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Sakshi Arya

Publications and source records attributed to Sakshi Arya.

12 recordsLinked to original sources
arXiv2026

Beyond Landmark Extraction: A Framework for Robust Geometric Feature Construction in Structured Image Classification

Much of the literature on structured image recognition has disproportionately focused on the comparison of classification algorithms. Rather than investigating which classifier performs best, this paper instead asks: what should a classifier know before it ever makes a prediction? In structured vision problems such as gesture recognition, facial expression categorization, and medical image analysis, discriminative information lies less in individual pixels and more in spatial relationships between semantic parts. Raw pixel spaces are high-dimensional, sensitive to nuisance variation, and often obfuscate the geometric structures that make visual tasks interpretable. Landmark extraction provides one form of dimension reduction, but it does not by itself determine the information preserved. This paper studies the post-landmark feature map as the central object of analysis and proposes a systematic framework for constructing and interpreting landmark-derived representations as an, informed, feature-based "dimension reduction" step. Using static hand gesture recognition as a case study, we evaluate coordinate, distance, angle, and hybrid representations through perturbation and ablation experiments. The results show that visually variable data exposes substantial gaps between raw coordinate features and their geometrically invariant counterparts, while hybrid representations achieve the strongest overall performance by combining complementary geometric components. These findings frame feature construction as a fundamental modeling decision and ultimately suggests that the question of what representation should a classifier learn from is one worth asking. The code used for feature construction and evaluation is available at https://github.com/ShivMaureeCWRU/Feature_based_dimension_reduction

cs.CV↗
arXiv2026

An Efficient Bayesian Framework for Uncertainty Quantification in Nonlinear Imaging Inverse Problems

Bayesian methods provide a natural framework for estimating a parameter in non-linear inverse problems and quantifying uncertainty in the estimation. However, when the forward model for such non-linear inverse problems is given by some Partial Differential Equation (PDE), Bayesian inference is typically carried out by resorting to MCMC methods. Since each MCMC iteration requires solving a PDE, these methods become computationally expensive and are often impractical for large-scale imaging problems. In this work, we develop a computationally efficient Bayesian framework for two such nonlinear imaging inverse problems: Quantitative Photoacoustic Tomography (QPAT) and Electrical Impedance Tomography (EIT). Building on a recently proposed two-stage pushforward methodology, we first formulate a Bayesian regression problem for an auxiliary variable whose posterior is available in closed form. This posterior is then pushed forward through a deterministic reconstruction map to obtain a posterior on the unknown parameter, avoiding MCMC sampling. We give a rigorous measure-theoretic justification to interpret the induced posterior as a Bayesian posterior and derive posterior contraction rates for both QPAT and EIT. Numerical results show that the proposed method provides accurate reconstructions and reliable uncertainty estimates at a arguably lower computational cost than standard Bayesian approaches.

math.ST↗
arXiv2026

Near-Optimal Nitrogen Recommendations for Precision Agriculture via Sequential Screening and Hierarchical Refinement

Nitrogen fertilizer management plays a central role in balancing agricultural productivity and environmental sustainability, yet identifying optimal application strategies remains difficult because treatment responses vary substantially across locations and many fertilizer choices are statistically indistinguishable near the optimum. This paper develops a hierarchical refinement procedure, built on sequential screening, for fertilizer recommendation in multi-site experiments that explicitly accounts for spatial heterogeneity while prioritizing parsimonious, decision-oriented selection. Rather than targeting a single estimated best treatment, the proposed method first conducts sequential screening at a higher aggregation level to eliminate clearly inferior fertilizer choices and then refines recommendations locally among the surviving candidates. We study the asymptotic properties of the proposed estimators and show that it provides screening-safety guaranteed recommendations. The efficacy of the new approach is investigated through a multi-state, multi-year corn nitrogen trial. The results show that no single fertilizer regime is uniformly optimal within a state; instead, each state is associated with multiple recommended choices, and the most common recommendation typically covers only about one-third to one-half of decision units, underscoring substantial within-state heterogeneity. Representative site-level comparisons further demonstrate that the proposed method often yields lower total nitrogen recommendations than state-level or hindsight benchmarks while maintaining competitive agronomic performance.

