Lecture

Robust Regression in Genomic Data Analysis

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In course

MATH-474: Statistics for genomic data analysis

After a short introduction to basic molecular biology and genomic technologies, this course covers the most useful statistical concepts and methods for the analysis of genomic data. ...

Description

This lecture covers the concept of robust regression in the context of genomic data analysis, focusing on downweighting observations with large residuals to improve estimation accuracy. Various loss and weight functions are discussed, including the Huber loss function. The lecture also delves into the use of M-estimators and the iterative reweighted least squares (IRLS) algorithm for robust regression estimation. Practical applications of robust regression in microarray data analysis, outlier detection, and quality assessment of gene expression measures are explored through examples and pseudo-images. Quality assessment metrics such as NUSE and RLE are explained, providing insights into chip quality and expression measurement error. The lecture concludes with a discussion on different quality assessment measures and their implementation in genomic data analysis tools.

Instructor

Darlene Goldstein

Official source

Ontological neighbourhood

Statistics

Statistical inference: Mathematical statistics

Data analysis: Regression analysis

Related concepts (32)

Loss function

In mathematical optimization and decision theory, a loss function or cost function (sometimes also called an error function) is a function that maps an event or values of one or more variables onto a real number intuitively representing some "cost" associated with the event. An optimization problem seeks to minimize a loss function. An objective function is either a loss function or its opposite (in specific domains, variously called a reward function, a profit function, a utility function, a fitness function, etc.

Robust regression

In robust statistics, robust regression seeks to overcome some limitations of traditional regression analysis. A regression analysis models the relationship between one or more independent variables and a dependent variable. Standard types of regression, such as ordinary least squares, have favourable properties if their underlying assumptions are true, but can give misleading results otherwise (i.e. are not robust to assumption violations).

M-estimator

In statistics, M-estimators are a broad class of extremum estimators for which the objective function is a sample average. Both non-linear least squares and maximum likelihood estimation are special cases of M-estimators. The definition of M-estimators was motivated by robust statistics, which contributed new types of M-estimators. However, M-estimators are not inherently robust, as is clear from the fact that they include maximum likelihood estimators, which are in general not robust.

Huber loss

In statistics, the Huber loss is a loss function used in robust regression, that is less sensitive to outliers in data than the squared error loss. A variant for classification is also sometimes used. The Huber loss function describes the penalty incurred by an estimation procedure f. Huber (1964) defines the loss function piecewise by This function is quadratic for small values of a, and linear for large values, with equal values and slopes of the different sections at the two points where .

Maximum likelihood estimation

In statistics, maximum likelihood estimation (MLE) is a method of estimating the parameters of an assumed probability distribution, given some observed data. This is achieved by maximizing a likelihood function so that, under the assumed statistical model, the observed data is most probable. The point in the parameter space that maximizes the likelihood function is called the maximum likelihood estimate. The logic of maximum likelihood is both intuitive and flexible, and as such the method has become a dominant means of statistical inference.

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