Variational Sequential Monte Carlo

Many recent advances in large scale probabilistic inference rely on variational methods. The success of variational approaches depends on (i) formulating a flexible parametric family of distributions, and (ii) optimizing the parameters to find the member of this family that most closely approximates the exact posterior. In this paper we present a new approximating family of distributions, the variational sequential Monte Carlo (VSMC) family, and show how to optimize it in variational inference. VSMC melds variational inference (VI) and sequential Monte Carlo (SMC), providing practitioners with flexible, accurate, and powerful Bayesian inference. The VSMC family is a variational family that can approximate the posterior arbitrarily well, while still allowing for efficient optimization of its parameters. We demonstrate its utility on state space models, stochastic volatility models for financial data, and deep Markov models of brain neural circuits

Boosting Black Box Variational Inference

Approximating a probability density in a tractable manner is a central task in Bayesian statistics. Variational Inference (VI) is a popular technique that achieves tractability by choosing a relatively simple variational family. Borrowing ideas from the classic boosting framework, recent approaches attempt to \emph{boost} VI by replacing the selection of a single density with a greedily constructed mixture of densities. In order to guarantee convergence, previous works impose stringent assumptions that require significant effort for practitioners. Specifically, they require a custom implementation of the greedy step (called the LMO) for every probabilistic model with respect to an unnatural variational family of truncated distributions. Our work fixes these issues with novel theoretical and algorithmic insights. On the theoretical side, we show that boosting VI satisfies a relaxed smoothness assumption which is sufficient for the convergence of the functional Frank-Wolfe (FW) algorithm. Furthermore, we rephrase the LMO problem and propose to maximize the Residual ELBO (RELBO) which replaces the standard ELBO optimization in VI. These theoretical enhancements allow for black box implementation of the boosting subroutine. Finally, we present a stopping criterion drawn from the duality gap in the classic FW analyses and exhaustive experiments to illustrate the usefulness of our theoretical and algorithmic contributions

Latent variable models for understanding user behavior in software applications

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2018.Cataloged from PDF version of thesis.Includes bibliographical references (pages 147-157).Understanding user behavior in software applications is of significant interest to software developers and companies. By having a better understanding of the user needs and usage patterns, the developers can design a more efficient workflow, add new features, or even automate the user's workflow. In this thesis, I propose novel latent variable models to understand, predict and eventually automate the user interaction with a software application. I start by analyzing users' clicks using time series models; I introduce models and inference algorithms for time series segmentation which are scalable to large-scale user datasets. Next, using a conditional variational autoencoder and some related models, I introduce a framework for automating the user interaction with a software application. I focus on photo enhancement applications, but this framework can be applied to any domain where segmentation, prediction and personalization is valuable. Finally, by combining sequential Monte Carlo and variational inference, I propose a new inference scheme which has better convergence properties than other reasonable baselines.by Ardavan Saeedi.Ph. D