arXiv subjects

Gautam Dasarathy

Publications and source records attributed to Gautam Dasarathy.

At least 19 recordsLinked to original sources

arXiv2026

Mixing-Free and Signal-Optimal Learning of Gaussian Graphical Models from Glauber Dynamics

Gaussian graphical model selection is usually studied under independent sampling, but in many applications the data arise as a single trajectory of a dependent stochastic process. We study exact recovery of the graph from one trajectory of random-scan Gaussian Glauber dynamics. Existing techniques for this problem either inherit the mixing time of the chain, which can be super-polynomial in the dimension $p$ without strong assumptions, or are suboptimal in the minimum normalized edge strength $κ$. We propose two algorithms that are mixing-free and attain the $κ^{-2}$ dependence of the information-theoretic lower bounds. Both instantiate a shared dueling-neighborhood search meta-algorithm with a local statistic built directly from the update sequence. For every fixed precision matrix and deterministic initialization, the first algorithm fits a least-squares regression at the updates of each node and has pointwise recovery horizon $\widetilde O(pd^{2}/κ^{2})$, where $d$ is the maximum degree. Its horizon depends logarithmically on a local conditioning quantity and on the initialization potential. The second algorithm is based on counting occurences of a specific update pattern and requires $\widetilde O(pd^{4}/κ^{2})$ updates, with no dependence on any condition number. The central technical challenge is that both statistics are built from dependent, non-stationary observations. Our analysis tackles this by demonstrating how to extract fresh Gaussian innovations from the update sequence, which yields mixing-free control of appropriate quantities. Neither the algorithms nor their analyses invoke stationarity, a spectral gap, or mixing conditions.

stat.ML↗

arXiv2026

Stochastic Linear Bandits with Partially Observed Actions

The stochastic linear bandit, where actions are represented as vectors and rewards are linear, is a central paradigm for sequential decision making. We study a partially observed variant of this problem in which the learning agent only sees a random subset of coordinates for each action. Such partial observability arises naturally in settings like recommendation and healthcare, where full action descriptions can be expensive or even impossible to obtain. In general, this makes sublinear regret information-theoretically impossible. However, we show that this barrier can be overcome when the action vectors have low intrinsic dimension. We propose an algorithm, TOFU-POV, that estimates the latent action subspace using the masked actions, imputes current actions using an epoch-wise frozen representation, and runs OFUL in the resulting low-dimensional coordinates. Our theory shows that TOFU-POV enjoys a $\sqrt{T}$ regret that scales with the intrinsic action subspace dimension as opposed to the ambient dimension and quantifies the interaction between these quantities and the missingness, decision set size, and subspace conditioning. We also devise a rank-adaptive algorithm that does not require the knowledge of the intrinsic dimension. We complement these guarantees with a lower bound based on a novel product construction that separates usual reward-learning uncertainty from a missingness-dependent cost intrinsic to partial observation. Synthetic and real data experiments support our theory and show that TOFU-POV can substantially improve upon natural baselines in this challenging problem.

cs.LG↗

arXiv2026

Local and Mixing-Based Algorithms for Gaussian Graphical Model Selection from Glauber Dynamics

Gaussian graphical model selection is usually studied under independent sampling, but in many applications observations arise from dependent dynamics. We study structure learning when the data consist of a single trajectory of Gaussian Glauber dynamics. We develop two complementary approaches. The first is a local edge-testing estimator based on an appropriately designed correlation test that reveals edges. This estimator does not require waiting for the chain to mix and admits an embarrassingly parallel edgewise implementation. The second is a burn-in/thinning reduction: under a Dobrushin contraction condition, we prove that a suitably subsampled Gaussian Gibbs trajectory is close in total variation to an i.i.d. product sample, allowing standard i.i.d. Gaussian graphical model learners to be used as black boxes. The key technical ingredient, which may be of independent interest, is a high-dimensional total-variation bound for random-scan Gaussian Gibbs samplers, obtained by combining Wasserstein contraction with an approximate Lipschitz smoothing argument. We prove finite-sample recovery guarantees for both approaches, establish information-theoretic lower bounds on the observation time, and empirically compare the resulting sample-computation tradeoffs.

