The recent rapid development of well-designed and powerful machine learning (ML) models has significantly transformed our lives. However, the success of these models is often evaluated based on the accuracy of their predictions, which, while important, is not sufficient in many real-world scenarios. In high-stakes applications, it is equally critical to assess the uncertainty of model outputs. Uncertainty quantification (UQ) has long been a central problem in fields like statistics and ML. Several well-established methods, such as Bayesian inference and resampling techniques, have been widely adopted to address UQ. However, Bayesian posterior intervals are only valid if the parametric assumptions of the model are correctly specified, which may not always be the case in practical applications.

Electronic commerce, or e-commerce, is the buying and selling of goods and services, or the transmitting of funds or data online. E-commerce platforms come in many kinds, with global players such as Amazon, Airbnb, Alibaba, eBay and platforms targeting specific geographic regions. Information retrieval has a natural role to play in e-commerce, especially in connecting people to goods and services. Information discovery in e-commerce concerns different types of search (e.g., exploratory search vs. lookup tasks), recommender systems, and natural language processing in e-commerce portals. The rise in popularity of e-commerce sites has made research on information discovery in e-commerce an increasingly active research area. This is witnessed by an increase in publications and dedicated workshops in this space. Methods for information discovery in e-commerce largely focus on improving the effectiveness of e-commerce search and recommender systems, on enriching and using knowledge graphs to support e-commerce, and on developing innovative question answering and bot-based solutions that help to connect people to goods and services. In this survey, an overview is given of the fundamental infrastructure, algorithms, and technical solutions for information discovery in e-commerce. The topics covered include user behavior and profiling, search, recommendation, and language technology in e-commerce.

Sampling from a target distribution π whose density is known up to a normalizing constant is a challenging problem in statistics and machine learning, and is currently the subject of intense interest due to applications in Bayesian statistics [19] and energy-based models in deep learning [68], among other areas. In these settings, the normalizing constant of the target distribution π is typically intractable, and Markov Chain Monte Carlo (MCMC) algorithms [58, 57] are commonly used to generate Markov chains in the ambient space, whose law eventually approximates the target distribution. Among MCMC algorithms, the Unadjusted Langevin Algorithm (ULA), which corresponds to a time discretization of a Langevin diffusion process, has attracted considerable attention due to its simplicity, theoretical grounding, and utility in practice [59, 76, 23, 66]. For example, ULA can be proven to converge quickly when the target distribution π is smooth and strongly log-concave [23]. However, many cases in practice require to sample from distributions which are not log-concave, and indeed potentially even multi-modal [54, 82]. In such settings, the convergence of ULA is governed by functional inequalities which effectively quantify the convexity, or lack thereof, of the target distribution [75]. Nonetheless, truly multi-modal target distributions generally have poor functional inequalities, thus leading to weak convergence guarantees for ULA. This phenomenon is not merely a theoretical artifact, and it is wellknown amongst practitioners that when sampling from multi-modal distributions, algorithms based on ULA can get stuck in local modes and suffer from slow convergence [20]. Tempering or annealing is a popular technique [51, 27, 69] to overcome the deficiencies of ULA and other MCMC methods in the multi-modal setting.

Although existing variational graph autoencoders (VGAEs) have been widely used for modeling and generating graph-structured data, most of them are still not flexible enough to approximate the sparse and skewed latent node representations, especially those of document relational networks (DRNs) with discrete observations. To analyze a collection of interconnected documents, a typical branch of Bayesian models, specifically relational topic models (RTMs), has proven their efficacy in describing both link structures and document contents of DRNs, which motives us to incorporate RTMs with existing VGAEs to alleviate their potential issues when modeling the generation of DRNs. In this paper, moving beyond the sophisticated approximate assumptions of traditional RTMs, we develop a graph Poisson factor analysis (GPFA), which provides analytic conditional posteriors to improve the inference accuracy, and extend GPFA to a multi-stochastic-layer version named graph Poisson gamma belief network (GPGBN) to capture the hierarchical document relationships at multiple semantic levels. Then, taking GPGBN as the decoder, we combine it with various Weibull-based graph inference networks, resulting in two variants of Weibull graph auto-encoder (WGAE), equipped with model inference algorithms. Experimental results demonstrate that our models can extract high-quality hierarchical latent document representations and achieve promising performance on various graph analytic tasks.