stat.ME↗
arXiv2026

Kernel Single-Index Bandits: Estimation, Inference, and Learning

We study contextual bandits with finitely many actions in which the reward of each arm follows a single-index model with an arm-specific index parameter and an unknown nonparametric link function. We consider a regime in which arms correspond to stable decision options and covariates evolve adaptively under the bandit policy. This setting creates significant statistical challenges: the sampling distribution depends on the allocation rule, observations are dependent over time, and inverse-propensity weighting induces variance inflation. We propose a kernelized $\varepsilon$-greedy algorithm that combines Stein-based estimation of the index parameters with inverse-propensity-weighted kernel ridge regression for the reward functions. This approach enables flexible semiparametric learning while retaining interpretability. Our analysis develops new tools for inference with adaptively collected data. We establish asymptotic normality for the single-index estimator under adaptive sampling, yielding valid confidence regions, and derive a directional functional central limit theorem for the RKHS estimator, which provides asymptotically valid pointwise confidence intervals. The analysis relies on concentration bounds for inverse-weighted Gram matrices together with martingale central limit theorems. We further obtain finite-time regret guarantees, including $\tilde{O}(\sqrt{T})$ rates under common-link Lipschitz conditions, showing that semiparametric structure can be exploited without sacrificing statistical efficiency. These results provide a unified framework for simultaneous learning and inference in single-index contextual bandits.

stat.ML↗
arXiv2025

Non-Linear Model-Based Sequential Decision-Making in Agriculture

Agricultural decision-making faces a dual challenge: sustaining high yields to meet global food security needs while reducing the environmental impacts of input use, including fertilizer losses and other agrochemical applications such as herbicides, insecticides, and fungicides. Nitrogen inputs are central to this tension. They are indispensable for crop growth yet major drivers of greenhouse gas emissions, nutrient runoff, and escalating production costs. Addressing these intertwined pressures requires adaptive decision-support tools that are statistically principled, economically sustainable and interpretable for practitioners. We develop nonlinear model-based bandit algorithms as a framework for adaptive fertilizer management under uncertainty. Building on classical mechanistic yield-response models, our approach links algorithmic exploration-exploitation strategies directly to interpretable biological processes such as maximum yield and nutrient efficiency. This grounding makes recommendations transparent for practitioners while supporting cost-effective and sustainable input use. Methodologically, we establish regret and sample complexity results for the well-specified nonlinear case, examine robustness under misspecification, and evaluate the proposed methods through profit-oriented simulations and an offline replay case study on publicly available multi-site corn nitrogen field trials from the U.S. Midwest. The results show that incorporating biologically meaningful mechanistic structure enables faster learning and higher profit as evidence accumulates, with flexible nonparametric baselines providing a competitive alternative in pooled and heterogeneous settings. Our findings illustrate how interpretable, uncertainty-aware sequential decision rules can support economically sustainable fertilizer recommendations and contribute to more efficient agricultural input use.

stat.ML↗
arXiv2025

Batched Nonparametric Bandits via k-Nearest Neighbor UCB

We study sequential decision-making in batched nonparametric contextual bandits, where actions are selected over a finite horizon divided into a small number of batches. Motivated by constraints in domains such as medicine and marketing -- where online feedback is limited -- we propose a nonparametric algorithm that combines adaptive k-nearest neighbor (k-NN) regression with the upper confidence bound (UCB) principle. Our method, BaNk-UCB, is fully nonparametric, adapts to the context dimension, and is simple to implement. Unlike prior work relying on parametric or binning-based estimators, BaNk-UCB uses local geometry to estimate rewards and adaptively balances exploration and exploitation. We provide near-optimal regret guarantees under standard Lipschitz smoothness and margin assumptions, using a theoretically motivated batch schedule that balances regret across batches and achieves minimax-optimal rates. Empirical evaluations on synthetic and real-world datasets demonstrate that BaNk-UCB consistently outperforms binning-based baselines.

stat.ML↗
arXiv2025

Predictions of damages from Atlantic tropical cyclones: a hierarchical Bayesian study on extremes

