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Lecture

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In course

PHYS-467: Machine learning for physicists

Machine learning and data analysis are becoming increasingly central in sciences including physics. In this course, fundamental principles and methods of machine learning will be introduced and practised. ...

Instructor

Lenka Zdeborová

Lenka Zdeborová is a Professor of Physics and of Computer Science in École Polytechnique Fédérale de Lausanne where she leads the Statistical Physics of Computation Laboratory. She received a PhD in physics from University Paris-Sud and from Charles University in Prague in 2008. She spent two years in the Los Alamos National Laboratory as the Director's Postdoctoral Fellow. Between 2010 and 2020 she was a researcher at CNRS working in the Institute of Theoretical Physics in CEA Saclay, France. In 2014, she was awarded the CNRS bronze medal, in 2016 Philippe Meyer prize in theoretical physics and an ERC Starting Grant, in 2018 the Irène Joliot-Curie prize, in 2021 the Gibbs lectureship of AMS. She is an editorial board member for Journal of Physics A, Physical Review E, Physical Review X, SIMODS, Machine Learning: Science and Technology, and Information and Inference. Lenka's expertise is in applications of concepts from statistical physics, such as advanced mean field methods, replica method and related message-passing algorithms, to problems in machine learning, signal processing, inference and optimization. She enjoys erasing the boundaries between theoretical physics, mathematics and computer science.

Official source

https://mediaspace.epfl.ch/media/0_ye17xter

Ontological neighbourhood

Statistics

Data analysis: Regression analysis

Related concepts (32)

Nuclear magnetic resonance

Nuclear magnetic resonance (NMR) is a physical phenomenon in which nuclei in a strong constant magnetic field are perturbed by a weak oscillating magnetic field (in the near field) and respond by producing an electromagnetic signal with a frequency characteristic of the magnetic field at the nucleus. This process occurs near resonance, when the oscillation frequency matches the intrinsic frequency of the nuclei, which depends on the strength of the static magnetic field, the chemical environment, and the magnetic properties of the isotope involved; in practical applications with static magnetic fields up to ca.

Least squares

The method of least squares is a standard approach in regression analysis to approximate the solution of overdetermined systems (sets of equations in which there are more equations than unknowns) by minimizing the sum of the squares of the residuals (a residual being the difference between an observed value and the fitted value provided by a model) made in the results of each individual equation. The most important application is in data fitting.

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.

Nuclear magnetic resonance spectroscopy

Nuclear magnetic resonance spectroscopy, most commonly known as NMR spectroscopy or magnetic resonance spectroscopy (MRS), is a spectroscopic technique to observe local magnetic fields around atomic nuclei. This spectroscopy is based on the measurement of absorption of electromagnetic radiations in the radio frequency region from roughly 4 to 900 MHz. Absorption of radio waves in the presence of magnetic field is accompanied by a special type of nuclear transition, and for this reason, such type of spectroscopy is known as Nuclear Magnetic Resonance Spectroscopy.

Linear least squares

Linear least squares (LLS) is the least squares approximation of linear functions to data. It is a set of formulations for solving statistical problems involved in linear regression, including variants for ordinary (unweighted), weighted, and generalized (correlated) residuals. Numerical methods for linear least squares include inverting the matrix of the normal equations and orthogonal decomposition methods. The three main linear least squares formulations are: Ordinary least squares (OLS) is the most common estimator.

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Probabilistic Models for Linear Regression

Covers the probabilistic model for linear regression and its applications in nuclear magnetic resonance and X-ray imaging.

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Explores linear regression from a statistical inference perspective, covering probabilistic models, ground truth, labels, and maximum likelihood estimators.

Linear Regression: Statistical Inference and Regularization

Covers the probabilistic model for linear regression and the importance of regularization techniques.

Probabilistic Linear Regression

Explores probabilistic linear regression, covering joint and conditional probability, ridge regression, and overfitting mitigation.

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