2018 — 2021 
Honnappa, Harsha Rao, Vinayak 
N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information 
Decision Theoretic Bayesian Computation
Decisionmakers, whether in business, policymaking, or engineering systems, face the problem of taking action without complete knowledge of the state of the world. Examples of such situations include controlling industrial plants, maneuvering autonomous vehicles, developing new drugs, making investment decisions or staffing decisions in service systems. Modern decisionmakers typically use sophisticated probabilistic models to capture uncertainty, and take optimal actions within the framework of such models. In general, the models themselves involve unknown parameters which must be estimated from data. While large datasets improve the estimation of the parameters, leading to more accurate decisions, these bigdata settings also raise computational challenges that call for approximations in the estimation. Current methodology typically proceeds in two steps: (1) use the vast statistical and machine learning literature to approximately estimate model parameters, and (2) use the resulting approximations to compute the best possible action. This twostage procedure can result in suboptimality of actions, as the approximations computed in the first stage are not tailored to the decisionmaking problem in the second stage. The objective of this project is to develop and study a methodological framework for approximate computation that puts decisionmaking at its center, recognizing that the ultimate goal of most bigdata analyses is to help decide among actions in the face of uncertainty. The project will provide tools and theory to accurately account for tradeoffs between statistical accuracy, decisiontheoretic utility and computational complexity, and will integrate decisionmaking into the computational revolution that has driven much of modern datascience. The tools and theory potentially impact a large range of datadriven decisionmaking problems.
This project works in the overarching framework of Bayesian statistics, where the primary object of interest is the posterior distribution over the unknown parameters and variables. The research focuses on theoretical and methodological challenges arising from approximate computation for Bayesian decision theory. The investigators consider two complementary problems, (a) Decisiontheoretic variational Bayes, and (b) Robust decisionmaking. The former task analyzes and extends variational methods, developed in the machine learning community to approximate intractable Bayesian posterior distributions, from a decisiontheoretic viewpoint. The investigators will theoretically study the optimality of such algorithms with respect to decisionmaking rather than prediction, and develop novel `losscalibrated' algorithms that search for approximations using decisiontheoretic, rather than inferential criteria. Task (b) recognizes that a model is always an approximation to reality, and is therefore misspecified. As a consequence, a Bayesian posterior distribution, even if calculated exactly, might not actually characterize the distribution over future observations. The investigators explore connections with approximations from the first task, and move from uncertainty about parameters and variables under a specified model, to uncertainty about the choice of model itself. They develop and analyze methodology that allows robust and principled decisions in the face of such `Knightian' uncertainty.
This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

0.961 
2018 — 2021 
Rao, Vinayak 
N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information 
Ri: Small: Dynamics of Repulsion and Reinforcement in Point Process, Latent Variable, and Trajectory Models
Most traditional ways of analyzing data assume that data points are sampled independently of one another. In many problems, however, this assumption is incorrect. This project focuses on data where one observation influences others, either as reinforcing (likely to have a similar value) or repulsing (likely to have a greatly different value). Such interactions might arise between static measurements, between trajectories evolving in space/on a network, or may be desirable biases in algorithms to promote goals like robustness, diversity or fairness. These might arise as a consequence of competition for finite resources, because of richgetricher dynamics from propagating social influence, because of interacting processes in physical and biological systems, or out of a desire to learn compact representations of complex systems. Examples include the locations of cells or service stations, interactions among particles or populations, traffic trajectories, users navigating social media, the spiking of neurons or the spread of disease. The research brings together applied problems and theoretical ideas from fields like machine learning, statistics, physics and computer science. Such tools open new avenues to datasummarization, exploration and visualization, and allow practitioners to explore tradeoffs between interpretability and predictive accuracy. The applied aspects of this project provide an opportunity for undergraduate research and for the integration of research and teaching through an undergraduate course on stochastic processes and simulation.
At a technical level, this project develops principled statistical models and efficient algorithms that relax assumptions of independence among observations lying on a shared space. It considers interactions for three classes of problems: 1) point process models, 2) latent variable models and 3) trajectory models. Central to the work are two kinds of stochastic process models: the Hawkes process for reinforcement, and the Matern typeIII process for repulsion. Both processes share intuitive and mechanistic generative schemes from an underlying Poisson process, whose rate is modulated by event history. This allows a framework that jointly models richer repulsive and reinforcing interactions in stationary and trajectory data. The connection with the Poisson process allows novel models and mechanisms of reinforcement and repulsion, as well as new, scalable algorithms, allowing investigations into the fundamental role of nonPoissonness in real applications. Incorporating repulsive priors into latent variables of hierarchical models also allow novel repulsive latent variable models with biases towards parsimony and interpretability.
This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

0.961 