Research

Research Interests

  • Bayesian Nonparametrics

  • Mixture and Hierarchical mixture models.

  • (Approximate) Bayesian Inference.

  • Geometric Topic modeling.

  • Optimal Transport.

  • Autonomous vehicles.

I am interested in various fields of Statistics and their applications to real data.

Bayesian Nonparametrics

Mixture models form very useful tools for density estimation, clustering and other Statistical applications. A commonly used approach towards using mixture models for Bayesian Inference is via the use of nonparametric priors such as the Dirichlet Process. However, even though density estimationis efficiently achieved with the DP priors, parameter estimations and estimation of the number of components with this prior are not very well-studied. A common misconception that might have led to the popularity of the BNP approach is that using a nonparametric prior eliminates the need to estimate the number of components, an idea that has been disproved by Miller & Harrison. However, we show in a recent work that there exist post-processing steps which can still recover the true number of components. In addition, we also show that the MFM prior works better for parameter estimation purposes. I am also interested in misspecification structures of mixture models. As George Box said “All models are worng, but some are useful”. In particular for mixture models, even if we use the incorrect kernel, can we still get close to the truth? Can we remedy that in some way? Most theoretical results deal witht he assumption that parameter space is compact? What happens if we misspecify the parameter space? Can we estimate the parameter space in an efficient way? We also explore some of these ideas in a collection of works.

Approximate Bayesian Inference is also an area I am currently working on.

Topic Modeling

I am also interested in Topic models, in particular in developing fast and efficient geometric algorithms for estimation of topics. MCMC methods provide accurate estimation with Topic models. However, being very generic as an approach, they compromise a lot in terms of speed. On the other hand, fast methods such as Stochastic Variational Inference maybe quite inaccurate in extreme cases. In a collection of works, with a collaborator we explore the estimation of topics as well as the number of true topics and provide geometric algorithms for the same, in addition to theoretical understanding of the approaches.

Autonomous Vehicles

Automated driving is a very popular area of research. Traffic encounters are driving scenarios which are often realised in real-life driving situations. One step towards completely automated cars is by understanding of the driving scenarios. In a recent work, we provide some techniques to identify such encounters and provide a method to evaluate outcomes.