arXiv subjects

Jhanvi Garg

Publications and source records attributed to Jhanvi Garg.

4 recordsLinked to original sources

arXiv2025

Restricted Spectral Gap Decomposition for Simulated Tempering Targeting Mixture Distributions

Simulated tempering is a widely used strategy for sampling from multimodal distributions. In this paper, we consider simulated tempering combined with an arbitrary local Markov chain Monte Carlo sampler and present a new decomposition theorem that provides a lower bound on the restricted spectral gap of the algorithm for sampling from mixture distributions. By working with the restricted spectral gap, the applicability of our results is extended to broader settings such as when the usual spectral gap is difficult to bound or becomes degenerate. We demonstrate the application of our theoretical results by analyzing simulated tempering combined with random walk Metropolis--Hastings for sampling from mixtures of Gaussian distributions. Our complexity bound scales polynomially with the separation between modes, logarithmically with $1/\varepsilon$, where $\varepsilon$ denotes the target accuracy in total variation distance, and exponentially with the dimension $d$.

math.ST↗

arXiv2024

Fragility Index for Time-to-Event Endpoints in Single-Arm Clinical Trials

The reliability of clinical trial outcomes is crucial, especially in guiding medical decisions. In this paper, we introduce the Fragility Index (FI) for time-to-event endpoints in single-arm clinical trials - a novel metric designed to quantify the robustness of study conclusions. The FI represents the smallest number of censored observations that, when reclassified as uncensored events, causes the posterior probability of the median survival time exceeding a specified threshold to fall below a predefined confidence level. While drug effectiveness is typically assessed by determining whether the posterior probability exceeds a specified confidence level, the FI offers a complementary measure, indicating how robust these conclusions are to potential shifts in the data. Using a Bayesian approach, we develop a practical framework for computing the FI based on the exponential survival model. To facilitate the application of our method, we developed an R package fi, which provides a tool to compute the Fragility Index. Through real world case studies involving time to event data from single arms clinical trials, we demonstrate the utility of this index. Our findings highlight how the FI can be a valuable tool for assessing the robustness of survival analyses in single-arm studies, aiding researchers and clinicians in making more informed decisions.

stat.ME↗

arXiv2024

Soft-constrained Schrodinger Bridge: a Stochastic Control Approach

Schrödinger bridge can be viewed as a continuous-time stochastic control problem where the goal is to find an optimally controlled diffusion process whose terminal distribution coincides with a pre-specified target distribution. We propose to generalize this problem by allowing the terminal distribution to differ from the target but penalizing the Kullback-Leibler divergence between the two distributions. We call this new control problem soft-constrained Schrödinger bridge (SSB). The main contribution of this work is a theoretical derivation of the solution to SSB, which shows that the terminal distribution of the optimally controlled process is a geometric mixture of the target and some other distribution. This result is further extended to a time series setting. One application is the development of robust generative diffusion models. We propose a score matching-based algorithm for sampling from geometric mixtures and showcase its use via a numerical example for the MNIST data set.

stat.ML↗

arXiv2022

A quickest detection problem with false negatives

We formulate and solve a variant of the quickest detection problem which features false negatives. A standard Brownian motion acquires a drift at an independent exponential random time which is not directly observable. Based on the observation in continuous time of the sample path of the process, an optimizer must detect the drift as quickly as possible after it has appeared. The optimizer can inspect the system multiple times upon payment of a fixed cost per inspection. If a test is performed on the system before the drift has appeared then, naturally, the test will return a negative outcome. However, if a test is performed after the drift has appeared, then the test may fail to detect it and return a false negative with probability $\epsilon\in(0,1)$. The optimisation ends when the drift is eventually detected. The problem is formulated mathematically as an optimal multiple stopping problem, and it is shown to be equivalent to a recursive optimal stopping problem. Exploiting such connection and free boundary methods we find explicit formulae for the expected cost and the optimal strategy. We also show that when $\epsilon = 0$ our expected cost is an affine transformation of the one in Shiryaev's classical optimal detection problem with a rescaled model parameter.

math.OC↗