Sooraj Bhat

Farther than you may think: an empirical investigation of the proximity of users to their mobile phones

Implicit in much research and application development for mobile phones is the assumption that the mobile phone is a suitable proxy for its owners location. We report an in-depth empirical investigation of this assumption in which we measured proximity of the phone to its owner over several weeks of continual observation. Our findings, summarizing results over 16 different subjects of a variety of ages and occupations, establish baseline statistics for the proximity relationship in a typical US metropolitan market. Supplemental interviews help us to establish reasons why the phone and owner are separated, leading to guidelines for developing mobile phone applications that can be smart with respect to the proximity assumption. We show it is possible to predict the proximity relationship with 86% confidence using simple parameters of the phone, such as current cell ID, current date and time, signal status, charger status and ring/vibrate mode.

Deriving probability density functions from probabilistic functional programs

The probability density function of a probability distribution is a fundamental concept in probability theory and a key ingredient in various widely used machine learning methods. However, the necessary framework for compiling probabilistic functional programs to density functions has only recently been developed. In this work, we present a density compiler for a probabilistic language with discrete and continuous distributions, and discrete observations, and provide a proof of its soundness. The compiler greatly reduces the development effort of domain experts, which we demonstrate by solving inference problems from various scientific applications, such as modelling the global carbon cycle, using a standard Markov chain Monte Carlo framework.

Towards adaptive programming: integrating reinforcement learning into a programming language

Current programming languages and software engineering paradigms are proving insufficient for building intelligent multi-agent systems--such as interactive games and narratives--where developers are called upon to write increasingly complex behavior for agents in dynamic environments. A promising solution is to build adaptive systems; that is, to develop software written specifically to adapt to its environment by changing its behavior in response to what it observes in the world. In this paper we describe a new programming language, An Adaptive Behavior Language (A2BL), that implements adaptive programming primitives to support partial programming, a paradigm in which a programmer need only specify the details of behavior known at code-writing time, leaving the run-time system to learn the rest. Partial programming enables programmers to more easily encode software agents that are difficult to write in existing languages that do not offer language-level support for adaptivity. We motivate the use of partial programming with an example agent coded in a cutting-edge, but non-adaptive agent programming language (ABL), and show how A2BL can encode the same agent much more naturally.

A globally optimal algorithm for TTD-MDPs

In this paper, we discuss the use of Targeted Trajectory Distribution Markov Decision Processes (TTD-MDPs)---a variant of MDPs in which the goal is to realize a specified distribution of trajectories through a state space---as a general agent-coordination framework. We present several advances to previous work on TTD-MDPs. We improve on the existing algorithm for solving TTD-MDPs by deriving a greedy algorithm that finds a policy that provably minimizes the global KL-divergence from the target distribution. We test the new algorithm by applying TTD-MDPs to drama management, where a system must coordinate the behavior of many agents to ensure that a game follows a coherent storyline, is in keeping with the authors desires, and offers a high degree of replayability. Although we show that suboptimal greedy strategies will fail in some cases, we validate previous work that suggests that they can work well in practice. We also show that our new algorithm provides guaranteed accuracy even in those cases, with little additional computational cost. Further, we illustrate how this new approach can be applied online, eliminating the memory-intensive offline sampling necessary in the previous approach.

A type theory for probability density functions

There has been great interest in creating probabilistic programming languages to simplify the coding of statistical tasks; however, there still does not exist a formal language that simultaneously provides (1) continuous probability distributions, (2) the ability to naturally express custom probabilistic models, and (3) probability density functions (PDFs). This collection of features is necessary for mechanizing fundamental statistical techniques. We formalize the first probabilistic language that exhibits these features, and it serves as a foundational framework for extending the ideas to more general languages. Particularly novel are our type system for absolutely continuous (AC) distributions (those which permit PDFs) and our PDF calculation procedure, which calculates PDF s for a large class of AC distributions. Our formalization paves the way toward the rigorous encoding of powerful statistical reformulations.

Automating mathematical program transformations

Mathematical programs (MPs) are a class of constrained optimization problems that include linear, mixed-integer, and disjunctive programs. Strategies for solving MPs rely heavily on various transformations between these subclasses, but most are not automated because MP theory does not presently treat programs as syntactic objects. In this work, we present the first syntactic definition of MP and of some widely used MP transformations, most notably the big-M and convex hull methods for converting disjunctive constraints. We use an embedded OCaml DSL on problems from chemical process engineering and operations research to compare our automated transformations to existing technology—finding that no one technique is always best—and also to manual reformulations—finding that our mechanizations are comparable to human experts. This work enables higher-level solution strategies that can use these transformations as subroutines.

Toward interactive statistical modeling

When solving machine learning problems, there is currently little automated support for easily experimenting with alternative statistical models or solution strategies. This is because this activity often requires expertise from several di erent fields (e.g., statistics, optimization, linear algebra), and the level of formalism required for automation is much higher than for a human solving problems on paper. We present a system toward addressing these issues, which we achieve by (1) formalizing a type theory for probability and optimization, and (2) providing an interactive rewrite system for applying problem reformulation theorems. Automating solution strategies this way enables not only manual experimentation but also higher-level, automated activities, such as autotuning.

Deriving Probability Density Functions from Probabilistic Functional Programs

The probability density function of a probability distribution is a fundamental concept in probability theory and a key ingredient in various widely used machine learning methods. However, the necessary framework for compiling probabilistic functional programs to density functions has only recently been developed. In this work, we present a density compiler for a probabilistic language with failure and both discrete and continuous distributions, and provide a proof of its soundness. The compiler greatly reduces the development effort of domain experts, which we demonstrate by solving inference problems from various scientific applications, such as modelling the global carbon cycle, using a standard Markov chain Monte Carlo framework.