arXiv subjects

Soumojit Das

Publications and source records attributed to Soumojit Das.

5 recordsLinked to original sources

arXiv2026

Differential Privacy Guarantees in Small Area Estimation

Statistical agencies increasingly rely on small area estimation to produce reliable estimates for subpopulations with limited sample sizes. These estimates are built from individual survey responses, so agencies must ensure that releasing them does not reveal information about any single respondent. We show that when a single draw from the posterior distribution of the Bayesian Fay-Herriot model is released, pure $\varepsilon$-differential privacy is unattainable, but the release satisfies formal privacy guarantees under R\'enyi differential privacy and zero-concentrated differential privacy without any noise being added, provided we treat the variance components as fixed. The key insight is that the posterior draw equals the posterior mean plus the Gaussian noise whose variance equals the posterior variance. The guarantee is thus governed by the sensitivity of the direct survey estimate and the posterior variance, and applies equally to a release of the posterior mean with that amount of noise added. For binary outcomes estimated with the H\'ajek estimator, the sensitivity equals the largest survey weight in the area divided by the sum of the weights. For the intercept-only model we derive exact coefficients describing how a change in one record propagates to every area's posterior mean, giving finite-sample per-area guarantees and a joint guarantee for releasing all areas at once that exceeds the largest per-area guarantee by at most a few percent in our applications. Two applications, poverty prevalence across 2,462 Public Use Microdata Areas in the American Community Survey and smoking prevalence across 52 substrata in the Washington state Behavioral Risk Factor Surveillance System, show that the guarantee is driven far more by the inequality of the survey weights than by the sample size, and that the shrinkage of the model tightens it substantially.

stat.ME↗

arXiv2025

Geometric Calibration and Neutral Zones for Uncertainty-Aware Multi-Class Classification

Modern artificial intelligence systems make critical decisions yet often fail silently when uncertain -- even well-calibrated models provide no mechanism to identify \textit{which specific predictions} are unreliable. We develop a geometric framework addressing both calibration and instance-level uncertainty quantification for neural network probability outputs. Treating probability vectors as points on the $(c-1)$-dimensional probability simplex equipped with the Fisher--Rao metric, we construct: (i) Additive Log-Ratio (ALR) calibration maps that reduce exactly to Platt scaling for binary problems while extending naturally to multi-class settings, and (ii) geometric reliability scores that translate calibrated probabilities into actionable uncertainty measures, enabling principled deferral of ambiguous predictions to human review. Theoretical contributions include: consistency of the calibration estimator at rate $O_p(n^{-1/2})$ via M-estimation theory (Theorem~1), and tight concentration bounds for reliability scores with explicit sub-Gaussian parameters enabling sample size calculations for validation set design (Theorem~2). We conjecture Neyman--Pearson optimality of our neutral zone construction based on connections to Bhattacharyya coefficients. Empirical validation on Adeno-Associated Virus classification demonstrates that the two-stage framework captures 72.5\% of errors while deferring 34.5\% of samples, reducing automated decision error rates from 16.8\% to 6.9\%. Notably, calibration alone yields marginal accuracy gains; the operational benefit arises primarily from the reliability scoring mechanism, which applies to any well-calibrated probability output. This work bridges information geometry and statistical learning, offering formal guarantees for uncertainty-aware classification in applications requiring rigorous validation.

stat.ML↗

arXiv2025

Multidimensional Poverty Mapping for Small Areas

Many countries measure poverty based only on income or consumption. However, there is a growing awareness of measuring poverty through multiple dimensions that captures a more reasonable status of poverty. Estimating poverty measure(s) for small geographical areas, commonly referred to as poverty mapping, is challenging due to small or no sample for the small areas. While there is a huge literature available on unidimensional poverty mapping, only a limited effort has been made to address special challenges that arise only in the multidimensional poverty mapping. For example, in multidimensional poverty mapping, a new problem arises involving estimation of relative contributions of different dimensions to overall poverty for small areas. This problem has been grossly ignored in the small area estimation (SAE) literature. We address this issue using a multivariate hierarchical model implemented via a Bayesian method. Moreover, we demonstrate how a multidimensional poverty composite measure can be estimated for small areas. In this paper, we demonstrate our proposed methodology using a survey data specially designed by one of us for multidimensional poverty mapping. This paper adds a new direction to poverty mapping literature.

stat.ME↗

arXiv2022

Approximate hierarchical Bayes small area estimation using NEF-QVF and poststratification

We propose an approximate hierarchical Bayes approach that uses the Natural Exponential Family with Quadratic Variance Function in combining information from multiple sources to improve traditional survey estimates of finite population means for small areas. Unlike other Bayesian approaches in finite population sampling, we do not assume a model for all units of the finite population and do not require linking sampled units to the finite population frame. We assume a model only for the finite population units in which the outcome variable is observed; because, for these units, the assumed model can be checked using existing statistical tools. We do not posit an elaborate model on the true means for unobserved units. Instead, we assume that population means of cells with the same combination of factor levels are identical across small areas, and that the population mean for a cell is identical to the mean of the observed units in that cell. We apply our proposed methodology to a real-life survey, linking information from multiple disparate data sources. We also provide practical ways of model selection that can be applied to a wider class of models under similar setting but for a diverse range of scientific problems.

stat.ME↗

arXiv2022

Imputation under Differential Privacy

The literature on differential privacy almost invariably assumes that the data to be analyzed are fully observed. In most practical applications this is an unrealistic assumption. A popular strategy to address this problem is imputation, in which missing values are replaced by estimated values given the observed data. In this paper we evaluate various approaches to answering queries on an imputed dataset in a differentially private manner, as well as discuss trade-offs as to where along the pipeline privacy is considered. We show that if imputation is done without consideration to privacy, the sensitivity of certain queries can increase linearly with the number of incomplete records. On the other hand, for a general class of imputation strategies, these worst case scenarios can be greatly reduced by ensuring privacy already during the imputation stage. We use a simulated dataset to demonstrate these results across a number of imputation schemes (both private and non-private) and examine their impact on the utility of a private query on the data.

cs.DB↗