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Ronak Mehta

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4 papers

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NeurIPS Conference 2025 Conference Paper

Stochastic Gradients under Nuisances

Facheng Yu
Ronak Mehta
Alex Luedtke
Zaid Harchaoui

Stochastic gradient optimization is the dominant learning paradigm for a variety of scenarios, from classical supervised learning to modern self-supervised learning. We consider stochastic gradient algorithms for learning problems whose objectives rely on unknown nuisance parameters, and establish non-asymptotic convergence guarantees. Our results show that, while the presence of a nuisance can alter the optimum and upset the optimization trajectory, the classical stochastic gradient algorithm may still converge under appropriate conditions, such as Neyman orthogonality. Moreover, even when Neyman orthogonality is not satisfied, we also show that an algorithm variant with approximately orthogonalized updates (with an approximately orthogonalized gradient oracle) may achieve similar convergence rates. Examples from orthogonal statistical learning/double machine learning and causal inference are discussed.

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NeurIPS Conference 2024 Conference Paper

Drago: Primal-Dual Coupled Variance Reduction for Faster Distributionally Robust Optimization

Ronak Mehta
Jelena Diakonikolas
Zaid Harchaoui

We consider the penalized distributionally robust optimization (DRO) problem with a closed, convex uncertainty set, a setting that encompasses learning using $f$-DRO and spectral/$L$-risk minimization. We present Drago, a stochastic primal-dual algorithm which combines cyclic and randomized components with a carefully regularized primal update to achieve dual variance reduction. Owing to its design, Drago enjoys a state-of-the-art linear convergence rate on strongly convex-strongly concave DRO problems witha fine-grained dependency on primal and dual condition numbers. The theoretical results are supported with numerical benchmarks on regression and classification tasks.

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TMLR Journal 2024 Journal Article

Independence Testing for Temporal Data

Cencheng Shen
Jaewon Chung
Ronak Mehta
Ting Xu
Joshua T Vogelstein

Temporal data are increasingly prevalent in modern data science. A fundamental question is whether two time series are related or not. Existing approaches often have limitations, such as relying on parametric assumptions, detecting only linear associations, and requiring multiple tests and corrections. While many non-parametric and universally consistent dependence measures have recently been proposed, directly applying them to temporal data can inflate the p-value and result in an invalid test. To address these challenges, this paper introduces the temporal dependence statistic with block permutation to test independence between temporal data. Under proper assumptions, the proposed procedure is asymptotically valid and universally consistent for testing independence between stationary time series, and capable of estimating the optimal dependence lag that maximizes the dependence. Moreover, it is compatible with a rich family of distance and kernel based dependence measures, eliminates the need for multiple testing, and exhibits excellent testing power in various simulation settings.

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NeurIPS Conference 2024 Conference Paper

The Benefits of Balance: From Information Projections to Variance Reduction

Lang Liu
Ronak Mehta
Soumik Pal
Zaid Harchaoui

Data balancing across multiple modalities and sources appears in various forms in foundation models in machine learning and AI, e. g. , in CLIP and DINO. We show that data balancing across modalities and sources actually offers an unsuspected benefit: variance reduction. We present a non-asymptotic statistical bound that quantifies this variance reduction effect and relates it to the eigenvalue decay of Markov operators. Furthermore, we describe how various forms of data balancing in contrastive multimodal learning and self-supervised clustering can be better understood, and even improved upon, owing to our variance reduction viewpoint.

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