Statistics and Probability Seminar
Speaker: Raghavendra Tripathi, NYU Abu Dhabi
Host: Parthanil Roy
Title: Efficient sampling from almost all monotone sets
Time, day and date: 11:00:00 AM – 12:00:00 PM, Thursday, August 06
Venue: Conference Room
Abstract: Sampling from the uniform measure on a monotone subset of Boolean hypercube arises in several contexts. For example, sampling a configuration in bond percolation with left to right crossing, or sampling a Knapsack. One popular and oft used method to sample from such sets is to restrict the random walk on the full hypercube to the monotone set. The random walk on the full hypercube mixes in $O(nlogn)$ time.Ding and Mossel (2014) conjectured that restricted chain on any monotone set with fixed positive measure also mixes in $O(nlogn)$ time and proved an upper bound $O(n^3)$. This was recently improved to $O(n^2)$ by proving a sharp Poincare inequality. We prove that for almost all monotone subsets, the log-Sobolev constant is order $n$ which in turn implies the Ding and Mossel’s conjecture for almost all monotone sets. This talk is based on joint work with Patrick O. Santos and Pierre Youssef.

Deep Learning in Finance – Lecture 2
Speaker: Prof. Ovidiu Calin, Eastern Michigan University
Host: S Baskar
Title: Machine Learning Methods for Financial Model Calibration
Time, day and date: 5:00:00 PM – 6:00:00 PM, Thursday, August 06
Venue: Ramanujan Hall
Abstract: This presentation introduced machine learning methods for the calibration of financial models, focusing on the recovery of unknown model parameters from observed market data. We began by formulating model calibration as an inverse problem in which parameters are estimated so that theoretical option prices closely match market prices. After reviewing the mathematical optimization framework, we showed how machine learning can replace repeated numerical optimization by directly learning the inverse mapping from market prices to model parameters, enabling fast real-time calibration. Samuelson's geometric Brownian motion model
was then presented as a fundamental example, together with its stochastic differential equation, probabilistic properties, and explicit maximum likelihood estimators for drift and volatility. To account for changing market conditions, we introduced sliding-window estimation, which produces time-dependent parameter estimates capable of identifying volatility clustering, market regimes, and trend changes. Finally, the limitations of constant-volatility models motivated the introduction of the Heston stochastic volatility model, whose additional parameters provide a more realistic description of financial markets. Throughout the presentation, interactive implementations demonstrated how modern machine learning techniques can efficiently estimate model parameters, visualize their evolution over time, and support practical applications in option pricing, hedging, and quantitative risk management.