Lecture

Statistical Physics of Computation: Insights and Applications

Graph Chat

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

Description

This lecture by the instructor delves into the application of statistical physics concepts to computational problems, exploring topics such as generating random variables, solving card games using principal component analysis, Bayesian inference, mean-field spin glass models, and first-order phase transitions. The lecture also discusses the challenges in achieving optimal estimation error, the computation of marginals, and the transition from physics to learning paradigms. Furthermore, it covers the concept of compressed sensing and nucleation in physics, providing insights into optimal decoding and benchmark data analysis.

Official source

Related concepts (29)

Computational problem

In theoretical computer science, a computational problem is a problem that may be solved by an algorithm. For example, the problem of factoring "Given a positive integer n, find a nontrivial prime factor of n." is a computational problem. A computational problem can be viewed as a set of instances or cases together with a, possibly empty, set of solutions for every instance/case. For example, in the factoring problem, the instances are the integers n, and solutions are prime numbers p that are the nontrivial prime factors of n.

Bayesian inference

Bayesian inference (ˈbeɪziən or ˈbeɪʒən ) is a method of statistical inference in which Bayes' theorem is used to update the probability for a hypothesis as more evidence or information becomes available. Bayesian inference is an important technique in statistics, and especially in mathematical statistics. Bayesian updating is particularly important in the dynamic analysis of a sequence of data. Bayesian inference has found application in a wide range of activities, including science, engineering, philosophy, medicine, sport, and law.

Principal component analysis

Principal component analysis (PCA) is a popular technique for analyzing large datasets containing a high number of dimensions/features per observation, increasing the interpretability of data while preserving the maximum amount of information, and enabling the visualization of multidimensional data. Formally, PCA is a statistical technique for reducing the dimensionality of a dataset. This is accomplished by linearly transforming the data into a new coordinate system where (most of) the variation in the data can be described with fewer dimensions than the initial data.

Computational complexity theory

In theoretical computer science and mathematics, computational complexity theory focuses on classifying computational problems according to their resource usage, and relating these classes to each other. A computational problem is a task solved by a computer. A computation problem is solvable by mechanical application of mathematical steps, such as an algorithm. A problem is regarded as inherently difficult if its solution requires significant resources, whatever the algorithm used.

Bayesian network

A Bayesian network (also known as a Bayes network, Bayes net, belief network, or decision network) is a probabilistic graphical model that represents a set of variables and their conditional dependencies via a directed acyclic graph (DAG). It is one of several forms of causal notation. Bayesian networks are ideal for taking an event that occurred and predicting the likelihood that any one of several possible known causes was the contributing factor. For example, a Bayesian network could represent the probabilistic relationships between diseases and symptoms.

Related lectures (64)

Density of States and Bayesian Inference in Computational Mathematics

Explores computing density of states and Bayesian inference using importance sampling, showcasing lower variance and parallelizability of the proposed method.

Monte Carlo: Markov Chains

Covers unsupervised learning, dimensionality reduction, SVD, low-rank estimation, PCA, and Monte Carlo Markov Chains.

Scientific Machine Learning: Introduction to Spin Glass Models

Introduces Scientific Machine Learning, emphasizing its application in various scientific fields and the connection between machine learning and physics.

Maximum Likelihood Inference

Explores maximum likelihood inference, comparing models based on likelihood ratios and demonstrating with a coin example.

Bayesian Inference: Optimal Estimation