that the proposed methods compare favorably to baseline models while also capturing useful time-event interactions.

Da Xu, Chuanwei Ruan, Kamiya Motwani et al.

Modeling generative process of growing graphs has wide applications in social networks and recommendation systems, where cold start problem leads to new nodes isolated from existing graph. Despite the emerging literature in learning graph representation and graph generation, most of them can not handle isolated new nodes without nontrivial modifications. The challenge arises due to the fact that learning to generate representations for nodes in observed graph relies heavily on topological features, whereas for new nodes only node attributes are available. Here we propose a unified generative graph convolutional network that learns node representations for all nodes adaptively in a generative model framework, by sampling graph generation sequences constructed from observed graph data. We optimize over a variational lower bound that consists of a graph reconstruction term and an adaptive Kullback-Leibler divergence regularization term. We demonstrate the superior performance of our approach on several benchmark citation network datasets.