Upcoming Seminars

No seminars are currently scheduled.

Past Seminars

Adaptive Wavelet Quantile Density Estimation Based on Biased Samples

Hassan Doosti, Macquarie University, Sydney, Australia.

24th April 2025

Abstract: Quantile density functions offer critical insights in fields ranging from economics to biomedical studies. However, their accurate estimation becomes challenging when data is biased or irregularly sampled. This talk presents a comparative evaluation of threshold selection methods—specifically hard and block thresholding—in adaptive wavelet-based quantile density estimation under such conditions. By integrating theoretical analysis grounded in minimax risk over Besov spaces and extensive simulation studies, we demonstrate the effectiveness of block thresholding in achieving optimal convergence rates, even in the presence of bias. Applications to real-world data further highlight the practical advantages of the proposed methodology. The findings provide actionable guidance for statisticians and data scientists dealing with biased data and looking for robust, adaptive estimation strategies.

Three-dimensional statistical inference using z-stacks of two-dimensional images of oral microbiome samples

Suman Majumder, ISRU, ISI Kolkata

16th April 2025

Abstract: The intra- and inter-taxon relationships present between different bacteria in human oral samples has been of interest to researchers for quite some time. The problem is similar to determining interspecies relationships between different animals in a region with some key challenges and restrictions. Spatial analysis of images of saliva or dental plaque samples allows us to quantify these relationships and the attached uncertainties. Such analyses are few in numbers and primarily utilize two-dimensional methods and infer about these relationships in a two-dimensional plane, followed by some sort of meta-analysis to infer over a collection of “slices” from a sample. In this talk, I will talk about challenges of using spatial analysis in microbiome image data, discuss how we can perform three-dimensional joint analysis of these “slices” using two-dimensional spatial isotropic models, and present more challenges we would need to deal with to make the model statistically prudent.

High-dimensional Inference using Random Projections

Minerva Mukhopadhyay, ISRU, ISI Kolkata

3rd April 2025

Abstract: With increasing availability of data, nowadays, we often encounter high-dimensional data from various fields of study. Almost all standard multivariate approaches fail in effectively analysing such data, both theoretically as well as computationally. Dimension reduction techniques are an essential pre-processing step towards dealing with such data. Among existing methods, the random projection ensemble approach has proven to be a promising approach. In this talk, we plan to discuss the fundamentals of random projections and some of its improvements that have been proposed in the literature. We will also explore implementations of random projections in some specific methods of classification and density estimation.

Spectra of random hypergraphs and contractions of random tensors

Soumendu Sundar Mukherjee, SMU, ISI Kolkata

5th December 2024

Abstract: We will discuss some results on the limit spectra of adjacency and Laplacian matrices of r-uniform Erdős-Rényi hypergraphs on n vertices, in an asymptotic regime where r/n → c ∈ [0,1). Unlike the case of Erdős-Rényi random graphs, the entries of hypergraph adjacency matrices exhibit long range correlations, which make spectral analysis more challenging. Using an ANOVA-style representation, we are able to obtain many results, including a Baik-Ben Arous-Péché phase transition for the largest eigenvalue at r = 3: An appropriately scaled largest eigenvalue converges in probability to 2 if r ∈ {2,3}, and to √(r-2) + 1/√(r-2), if r ≥ 4. Time permitting, we will discuss some related results on contractions of random tensors, which show up in the context of tensor PCA and when studying the so-called p-spin spherical spin glass.

This talk will be based on several joint works with Dipranjan Pal and Himasish Talukdar, both PhD students at ISI Kolkata.

MCMC Importance Sampling via Moreau-Yosida Envelopes

Dootika Vats, Department of Mathematics and Statistics, IIT Kanpur

18th November 2024

Abstract: Markov chain Monte Carlo (MCMC) is the workhorse computational algorithm employed for inference in Bayesian statistics. Gradient-based MCMC algorithms are known to yield faster converging Markov chains. In modern parsimonious models, the use of non-differentiable priors is fairly standard, yielding non-differentiable posteriors. Without differentiability, gradient-based MCMC algorithms cannot be employed effectively. Recently proposed proximal MCMC approaches, however, can partially remedy this limitation. These approaches employ the Moreau-Yosida (MY) envelope to smooth the nondifferentiable prior enabling sampling from an approximation to the target posterior. In this work, we leverage properties of the MY envelope to construct an importance sampling paradigm to correct for this approximation error. We establish asymptotic normality of the importance sampling estimators with an explicit expression for the asymptotic variance which we use to derive a practical metric of sampling efficiency. Numerical studies show that the proposed scheme can yield lower variance estimators compared to existing proximal MCMC alternatives.