arXiv subjects

Aytijhya Saha

Publications and source records attributed to Aytijhya Saha.

10 recordsLinked to original sources

arXiv2026

Non-partitioned e-detectors for nonparametric sequential change detection

We study the problem of sequential change detection over a general class of probability distributions ($\mathcal P$), where both the pre-change and post-change distributions are unknown and belong to $\mathcal P$. We do not assume a pre-specified partition of $\mathcal P$ into pre- and post-change families. We propose a general class of sequential change detectors obtained by aggregating point-null e-processes over possible changepoints and taking an infimum over candidate no-change distributions. The weights in the aggregation scheme determine whether they attain average run length (ARL) control and probability-of-false-alarm (PFA) control. Under suitable assumptions, we prove that our methods achieve first-order asymptotically optimal detection delay. Concrete examples include sub-Gaussian and bounded mean changes, Gaussian mean changes with unknown variance, as well as changes in Markov transition matrices.

stat.ME↗

arXiv2026

Distribution-free changepoint localization after sequential change detection

This paper introduces a distribution-free framework for constructing post-detection confidence sets for changepoints after stopping a sequential change detection procedure. It is well known that conformal test martingales can be used to sequentially detect changes in distribution, but by themselves provide no inference for the time at which a proclaimed change occurred. Past work on post-detection inference requires pre- and post-change classes of distributions to be known, but this paper accomplishes localization of the changepoint without any distributional assumptions. We establish finite-sample coverage guarantees (conditional on correct detection). We provide non-asymptotic bounds on the conditional expected size of the confidence sets. Under suitable asymptotic regimes, we prove that the conditional expected size of the confidence set remains uniformly bounded and demonstrate strong empirical performance on simulated and real data. To the best of our knowledge, this is the first general distribution-free framework for sequential changepoint localization with valid post-detection coverage.

stat.ML↗

arXiv2026

Causal Inference with Categorical Unobserved Confounder via Mixture Learning

Unobserved confounding is a fundamental challenge for estimating causal effects. To address unobserved confounding, recent literature has turned to two different approaches -- proxy variables and the use of multiple treatments. The first approach, commonly referred to as proximal causal inference, requires proxies to be assigned to specific asymmetric roles: treatment-inducing proxies (negative control exposures), variables that act as common causes of the treatment and outcome, and outcome-inducing proxies (negative control outcomes). In practice, however, identifying variables that satisfy these asymmetric roles can be difficult depending on the application domain. The second approach, commonly referred to as the ``Deconfounder," deals with multiple conditionally independent treatments. There has been limited progress towards developing a consistent estimation method for this setting. As the primary contribution of this work, we establish that causal effects are identifiable in both settings when the unobserved confounder is categorical under suitable conditions. Our approach builds on a mixture learning perspective: we show that the underlying confounding structure can be recovered by identifying the corresponding mixture distribution. We propose an estimation procedure based on tensor decomposition, which allows consistent recovery of the latent structure and comes with non-asymptotic guarantees. Simulation studies and real data experiments demonstrate that the proposed method performs well even with limited data.

stat.ME↗

arXiv2026

Optimal e-variables under constraints

E-variables enable safe and anytime-valid inference, with log-optimal e-variables given by the likelihood ratio of the least favorable distributions (LFDs) when they exist in composite settings. While this unconstrained theory is well understood, one may need/wish to impose additional structural constraints, including differential privacy, quantization, boundedness, or moment restrictions. We show that under these constraints, log-optimal constrained e-variables can often be constructed by a simple \emph{optimize-then-constrain} principle: first compute the unconstrained log-optimal e-variable, then impose the constraint via an appropriate transformation. Thus, the constrained growth-rate optimization problem does not require solving for a different LFD pair; the constrained optimal solution is just a post-processing of the unconstrained optimal solution.

stat.ME↗

arXiv2025

Density estimation with atoms, and functional estimation for mixed discrete-continuous data

In classical density (or density-functional) estimation, it is standard to assume that the underlying distribution has a density with respect to the Lebesgue measure. However, when the data distribution is a mixture of continuous and discrete components, the resulting methods are inconsistent in theory and perform poorly in practice. In this paper, we point out that a minor modification of existing methods for nonparametric density (functional) estimation can allow us to fully remove this assumption while retaining nearly identical theoretical guarantees and improved empirical performance. Our approach is very simple: data points that appear exactly once are likely to originate from the continuous component, whereas repeated observations are indicative of the discrete part. Leveraging this observation, we modify existing estimators for a broad class of functionals of the continuous component of the mixture; this modification is a "wrapper" in the sense that the user can use any underlying method of their choice for continuous density functional estimation. Our modifications deliver consistency without requiring knowledge of the discrete support, the mixing proportion, and without imposing additional assumptions beyond those needed in the absence of the discrete part. Thus, various theorems and existing software packages can be made automatically more robust, with absolutely no additional price when the data is not truly mixed.

