Statistical approximations | Stochastic optimization
Stochastic approximation methods are a family of iterative methods typically used for root-finding problems or for optimization problems. The recursive update rules of stochastic approximation methods can be used, among other things, for solving linear systems when the collected data is corrupted by noise, or for approximating extreme values of functions which cannot be computed directly, but only estimated via noisy observations. In a nutshell, stochastic approximation algorithms deal with a function of the form which is the expected value of a function depending on a random variable . The goal is to recover properties of such a function without evaluating it directly. Instead, stochastic approximation algorithms use random samples of to efficiently approximate properties of such as zeros or extrema. Recently, stochastic approximations have found extensive applications in the fields of statistics and machine learning, especially in settings with big data. These applications range from stochastic optimization methods and algorithms, to online forms of the EM algorithm, reinforcement learning via temporal differences, and deep learning, and others.Stochastic approximation algorithms have also been used in the social sciences to describe collective dynamics: fictitious play in learning theory and consensus algorithms can be studied using their theory. The earliest, and prototypical, algorithms of this kind are the Robbins–Monro and Kiefer–Wolfowitz algorithms introduced respectively in 1951 and 1952. (Wikipedia).
Stochastic Approximation-based algorithms, when the Monte (...) - Fort - Workshop 2 - CEB T1 2019
Gersende Fort (CNRS, Univ. Toulouse) / 13.03.2019 Stochastic Approximation-based algorithms, when the Monte Carlo bias does not vanish. Stochastic Approximation algorithms, whose stochastic gradient descent methods with decreasing stepsize are an example, are iterative methods to comput
From playlist 2019 - T1 - The Mathematics of Imaging
Jana Cslovjecsek: Efficient algorithms for multistage stochastic integer programming using proximity
We consider the problem of solving integer programs of the form min {c^T x : Ax = b; x geq 0}, where A is a multistage stochastic matrix. We give an algorithm that solves this problem in fixed-parameter time f(d; ||A||_infty) n log^O(2d) n, where f is a computable function, d is the treed
From playlist Workshop: Parametrized complexity and discrete optimization
Numeric Modeling in Mathematica: Q&A with Mathematica Experts
Mathematica experts answer user-submitted questions about numeric computations during Mathematica Experts Live: Numeric Modeling in Mathematica. For more information about Mathematica, please visit: http://www.wolfram.com/mathematica
From playlist Mathematica Experts Live: Numeric Modeling in Mathematica
Anthony Nouy: Adaptive low-rank approximations for stochastic and parametric equations [...]
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Numerical Analysis and Scientific Computing
Basic stochastic simulation b: Stochastic simulation algorithm
(C) 2012-2013 David Liao (lookatphysics.com) CC-BY-SA Specify system Determine duration until next event Exponentially distributed waiting times Determine what kind of reaction next event will be For more information, please search the internet for "stochastic simulation algorithm" or "kin
From playlist Probability, statistics, and stochastic processes
Approximating Functions in a Metric Space
Approximations are common in many areas of mathematics from Taylor series to machine learning. In this video, we will define what is meant by a best approximation and prove that a best approximation exists in a metric space. Chapters 0:00 - Examples of Approximation 0:46 - Best Aproximati
From playlist Approximation Theory
Linear Approximations and Differentials
Linear Approximation In this video, I explain the concept of a linear approximation, which is just a way of approximating a function of several variables by its tangent planes, and I illustrate this by approximating complicated numbers f without using a calculator. Enjoy! Subscribe to my
From playlist Partial Derivatives
Francis Bach: Large-scale machine learning and convex optimization 2/2
Abstract: Many machine learning and signal processing problems are traditionally cast as convex optimization problems. A common difficulty in solving these problems is the size of the data, where there are many observations ("large n") and each of these is large ("large p"). In this settin
From playlist Probability and Statistics
Elias Khalil - Neur2SP: Neural Two-Stage Stochastic Programming - IPAM at UCLA
Recorded 02 March 2023. Elias Khalil of the University of Toronto presents "Neur2SP: Neural Two-Stage Stochastic Programming" at IPAM's Artificial Intelligence and Discrete Optimization Workshop. Abstract: Stochastic Programming is a powerful modeling framework for decision-making under un
From playlist 2023 Artificial Intelligence and Discrete Optimization
Jorge Nocedal: "Tutorial on Optimization Methods for Machine Learning, Pt. 3"
Graduate Summer School 2012: Deep Learning, Feature Learning "Tutorial on Optimization Methods for Machine Learning, Pt. 3" Jorge Nocedal, Northwestern University Institute for Pure and Applied Mathematics, UCLA July 18, 2012 For more information: https://www.ipam.ucla.edu/programs/summ
From playlist GSS2012: Deep Learning, Feature Learning
FinMath L2-2: The general Ito integral 2
Welcome to the second part of lesson 2. In this video we discuss some properties of the (general) Ito integral and introduce the necessary notions to deal with the Ito-Doeblin formula, which will be treated in Lesson 3. Topics: 00:00 A little exercise for you 06:46 Definition of the integ
From playlist Financial Mathematics
Dr Lukasz Szpruch, University of Edinburgh
Bio I am a Lecturer at the School of Mathematics, University of Edinburgh. Before moving to Scotland I was a Nomura Junior Research Fellow at the Institute of Mathematics, University of Oxford, and a member of Oxford-Man Institute for Quantitative Finance. I hold a Ph.D. in mathematics fr
From playlist Short Talks
DeepMind x UCL | Deep Learning Lectures | 5/12 | Optimization for Machine Learning
Optimization methods are the engines underlying neural networks that enable them to learn from data. In this lecture, DeepMind Research Scientist James Martens covers the fundamentals of gradient-based optimization methods, and their application to training neural networks. Major topics in
From playlist Learning resources
Stochastic Gradient Descent: where optimization meets machine learning- Rachel Ward
2022 Program for Women and Mathematics: The Mathematics of Machine Learning Topic: Stochastic Gradient Descent: where optimization meets machine learning Speaker: Rachel Ward Affiliation: University of Texas, Austin Date: May 26, 2022 Stochastic Gradient Descent (SGD) is the de facto op
From playlist Mathematics
Introduction to the paper https://arxiv.org/abs/2002.06707
From playlist Research
Stochastic processes by VijayKumar Krishnamurthy
Winter School on Quantitative Systems Biology DATE: 04 December 2017 to 22 December 2017 VENUE: Ramanujan Lecture Hall, ICTS, Bengaluru The International Centre for Theoretical Sciences (ICTS) and the Abdus Salam International Centre for Theoretical Physics (ICTP), are organizing a Wint
From playlist Winter School on Quantitative Systems Biology
Deep Learning 5: Optimization for Machine Learning
James Martens, Research Scientist, discusses optimization for machine learning as part of the Advanced Deep Learning & Reinforcement Learning Lectures.
From playlist Learning resources
Francis Bach : Large-scale machine learning and convex optimization 1/2
Abstract: Many machine learning and signal processing problems are traditionally cast as convex optimization problems. A common difficulty in solving these problems is the size of the data, where there are many observations ("large n") and each of these is large ("large p"). In this settin
From playlist Probability and Statistics
Peter Kratz : Large deviations for Poisson driven processes in epidemiology
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Probability and Statistics