I’m a third year graduate student at Lab for Information and Decision Systems (LIDS) at MIT. I work with Prof. Guy Bresler on Applied Probability and Statistics.

I seek to solve theoretical machine learning problems([1]) using ideas from Probability Theory and Statistics and in the process, obtain novel insights into Probability Theory itself. I am currently devising methods to compare two different probability distributions over high dimensional spaces using associated Markov processes. I am also interested in understanding various local, randomized optimization algorithms.

Previously I was an undergraduate student at IIT Madras.


Email:
dheeraj[at]mit[dot]edu

 

[1] “आकाशात् पतितं तोयं यथा गच्छति सागरम्” 

 

Publications:

In Preparation:

  • Total Variation Convergence of Random Graphs. (2019)
    with Matthew Brennan and Guy Bresler

Manuscripts:

Journal Publications:

  • Stein’s Method for Stationary Distributions of Markov Chains and Application to Ising Models. (2019)
    arXiv preprint, to appear in Annals of Applied Probability
    with Guy Bresler
    Description: We give a method to bound the Wasserstein distance of binary random vectors by comparing their associated Glauber dynamics. The method is applied to show that two randomly picked sites in an Ising model over a d-regular expander graph behave very similar to two randomly picked sites over a Curie-Weiss model at the same temperature in the low temperature phase.
  •  Continuous limit of discrete quantum walks. (2015)
    Physical Review A, arxiv:1501.06950
    with Todd A. Brun
    Description: We give a general method to obtain continuous time analogues of discrete time quantum walks under certain assumptions by mapping it to a different space. We illustrate our method by showing that the grid-walk variant of Grover’s algorithm performs just as well in  continuous time as it does in the discrete time.

Conference Publications: