Discrete distributions | Continuous distributions | Types of probability distributions | Exponentials

Exponential family

In probability and statistics, an exponential family is a parametric set of probability distributions of a certain form, specified below. This special form is chosen for mathematical convenience, including the enabling of the user to calculate expectations, covariances using differentiation based on some useful algebraic properties, as well as for generality, as exponential families are in a sense very natural sets of distributions to consider. The term exponential class is sometimes used in place of "exponential family", or the older term Koopman–Darmois family. The terms "distribution" and "family" are often used loosely: specifically, an exponential family is a set of distributions, where the specific distribution varies with the parameter; however, a parametric family of distributions is often referred to as "a distribution" (like "the normal distribution", meaning "the family of normal distributions"), and the set of all exponential families is sometimes loosely referred to as "the" exponential family. They are distinct because they possess a variety of desirable properties, most importantly the existence of a sufficient statistic. The concept of exponential families is credited to E. J. G. Pitman, G. Darmois, and B. O. Koopman in 1935–1936. Exponential families of distributions provides a general framework for selecting a possible alternative parameterisation of a parametric family of distributions, in terms of natural parameters, and for defining useful sample statistics, called the natural sufficient statistics of the family. (Wikipedia).

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(ML 5.1) Exponential families (part 1)

Definition of exponential families, and examples. We look at the Exponential distribution and Bernoulli distribution as examples of exponential families. A playlist of these Machine Learning videos is available here: http://www.youtube.com/view_play_list?p=D0F06AA0D2E8FFBA

From playlist Machine Learning

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(ML 5.3) MLE for an exponential family (part 1)

Characterization of the MLE for an exponential family. A playlist of these Machine Learning videos is available here: http://www.youtube.com/view_play_list?p=D0F06AA0D2E8FFBA

From playlist Machine Learning

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(ML 5.2) Exponential families (part 2)

Definition of exponential families, and examples. We look at the Exponential distribution and Bernoulli distribution as examples of exponential families. A playlist of these Machine Learning videos is available here: http://www.youtube.com/view_play_list?p=D0F06AA0D2E8FFBA

From playlist Machine Learning

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Algebra Ch 46: Exponential Function (1 of 12) What is an Exponential Function?

Visit http://ilectureonline.com for more math and science lectures! To donate: http://www.ilectureonline.com/donate https://www.patreon.com/user?u=3236071 We will learn an exponential function is a function in the form of f(x)=b^x where b=base (b(greater than)0, and b does not=1) and x=e

From playlist THE "WHAT IS" PLAYLIST

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Learn the basics for solve an exponential equation using a calculator

👉 Learn how to solve exponential equations. An exponential equation is an equation in which a variable occurs as an exponent. To solve an exponential equation, we isolate the exponential part of the equation. Then we take the log of both sides. Note that the base of the log should correspo

From playlist Solve Exponential Equations with Logarithms

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Learn basics for solving an exponential equation by using one to one property

👉 Learn how to solve exponential equations. An exponential equation is an equation in which a variable occurs as an exponent. To solve an exponential equation, we isolate the exponential part of the equation. Then we take the log of both sides. Note that the base of the log should correspo

From playlist Solve Exponential Equations with Logarithms

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Solving exponential equations using the one to one property

👉 Learn how to solve exponential equations. An exponential equation is an equation in which a variable occurs as an exponent. To solve an exponential equation, we isolate the exponential part of the equation. Then we take the log of both sides. Note that the base of the log should correspo

From playlist Solve Exponential Equations with Logarithms

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Stanford CS229: Machine Learning | Summer 2019 | Lecture 6 - Exponential Family & GLM

For more information about Stanford’s Artificial Intelligence professional and graduate programs, visit: https://stanford.io/3Eb7mIi Anand Avati Computer Science, PhD To follow along with the course schedule and syllabus, visit: http://cs229.stanford.edu/syllabus-summer2019.html

From playlist Stanford CS229: Machine Learning Course | Summer 2019 (Anand Avati)

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21. Generalized Linear Models

MIT 18.650 Statistics for Applications, Fall 2016 View the complete course: http://ocw.mit.edu/18-650F16 Instructor: Philippe Rigollet In this lecture, Prof. Rigollet talked about linear model, generalization, and examples of disease occurring rate, prey capture rate, Kyphosis data, etc.

From playlist MIT 18.650 Statistics for Applications, Fall 2016

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Lecture 4 - Perceptron & Generalized Linear Model | Stanford CS229: Machine Learning (Autumn 2018)

For more information about Stanford’s Artificial Intelligence professional and graduate programs, visit: https://stanford.io/3GnSw3o Anand Avati PhD Candidate and CS229 Head TA To follow along with the course schedule and syllabus, visit: http://cs229.stanford.edu/syllabus-autumn2018.h

From playlist Stanford CS229: Machine Learning Full Course taught by Andrew Ng | Autumn 2018

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Guido Montúfar : Fisher information metric of the conditional probability politopes

Recording during the thematic meeting : "Geometrical and Topological Structures of Information" the September 01, 2017 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent

From playlist Geometry

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Solve an exponential equation using one to one property and isolating the exponent

👉 Learn how to solve exponential equations. An exponential equation is an equation in which a variable occurs as an exponent. To solve an exponential equation, we isolate the exponential part of the equation. Then we take the log of both sides. Note that the base of the log should correspo

From playlist Solve Exponential Equations with Logarithms

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Generalized Linear Model (Part A)

Regression Analysis by Dr. Soumen Maity,Department of Mathematics,IIT Kharagpur.For more details on NPTEL visit http://nptel.ac.in

From playlist IIT Kharagpur: Regression Analysis | CosmoLearning.org Mathematics

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Solving an exponential equation using the one to one property

👉 Learn how to solve exponential equations. An exponential equation is an equation in which a variable occurs as an exponent. To solve an exponential equation, we isolate the exponential part of the equation. Then we take the log of both sides. Note that the base of the log should correspo

From playlist Solve Exponential Equations with Logarithms

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Lecture 4 | Machine Learning (Stanford)

Lecture by Professor Andrew Ng for Machine Learning (CS 229) in the Stanford Computer Science department. Professor Ng lectures on Newton's method, exponential families, and generalized linear models and how they relate to machine learning. This course provides a broad introduction to

From playlist Lecture Collection | Machine Learning

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Lecture 11: Sheaves form a topos (Part 2)

In this talk Patrick Elliott proves that the category of sheaves on a site is a topos, by discussing the exponentials and subobject classifier in detail. The notes are already online: The lecture notes are available here: http://therisingsea.org/notes/ch2018-lecture11.pdf. For the genera

From playlist Topos theory seminar

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Solving an exponential equation using the one to one property 16^x + 2 = 6

👉 Learn how to solve exponential equations. An exponential equation is an equation in which a variable occurs as an exponent. To solve an exponential equation, we isolate the exponential part of the equation. Then we take the log of both sides. Note that the base of the log should correspo

From playlist Solve Exponential Equations with Logarithms

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Generalized Linear Model (Part B)

Regression Analysis by Dr. Soumen Maity,Department of Mathematics,IIT Kharagpur.For more details on NPTEL visit http://nptel.ac.in

From playlist IIT Kharagpur: Regression Analysis | CosmoLearning.org Mathematics

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