Combinatorics seminar
Speaker: Nitesh Prajapati, IIT Bhilai
Host: Niranjan Balachandran
Title: Some Direct and Inverse Problems for Sumsets, Restricted Sumsets, and Product Sets
Time, day and date: 11:30:00 AM - 12:30:00 PM, Tuesday, August 11
Venue: Online (meet.google.com/jwm-qugk-hmu)
Abstract: Attached https://drive.google.com/open?id=1rQbYHeVo2HChZTTNjMldNDPOwk0AShj3

Statistics/Probability Seminar
Speaker: Sabyasachi Chatterjee, University of Illinois Urbana-Champaign
Host: Parthanil Roy
Title: A New Min–Max Representation for Univariate Total Variation Denoising
Time, day and date: 4:00:00 PM – 5:00:00 PM, Tuesday, August 11
Venue: Ramanujan Hall
Abstract: Total variation denoising (TVD) is a classical and widely used method for estimating signals with piecewise constant structure. Although the estimator is defined through a simple convex optimization problem and has been studied extensively, no explicit pointwise characterization of the fitted values was previously known.
In this talk, I will present a new min–max/max–min representation for TVD that gives an explicit pointwise description of the fitted values in terms of local averages over intervals. This representation reveals a hidden multiscale structure underlying the estimator, provides new insight into its bias and variance, and leads to sharp pointwise risk bounds that adapt to the local smoothness of the underlying signal.
I will then show that this pointwise perspective extends naturally to quantile regression. In this setting, the fitted values admit an exact characterization as an interval determined by local order statistics, reflecting the non-strict convexity of the quantile loss. This characterization yields new structural insights into quantile TVD, including automatically non-crossing quantile curves without the need for additional constraints.
The talk is based on the following two papers:
(1) https://arxiv.org/pdf/2410.03041
(2) https://arxiv.org/pdf/2605.01237

Deep Learning in Finance – Lecture 3
Speaker: Prof. Ovidiu Calin, Eastern Michigan University
Host: S Baskar
Title: Learning Stochastic Processes Part I: Calibration
Time, day and date: 5:00:00 PM – 6:00:00 PM, Tuesday, August 11
Venue: Ramanujan Hall
Abstract: This presentation introduced modern approaches for learning and calibrating stochastic processes from data using machine learning. Beginning with Gaussian processes, we showed how neural networks can be used to approximate the time-dependent mean and variance functions, transforming the observations into a standardized process that should follow a standard normal distribution. This viewpoint naturally leads to calibration methods based on quantile matching, which compare the entire empirical distribution rather than only its first moments, providing a more robust alternative to classical moment-matching techniques. We then extended the framework to learning covariance kernels, enabling the recovery of temporal dependence in Gaussian processes, with simplified formulations for stationary models. The second part focused on the calibration of stochastic differential equations, using the Langevin (Ornstein–Uhlenbeck) process as a representative example. After deriving its explicit solution and statistical properties, we discussed several calibration strategies, including moment matching, quantile matching, and autoregressive estimation. Throughout the presentation, neural-network-based calibration was presented as a flexible and powerful alternative to traditional estimation methods, capable of learning unknown statistical quantities directly from observed trajectories while providing a unified framework applicable to a broad class of stochastic models encountered in finance, physics, engineering, and data science.