Ankit Pensia
PhD candidate
Department of Computer Sciences

Hi! I am a final-year PhD student in the Computer Sciences department at UW-Madison.

I am advised by Prof. Po-Ling Loh and Prof. Varun Jog. I also work closely with Prof. Ilias Diakonikolas. During Summer 2022, I was a research intern at Google Research NYC with Dr. Pranjal Awasthi and Dr. Satyen Kale. Before coming to the lovely town of Madison, I spent five memorable years at IIT Kanpur.

Please feel free to contact me at ankitp@cs.wisc.edu.

## Research

My research interests include:

Please see below for more details.

## Selected Publications

A comprehensive list of my published works can be found here. Relevant information can also be found on my profiles at Google Scholar, dblp, and Semantic Scholar.

### Robust and Heavy-Tailed Statistics

Outliers and heavy-tailed distributions can pose significant challenges to standard inference procedures. These challenges are addressed in the field of robust statistics, which focuses on developing algorithms that are resistant to the effects of these extreme and atypical data points. I am interested in exploring the statistical and computational landscapes of such algorithms.

• Outlier Robust Mean Estimation with Subgaussian Rates via Stability [link] [abstract]
with I. Diakonikolas and D. M. Kane. NeurIPS, 2020
We show that recent outlier-robust algorithms also achieve subgaussian confidence intervals for heavy-tailed distributions, and vice-versa. In particular, we identify the "stability" condition as the bridge between these two contamination models. In a recent paper at NeurIPS 2022, we extended these results to when the mean is further constrained to be sparse, i.e., robust sparse mean estimation.
• Robust regression with covariate filtering: Heavy tails and adversarial contamination [link] [abstract]
with V. Jog and P. Loh. Manuscript, 2020
We propose a simple (computationally-efficient) filtering step to remove potentially harmful covariates for robust regression. Combined with Huber Regression or Least Trimmed Squares, we obtain simple, fast, and provable algorithms for robust regression.

### Inference under Communication, Memory, and Privacy Constraints

The proliferation of big data has led to the development of distributed inference paradigms such as federated learning and the use of edge devices. These distributed setups impose constraints on communication bandwidth, memory usage, and privacy. My research focuses on understanding the impact of these constraints on sample complexity and developing computationally-efficient algorithms.

• Simple Binary Hypothesis Testing under Local Differential Privacy and Communication Constraints [link] [abstract]
with A. R. Asadi, V. Jog, and P. Loh. Manuscript, 2023
We characterizes the minmax optimal sample complexity of hypothesis testing under local differential privacy and communication constraints, develops instance-optimal algorithms, and shows separation between the sample complexity for binary and ternary distributions. In this paper, we build on our recent prior work, where we had shown that the cost of only the communication constraints is mild (at most logarithmic) for binary hypothesis testing but severe (exponential) for $M$-ary hypothesis testing.
• Streaming Algorithms for High-Dimensional Robust Statistics [link] [abstract]
with I. Diakonikolas, D. M. Kane, and T. Pittas. ICML, 2022
We develop the first (computationally-efficient and sample-efficient) streaming algorithm with $o(d^2)$ memory usage for a variety of robust estimation tasks; in fact, our algorithm uses only $\tilde{O}(d)$ space. All the prior robust algorithms needed to store the entire dataset in memory, which leads to super-quadratic memory. We also develop near linear-time robust mean estimation algorithm under a unified notion of "stability".

### Machine Learning and Statistics

I have a broad interest in the fields of machine learning and statistics. In particular, I have explored the representation power of neural networks and the generalization error of learning algorithms in my research.

• Optimal Lottery Tickets via SubsetSum: Logarithmic Over-Parameterization is Sufficient [link] [abstract]
with S. Rajput, A. Nagle, H. Vishwakarma, and D. Papailiopoulos. NeurIPS, 2020
We prove the strong lottery ticket hypothesis with optimal bounds on over-parameterization. We prove these results by connecting pruning of neural networks to random subset sum, a well-studied topic in TCS. This leads to an exponential improvement in the required over-parameterization in the width.
• Generalization Error Bounds for Noisy, Iterative Algorithms [link] [abstract]
with V. Jog and P. Loh. ISIT, 2018
We provide a general recipe to bound generalization error of noisy, iterative algorithms using information-theoretic tools. One prominent example of such algorithms is Stochastic Gradient Langevin Dynamics (SGLD).

## Teaching Experience

1. Graduate Teaching Assistant

1. Mathematical Foundations of Machine Learning, UW-Madison, Fall 2018

2. Introduction to Bioinformatics, UW-Madison, Fall 2017

3. Probabilistic Mobile Robotics, IIT Kanpur, Fall 2016, Spring 2016

4. Communication Systems, IIT Kanpur, Summer 2016