Research

Our research focuses on statistical and computational aspects of learning, with current emphasis on over-parameterized models including deep learning and generative models. Some of the themes of current focus include:
Deep Learning: Optimization, Generalization, and Geometry
Sequential Decision Making, Bandits
Generative Models, Graphical Models
High-dimensional Statistics, Sparsity, Structure
Optimization

We also work on applications of machine learning on problems in several areas inclduing:
Climate science
Ecology
Recommendation systems
Finance

A brief summary and a few selected papers on each of these themes are below. Please see our Publications for more details.


Deep Learning: Optimization, Generalization, and Geometry

Deep learning models have emerged as the state-of-the-art in many domains, but such models also have the capacity to perfectly fit random data. The focus of of our work is to understand optimization and generalization in deep learning, and use such understanding to improve algorithms and design choices, e.g., effect of width, effect of noisy training algorithms, etc.

Selected Papers


Sequential Decision Making, Bandits

Sequential decision making paradigms, such as context bandits, have been successfully used in a variety of applications. Our work focuses on new families of contextual bandit algorithms which can leverage neural representations, can handle constraints, can have simpler algorithms for smoothed analysis, i.e., less powerful adversaries due to noise.

Selected Papers


Generative Models, Graphical Models

Generative and graphical models enable probabilistic modeling of data, suitable uncertainty quantification, and inference. Such models have also been effective in learning suitable representations of data based on deep generative models. We have worked extensively on directed and undirected graphical models, including dependency structure learning, parameter estimation, and inference. Our recent work has been focusing on more flexible deep generative models, with current emphasis on likelihood based methods such as normalizing flows and variational autoencoders. Generative models will be an ongoing focus area with certain problems being motivated by applications in climate science, ecology, and finance.

Selected Papers


High-dimensional Statistics, Sparsity, Structure

High-dimensional over-parameterized models, where the number of parameters is much larger than the number of training samples, have been shown to effective in a wide variety of scenarios. Such models include sparse and structured estimation based on explicit regularization, e.g., Lasso, Dantzig selector, etc., as well as their non-linear, non-convex, and semi-parametric extensions. Our work has focused on statistical and computational guarantees for such models, often based on geometric ideas and associated tools from empirical processes such as generic chaining.

Selected Papers


Optimization

Optimization plays a key role in several facets of machine learning. In addition to using optimization for several projects, we have done work on certain themes in optimization including augmented Lagrangian and primal dual methods, sketched iterative algorithms, and accelerated first order methods. Our current work focuses on noisy gradient methods and optimization for overparametereized deep models.

Selected Papers



Applications

We work on applications of machine learning on problems in several areas inclduing:
Climate science
Ecology
Recommendation systems
Finance


Climate Science

There are several challenging problems in climate science where progress can potentially be made based on machine learning. We have worked on several problems in this context including better design of climate model ensembles, understanding statistical dependencies for physical processes, and interpretable predictive models for predicting climate variables. Our current work focuses on sub-seasonal climate forecasting which focuses on prediction of key climate variables such as temperature and precipitation in the 2 week to 2 month time horizon.

Selected Papers


Ecology

Our work in ecology has focused on modeling of plant functional traits as a predictive or gap-filling problem, similar to ratings prediction in recommendation systems. Such work has been extended to uncertainty quantified plant trait prediction, and use of such predicted plant trait distributions in terrestrial land surface model. Our current work is focused on spectral biology which uses hyper-spectral data from drones and sattelites to characterize biodiversity across scales.

Selected Papers


Recommendation Systems

We have worked on several aspects of recommendation systems over the years.

Selected Papers


Finance

We have worked on certain aspects of portfolio selection from the perspective of online learning and full-information sequential decision making.

Selected Papers