Bayesian hierarchical models are proposed for modeling tropical cyclone characteristics and their damage potential in the Atlantic basin. We model the joint probability distribution of tropical cyclone characteristics and their damage potential at two different temporal scales, while taking several climate indices into account. First, a predictive model for an entire season is developed that forecasts the number of cyclone events that will take place, the probability of each cyclone causing some amount of damage, and the monetized value of damages. Then, specific characteristics of individual cyclones are considered to predict the monetized value of the damage it will cause. Robustness studies are conducted and excellent prediction power is demonstrated across different data science models and evaluation techniques.

stat.AP↗
arXiv2025

Kernel $ε$-Greedy for Multi-Armed Bandits with Covariates

We consider the $ε$-greedy strategy for the multi-arm bandit with covariates (MABC) problem, where the mean reward functions are assumed to lie in a reproducing kernel Hilbert space (RKHS). We propose to estimate the unknown mean reward functions using an online weighted kernel ridge regression estimator, and show the resultant estimator to be consistent under appropriate decay rates of the exploration probability sequence, $\{ε_t\}_t$, and regularization parameter, $\{λ_t\}_t$. Moreover, we show that for any choice of kernel and the corresponding RKHS, we achieve a sub-linear regret rate depending on the intrinsic dimensionality of the RKHS. Furthermore, we achieve the optimal regret rate of $\sqrt{T}$ under a margin condition for finite-dimensional RKHS.

stat.ML↗
arXiv2025

Batched Single-Index Global Multi-Armed Bandits with Covariates

The multi-armed bandits (MAB) framework is a widely used approach for sequential decision-making, where a decision-maker selects an arm in each round with the goal of maximizing long-term rewards. In many practical applications, such as personalized medicine and recommendation systems, contextual information is available at the time of decision-making, rewards from different arms are related rather than independent, and feedback is provided in batches. We propose a novel semi-parametric framework for batched bandits with covariates that incorporates a shared parameter across arms. We leverage the single-index regression (SIR) model to capture relationships between arm rewards while balancing interpretability and flexibility. Our algorithm, Batched single-Index Dynamic binning and Successive arm elimination (BIDS), employs a batched successive arm elimination strategy with a dynamic binning mechanism guided by the single-index direction. We consider two settings: one where a pilot direction is available and another where the direction is estimated from data, deriving theoretical regret bounds for both cases. When a pilot direction is available with sufficient accuracy and the number of arms $K$ is fixed, our approach achieves minimax-optimal rates (with $d = 1$) for nonparametric batched bandits, circumventing the curse of dimensionality. Extensive experiments on simulated and real-world datasets demonstrate the effectiveness of our algorithm compared to the nonparametric batched bandit method introduced by \cite{jiang2025batched}.

stat.ML↗
arXiv2020

Adaptive estimation of a function from its Exponential Radon Transform in presence of noise

In this article we propose a locally adaptive strategy for estimating a function from its Exponential Radon Transform (ERT) data, without prior knowledge of the smoothness of functions that are to be estimated. We build a non-parametric kernel type estimator and show that for a class of functions comprising a wide Sobolev regularity scale, our proposed strategy follows the minimax optimal rate up to a $\log{n}$ factor. We also show that there does not exist an optimal adaptive estimator on the Sobolev scale when the pointwise risk is used and in fact the rate achieved by the proposed estimator is the adaptive rate of convergence.

math.ST↗
arXiv2020

To update or not to update? Delayed Nonparametric Bandits with Randomized Allocation

Delayed rewards problem in contextual bandits has been of interest in various practical settings. We study randomized allocation strategies and provide an understanding on how the exploration-exploitation tradeoff is affected by delays in observing the rewards. In randomized strategies, the extent of exploration-exploitation is controlled by a user-determined exploration probability sequence. In the presence of delayed rewards, one may choose between using the original exploration sequence that updates at every time point or update the sequence only when a new reward is observed, leading to two competing strategies. In this work, we show that while both strategies may lead to strong consistency in allocation, the property holds for a wider scope of situations for the latter. However, for finite sample performance, we illustrate that both strategies have their own advantages and disadvantages, depending on the severity of the delay and underlying reward generating mechanisms.

stat.ML↗