Lecture

Optimal Errors and Phase Transitions in Generalized Linear Models

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.

In course

PHYS-754: Lecture series on scientific machine learning

This lecture presents ongoing work on how scientific questions can be tackled using machine learning. Machine learning enables extracting knowledge from data computationally and in an automatized way. We will learn on examples how this is influencing the v ...

Description

This lecture discusses the concept of optimal errors and phase transitions in high-dimensional generalized linear models. It covers the definition of generalized linear estimation models, the recovery of signals, and the interpretation of phase transitions in different regions. The speaker explains the significance of first-order phase transitions and the performance comparison of different algorithms in logistic regression and compressed sensing.

Instructors (10)

Anne-Clémence Corminboeuf

Teaching & PhD PhD Students Liam Oliver Marsh, Pratham Pushparaj Deshmukh, Roel Christiaan M Raike, Thanapat Worakul, Osvaldo Hernandez Cuellar, Juliette Veronique Schleicher, Yannick Calvino Alonso, Sara Bassetta, Yuri Cho, Kelian Dietmar Marc Gaedecke, Guoyuan Liu Past EPFL PhD Students Fabrice Avaltroni, Daniel Filipe Jana, Stephan Niklaus Steinmann, Jérôme Florian Gonthier, Riccardo Petraglia, Antonio Prlj, Laurent Alexis Clément Vannay, Alberto Fabrizio, Kun-Han Lin, Boodsarin Sawatlon, Raimon Fabreg

Philippe Schwaller

Michele Ceriotti

Michele Ceriotti received his Ph.D. in Physics from ETH Zürich in 2010. He spent three years in Oxford as a Junior Research Fellow at Merton College. Since 2013 he leads the laboratory for Computational Science and Modeling in the Institute of Materials at EPFL. His research revolves around the atomic-scale modelling of materials, based on the sampling of quantum and thermal fluctuations and on the use of machine learning to predict and rationalize structure-property relations. He has been awarded the IBM Research Forschungspreis in 2010, the Volker Heine Young Investigator Award in 2013, an ERC Starting Grant in 2016, and the IUPAP C10 Young Scientist Prize in 2018.

David Richard Harvey

Expertise CosmologyDark MatterGalaxy ClustersStrong Gravitational LensingWeak Gravitational Lensing I am an observational and theoretical astrophysicist at EPFL. My main area of research is dark matter and trying to understand its properties and dynamics. I love to use deep learning in my work and understand how fondation models and generative AI can help us understand the Universe. I am a member of Euclid and ARRAKIHS and the lead of the self interacting dark matter Key Project in Euclid. Outside of my r

Matthieu Wyart

Teaching & PhD Past EPFL PhD Students Riccardo Ravasio, Mario Geiger, Wencheng Ji, Leonardo Petrini, Umberto Maria Tomasini, Alessandro Favero Courses Systèmes complexes PHYS-343 This courses show how known (entropy, phase transitions) and new (glasses, percolation, avalanche-type response) physical concepts can be used in various fields (including Computer science, neuroscience, social sciences).

Official source

Related concepts (12)

Logistic regression

In statistics, the logistic model (or logit model) is a statistical model that models the probability of an event taking place by having the log-odds for the event be a linear combination of one or more independent variables. In regression analysis, logistic regression (or logit regression) is estimating the parameters of a logistic model (the coefficients in the linear combination).

Multinomial logistic regression

In statistics, multinomial logistic regression is a classification method that generalizes logistic regression to multiclass problems, i.e. with more than two possible discrete outcomes. That is, it is a model that is used to predict the probabilities of the different possible outcomes of a categorically distributed dependent variable, given a set of independent variables (which may be real-valued, binary-valued, categorical-valued, etc.).

Phase transition

In chemistry, thermodynamics, and other related fields, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic states of matter: solid, liquid, and gas, and in rare cases, plasma. A phase of a thermodynamic system and the states of matter have uniform physical properties. During a phase transition of a given medium, certain properties of the medium change as a result of the change of external conditions, such as temperature or pressure.

Generalized linear model

In statistics, a generalized linear model (GLM) is a flexible generalization of ordinary linear regression. The GLM generalizes linear regression by allowing the linear model to be related to the response variable via a link function and by allowing the magnitude of the variance of each measurement to be a function of its predicted value. Generalized linear models were formulated by John Nelder and Robert Wedderburn as a way of unifying various other statistical models, including linear regression, logistic regression and Poisson regression.

Linear regression

In statistics, linear regression is a linear approach for modelling the relationship between a scalar response and one or more explanatory variables (also known as dependent and independent variables). The case of one explanatory variable is called simple linear regression; for more than one, the process is called multiple linear regression. This term is distinct from multivariate linear regression, where multiple correlated dependent variables are predicted, rather than a single scalar variable.

Related lectures (64)

Generalized Linear Regression: Classification

Explores Generalized Linear Regression, Classification, confusion matrices, ROC curves, and noise in data.

Generalized Linear Models: GLMs for Non-Gaussian Data

Explores Generalized Linear Models for non-Gaussian data, covering interpretation of natural link function, MLE asymptotic normality, deviance measures, residuals, and logistic regression.

Linear Models for Classification: Multi-Class Extensions

Covers linear models for multi-class classification, focusing on logistic regression and evaluation metrics.

Generalized Linear Models: Examples and Applications

Explores special examples of Generalized Linear Models, covering logistic regression, count data models, separation issues, and nonparametric relationships.

Linear Models for Classification