arXiv subjects

Ronak Mehta

Publications and source records attributed to Ronak Mehta.

At least 19 recordsLinked to original sources

arXiv2025

Stochastic Gradients under Nuisances

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 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.

stat.ML↗

arXiv2025

Supervised Stochastic Gradient Algorithms for Multi-Trial Source Separation

We develop a stochastic algorithm for independent component analysis that incorporates multi-trial supervision, which is available in many scientific contexts. The method blends a proximal gradient-type algorithm in the space of invertible matrices with joint learning of a prediction model through backpropagation. We illustrate the proposed algorithm on synthetic and real data experiments. In particular, owing to the additional supervision, we observe an increased success rate of the non-convex optimization and the improved interpretability of the independent components.

cs.LG↗

arXiv2025

A Generalization Theory for Zero-Shot Prediction

A modern paradigm for generalization in machine learning and AI consists of pre-training a task-agnostic foundation model, generally obtained using self-supervised and multimodal contrastive learning. The resulting representations can be used for prediction on a downstream task for which no labeled data is available. We present a theoretical framework to better understand this approach, called zero-shot prediction. We identify the target quantities that zero-shot prediction aims to learn, or learns in passing, and the key conditional independence relationships that enable its generalization ability.

stat.ML↗

arXiv2025

Efficient Methods for Min-Max Optimization with Dual-Linear Coupling

We study a class of convex-concave min-max problems in which the coupled component of the objective is linear in at least one of the two decision vectors. We identify such problem structure as interpolating between the bilinearly and nonbilinearly coupled problems, motivated by key applications in areas such as distributionally robust optimization and convex optimization with functional constraints. Leveraging the considered nonlinear-linear coupling of the primal and the dual decision vectors, we develop a general algorithmic framework leading to fine-grained complexity bounds exploiting separability properties of the problem, whenever present. The obtained complexity bounds offer potential improvements over state-of-the-art scaling with $\sqrt{n}$ or $n$ in some of the considered problem settings, which even include bilinearly coupled problems, where $n$ is the dimension of the dual decision vector. On the algorithmic front, our work provides novel strategies for combining randomization with extrapolation and multi-point anchoring in the mirror descent-style updates in the primal and the dual, which we hope will find further applications in addressing related optimization problems.

math.OC↗

arXiv2025

What do Large Language Models Say About Animals? Investigating Risks of Animal Harm in Generated Text

As machine learning systems become increasingly embedded in society, their impact on human and nonhuman life continues to escalate. Technical evaluations have addressed a variety of potential harms from large language models (LLMs) towards humans and the environment, but there is little empirical work regarding harms towards nonhuman animals. Following the growing recognition of animal protection in regulatory and ethical AI frameworks, we present AnimalHarmBench (AHB), a benchmark for risks of animal harm in LLM-generated text. Our benchmark dataset comprises 1,850 curated questions from Reddit post titles and 2,500 synthetic questions based on 50 animal categories (e.g., cats, reptiles) and 50 ethical scenarios with a 70-30 public-private split. Scenarios include open-ended questions about how to treat animals, practical scenarios with potential animal harm, and willingness-to-pay measures for the prevention of animal harm. Using the LLM-as-a-judge framework, responses are evaluated for their potential to increase or decrease harm, and evaluations are debiased for the tendency of judges to judge their own outputs more favorably. AHB reveals significant differences across frontier LLMs, animal categories, scenarios, and subreddits. We conclude with future directions for technical research and addressing the challenges of building evaluations on complex social and moral topics.

cs.CY↗

arXiv2025

Proving the Coding Interview: A Benchmark for Formally Verified Code Generation

We introduce the Formally Verified Automated Programming Progress Standards, or FVAPPS, a benchmark of 4715 samples for writing programs and proving their correctness, the largest formal verification benchmark, including 1083 curated and quality controlled samples. Previously, APPS provided a benchmark and dataset for programming puzzles to be completed in Python and checked against unit tests, of the kind seen in technical assessments in the software engineering industry. Building upon recent approaches for benchmarks in interactive theorem proving, we generalize the unit tests to Lean 4 theorems given without proof (i.e., using Lean's "sorry" keyword). On the 406 theorems of 100 randomly selected samples, Sonnet correctly proves 30% and Gemini correctly proves 18%. We challenge the machine learning and program synthesis communities to solve both each general purpose programming problem and its associated correctness specifications. The benchmark is available at https://huggingface.co/datasets/quinn-dougherty/fvapps.

cs.SE↗

arXiv2024

The Benefits of Balance: From Information Projections to Variance Reduction

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.

stat.ML↗

arXiv2024

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

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 that 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 with a fine-grained dependency on primal and dual condition numbers. Theoretical results are supported by numerical benchmarks on regression and classification tasks.

