arXiv subjects

Soham Bakshi

Publications and source records attributed to Soham Bakshi.

7 recordsLinked to original sources

arXiv2026

Selective Inference for Time-Varying Moderated Effects

Causal effect moderation investigates how the effect of interventions (or treatments) on outcome variables changes based on observed characteristics of individuals, known as potential effect moderators. With advances in data collection, datasets containing many observed features as potential moderators have become increasingly common. High-dimensional analyses often lack interpretability, with important moderators masked by noise, while low-dimensional, marginal analyses yield many false positives due to strong correlations with true moderators. In this paper, we propose a two-step method for selective inference on time-varying causal effect moderation that addresses the limitations of both high-dimensional and marginal analyses. Our method first selects a relatively smaller, more interpretable model to estimate a linear causal effect moderation using a Gaussian randomization approach. We then condition on the selection event to construct a pivot, enabling uniformly asymptotic semi-parametric inference in the selected model. Our numerical results show that our method achieves valid coverage rates, even when existing conditional methods and common sample splitting techniques fail. Moreover, our method yields shorter, bounded intervals, unlike existing methods that may produce infinitely long intervals.

stat.ME↗

arXiv2026

Flexible Inference for Winners with Conditional Validity

Researchers often select top-performing options or winners, based on a data-driven criterion, such as treatments, models, or model features and then report effect estimates for the selected winners. Naive post-selection estimates, however, are known to suffer from the winner's curse, producing systematically overoptimistic results. We introduce a flexible conditional inference method that corrects for this overoptimism through an adaptive exponential randomization scheme. Our method achieves selection quality that closely matches that of standard top-k selection, while also yielding shorter confidence intervals than existing approaches. Furthermore, our approach applies broadly to nonparametric settings with asymptotically linear selection statistics, covering wide-ranging applications such as inference for the efficacy of the most promising treatments in clinical trials, the abilities of top-ranked models on leaderboards, and the importance of the most predictive features in a model.

stat.ME↗

arXiv2026

Classification Trees with Valid Inference via the Exponential Mechanism

Decision trees are widely used for non-linear modeling, as they capture interactions between predictors while producing inherently interpretable models. Despite their popularity, performing inference on the non-linear fit remains largely unaddressed. This paper focuses on classification trees and makes two key contributions. First, we introduce a novel tree-fitting method that replaces the greedy splitting of the predictor space in standard tree algorithms with a probabilistic approach. Each split in our approach is selected according to sampling probabilities defined by an exponential mechanism, with a temperature parameter controlling its deviation from the deterministic choice given data. Second, while our approach can fit a tree that with high probability coincides with the fit produced by standard tree algorithms at low temperatures, it is not merely predictive; unlike standard algorithms, it enables inference by taking into account the highly adaptive tree structure. Our method produces pivots directly from the sampling probabilities in the exponential mechanism. In theory, our pivots allow asymptotically valid inference on the parameters in the predictive fit, and in practice, our method delivers powerful inference without sacrificing predictive accuracy, in contrast to data splitting methods.

stat.ME↗

arXiv2026

From Collapse to Improvement: Statistical Perspectives on the Evolutionary Dynamics of Iterative Training on Contaminated Sources

The problem of model collapse has presented new challenges in iterative training of generative models, where such training with synthetic data leads to an overall degradation of performance. This paper looks at the problem from a statistical viewpoint, illustrating that one can actually hope for improvement when models are trained on data contaminated with synthetic samples, as long as there is some amount of fresh information from the true target distribution. In particular, we consider iterative training on samples sourced from a mixture of the true target and synthetic distributions. We analyze the entire iterative evolution in a next-token prediction language model, capturing how the interplay between the mixture weights and the sample size controls the overall long-term performance. With non-trivial mixture weight of the true distribution, even if it decays over time, simply training the model in a contamination-agnostic manner with appropriate sample sizes can avoid collapse and even recover the true target distribution under certain conditions. Simulation studies support our findings and also show that such behavior is more general for other classes of models.

stat.ML↗

arXiv2025

Inference with Randomized Regression Trees

Regression trees are a popular machine learning algorithm that fit piecewise constant models by recursively partitioning the predictor space. This paper focuses on statistical inference for a data-dependent model obtained from a fitted regression tree. We introduce Randomized Regression Trees (RRT), a novel selective inference method that adds independent Gaussian noise to the gain function underlying the splitting rules of classic regression trees. The RRT method offers several advantages over existing methods. First, added randomization is used to obtain a closed-form pivot while accounting for the data-dependent tree structure. Second, RRT with a small amount of randomization achieves predictive accuracy similar to a model trained on the entire dataset, while also providing significantly more powerful inference than existing selective inference methods, such as data splitting. Third, RRT yields intervals that automatically adapt to the signal strength in the data. Our empirical analyses highlight these advantages of the RRT method and its ability to convert a purely predictive algorithm into a method capable of performing powerful inference in the non-linear tree model.

stat.ME↗

arXiv2023

Bayes classifier cannot be learned from noisy responses with unknown noise rates

Training a classifier with noisy labels typically requires the learner to specify the distribution of label noise, which is often unknown in practice. Although there have been some recent attempts to relax that requirement, we show that the Bayes decision rule is unidentified in most classification problems with noisy labels. This suggests it is generally not possible to bypass/relax the requirement. In the special cases in which the Bayes decision rule is identified, we develop a simple algorithm to learn the Bayes decision rule, that does not require knowledge of the noise distribution.

stat.ML↗

arXiv2022

How to approximate irrational numbers nicely?

In the literature, we have various ways of proving irrationality of a real number. In this survey article, we shall emphasize on a particular criterion to prove irrationality. This is called nice approximation of a number by a sequence of rational numbers. This criterion of irrationality is easy to prove and is of great importance. Using it, irrationality of a large class of numbers is proved. We shall apply this method to prove irrationality of algebraic, exponential and trigonometric irrational numbers. Most of the times, explicit constructions are done of the nice sequence of rational numbers. Arguments used are basic like the binomial theorem and maxima and minima of functions. Thus, this survey article is accessible to undergraduate students and has a broad appeal for anyone looking for entertaining mathematics. This article brings out classically known beautiful mathematics without using any heavyweight machinery.

math.NT↗