Black Box Variational Inference

Variational inference has become a widely used method to approximate posteriors in complex latent variables models. However, deriving a variational inference algorithm generally requires significant model-specific analysis, and these efforts can hinder and deter us from quickly developing and exploring a variety of models for a problem at hand. In this paper, we present a "black box" variational inference algorithm, one that can be quickly applied to many models with little additional derivation. Our method is based on a stochastic optimization of the variational objective where the noisy gradient is computed from Monte Carlo samples from the variational distribution. We develop a number of methods to reduce the variance of the gradient, always maintaining the criterion that we want to avoid difficult model-based derivations. We evaluate our method against the corresponding black box sampling based methods. We find that our method reaches better predictive likelihoods much faster than sampling methods. Finally, we demonstrate that Black Box Variational Inference lets us easily explore a wide space of models by quickly constructing and evaluating several models of longitudinal healthcare data

Monomial Nonnegativity and the Bruhat Order

We show that five nonnegativity properties of polynomials coincide when restricted to polynomials of the form x1, pi(1) ... xn,pi(n) - x1, sigma(1) ... xn, sigma(n), where $\pi and sigma are permutations in Sn. In particular, we show that each of these properties may be used to characterize the Bruhat order on Sn

How Smart Machines Think

The future is here: Self-driving cars are on the streets, an algorithm gives you movie and TV recommendations, IBM\u27s Watson triumphed on Jeopardy over puny human brains, computer programs can be trained to play Atari games. But how do all these things work? In this book, Sean Gerrish offers an engaging and accessible overview of the breakthroughs in artificial intelligence and machine learning that have made today\u27s machines so smart. Gerrish outlines some of the key ideas that enable intelligent machines to perceive and interact with the world. He describes the software architecture that allows self-driving cars to stay on the road and to navigate crowded urban environments; the million-dollar Netflix competition for a better recommendation engine (which had an unexpected ending); and how programmers trained computers to perform certain behaviors by offering them treats, as if they were training a dog. He explains how artificial neural networks enable computers to perceive the world?and to play Atari video games better than humans. He explains Watson\u27s famous victory on Jeopardy, and he looks at how computers play games, describing AlphaGo and Deep Blue, which beat reigning world champions at the strategy games of Go and chess. Computers have not yet mastered everything, however; Gerrish outlines the difficulties in creating intelligent agents that can successfully play video games like StarCraft that have evaded solution?at least for now. Gerrish weaves the stories behind these breakthroughs into the narrative, introducing readers to many of the researchers involved, and keeping technical details to a minimum. Science and technology buffs will find this book an essential guide to a future in which machines can outsmart people

Applications of Latent Variable Models for Modeling Influence and Decision Making

The past twenty years have seen an avalanche of digital information which is overwhelming people in industry, government, and academics. This avalanche is two-sided: while the past decade has seen an onslaught of digitized records -- as governments, publishers, and researchers race to make their records digital, the electronic and software tools for computationally analyzing this data have quickly evolved to face this challenge. Many of these challenges evolve around recurring patterns, including the presence of text, bits of information about pairs of items, and sequential observations. In this work we present several methods to address these challenges in data analysis which take advantage of these recurring patterns. We begin with a method for identifying influential documents in a collection which evolves over time. We demonstrate that by encoding our assumptions about influential documents in a statistical model of the changes in textual themes, we are able to provide an alternative bibliometric which provides results consistent with---yet different from---traditional metrics of influence such as citation counts. We then introduce a model for measuring the relationships between pairs of countries over time. We will demonstrate that this model is able to learn meaningful relationships between countries which is extraordinarily consistent across different human labels. We next address limitations in existing models of legislative voting. In one extention we predict legislators' votes by using the text of the bills they are voting on combined with individual legislators' past voting behavior. We then introduce a method for inferring these lawmakers' positions on specific issues. A recurring theme in the methods we present is that by using a small set of statistical primitives, we are able to apply known (or mildly adapted) methods to new problems. Several advances in the past few decades in statistical modeling will make the development and discussion of our models easier, as they will provide both this set of primitives (which can be interchanged easily) and the tools for working with them. As a final contribution, we describe a new method for fitting a statistical model with variational inference, without the time investment typically required of practitioners

How They Vote: Issue-Adjusted Models of Legislative Behavior

We develop a probabilistic model of legislative data that uses the text of the bills to uncover lawmakers ’ positions on specific political issues. Our model can be used to explore how a lawmaker’s voting patterns deviate from what is expected and how that deviation depends on what is being voted on. We derive approximate posterior inference algorithms based on variational methods. Across 12 years of legislative data, we demonstrate both improvement in heldout predictive performance and the model’s utility in interpreting an inherently multi-dimensional space.

Two new criteria for comparison in the Bruhat order

We give two new criteria by which pairs of permutations may be compared in defining the Bruhat order (of type A). One criterion uses totally nonnegative polynomials and the other uses Schur functions

Predicting legislative roll calls from text

We develop several predictive models linking legislative sentiment to legislative text. Our models, which draw on ideas from ideal point estimation and topic models, predict voting patterns based on the contents of bills and infer the political leanings of legislators. With supervised topics, we provide an exploratory window into how the language of the law is correlated with political support. We also derive approximate posterior inference algorithms based on variational methods. Across 12 years of legislative data, we predict specific voting patterns with high accuracy. 1

Black Box Variational Inference

Variational inference has become a widely used method to approximate posteriors in complex latent variables models. However, deriving a variational inference algorithm generally requires significant model-specific analysis, and these efforts can hinder and deter us from quickly developing and exploring a variety of models for a problem at hand. In this paper, we present a "black box" variational inference algorithm, one that can be quickly applied to many models with little additional derivation. Our method is based on a stochastic optimization of the variational objective where the noisy gradient is computed from Monte Carlo samples from the variational distribution. We develop a number of methods to reduce the variance of the gradient, always maintaining the criterion that we want to avoid difficult model-based derivations. We evaluate our method against the corresponding black box sampling based methods. We find that our method reaches better predictive likelihoods much faster than sampling methods. Finally, we demonstrate that Black Box Variational Inference lets us easily explore a wide space of models by quickly constructing and evaluating several models of longitudinal healthcare data