My research focuses on developing principled statistical and computational foundations for modern data science, with an emphasis on understanding and improving the performance of deep learning systems in high-dimensional and heterogeneous environments. I use tools from statistical learning theory, high-dimensional probability, optimal transport, and information theory to analyze how neural networks learn complex distributions and why their convergence and generalization behavior is governed by low-dimensional intrinsic structure rather than ambient dimensionality. Methodologically, my work combines nonparametric analysis, minimax theory, and geometric insights from optimal transport to derive sharp error bounds and to design architectures that adapt to underlying data geometry.
A complementary line of my research develops robust tools for unsupervised learning, including clustering, dimensionality reduction, and distributional estimation in the presence of outliers, misspecification, and low signal-to-noise ratios. I leverage convex and nonconvex optimization techniques, spectral and kernel methods, and novel divergence measures to obtain algorithms with strong theoretical guarantees and practical scalability.
Across these directions, my goal is to bridge modern deep learning practice with rigorous mathematical understanding. By integrating theory, computation, and scalable algorithm design, my research aims to provide data-driven methodologies that are reliable, interpretable, and robust in large-scale scientific and industrial applications.
Please describe one or two of your most interesting projects.
Deep Learning Beyond Ambient Dimension: Sharp Rates via Intrinsic Geometry
A central project in my research develops a rigorous mathematical framework explaining why deep generative models—such as GANs and VAEs—achieve superior performance in high-dimensional distribution learning. Using tools from statistical learning theory, optimal transport, and measure theory, I show that the convergence rates of deep learners depend not on the ambient dimension of the data, but on its intrinsic low-dimensional structure. The project combines minimax analysis, nonparametric statistics, and tensorized optimal transport to derive the sharpest known error bounds for deep generative modeling, cycle-consistent architectures, and supervised learning with deep networks. This work not only advances theoretical understanding but also provides practical guidance for designing architectures that are stable, sample-efficient, and aligned with the geometry of real-world data.
Outlier-Robust Clustering and Dimensionality Reduction in High Dimensions
One of my core projects develops statistically principled methods for clustering and dimensionality reduction in high-dimensional, noisy, and heterogeneous data environments. Traditional clustering algorithms often fail when data contain outliers, exhibit low signal-to-noise ratios, or lie on complex low-dimensional structures embedded in very high-dimensional spaces. To address these challenges, I design algorithms that combine ideas from robust statistics, spectral methods, and information-theoretic divergence measures. A key component of this work is the development of outlier-robust estimators that remain stable even when a non-negligible fraction of data points are adversarial or corrupted. I introduce new divergence measures and entropy-like functionals tailored to high-dimensional geometry, allowing the algorithms to isolate well-behaved clusters while suppressing the influence of noisy points. These methods leverage convex relaxations, nonconvex optimization landscapes with benign geometry, and concentration inequalities for random matrices to achieve strong theoretical guarantees on recovery, sample complexity, and robustness.
How did you end up where you are today? (Your research journey)
My research journey began in 2015 at the Indian Statistical Institute, where early exposure to high-dimensional probability and unsupervised learning shaped my interest in the mathematical foundations of data science. In 2020, I moved to the University of California, Berkeley for my doctoral studies, where I became deeply engaged in understanding why modern deep learning methods succeed in complex, high-dimensional environments. Over these years, I developed a research agenda that blends statistical learning theory, optimal transport, and robust optimization to study deep generative models, federated learning, and clustering under noise and misspecification. Throughout this trajectory, my overarching goal has remained consistent: to build rigorous theoretical frameworks that explain and improve the behavior of contemporary machine learning systems.
What makes you excited about your data science and AI research?
What excites me most about my research in data science and AI is the opportunity to uncover the mathematical principles that explain why modern learning systems work as well as they do—and to push those systems toward greater reliability, efficiency, and interpretability. I am drawn to problems where deep learning, high-dimensional statistics, data science and AI intersect, because these areas reveal surprising structure beneath complex data. Developing rigourous frameworks that not only clarifies fundamental limits but also guides practical algorithm design is deeply motivating. Ultimately, the most exciting aspect of this work is its potential to impact real scientific and societal applications while remaining grounded in rigorous mathematics.