cs.LG↗

arXiv2026

Statistically Valid Post-Deployment Monitoring Should Be Standard for AI-Based Digital Health

This position paper argues that post-deployment monitoring in clinical AI is underdeveloped and proposes statistically valid and label-efficient testing frameworks as a principled foundation for ensuring reliability and safety in real-world deployment. A recent review found that only 9% of FDA-registered AI-based healthcare tools include a post-deployment surveillance plan. Existing monitoring approaches are often manual, sporadic, and reactive, making them ill-suited for the dynamic environments in which clinical models operate. We contend that post-deployment monitoring should be grounded in label-efficient and statistically valid testing frameworks, offering a principled alternative to current practices. We use the term "statistically valid" to refer to methods that provide explicit guarantees on error rates (e.g., Type I/II error), enable formal inference under pre-defined assumptions, and support reproducibility--features that align with regulatory requirements. Specifically, we propose that the detection of changes in the data and model performance degradation should be framed as distinct statistical hypothesis testing problems. Grounding monitoring in statistical rigor ensures a reproducible and scientifically sound basis for maintaining the reliability of clinical AI systems. Importantly, it also opens new research directions for the technical community--spanning theory, methods, and tools for statistically principled detection, attribution, and mitigation of post-deployment model failures in real-world settings.

cs.LG↗

arXiv2025

Matched-Pair Experimental Design with Active Learning

Matched-pair experimental designs aim to detect treatment effects by pairing participants and comparing within-pair outcome differences. In many situations, the overall effect size across the entire population is small. Then, the focus naturally shifts to identifying and targeting high treatment-effect regions where the intervention is most effective. This paper proposes a matched-pair experimental design that sequentially and actively enrolls patients in high treatment-effect regions. Importantly, we frame the identification of the target region as a classification problem and propose an active learning framework tailored to matched-pair designs. Our design not only reduces the experimental cost of detecting treatment efficacy, but also ensures that the identified regions enclose the entire high-treatment-effect regions. Our theoretical analysis of the framework's label complexity and experiments in practical scenarios demonstrate the efficiency and advantages of the approach.

cs.LG↗

arXiv2025

Learning Networks from Wide-Sense Stationary Stochastic Processes

Complex networked systems driven by latent inputs are common in fields like neuroscience, finance, and engineering. A key inference problem here is to learn edge connectivity from node outputs (potentials). We focus on systems governed by steady-state linear conservation laws: $X_t = {L^{\ast}}Y_{t}$, where $X_t, Y_t \in \mathbb{R}^p$ denote inputs and potentials, respectively, and the sparsity pattern of the $p \times p$ Laplacian $L^{\ast}$ encodes the edge structure. Assuming $X_t$ to be a wide-sense stationary stochastic process with a known spectral density matrix, we learn the support of $L^{\ast}$ from temporally correlated samples of $Y_t$ via an $\ell_1$-regularized Whittle's maximum likelihood estimator (MLE). The regularization is particularly useful for learning large-scale networks in the high-dimensional setting where the network size $p$ significantly exceeds the number of samples $n$. We show that the MLE problem is strictly convex, admitting a unique solution. Under a novel mutual incoherence condition and certain sufficient conditions on $(n, p, d)$, we show that the ML estimate recovers the sparsity pattern of $L^\ast$ with high probability, where $d$ is the maximum degree of the graph underlying $L^{\ast}$. We provide recovery guarantees for $L^\ast$ in element-wise maximum, Frobenius, and operator norms. Finally, we complement our theoretical results with several simulation studies on synthetic and benchmark datasets, including engineered systems (power and water networks), and real-world datasets from neural systems (such as the human brain).