We study minimax optimal reinforcement learning in episodic factored Markov decision processes (FMDPs), which are MDPs with conditionally independent transition components. Assuming the factorization is known, we propose two model-based algorithms. The first one achieves minimax optimal regret guarantees for a rich class of factored structures, while the second one enjoys better computational complexity with a slightly worse regret. A key new ingredient of our algorithms is the design of a bonus term to guide exploration. We complement our algorithms by presenting several structure dependent lower bounds on regret for FMDPs that reveal the difficulty hiding in the intricacy of the structures.

Exact multi-label classification is the task of assigning each datapoint a set of class labels such that the assigned set exactly matches the ground truth. Optimizing for exact multi-label classification is important in domains where missing a single label can be especially costly, such as in object detection for autonomous vehicles or symptom classification for disease diagnosis. Recurrent Classifier Chains (RCCs), a recurrent neural network extension of ensemble-based classifier chains, are the state-of-the-art exact multi-label classification method for maximizing subset accuracy. However, RCCs iteratively predict classes with an unprincipled ordering, and therefore indiscriminately condition class probabilities. These disadvantages make RCCs prone to predicting inaccurate label sets. In this work we propose Recurrent Bayesian Classifier Chains (RBCCs), which learn a Bayesian network of class dependencies and leverage this network in order to condition the prediction of child nodes only on their parents.

We present two elegant solutions for modeling continuous-time dynamics, in a novel model-based reinforcement learning (RL) framework for semi-Markov decision processes (SMDPs), using neural ordinary differential equations (ODEs). Our models accurately characterize continuous-time dynamics and enable us to develop high-performing policies using a small amount of data. We also develop a model-based approach for optimizing time schedules to reduce interaction rates with the environment while maintaining the near-optimal performance, which is not possible for model-free methods. We experimentally demonstrate the efficacy of our methods across various continuous-time domains.

This paper considers the challenging tasks of Multi-Agent Reinforcement Learning (MARL) under partial observability, where each agent only sees her own individual observations and actions that reveal incomplete information about the underlying state of system. This paper studies these tasks under the general model of multiplayer general-sum Partially Observable Markov Games (POMGs), which is significantly larger than the standard model of Imperfect Information Extensive-Form Games (IIEFGs). We identify a rich subclass of POMGs---weakly revealing POMGs---in which sample-efficient learning is tractable. In the self-play setting, we prove that a simple algorithm combining optimism and Maximum Likelihood Estimation (MLE) is sufficient to find approximate Nash equilibria, correlated equilibria, as well as coarse correlated equilibria of weakly revealing POMGs, in a polynomial number of samples when the number of agents is small. In the setting of playing against adversarial opponents, we show that a variant of our optimistic MLE algorithm is capable of achieving sublinear regret when being compared against the optimal maximin policies.

Sparse models are desirable for many applications across diverse domains as they can perform automatic variable selection, aid interpretability, and provide regularization. When fitting sparse models in a Bayesian framework, however, analytically obtaining a posterior distribution over the parameters of interest is intractable for all but the simplest cases. As a result practitioners must rely on either sampling algorithms such as Markov chain Monte Carlo or variational methods to obtain an approximate posterior. Mean field variational inference is a particularly simple and popular framework that is often amenable to analytically deriving closed-form parameter updates. When all distributions in the model are members of exponential families and are conditionally conjugate, optimization schemes can often be derived by hand.

We consider the question of learning the natural parameters of a k parameter \textit{minimal} exponential family from i.i.d. We focus on the setting where the support as well as the natural parameters are appropriately bounded. While the traditional maximum likelihood estimator for this class of exponential family is consistent, asymptotically normal, and asymptotically efficient, evaluating it is computationally hard. In this work, we propose a computationally efficient estimator that is consistent as well as asymptotically normal under mild conditions. We provide finite sample guarantees to achieve an ( \ell_2) error of \alpha in the parameter estimation with sample complexity O(\mathrm{poly}(k/\alpha)) and computational complexity {O}(\mathrm{poly}(k/\alpha)) .