stat.ME↗

arXiv2025

Post-detection inference for sequential changepoint localization

This paper addresses a fundamental but largely unexplored challenge in sequential changepoint analysis: conducting inference following a detected change. We develop a very general framework to construct confidence sets for the unknown changepoint using only the data observed up to a data-dependent stopping time at which an arbitrary sequential detection algorithm declares a change. Our framework is nonparametric, making no assumption on the composite post-change class, the observation space, or the sequential detection procedure used, and is non-asymptotically valid. We also extend it to handle composite pre-change classes under a suitable assumption, and also derive confidence sets for the change magnitude in parametric settings. We provide theoretical guarantees on the width of our confidence intervals. Extensive simulations demonstrate that the produced sets have reasonable size, and slightly conservative coverage. In summary, we present the first general method for sequential changepoint localization, which is theoretically sound and broadly applicable in practice.

stat.ML↗

arXiv2024

Huber-robust likelihood ratio tests for composite nulls and alternatives

We propose an e-value based framework for testing arbitrary composite nulls against composite alternatives, when an $\epsilon$ fraction of the data can be arbitrarily corrupted. Our tests are inherently sequential, being valid at arbitrary data-dependent stopping times, but they are new even for fixed sample sizes, giving type-I error control without any regularity conditions. We first prove that least favourable distribution (LFD) pairs, when they exist, yield optimal e-values for testing arbitrary composite nulls against composite alternatives. Then we show that if an LFD pair exists for some composite null and alternative, then the LFDs of Huber's $\epsilon$-contamination or total variation (TV) neighborhoods around that specific pair form the optimal LFD pair for the corresponding robustified composite hypotheses. Furthermore, where LFDs do not exist, we develop new robust composite tests for general settings. Our test statistics are a nonnegative supermartingale under the (robust) null, even under a sequentially adaptive (non-i.i.d.) contamination model where the conditional distribution of each observation given the past data lies within an $\epsilon$ TV ball of some distribution in the original composite null. When LFDs exist, our supermartingale grows to infinity exponentially fast under any distribution in the ($\epsilon$ TV-corruption of the) alternative at the optimal rate. When LFDs do not exist, we provide an asymptotic growth rate analysis, showing that as $\epsilon \to 0$, the exponent converges to the corresponding Kullback-Leibler divergence, recovering the classical optimal non-robust rate. Simulations validate the theory and demonstrate reasonable practical performance.

stat.ME↗

arXiv2023

Group-Feature (Sensor) Selection With Controlled Redundancy Using Neural Networks

In this paper, we present a novel embedded feature selection method based on a Multi-layer Perceptron (MLP) network and generalize it for group-feature or sensor selection problems, which can control the level of redundancy among the selected features or groups. Additionally, we have generalized the group lasso penalty for feature selection to encompass a mechanism for selecting valuable group features while simultaneously maintaining a control over redundancy. We establish the monotonicity and convergence of the proposed algorithm, with a smoothed version of the penalty terms, under suitable assumptions. Experimental results on several benchmark datasets demonstrate the promising performance of the proposed methodology for both feature selection and group feature selection over some state-of-the-art methods.

cs.LG↗

arXiv2023

Testing exchangeability by pairwise betting

In this paper, we address the problem of testing exchangeability of a sequence of random variables, $X_1, X_2,\cdots$. This problem has been studied under the recently popular framework of testing by betting. But the mapping of testing problems to game is not one to one: many games can be designed for the same test. Past work established that it is futile to play single game betting on every observation: test martingales in the data filtration are powerless. Two avenues have been explored to circumvent this impossibility: betting in a reduced filtration (wealth is a test martingale in a coarsened filtration), or playing many games in parallel (wealth is an e-process in the data filtration). The former has proved to be difficult to theoretically analyze, while the latter only works for binary or discrete observation spaces. Here, we introduce a different approach that circumvents both drawbacks. We design a new (yet simple) game in which we observe the data sequence in pairs. Despite the fact that betting on individual observations is futile, we show that betting on pairs of observations is not. To elaborate, we prove that our game leads to a nontrivial test martingale, which is interesting because it has been obtained by shrinking the filtration very slightly. We show that our test controls type-1 error despite continuous monitoring, and achieves power one for both binary and continuous observations, under a broad class of alternatives. Due to the shrunk filtration, optional stopping is only allowed at even stopping times, not at odd ones: a relatively minor price. We provide a wide array of simulations that align with our theoretical findings.

stat.ME↗

arXiv2023

Robust Classification of High-Dimensional Data using Data-Adaptive Energy Distance

Classification of high-dimensional low sample size (HDLSS) data poses a challenge in a variety of real-world situations, such as gene expression studies, cancer research, and medical imaging. This article presents the development and analysis of some classifiers that are specifically designed for HDLSS data. These classifiers are free of tuning parameters and are robust, in the sense that they are devoid of any moment conditions of the underlying data distributions. It is shown that they yield perfect classification in the HDLSS asymptotic regime, under some fairly general conditions. The comparative performance of the proposed classifiers is also investigated. Our theoretical results are supported by extensive simulation studies and real data analysis, which demonstrate promising advantages of the proposed classification techniques over several widely recognized methods.

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