Efficient Probabilistic Inference in the Quest for Physics Beyond the Standard Model

We present a novel framework that enables efficient probabilistic inference in large-scale scientific models by allowing the execution of existing domain-specific simulators as probabilistic programs, resulting in highly interpretable posterior inference. Our framework is general purpose and scalable, and is based on a cross-platform probabilistic execution protocol through which an inference engine can control simulators in a language-agnostic way. We demonstrate the technique in particle physics, on a scientifically accurate simulation of the tau lepton decay, which is a key ingredient in establishing the properties of the Higgs boson. High-energy physics has a rich set of simulators based on quantum field theory and the interaction of particles in matter. We show how to use probabilistic programming to perform Bayesian inference in these existing simulator codebases directly, in particular conditioning on observable outputs from a simulated particle detector to directly produce an interpretable posterior distribution over decay pathways. Inference efficiency is achieved via inference compilation where a deep recurrent neural network is trained to parameterize proposal distributions and control the stochastic simulator in a sequential importance sampling scheme, at a fraction of the computational cost of Markov chain Monte Carlo sampling.

Tighter Variational Bounds are Not Necessarily Better

We provide theoretical and empirical evidence that using tighter evidence lower bounds (ELBOs) can be detrimental to the process of learning an inference network by reducing the signal-to-noise ratio of the gradient estimator. Our results call into question common implicit assumptions that tighter ELBOs are better variational objectives for simultaneous model learning and inference amortization schemes. Based on our insights, we introduce three new algorithms: the partially importance weighted auto-encoder (PIWAE), the multiply importance weighted auto-encoder (MIWAE), and the combination importance weighted auto-encoder (CIWAE), each of which includes the standard importance weighted auto-encoder (IWAE) as a special case. We show that each can deliver improvements over IWAE, even when performance is measured by the IWAE target itself. Furthermore, our results suggest that PIWAE may be able to deliver simultaneous improvements in the training of both the inference and generative networks.

Inference Trees: Adaptive Inference with Exploration

We introduce inference trees (ITs), a new class of inference methods that build on ideas from Monte Carlo tree search to perform adaptive sampling in a manner that balances exploration with exploitation, ensures consistency, and alleviates pathologies in existing adaptive methods. ITs adaptively sample from hierarchical partitions of the parameter space, while simultaneously learning these partitions in an online manner. This enables ITs to not only identify regions of high posterior mass, but also maintain uncertainty estimates to track regions where significant posterior mass may have been missed. ITs can be based on any inference method that provides a consistent estimate of the marginal likelihood. They are particularly effective when combined with sequential Monte Carlo, where they capture long-range dependencies and yield improvements beyond proposal adaptation alone.

Deep Variational Reinforcement Learning for POMDPs

Many real-world sequential decision making problems are partially observable by nature, and the environment model is typically unknown. Consequently, there is great need for reinforcement learning methods that can tackle such problems given only a stream of incomplete and noisy observations. In this paper, we propose deep variational reinforcement learning (DVRL), which introduces an inductive bias that allows an agent to learn a generative model of the environment and perform inference in that model to effectively aggregate the available information. We develop an n-step approximation to the evidence lower bound (ELBO), allowing the model to be trained jointly with the policy. This ensures that the latent state representation is suitable for the control task. In experiments on Mountain Hike and flickering Atari we show that our method outperforms previous approaches relying on recurrent neural networks to encode the past.

Revisiting Reweighted Wake-Sleep

Discrete latent-variable models, while applicable in a variety of settings, can often be difficult to learn. Sampling discrete latent variables can result in high-variance gradient estimators for two primary reasons: 1. branching on the samples within the model, and 2. the lack of a pathwise derivative for the samples. While current state-of-the-art methods employ control-variate schemes for the former and continuous-relaxation methods for the latter, their utility is limited by the complexities of implementing and training effective control-variate schemes and the necessity of evaluating (potentially exponentially) many branch paths in the model. Here, we revisit the reweighted wake-sleep (RWS) (Bornschein and Bengio, 2015) algorithm, and through extensive evaluations, show that it circumvents both these issues, outperforming current state-of-the-art methods in learning discrete latent-variable models. Moreover, we observe that, unlike the importance weighted autoencoder, RWS learns better models and inference networks with increasing numbers of particles, and that its benefits extend to continuous latent-variable models as well. Our results suggest that RWS is a competitive, often preferable, alternative for learning deep generative models.

