Deep latent variable models (DLVMs) combine the approximation abilities of deep neural networks and the statistical foundations of generative models. Variational methods are commonly used for inference; however, the exact likelihood of these models has been largely overlooked. The purpose of this work is to study the general properties of this quantity and to show how they can be leveraged in practice. We focus on important inferential problems that rely on the likelihood: estimation and missing data imputation. First, we investigate maximum likelihood estimation for DLVMs: in particular, we show that most unconstrained models used for continuous data have an unbounded likelihood function. This problematic behaviour is demonstrated to be a source of mode collapse. We also show how to ensure the existence of maximum likelihood estimates, and draw useful connections with nonparametric mixture models. Finally, we describe an algorithm for missing data imputation using the exact conditional likelihood of a DLVM. On several data sets, our algorithm consistently and significantly outperforms the usual imputation scheme used for DLVMs.

Maximum mean discrepancy (MMD) has been successfully applied to learn deep generative models for characterizing a joint distribution of variables via kernel mean embedding. In this paper, we present conditional generative moment-matching networks (CGMMN), which learn a conditional distribution given some input variables based on a conditional maximum mean discrepancy (CMMD) criterion. The learning is performed by stochastic gradient descent with the gradient calculated by back-propagation. We evaluate CGMMN on a wide range of tasks, including predictive modeling, contextual generation, and Bayesian dark knowledge, which distills knowledge from a Bayesian model by learning a relatively small CGMMN student network. Our results demonstrate competitive performance in all the tasks.

Latent Dirichlet Allocation (LDA) is a very popular model for topic modeling as well as many other problems with latent groups. It is both simple and effective. When the number of topics (or latent groups) is unknown, the Hierarchical Dirichlet Process (HDP) provides an elegant non-parametric extension; however, it is a complex model and it is difficult to incorporate prior knowledge since the distribution over topics is implicit. We propose two new models that extend LDA in a simple and intuitive fashion by directly expressing a distribution over the number of topics. We also propose a new online Bayesian moment matching technique to learn the parameters and the number of topics of those models based on streaming data. The approach achieves higher log-likelihood than batch and online HDP with fixed hyperparameters on several corpora. The code is publicly available at https://github.com/whsu/bmm .

Models for collecting and aggregating categorical data on crowdsourcing platforms typically fall into two broad categories: those assuming agents honest and consistent but with heterogeneous error rates, and those assuming agents strategic and seek to maximize their expected reward. The former often leads to tractable aggregation of elicited data, while the latter usually focuses on optimal elicitation and does not consider aggregation. In this paper, we develop a Bayesian model, wherein agents have differing quality of information, but also respond to incentives. Our model generalizes both categories and enables the joint exploration of optimal elicitation and aggregation. This model enables our exploration, both analytically and experimentally, of optimal aggregation of categorical data and optimal multiple-choice interface design.

Hamiltonian system built on the distribution of interest.

In addition, there is also a performance objective to optimize, i.e. a reward to be maximized, or

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Creating an agent that performs well across multiple tasks and continuously incorporates new knowledge has been a longstanding goal of research on artificial intelligence.

We theoretically prove that RIL is able to incentivize rational workers to provide high-quality labels.

Event datasets involve irregular occurrences of events over the timeline and are prevalent in numerous domains.