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Lecture# Regularization in Machine Learning

Description

This lecture covers the concepts of Ridge Regression and Lasso Regression, focusing on regularization techniques to prevent overfitting in machine learning models. It explains how regularization impacts model flexibility and parameter values. The examples demonstrate the application of regularization in Julia code, emphasizing the importance of tuning hyperparameters and interpreting the results. Additionally, it discusses the use of Lasso paths to visualize the effect of different regularization values on parameter coefficients. The lecture concludes with practical exercises on implementing and understanding regularization in machine learning models.

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Related concepts (149)

BIO-322: Introduction to machine learning for bioengineers

Students understand basic concepts and methods of machine learning. They can describe them in mathematical terms and can apply them to data using a high-level programming language (julia/python/R).

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.

Regularized least squares

Regularized least squares (RLS) is a family of methods for solving the least-squares problem while using regularization to further constrain the resulting solution. RLS is used for two main reasons. The first comes up when the number of variables in the linear system exceeds the number of observations. In such settings, the ordinary least-squares problem is ill-posed and is therefore impossible to fit because the associated optimization problem has infinitely many solutions.

Regularization (physics)

In physics, especially quantum field theory, regularization is a method of modifying observables which have singularities in order to make them finite by the introduction of a suitable parameter called the regulator. The regulator, also known as a "cutoff", models our lack of knowledge about physics at unobserved scales (e.g. scales of small size or large energy levels). It compensates for (and requires) the possibility that "new physics" may be discovered at those scales which the present theory is unable to model, while enabling the current theory to give accurate predictions as an "effective theory" within its intended scale of use.

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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