


PreSynopsis Seminar
Date: 27 September, 2023 (Wednesday),
Time: 11:00 AM to 12:00 noon
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Venue: Room 105
Host: Niranjan Balachandran
Speaker: Brahadeesh Sankarnarayanan
Title: Some problems in combinatorics: Excursions in graph colorings and
extremal set theory
All are cordially invited.
Lecture series on Hodge Theory Wednesday 27 September, 11:30 am and 3.30 pm  Venue: Ramanujan Hall at 11.30 and 215 at 3.30 Host: Sudarshan Gurjar Speaker: V. Srinivas Affiliation: IIT Bombay Title: Introduction to Hodge Theory Abstract : These are part of an ongoing series of lectures on the basics of Hodge theory. We will finish the proof of the de Rham theorem, via sheaf cohomology, and discuss some linear algebra needed for the Hodge theory, as in Chapter 1 of Huybrechts' book.
Annual Progress Seminar Wednesday, 27th September 2023, 12 noon ======================================= Venue: Room 105 Host: Debraj Das Speaker: Ms. Janhvi Patel Affiliation: IIT Bombay Title: HighDimensional Berry Essen Bounds for Mestimators Abstract: Mestimation refers to a general method of estimation methods, where the estimators are obtained by maximizing certain criterion functions. Mestimators include the maximum likelihood estimator, lease square estimator, and many other estimators that appear in robust regression. Here we are interested in high dimensional asymptotics of Mestimators. More precisely, our goal is to find the BerryEssen bound on the difference between the law of properly centered and scaled M estimator and an appropriate Gaussian distribution.
Annual Progress Seminar Wednesday, 27th September 2023, 3.00 pm ===================================== Venue: Ramanujan Hall Host: Debraj Das Speaker: Mr. Mayukh Choudhury Affiliation: IIT Bombay Title: Bootstrapping LASSO in Generalized Linear Models Abstract: Generalized linear models or GLM is an important set of models that generalizes the ordinary linear regression by connecting the response variable with the covariates through arbitrary link functions and thus allowing the responses to have arbitrary distributions. On the other hand, the Least Absolute Shrinkage and Selection Operator or the Lasso is a popular and easytoimplement penalization method in regression especially when all the covariates are not relevant. However, Lasso has complicated asymptotic distribution which is not useful in practice and hence development of an alternative method of distributional approximation is required for the purpose of statistical inference. Bootstrap generally works as an alternative in most of the inference problems. In that spirit, here we develop a Bootstrap method that works as an approximation of the distribution of the Lasso estimator for all the submodels of GLM. However, it is the usual practice that crossvalidation is used to choose a datadependent choice of the penalty parameter in Lasso. To bridge the gap between the developed Bootstrap theory and the use of crossvalidation, we also establish the asymptotic property of the Kfold crossvalidated choice of the penalty parameter.
Lecture series on Hodge Theory Wednesday 27 September, 11:30 am and 3.30 pm  Venue: Ramanujan Hall at 11.30 and 215 at 3.30 Host: Sudarshan Gurjar Speaker: V. Srinivas Affiliation: IIT Bombay Title: Introduction to Hodge Theory Abstract : These are part of an ongoing series of lectures on the basics of Hodge theory. We will finish the proof of the de Rham theorem, via sheaf cohomology, and discuss some linear algebra needed for the Hodge theory, as in Chapter 1 of Huybrechts' book.