Hamiltonian Monte Carlo (HMC) is a powerful algorithm to sample latent variables from Bayesian models. The advent of probabilistic programming languages (PPLs) frees users from writing inference algorithms and lets users focus on modeling. However, many models are difficult for HMC to solve directly, and often require tricks like model reparameterization. We are motivated by the fact that many of those models could be simplified by marginalization. We propose to use automatic marginalization as part of the sampling process using HMC in a graphical model extracted from a PPL, which substantially improves sampling from real-world hierarchical models.

We present a novel approach for black-box VI that bypasses the difficulties of stochastic gradient ascent, including the task of selecting step-sizes. Our approach involves using a sequence of sample average approximation (SAA) problems. SAA approximates the solution of stochastic optimization problems by transforming them into deterministic ones. We use quasi-Newton methods and line search to solve each deterministic optimization problem and present a heuristic policy to automate hyperparameter selection. Our experiments show that our method simplifies the VI problem and achieves faster performance than existing methods.

We propose the use of U-statistics to reduce variance for gradient estimation in importance-weighted variational inference. The key observation is that, given a base gradient estimator that requires $m > 1$ samples and a total of $n > m$ samples to be used for estimation, lower variance is achieved by averaging the base estimator on overlapping batches of size $m$ than disjoint batches, as currently done. We use classical U-statistic theory to analyze the variance reduction, and propose novel approximations with theoretical guarantees to ensure computational efficiency. We find empirically that U-statistic variance reduction can lead to modest to significant improvements in inference performance on a range of models, with little computational cost.

We develop a likelihood free inference procedure for conditioning a probabilistic model on a predicate. A predicate is a Boolean valued function which expresses a yes/no question about a domain. Our contribution, which we call predicate exchange, constructs a softened predicate which takes value in the unit interval [0, 1] as opposed to a simply true or false. Intuitively, 1 corresponds to true, and a high value (such as 0.999) corresponds to "nearly true" as determined by a distance metric. We define Boolean algebra for soft predicates, such that they can be negated, conjoined and disjoined arbitrarily. A softened predicate can serve as a tractable proxy to a likelihood function for approximate posterior inference. However, to target exact inference, we temper the relaxation by a temperature parameter, and add a accept/reject phase use to replica exchange Markov Chain Mont Carlo, which exchanges states between a sequence of models conditioned on predicates at varying temperatures. We describe a lightweight implementation of predicate exchange that it provides a language independent layer that can be implemented on top of existingn modeling formalisms.

Deep probabilistic programming combines deep neural networks (for automatic hierarchical representation learning) with probabilistic models (for principled handling of uncertainty). Unfortunately, it is difficult to write deep probabilistic models, because existing programming frameworks lack concise, high-level, and clean ways to express them. To ease this task, we extend Stan, a popular high-level probabilistic programming language, to use deep neural networks written in PyTorch. Training deep probabilistic models works best with variational inference, so we also extend Stan for that. We implement these extensions by translating Stan programs to Pyro. Our translation clarifies the relationship between different families of probabilistic programming languages. Overall, our paper is a step towards making deep probabilistic programming easier.

We present an application of Artificial Intelligence techniques to the field of Information Security. The problem of remote Operating System (OS) Detection, also called OS Fingerprinting, is a crucial step of the penetration testing process, since the attacker (hacker or security professional) needs to know the OS of the target host in order to choose the exploits that he will use. OS Detection is accomplished by passively sniffing network packets and actively sending test packets to the target host, to study specific variations in the host responses revealing information about its operating system. The first fingerprinting implementations were based on the analysis of differences between TCP/IP stack implementations. The next generation focused the analysis on application layer data such as the DCE RPC endpoint information. Even though more information was analyzed, some variation of the "best fit" algorithm was still used to interpret this new information. Our new approach involves an analysis of the composition of the information collected during the OS identification process to identify key elements and their relations. To implement this approach, we have developed tools using Neural Networks and techniques from the field of Statistics. These tools have been successfully integrated in a commercial software (Core Impact).