On Nesting Monte Carlo Estimators

Many problems in machine learning and statistics involve nested expectations and thus do not permit conventional Monte Carlo (MC) estimation. For such problems, one must nest estimators, such that terms in an outer estimator themselves involve calculation of a separate, nested, estimation. We investigate the statistical implications of nesting MC estimators, including cases of multiple levels of nesting, and establish the conditions under which they converge. We derive corresponding rates of convergence and provide empirical evidence that these rates are observed in practice. We further establish a number of pitfalls that can arise from naive nesting of MC estimators, provide guidelines about how these can be avoided, and lay out novel methods for reformulating certain classes of nested expectation problems into single expectations, leading to improved convergence rates. We demonstrate the applicability of our work by using our results to develop a new estimator for discrete Bayesian experimental design problems and derive error bounds for a class of variational objectives.

Discontinuous Hamiltonian Monte Carlo for Probabilistic Programs

Hamiltonian Monte Carlo (HMC) is the dominant statistical inference algorithm used in most popular first-order differentiable probabilistic programming languages. HMC requires that the joint density be differentiable with respect to all latent variables. This complicates expressing some models in such languages and prohibits others. A recently proposed new integrator for HMC yielded a new Discontinuous HMC (DHMC) algorithm that can be used for inference in models with joint densities that have discontinuities. In this paper we show how to use DHMC for inference in probabilistic programs. To do this we introduce a sufficient set of language restrictions, a corresponding mathematical formalism that ensures that any joint density denoted in such a language has a suitably low measure of discontinuous points, and a recipe for how to apply DHMC in the more general probabilistic-programming context. Our experimental findings demonstrate the correctness of this approach.

Auto-Encoding Sequential Monte Carlo

We build on auto-encoding sequential Monte Carlo (AESMC): a method for model and proposal learning based on maximizing the lower bound to the log marginal likelihood in a broad family of structured probabilistic models. Our approach relies on the efficiency of sequential Monte Carlo (SMC) for performing inference in structured probabilistic models and the flexibility of deep neural networks to model complex conditional probability distributions. We develop additional theoretical insights and introduce a new training procedure which improves both model and proposal learning. We demonstrate that our approach provides a fast, easy-to-implement and scalable means for simultaneous model learning and proposal adaptation in deep generative models.

High Throughput Synchronous Distributed Stochastic Gradient Descent

We introduce a new, high-throughput, synchronous, distributed, data-parallel, stochastic-gradient-descent learning algorithm. This algorithm uses amortized inference in a compute-cluster-specific, deep, generative, dynamical model to perform joint posterior predictive inference of the mini-batch gradient computation times of all worker-nodes in a parallel computing cluster. We show that a synchronous parameter server can, by utilizing such a model, choose an optimal cutoff time beyond which mini-batch gradient messages from slow workers are ignored that maximizes overall mini-batch gradient computations per second. In keeping with earlier findings we observe that, under realistic conditions, eagerly discarding the mini-batch gradient computations of stragglers not only increases throughput but actually increases the overall rate of convergence as a function of wall-clock time by virtue of eliminating idleness. The principal novel contribution and finding of this work goes beyond this by demonstrating that using the predicted run-times from a generative model of cluster worker performance to dynamically adjust the cutoff improves substantially over the static-cutoff prior art, leading to, among other things, significantly reduced deep neural net training times on large computer clusters.

Inference Networks for Sequential Monte Carlo in Graphical Models

We introduce a new approach for amortizing inference in directed graphical models by learning heuristic approximations to stochastic inverses, designed specifically for use as proposal distributions in sequential Monte Carlo methods. We describe a procedure for constructing and learning a structured neural network which represents an inverse factorization of the graphical model, resulting in a conditional density estimator that takes as input particular values of the observed random variables, and returns an approximation to the distribution of the latent variables. This recognition model can be learned offline, independent from any particular dataset, prior to performing inference. The output of these networks can be used as automatically-learned high-quality proposal distributions to accelerate sequential Monte Carlo across a diverse range of problem settings.