stat.ML↗

arXiv2025

Advanced Tutorial: Label-Efficient Two-Sample Tests

Hypothesis testing is a statistical inference approach used to determine whether data supports a specific hypothesis. An important type is the two-sample test, which evaluates whether two sets of data points are from identical distributions. This test is widely used, such as by clinical researchers comparing treatment effectiveness. This tutorial explores two-sample testing in a context where an analyst has many features from two samples, but determining the sample membership (or labels) of these features is costly. In machine learning, a similar scenario is studied in active learning. This tutorial extends active learning concepts to two-sample testing within this \textit{label-costly} setting while maintaining statistical validity and high testing power. Additionally, the tutorial discusses practical applications of these label-efficient two-sample tests.

cs.LG↗

arXiv2024

Communication-Efficient Federated Learning over Wireless Channels via Gradient Sketching

Large-scale federated learning (FL) over wireless multiple access channels (MACs) has emerged as a crucial learning paradigm with a wide range of applications. However, its widespread adoption is hindered by several major challenges, including limited bandwidth shared by many edge devices, noisy and erroneous wireless communications, and heterogeneous datasets with different distributions across edge devices. To overcome these fundamental challenges, we propose Federated Proximal Sketching (FPS), tailored towards band-limited wireless channels and handling data heterogeneity across edge devices. FPS uses a count sketch data structure to address the bandwidth bottleneck and enable efficient compression while maintaining accurate estimation of significant coordinates. Additionally, we modify the loss function in FPS such that it is equipped to deal with varying degrees of data heterogeneity. We establish the convergence of the FPS algorithm under mild technical conditions and characterize how the bias induced due to factors like data heterogeneity and noisy wireless channels play a role in the overall result. We complement the proposed theoretical framework with numerical experiments that demonstrate the stability, accuracy, and efficiency of FPS in comparison to state-of-the-art methods on both synthetic and real-world datasets. Overall, our results show that FPS is a promising solution to tackling the above challenges of FL over wireless MACs.

cs.LG↗

arXiv2024

Unraveling overoptimism and publication bias in ML-driven science

Machine Learning (ML) is increasingly used across many disciplines with impressive reported results. However, recent studies suggest published performance of ML models are often overoptimistic. Validity concerns are underscored by findings of an inverse relationship between sample size and reported accuracy in published ML models, contrasting with the theory of learning curves where accuracy should improve or remain stable with increasing sample size. This paper investigates factors contributing to overoptimism in ML-driven science, focusing on overfitting and publication bias. We introduce a novel stochastic model for observed accuracy, integrating parametric learning curves and the aforementioned biases. We construct an estimator that corrects for these biases in observed data. Theoretical and empirical results show that our framework can estimate the underlying learning curve, providing realistic performance assessments from published results. Applying the model to meta-analyses of classifications of neurological conditions, we estimate the inherent limits of ML-based prediction in each domain.

cs.LG↗

arXiv2024

Active Sequential Two-Sample Testing

A two-sample hypothesis test is a statistical procedure used to determine whether the distributions generating two samples are identical. We consider the two-sample testing problem in a new scenario where the sample measurements (or sample features) are inexpensive to access, but their group memberships (or labels) are costly. To address the problem, we devise the first \emph{active sequential two-sample testing framework} that not only sequentially but also \emph{actively queries}. Our test statistic is a likelihood ratio where one likelihood is found by maximization over all class priors, and the other is provided by a probabilistic classification model. The classification model is adaptively updated and used to predict where the (unlabelled) features have a high dependency on labels; labeling the ``high-dependency'' features leads to the increased power of the proposed testing framework. In theory, we provide the proof that our framework produces an \emph{anytime-valid} $p$-value. In addition, we characterize the proposed framework's gain in testing power by analyzing the mutual information between the feature and label variables in asymptotic and finite-sample scenarios. In practice, we introduce an instantiation of our framework and evaluate it using several experiments; the experiments on the synthetic, MNIST, and application-specific datasets demonstrate that the testing power of the instantiated active sequential test significantly increases while the Type I error is under control.

cs.LG↗

arXiv2024

On Characterizations of Potential and Ordinal Potential Games

This paper investigates some necessary and sufficient conditions for a game to be a potential game. At first, we extend the classical results of Slade and Monderer and Shapley from games with one-dimensional action spaces to games with multi-dimensional action spaces, which require differentiable cost functions. Then, we provide a necessary and sufficient conditions for a game to have a potential function by investigating the structure of a potential function in terms of the players' cost differences, as opposed to differentials. This condition provides a systematic way for construction of a potential function, which is applied to network congestion games, as an example. Finally, we provide some sufficient conditions for a game to be ordinal potential and generalized ordinal potential.

