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.

Lifted inference algorithms exploit symmetries in probabilistic models to speed up inference. They show impressive performance when calculating unconditional probabilities in relational models, but often resort to non-lifted inference when computing conditional probabilities. The reason is that conditioning on evidence breaks many of the model's symmetries, which preempts standard lifting techniques. Recent theoretical results show, for example, that conditioning on evidence which corresponds to binary relations is #P-hard, suggesting that no lifting is to be expected in the worst case. In this paper, we balance this grim result by identifying the Boolean rank of the evidence as a key parameter for characterizing the complexity of conditioning in lifted inference.

Learning the directed acyclic graph (DAG) structure of a Bayesian network from observational data is a notoriously difficult problem for which many non-identifiability and hardness results are known. In this paper we propose a provably polynomial-time algorithm for learning sparse Gaussian Bayesian networks with equal noise variance --- a class of Bayesian networks for which the DAG structure can be uniquely identified from observational data --- under high-dimensional settings. We show that $O(k 4 \log p)$ number of samples suffices for our method to recover the true DAG structure with high probability, where $p$ is the number of variables and $k$ is the maximum Markov blanket size. We obtain our theoretical guarantees under a condition called \emph{restricted strong adjacency faithfulness} (RSAF), which is strictly weaker than strong faithfulness --- a condition that other methods based on conditional independence testing need for their success. The sample complexity of our method matches the information-theoretic limits in terms of the dependence on $p$.

With simultaneous measurements from ever increasing populations of neurons, there is a growing need for sophisticated tools to recover signals from individual neurons. In electrophysiology experiments, this classically proceeds in a two-step process: (i) threshold the waveforms to detect putative spikes and (ii) cluster the waveforms into single units (neurons). We extend previous Bayesian nonparamet- ric models of neural spiking to jointly detect and cluster neurons using a Gamma process model. Importantly, we develop an online approximate inference scheme enabling real-time analysis, with performance exceeding the previous state-of-the- art. Via exploratory data analysis--using data with partial ground truth as well as two novel data sets--we find several features of our model collectively contribute to our improved performance including: (i) accounting for colored noise, (ii) de- tecting overlapping spikes, (iii) tracking waveform dynamics, and (iv) using mul- tiple channels.

Decoding sensory stimuli from neural signals can be used to reveal how we sense our physical environment, and is valuable for the design of brain-machine interfaces. However, existing linear techniques for neural decoding may not fully reveal or exploit the fidelity of the neural signal. Here we develop a new approximate Bayesian method for decoding natural images from the spiking activity of populations of retinal ganglion cells (RGCs). We sidestep known computational challenges with Bayesian inference by exploiting artificial neural networks developed for computer vision, enabling fast nonlinear decoding that incorporates natural scene statistics implicitly. We use a decoder architecture that first linearly reconstructs an image from RGC spikes, then applies a convolutional autoencoder to enhance the image.

Stochastic gradient Markov chain Monte Carlo (SGMCMC) has become a popular method for scalable Bayesian inference. These methods are based on sampling a discrete-time approximation to a continuous time process, such as the Langevin diffusion. When applied to distributions defined on a constrained space the time-discretization error can dominate when we are near the boundary of the space. We demonstrate that because of this, current SGMCMC methods for the simplex struggle with sparse simplex spaces; when many of the components are close to zero. Unfortunately, many popular large-scale Bayesian models, such as network or topic models, require inference on sparse simplex spaces.

Conditional probabilities are a core concept in machine learning. For example, optimal prediction of a label $Y$ given an input $X$ corresponds to maximizing the conditional probability of $Y$ given $X$. A common approach to inference tasks is learning a model of conditional probabilities. However, these models are often based on strong assumptions (e.g., log-linear models), and hence their estimate of conditional probabilities is not robust and is highly dependent on the validity of their assumptions. Here we propose a framework for reasoning about conditional probabilities without assuming anything about the underlying distributions, except knowledge of their second order marginals, which can be estimated from data. We show how this setting leads to guaranteed bounds on conditional probabilities, which can be calculated efficiently in a variety of settings, including structured-prediction.

Sampling inference methods are computationally difficult to scale for many models in part because global dependencies can reduce opportunities for parallel computation. Without strict conditional independence structure among variables, standard Gibbs sampling theory requires sample updates to be performed sequentially, even if dependence between most variables is not strong. Empirical work has shown that some models can be sampled effectively by going Hogwild'' and simply running Gibbs updates in parallel with only periodic global communication, but the successes and limitations of such a strategy are not well understood. As a step towards such an understanding, we study the Hogwild Gibbs sampling strategy in the context of Gaussian distributions. We develop a framework which provides convergence conditions and error bounds along with simple proofs and connections to methods in numerical linear algebra.