stat.ML↗

arXiv2023

Distributionally Robust Optimization with Bias and Variance Reduction

We consider the distributionally robust optimization (DRO) problem with spectral risk-based uncertainty set and $f$-divergence penalty. This formulation includes common risk-sensitive learning objectives such as regularized condition value-at-risk (CVaR) and average top-$k$ loss. We present Prospect, a stochastic gradient-based algorithm that only requires tuning a single learning rate hyperparameter, and prove that it enjoys linear convergence for smooth regularized losses. This contrasts with previous algorithms that either require tuning multiple hyperparameters or potentially fail to converge due to biased gradient estimates or inadequate regularization. Empirically, we show that Prospect can converge 2-3$\times$ faster than baselines such as stochastic gradient and stochastic saddle-point methods on distribution shift and fairness benchmarks spanning tabular, vision, and language domains.

stat.ML↗

arXiv2022

Stochastic Optimization for Spectral Risk Measures

Spectral risk objectives - also called $L$-risks - allow for learning systems to interpolate between optimizing average-case performance (as in empirical risk minimization) and worst-case performance on a task. We develop stochastic algorithms to optimize these quantities by characterizing their subdifferential and addressing challenges such as biasedness of subgradient estimates and non-smoothness of the objective. We show theoretically and experimentally that out-of-the-box approaches such as stochastic subgradient and dual averaging are hindered by bias and that our approach outperforms them.

stat.ML↗

arXiv2022

Deep Unlearning via Randomized Conditionally Independent Hessians

Recent legislation has led to interest in machine unlearning, i.e., removing specific training samples from a predictive model as if they never existed in the training dataset. Unlearning may also be required due to corrupted/adversarial data or simply a user's updated privacy requirement. For models which require no training (k-NN), simply deleting the closest original sample can be effective. But this idea is inapplicable to models which learn richer representations. Recent ideas leveraging optimization-based updates scale poorly with the model dimension d, due to inverting the Hessian of the loss function. We use a variant of a new conditional independence coefficient, L-CODEC, to identify a subset of the model parameters with the most semantic overlap on an individual sample level. Our approach completely avoids the need to invert a (possibly) huge matrix. By utilizing a Markov blanket selection, we premise that L-CODEC is also suitable for deep unlearning, as well as other applications in vision. Compared to alternatives, L-CODEC makes approximate unlearning possible in settings that would otherwise be infeasible, including vision models used for face recognition, person re-identification and NLP models that may require unlearning samples identified for exclusion. Code can be found at https://github.com/vsingh-group/LCODEC-deep-unlearning/

cs.CV↗

arXiv2021

Towards a theory of out-of-distribution learning

Learning is a process wherein a learning agent enhances its performance through exposure of experience or data. Throughout this journey, the agent may encounter diverse learning environments. For example, data may be presented to the leaner all at once, in multiple batches, or sequentially. Furthermore, the distribution of each data sample could be either identical and independent (iid) or non-iid. Additionally, there may exist computational and space constraints for the deployment of the learning algorithms. The complexity of a learning task can vary significantly, depending on the learning setup and the constraints imposed upon it. However, it is worth noting that the current literature lacks formal definitions for many of the in-distribution and out-of-distribution learning paradigms. Establishing proper and universally agreed-upon definitions for these learning setups is essential for thoroughly exploring the evolution of ideas across different learning scenarios and deriving generalized mathematical bounds for these learners. In this paper, we aim to address this issue by proposing a chronological approach to defining different learning tasks using the provably approximately correct (PAC) learning framework. We will start with in-distribution learning and progress to recently proposed lifelong or continual learning. We employ consistent terminology and notation to demonstrate how each of these learning frameworks represents a specific instance of a broader, more generalized concept of learnability. Our hope is that this work will inspire a universally agreed-upon approach to quantifying different types of learning, fostering greater understanding and progress in the field.

stat.ML↗

arXiv2019

Manifold Oblique Random Forests: Towards Closing the Gap on Convolutional Deep Networks