cs.GT↗

arXiv2024

Robust Model Selection of Gaussian Graphical Models

In Gaussian graphical model selection, noise-corrupted samples present significant challenges. It is known that even minimal amounts of noise can obscure the underlying structure, leading to fundamental identifiability issues. A recent line of work addressing this "robust model selection" problem narrows its focus to tree-structured graphical models. Even within this specific class of models, exact structure recovery is shown to be impossible. However, several algorithms have been developed that are known to provably recover the underlying tree-structure up to an (unavoidable) equivalence class. In this paper, we extend these results beyond tree-structured graphs. We first characterize the equivalence class up to which general graphs can be recovered in the presence of noise. Despite the inherent ambiguity (which we prove is unavoidable), the structure that can be recovered reveals local clustering information and global connectivity patterns in the underlying model. Such information is useful in a range of real-world problems, including power grids, social networks, protein-protein interactions, and neural structures. We then propose an algorithm which provably recovers the underlying graph up to the identified ambiguity. We further provide finite sample guarantees in the high-dimensional regime for our algorithm and validate our results through numerical simulations.

stat.ML↗

arXiv2023

Graph quilting: graphical model selection from partially observed covariances

Graphical model selection is a seemingly impossible task when many pairs of variables are never jointly observed; this requires inference of conditional dependencies with no observations of corresponding marginal dependencies. This under-explored statistical problem arises in neuroimaging, for example, when different partially overlapping subsets of neurons are recorded in non-simultaneous sessions. We call this statistical challenge the "Graph Quilting" problem. We study this problem in the context of sparse inverse covariance learning, and focus on Gaussian graphical models where we show that missing parts of the covariance matrix yields an unidentifiable precision matrix specifying the graph. Nonetheless, we show that, under mild conditions, it is possible to correctly identify edges connecting the observed pairs of nodes. Additionally, we show that we can recover a minimal superset of edges connecting variables that are never jointly observed. Thus, one can infer conditional relationships even when marginal relationships are unobserved, a surprising result! To accomplish this, we propose an $\ell_1$-regularized partially observed likelihood-based graph estimator and provide performance guarantees in population and in high-dimensional finite-sample settings. We illustrate our approach using synthetic data, as well as for learning functional neural connectivity from calcium imaging data.

math.ST↗

arXiv2023

Differential Analysis for Networks Obeying Conservation Laws

Networked systems that occur in various domains, such as the power grid, the brain, and opinion networks, are known to obey conservation laws. For instance, electric networks obey Kirchoff's laws, and social networks display opinion consensus. Such conservation laws are often modeled as balance equations that relate appropriate injected flows and potentials at the nodes of the networks. A recent line of work considers the problem of estimating the unknown structure of such networked systems from observations of node potentials (and only the knowledge of the statistics of injected flows). Given the dynamic nature of the systems under consideration, an equally important task is estimating the change in the structure of the network from data -- the so called differential network analysis problem. That is, given two sets of node potential observations, the goal is to estimate the structural differences between the underlying networks. We formulate this novel differential network analysis problem for systems obeying conservation laws and devise a convex estimator to learn the edge changes directly from node potentials. We derive conditions under which the estimate is unique in the high-dimensional regime and devise an efficient ADMM-based approach to perform the estimation. Finally, we demonstrate the performance of our approach on synthetic and benchmark power network data.

eess.SY↗

arXiv2022

A Tunable Loss Function for Robust Classification: Calibration, Landscape, and Generalization

