Lecture

Mutual Information in Biological Data

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

BIO-369: Randomness and information in biological data

Biology is becoming more and more a data science, as illustrated by the explosion of available genome sequences. This course aims to show how we can make sense of such data and harness it in order to understand biological processes in a quantitative way. ...

Description

This lecture covers the concept of mutual information applied to biological data, focusing on quantifying randomness and information in data, statistical dependence, and inferring probability distributions. It delves into the relationship between covariance, correlation, and mutual information, highlighting the ability of mutual information to detect nonlinear forms of statistical dependence. The lecture also explores the use of mutual information in analyzing protein sequence data, emphasizing its independence from specific values. Additionally, it discusses the application of mutual information in understanding positional information in development and the rewiring of two-component signaling systems in biological contexts.

Instructor

Anne-Florence Raphaëlle Bitbol

I was trained in physics, and always had a strong interest in biology. I am broadly interested in understanding biological phenomena in a quantitative way, through physical concepts and mathematical and computational tools. I investigate the relative impacts of optimization and historical contingency in biological evolution, both at the scale of protein sequences and at the scale of microbial populations.Here is my research group website.Curriculum vitae Here is my complete CV. Professional experience:Since

Official source

Ontological neighbourhood

Statistics

Statistical inference: Mathematical statistics

Information engineering

Information theory: Channel capacity

Related concepts (32)

Entropy (information theory)

In information theory, the entropy of a random variable is the average level of "information", "surprise", or "uncertainty" inherent to the variable's possible outcomes. Given a discrete random variable , which takes values in the alphabet and is distributed according to : where denotes the sum over the variable's possible values. The choice of base for , the logarithm, varies for different applications. Base 2 gives the unit of bits (or "shannons"), while base e gives "natural units" nat, and base 10 gives units of "dits", "bans", or "hartleys".

Mutual information

In probability theory and information theory, the mutual information (MI) of two random variables is a measure of the mutual dependence between the two variables. More specifically, it quantifies the "amount of information" (in units such as shannons (bits), nats or hartleys) obtained about one random variable by observing the other random variable. The concept of mutual information is intimately linked to that of entropy of a random variable, a fundamental notion in information theory that quantifies the expected "amount of information" held in a random variable.

Correlation

In statistics, correlation or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data. Although in the broadest sense, "correlation" may indicate any type of association, in statistics it usually refers to the degree to which a pair of variables are linearly related. Familiar examples of dependent phenomena include the correlation between the height of parents and their offspring, and the correlation between the price of a good and the quantity the consumers are willing to purchase, as it is depicted in the so-called demand curve.

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.

Covariance

In probability theory and statistics, covariance is a measure of the joint variability of two random variables. If the greater values of one variable mainly correspond with the greater values of the other variable, and the same holds for the lesser values (that is, the variables tend to show similar behavior), the covariance is positive. In the opposite case, when the greater values of one variable mainly correspond to the lesser values of the other, (that is, the variables tend to show opposite behavior), the covariance is negative.

Related lectures (64)

Mutual Information: Continued

Explores mutual information for quantifying statistical dependence between variables and inferring probability distributions from data.

Information Measures

Covers information measures like entropy, Kullback-Leibler divergence, and data processing inequality, along with probability kernels and mutual information.

Quantifying Statistical Dependence

Delves into quantifying statistical dependence through covariance, correlation, and mutual information.

Mutual Information: Understanding Random Variables

Explores mutual information, quantifying relationships between random variables and measuring information gain and statistical dependence.

Quantifying Statistical Dependence: Covariance and Correlation