Approximate Bayesian computation (ABC) is an important methodology for Bayesian inference when the likelihood function is intractable. Sampling-based ABC algorithms such as rejection- and K2-ABC are inefficient when the parameters have high dimensions, while the regression-based algorithms such as K- and DR-ABC are hard to scale. In this paper, we introduce an optimization-based ABC framework that addresses these deficiencies. Leveraging a generative model for posterior and joint distribution matching, we show that ABC can be framed as saddle point problems, whose objectives can be accessed directly with samples. We present the predictive ABC algorithm (P-ABC), and provide a probabilistically approximately correct (PAC) bound that guarantees its learning consistency.

Potential based reward shaping is a powerful technique for accelerating convergence of reinforcement learning algorithms. Typically, such information includes an estimate of the optimal value function and is often provided by a human expert or other sources of domain knowledge. However, this information is often biased or inaccurate and can mislead many reinforcement learning algorithms. In this paper, we apply Bayesian Model Combination with multiple experts in a way that learns to trust a good combination of experts as training progresses. This approach is both computationally efficient and general, and is shown numerically to improve convergence across discrete and continuous domains and different reinforcement learning algorithms.

Continuous-time Bayesian networks (CTBNs) constitute a general and powerful framework for modeling continuous-time stochastic processes on networks. This makes them particularly attractive for learning the directed structures among interacting entities. However, if the available data is incomplete, one needs to simulate the prohibitively complex CTBN dynamics. Existing approximation techniques, such as sampling and low-order variational methods, either scale unfavorably in system size, or are unsatisfactory in terms of accuracy. Inspired by recent advances in statistical physics, we present a new approximation scheme based on cluster-variational methods that significantly improves upon existing variational approximations.

We consider maximum likelihood estimation of linear dynamical systems with generalized-linear observation models. Maximum likelihood is typically considered to be hard in this setting since latent states and transition parameters must be inferred jointly. Given that expectation-maximization does not scale and is prone to local minima, moment-matching approaches from the subspace identification literature have become standard, despite known statistical efficiency issues. In this paper, we instead reconsider likelihood maximization and develop an optimization based strategy for recovering the latent states and transition parameters. Key to the approach is a two-view reformulation of maximum likelihood estimation for linear dynamical systems that enables the use of global optimization algorithms for matrix factorization.

Generative adversarial training for imitation learning has shown promising results on high-dimensional and continuous control tasks. This paradigm is based on reducing the imitation learning problem to the density matching problem, where the agent iteratively refines the policy to match the empirical state-action visitation frequency of the expert demonstration. Although this approach has shown to robustly learn to imitate even with scarce demonstration, one must still address the inherent challenge that collecting trajectory samples in each iteration is a costly operation. To address this issue, we first propose a Bayesian formulation of generative adversarial imitation learning (GAIL), where the imitation policy and the cost function are represented as stochastic neural networks. Then, we show that we can significantly enhance the sample efficiency of GAIL leveraging the predictive density of the cost, on an extensive set of imitation learning tasks with high-dimensional states and actions.

Due to the inherent model uncertainty, learning to infer Bayesian posterior from a few-shot dataset is an important step towards robust meta-learning. In this paper, we propose a novel Bayesian model-agnostic meta-learning method. The proposed method combines efficient gradient-based meta-learning with nonparametric variational inference in a principled probabilistic framework. Unlike previous methods, during fast adaptation, the method is capable of learning complex uncertainty structure beyond a simple Gaussian approximation, and during meta-update, a novel Bayesian mechanism prevents meta-level overfitting. Remaining a gradient-based method, it is also the first Bayesian model-agnostic meta-learning method applicable to various tasks including reinforcement learning.

State-space models are successfully used in many areas of science, engineering and economics to model time series and dynamical systems. We present a fully Bayesian approach to inference and learning in nonlinear nonparametric state-space models. We place a Gaussian process prior over the transition dynamics, resulting in a flexible model able to capture complex dynamical phenomena. However, to enable efficient inference, we marginalize over the dynamics of the model and instead infer directly the joint smoothing distribution through the use of specially tailored Particle Markov Chain Monte Carlo samplers. Once an approximation of the smoothing distribution is computed, the state transition predictive distribution can be formulated analytically.

We describe a class of algorithms for amortized inference in Bayesian networks. In this setting, we invest computation upfront to support rapid online inference for a wide range of queries. Our approach is based on learning an inverse factorization of a model's joint distribution: a factorization that turns observations into root nodes. Our algorithms accumulate information to estimate the local conditional distributions that constitute such a factorization. These stochastic inverses can be used to invert each of the computation steps leading to an observation, sampling backwards in order to quickly find a likely explanation.

We propose a general formalism of iterated random functions with semigroup property, under which exact and approximate Bayesian posterior updates can be viewed as specific instances. A convergence theory for iterated random functions is presented. As an application of the general theory we analyze convergence behaviors of exact and approximate message-passing algorithms that arise in a sequential change point detection problem formulated via a latent variable directed graphical model. The sequential inference algorithm and its supporting theory are illustrated by simulated examples. Papers published at the Neural Information Processing Systems Conference.

When used as a surrogate objective for maximum likelihood estimation in latent variable models, the evidence lower bound (ELBO) produces state-of-the-art results. Inspired by this, we consider the extension of the ELBO to a family of lower bounds defined by a particle filter's estimator of the marginal likelihood, the filtering variational objectives (FIVOs). FIVOs take the same arguments as the ELBO, but can exploit a model's sequential structure to form tighter bounds. We present results that relate the tightness of FIVO's bound to the variance of the particle filter's estimator by considering the generic case of bounds defined as log-transformed likelihood estimators. Experimentally, we show that training with FIVO results in substantial improvements over training the same model architecture with the ELBO on sequential data.