We introduce a tunable loss function called $α$-loss, parameterized by $α\in (0,\infty]$, which interpolates between the exponential loss ($α= 1/2$), the log-loss ($α= 1$), and the 0-1 loss ($α= \infty$), for the machine learning setting of classification. Theoretically, we illustrate a fundamental connection between $α$-loss and Arimoto conditional entropy, verify the classification-calibration of $α$-loss in order to demonstrate asymptotic optimality via Rademacher complexity generalization techniques, and build-upon a notion called strictly local quasi-convexity in order to quantitatively characterize the optimization landscape of $α$-loss. Practically, we perform class imbalance, robustness, and classification experiments on benchmark image datasets using convolutional-neural-networks. Our main practical conclusion is that certain tasks may benefit from tuning $α$-loss away from log-loss ($α= 1$), and to this end we provide simple heuristics for the practitioner. In particular, navigating the $α$ hyperparameter can readily provide superior model robustness to label flips ($α> 1$) and sensitivity to imbalanced classes ($α< 1$).

cs.LG↗

arXiv2022

Maximizing and Satisficing in Multi-armed Bandits with Graph Information

Pure exploration in multi-armed bandits has emerged as an important framework for modeling decision-making and search under uncertainty. In modern applications, however, one is often faced with a tremendously large number of options. Even obtaining one observation per option may be too costly rendering traditional pure exploration algorithms ineffective. Fortunately, one often has access to similar relationships amongst the options that can be leveraged. In this paper, we consider the pure exploration problem in stochastic multi-armed bandits where the similarities between the arms are captured by a graph and the rewards may be represented as a smooth signal on this graph. In particular, we consider the problem of finding the arm with the maximum reward (i.e., the maximizing problem) or one with a sufficiently high reward (i.e., the satisficing problem) under this model. We propose novel algorithms \textbf{\algoname{}} (GRaph-based UcB) and $ζ$-\textbf{\algoname{}} for these problems and provide a theoretical characterization of their performance which specifically elicits the benefit of the graph side information. We also prove a lower bound on the data requirement, showing a large class of problems where these algorithms are near-optimal. We complement our theory with experimental results that show the benefit of capitalizing on such side information.

cs.LG↗

arXiv2022

A Machine Learning Framework for Event Identification via Modal Analysis of PMU Data

Power systems are prone to a variety of events (e.g. line trips and generation loss) and real-time identification of such events is crucial in terms of situational awareness, reliability, and security. Using measurements from multiple synchrophasors, i.e., phasor measurement units (PMUs), we propose to identify events by extracting features based on modal dynamics. We combine such traditional physics-based feature extraction methods with machine learning to distinguish different event types. Including all measurement channels at each PMU allows exploiting diverse features but also requires learning classification models over a high-dimensional space. To address this issue, various feature selection methods are implemented to choose the best subset of features. Using the obtained subset of features, we investigate the performance of two well-known classification models, namely, logistic regression (LR) and support vector machines (SVM) to identify generation loss and line trip events in two datasets. The first dataset is obtained from simulated generation loss and line trip events in the Texas 2000-bus synthetic grid. The second is a proprietary dataset with labeled events obtained from a large utility in the USA involving measurements from nearly 500 PMUs. Our results indicate that the proposed framework is promising for identifying the two types of events.

eess.SY↗

arXiv2022

Transmission Line Parameter Estimation Under Non-Gaussian Measurement Noise

Accurate knowledge of transmission line parameters is essential for a variety of power system monitoring, protection, and control applications. The use of phasor measurement unit (PMU) data for transmission line parameter estimation (TLPE) is well-documented. However, existing literature on PMU-based TLPE implicitly assumes the measurement noise to be Gaussian. Recently, it has been shown that the noise in PMU measurements (especially in the current phasors) is better represented by Gaussian mixture models (GMMs), i.e., the noises are non-Gaussian. We present a novel approach for TLPE that can handle non-Gaussian noise in the PMU measurements. The measurement noise is expressed as a GMM, whose components are identified using the expectation-maximization (EM) algorithm. Subsequently, noise and parameter estimation is carried out by solving a maximum likelihood estimation problem iteratively until convergence. The superior performance of the proposed approach over traditional approaches such as least squares and total least squares as well as the more recently proposed minimum total error entropy approach is demonstrated by performing simulations using the IEEE 118-bus system as well as proprietary PMU data obtained from a U.S. power utility.

eess.SP↗