I’m a fourth 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:

Manuscripts:

• A Corrective View of Neural Networks: Representation, Memorization and Learning. (2020)
  arXiv preprint
  with Guy Bresler.
  Description: We develop a corrective mechanism for neural network approximation: the total available non-linear units are divided into multiple groups and the first group approximates the function under consideration, the second group approximates the error in approximation produced by the first group and corrects it, the third group approximates the error produced by the first and second groups together and so on. This technique yields several new representation and learning results for neural networks.
• Phase Transition for Detecting Latent Geometry in Random Graphs. (2019)
  arXiv preprint
  with Matthew Brennan and Guy Bresler.
  Description: We consider sparse Random Intersection Graphs and Random Geometric Graphs and give sharp (and sharper) conditions on their dimensionality which ensure their convergence to Erdos Renyi random graphs in terms of total variation distance.

Journal Publications: 

• Stein’s Method for Stationary Distributions of Markov Chains and Application to Ising Models. (2019)
  Annals of Applied Probability 
  arXiv preprint: arxiv:1712.05743, 
  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:

• Making Last Iterate of Stochastic Gradient Descent Information Theoretically Optimal. (2019)
  COLT 2019
  with Praneeth Netrapalli and Prateek Jain
• SGD without Replacement: Sharper Rates for General Smooth Convex Functions. (2019)
  ICML 2019
  with Praneeth Netrapalli and Prateek Jain
  Description: Standard theoretical analysis of SGD is carried out assuming with replacement sampling techniques. We give the first general bounds for without replacement sampled SGD for convex functions assuming only gradient smoothness for the objective and match the error rates for with replacement sampling for a small number of epochs and better-than-without replacement sampling rates after a large number of epochs.
• Optimal Single Sample Tests for Structured versus Unstructured Network Data. (2018)
  COLT 2018.
  arxiv preprint 
  with Guy Bresler
  Description: We give a general, optimal single sample test to distinguish between unstructured models (Curie-Weiss, Erdos-Renyi etc) to structured models (Ising model, Exponential Random Graphs etc) when temperature parameters are unknown. We use distributional approximation as the main tool to prove the guarantees of this test.