Lecture

Probability Theory: Joint Marginals and Granger Causality

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In course

MGT-416: Causal inference

Students will learn the core concepts and techniques of network analysis with emphasis on causal inference. Theory and application will be balanced, with students working directly with network data throughout the course. ...

Description

This lecture covers the concepts of joint marginals and Granger causality in probability theory, explaining how to calculate joint marginals and the implications of Granger causality in predicting outcomes. The instructor discusses the calculation of conditional entropies, directed information, and the sequential prediction framework.

Instructor

Negar Kiyavash

Teaching & PhD PhD Students Mohammad Shahverdikondori, Badri Mohammad Reza, Arefe Boushehrian, Sepehr Elahi, Mohammadsadegh Khorasani, Mohammadsaeed Masiha, Amir Mohammad Aboueimehrizi Past EPFL PhD Students Sina Akbari, Ehsan Mokhtarian, Yaroslav Kivva, Fateme Jamshidi Courses Causal inference MGT-416 Students will learn the core concepts and techniques of network analysis with emphasis on causal inference. Theory andapplication will be balanced, with students working directly with networ

Official source

Ontological neighbourhood

Information engineering

Information theory: Channel capacity

Related concepts (31)

Probability theory

Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms. Typically these axioms formalise probability in terms of a probability space, which assigns a measure taking values between 0 and 1, termed the probability measure, to a set of outcomes called the sample space.

Probability

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty. The higher the probability of an event, the more likely it is that the event will occur. A simple example is the tossing of a fair (unbiased) coin.

Rényi entropy

In information theory, the Rényi entropy is a quantity that generalizes various notions of entropy, including Hartley entropy, Shannon entropy, collision entropy, and min-entropy. The Rényi entropy is named after Alfréd Rényi, who looked for the most general way to quantify information while preserving additivity for independent events. In the context of fractal dimension estimation, the Rényi entropy forms the basis of the concept of generalized dimensions. The Rényi entropy is important in ecology and statistics as index of diversity.

Min-entropy

The min-entropy, in information theory, is the smallest of the Rényi family of entropies, corresponding to the most conservative way of measuring the unpredictability of a set of outcomes, as the negative logarithm of the probability of the most likely outcome. The various Rényi entropies are all equal for a uniform distribution, but measure the unpredictability of a nonuniform distribution in different ways.

Probability axioms

The Kolmogorov axioms are the foundations of probability theory introduced by Russian mathematician Andrey Kolmogorov in 1933. These axioms remain central and have direct contributions to mathematics, the physical sciences, and real-world probability cases. An alternative approach to formalising probability, favoured by some Bayesians, is given by Cox's theorem. The assumptions as to setting up the axioms can be summarised as follows: Let be a measure space with being the probability of some event , and .

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