Related papers: High-Dimensional Statistics
This article is based upon lectures given at the 2013 IAS/Park City Mathematics Institute summer program in geometric analysis.
Measuring the distance between data points is fundamental to many statistical techniques, such as dimension reduction or clustering algorithms. However, improvements in data collection technologies has led to a growing versatility of…
These lecture notes focus on the recent advancements in neural information retrieval, with particular emphasis on the systems and models exploiting transformer networks. These networks, originally proposed by Google in 2017, have seen a…
Lecture notes accompanying an 8hr hour mini-course on SPDE given at Bo\u{g}azi\c{c}i University, Istanbul in June/July 2025. They are based on earlier notes of a shorter mini-course given at the University of Oxford in 2021. The main focus…
Late Winter Lecture Notes, Short Course (10 hours) of Relativistic Astrophysics held at the Department of Physics and Astronomy of the University of Padova, March 13-17, 2017. Third version.
This document contains the notes of a lecture I gave at the "Journ\'ees Nationales du Calcul Formel" (JNCF) on January 2017. The aim of the lecture was to discuss low-level algorithmics for p-adic numbers. It is divided into two main parts:…
Descriptive Analytics is the summarization of the past data and generates some useful patterns from that data. This work focuses on analyzing and querying large academic dataset for generating Student Progression using visualization and…
The need for new methods to deal with big data is a common theme in most scientific fields, although its definition tends to vary with the context. Statistical ideas are an essential part of this, and as a partial response, a thematic…
Comment: Fisher Lecture: Dimension Reduction in Regression [arXiv:0708.3774]
Comment: Fisher Lecture: Dimension Reduction in Regression [arXiv:0708.3774]
Comment: Fisher Lecture: Dimension Reduction in Regression [arXiv:0708.3774]
Lecture notes from the Jerusalem Winter School on Theoretical Physics "Correlated Electron Systems", Dec. 1991 -- Jan. 1992. Contains a review of recent and not so recent results in the theory of correlated fermions in one dimension.
These notes, associated with a topics course, deal with some special cases involving norms and linear transformations.
These are the preparatory notes for a Science & Music essay, "Playing by numbers", appeared in Nature 453 (2008) 988-989.
These are the lecture notes for the introductory graduate course I taught at Yale during Spring 2007. I mostly followed [GS], [BGV], [AB], [Par2], and there are no original results in these notes.
These are notes on adic spaces. They are made available upon some requests in order to make quoting them easier.
These are yet another lecture notes on Seiberg-Witten invariants, where no claim of originality is made, they contain a discussion of some related results from the recent literature.
Variational representations of divergences and distances between high-dimensional probability distributions offer significant theoretical insights and practical advantages in numerous research areas. Recently, they have gained popularity in…
This document collects the lecture notes from my course "Communication Complexity (for Algorithm Designers),'' taught at Stanford in the winter quarter of 2015. The two primary goals of the course are: 1. Learn several canonical problems…
These notes discuss, in a style intended for physicists, how to average data and fit it to some functional form. I try to make clear what is being calculated, what assumptions are being made, and to give a derivation of results rather than…