Decision forests (Forests), in particular random forests and gradient boosting trees, have demonstrated state-of-the-art accuracy compared to other methods in many supervised learning scenarios. In particular, Forests dominate other methods in tabular data, that is, when the feature space is unstructured, so that the signal is invariant to a permutation of the feature indices. However, in structured data lying on a manifold (such as images, text, and speech) deep networks (Networks), specifically convolutional deep networks (ConvNets), tend to outperform Forests. We conjecture that at least part of the reason for this is that the input to Networks is not simply the feature magnitudes, but also their indices. In contrast, naive Forest implementations fail to explicitly consider feature indices. A recently proposed Forest approach demonstrates that Forests, for each node, implicitly sample a random matrix from some specific distribution. These Forests, like some classes of Networks, learn by partitioning the feature space into convex polytopes corresponding to linear functions. We build on that approach and show that one can choose distributions in a manifold-aware fashion to incorporate feature locality. We demonstrate the empirical performance on data whose features live on three different manifolds: a torus, images, and time-series. Moreover, we demonstrate its strength in multivariate simulated settings and also show superiority in predicting surgical outcome in epilepsy patients and predicting movement direction from raw stereotactic EEG data from non-motor brain regions. In all simulations and real data, Manifold Oblique Random Forest (MORF) algorithm outperforms approaches that ignore feature space structure and challenges the performance of ConvNets. Moreover, MORF runs fast and maintains interpretability and theoretical justification.

cs.LG↗

arXiv2019

DUAL-GLOW: Conditional Flow-Based Generative Model for Modality Transfer

Positron emission tomography (PET) imaging is an imaging modality for diagnosing a number of neurological diseases. In contrast to Magnetic Resonance Imaging (MRI), PET is costly and involves injecting a radioactive substance into the patient. Motivated by developments in modality transfer in vision, we study the generation of certain types of PET images from MRI data. We derive new flow-based generative models which we show perform well in this small sample size regime (much smaller than dataset sizes available in standard vision tasks). Our formulation, DUAL-GLOW, is based on two invertible networks and a relation network that maps the latent spaces to each other. We discuss how given the prior distribution, learning the conditional distribution of PET given the MRI image reduces to obtaining the conditional distribution between the two latent codes w.r.t. the two image types. We also extend our framework to leverage 'side' information (or attributes) when available. By controlling the PET generation through 'conditioning' on age, our model is also able to capture brain FDG-PET (hypometabolism) changes, as a function of age. We present experiments on the Alzheimers Disease Neuroimaging Initiative (ADNI) dataset with 826 subjects, and obtain good performance in PET image synthesis, qualitatively and quantitatively better than recent works.

eess.IV↗

arXiv2019

Independence Testing for Temporal Data

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.

stat.ML↗

arXiv2019

hyppo: A Multivariate Hypothesis Testing Python Package

We introduce hyppo, a unified library for performing multivariate hypothesis testing, including independence, two-sample, and k-sample testing. While many multivariate independence tests have R packages available, the interfaces are inconsistent and most are not available in Python. hyppo includes many state of the art multivariate testing procedures. The package is easy-to-use and is flexible enough to enable future extensions. The documentation and all releases are available at https://hyppo.neurodata.io.

stat.CO↗

arXiv2019

Random Forests for Adaptive Nearest Neighbor Estimation of Information-Theoretic Quantities

Information-theoretic quantities, such as conditional entropy and mutual information, are critical data summaries for quantifying uncertainty. Current widely used approaches for computing such quantities rely on nearest neighbor methods and exhibit both strong performance and theoretical guarantees in certain simple scenarios. However, existing approaches fail in high-dimensional settings and when different features are measured on different scales.We propose decision forest-based adaptive nearest neighbor estimators and show that they are able to effectively estimate posterior probabilities, conditional entropies, and mutual information even in the aforementioned settings.We provide an extensive study of efficacy for classification and posterior probability estimation, and prove certain forest-based approaches to be consistent estimators of the true posteriors and derived information-theoretic quantities under certain assumptions. In a real-world connectome application, we quantify the uncertainty about neuron type given various cellular features in the Drosophila larva mushroom body, a key challenge for modern neuroscience.

cs.LG↗

arXiv2019

Resource Constrained Neural Network Architecture Search: Will a Submodularity Assumption Help?

The design of neural network architectures is frequently either based on human expertise using trial/error and empirical feedback or tackled via large scale reinforcement learning strategies performed over distinct discrete architecture choices. In the latter case, the optimization is often non-differentiable and also not very amenable to derivative-free optimization methods. Most methods in use today require sizable computational resources. And if we want networks that additionally satisfy resource constraints, the above challenges are exacerbated because the search must now balance accuracy with certain budget constraints on resources. We formulate this problem as the optimization of a set function -- we find that the empirical behavior of this set function often (but not always) satisfies marginal gain and monotonicity principles -- properties central to the idea of submodularity. Based on this observation, we adapt algorithms within discrete optimization to obtain heuristic schemes for neural network architecture search, where we have resource constraints on the architecture. This simple scheme when applied on CIFAR-100 and ImageNet, identifies resource-constrained architectures with quantifiably better performance than current state-of-the-art models designed for mobile devices. Specifically, we find high-performing architectures with fewer parameters and computations by a search method that is much faster.

cs.CV↗