Spanning tree | Markov processes
In the mathematical theory of Markov chains, the Markov chain tree theorem is an expression for the stationary distribution of a Markov chain with finitely many states. It sums up terms for the rooted spanning trees of the Markov chain, with a positive combination for each tree. The Markov chain tree theorem is closely related to Kirchhoff's theorem on counting the spanning trees of a graph, from which it can be derived. It was first stated by , for certain Markov chains arising in thermodynamics, and proved in full generality by , motivated by an application in limited-memory estimation of the probability of a biased coin. A finite Markov chain consists of a finite set of states, and a transition probability for changing from state to state , such that for each state the outgoing transition probabilities sum to one. From an initial choice of state (which turns out to be irrelevant to this problem), each successive state is chosen at random according to the transition probabilities from the previous state. A Markov chain is said to be irreducible when every state can reach every other state through some sequence of transitions, and aperiodic if, for every state, the possible numbers of steps in sequences that start and end in that state have greatest common divisor one. An irreducible and aperiodic Markov chain necessarily has a stationary distribution, a probability distribution on its states that describes the probability of being on a given state after many steps, regardless of the initial choice of state. The Markov chain tree theorem considers spanning trees for the states of the Markov chain, defined to be trees, directed toward a designated root, in which all directed edges are valid transitions of the given Markov chain. If a transition from state to state has transition probability , then a tree with edge set is defined to have weight equal to the product of its transition probabilities: Let denote the set of all spanning trees having state at their root. Then, according to the Markov chain tree theorem, the stationary probability for state is proportional to the sum of the weights of the trees rooted at . That is,where the normalizing constant is the sum of over all spanning trees. (Wikipedia).
(ML 14.3) Markov chains (discrete-time) (part 2)
Definition of a (discrete-time) Markov chain, and two simple examples (random walk on the integers, and a oversimplified weather model). Examples of generalizations to continuous-time and/or continuous-space. Motivation for the hidden Markov model.
From playlist Machine Learning
Prob & Stats - Markov Chains (8 of 38) What is a Stochastic Matrix?
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what is a stochastic matrix. Next video in the Markov Chains series: http://youtu.be/YMUwWV1IGdk
From playlist iLecturesOnline: Probability & Stats 3: Markov Chains & Stochastic Processes
(ML 18.4) Examples of Markov chains with various properties (part 1)
A very simple example of a Markov chain with two states, to illustrate the concepts of irreducibility, aperiodicity, and stationary distributions.
From playlist Machine Learning
Prob & Stats - Markov Chains (10 of 38) Regular Markov Chain
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what is a regular Markov chain. Next video in the Markov Chains series: http://youtu.be/DeG8MlORxRA
From playlist iLecturesOnline: Probability & Stats 3: Markov Chains & Stochastic Processes
(ML 14.2) Markov chains (discrete-time) (part 1)
Definition of a (discrete-time) Markov chain, and two simple examples (random walk on the integers, and a oversimplified weather model). Examples of generalizations to continuous-time and/or continuous-space. Motivation for the hidden Markov model.
From playlist Machine Learning
11e Machine Learning: Markov Chain Monte Carlo
A lecture on the basics of Markov Chain Monte Carlo for sampling posterior distributions. For many Bayesian methods we must sample to explore the posterior. Here's some basics.
From playlist Machine Learning
Markov Chains : Data Science Basics
The basics of Markov Chains, one of my ALL TIME FAVORITE objects in data science.
From playlist Data Science Basics
Matrix Limits and Markov Chains
In this video I present a cool application of linear algebra in which I use diagonalization to calculate the eventual outcome of a mixing problem. This process is a simple example of what's called a Markov chain. Note: I just got a new tripod and am still experimenting with it; sorry if t
From playlist Eigenvalues
Cécile Mailler : Processus de Pólya à valeur mesure
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From playlist Probability and Statistics
18. Countable-state Markov Chains and Processes
MIT 6.262 Discrete Stochastic Processes, Spring 2011 View the complete course: http://ocw.mit.edu/6-262S11 Instructor: Robert Gallager License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 6.262 Discrete Stochastic Processes, Spring 2011
19. Countable-state Markov Processes
MIT 6.262 Discrete Stochastic Processes, Spring 2011 View the complete course: http://ocw.mit.edu/6-262S11 Instructor: Robert Gallager License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 6.262 Discrete Stochastic Processes, Spring 2011
Zeros of polynomials, decay of correlations, and algorithms by Piyush Srivastava
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From playlist Statistical Physics of Machine Learning 2020
Tom Hutchcroft: Interlacements and the uniform spanning forest
Abstract: The Aldous-Broder algorithm allows one to sample the uniform spanning tree of a finite graph as the set of first-entry edges of a simple random walk. In this talk, I will discuss how this can be extended to infinite transient graphs by replacing the random walk with the random in
From playlist Probability and Statistics
High dimensional expanders - Part 2 - Irit Dinur
Computer Science/Discrete Mathematics Seminar II Topic: High dimensional expanders - Part 2 Speaker: Irit Dinur Affiliation: Weizmann Institute of Science; Visiting Professor, School of Mathematics Date: March 24, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
Johan Segers: Modelling multivariate extreme value distributions via Markov trees
CONFERENCE Recording during the thematic meeting : "Adaptive and High-Dimensional Spatio-Temporal Methods for Forecasting " the September 26, 2022 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks
From playlist Probability and Statistics
Prob & Stats - Markov Chains (9 of 38) What is a Regular Matrix?
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what is a regular matrix. Next video in the Markov Chains series: http://youtu.be/loBUEME5chQ
From playlist iLecturesOnline: Probability & Stats 3: Markov Chains & Stochastic Processes
Linear cover time is exponentially unlikely - Quentin Dubroff
Computer Science/Discrete Mathematics Seminar I Topic: Linear cover time is exponentially unlikely Speaker: Quentin Dubroff Affiliation: Rutgers University Date: March 28, 2022 Proving a 2009 conjecture of Itai Benjamini, we show: For any C, there is a greater than 0 such that for any s
From playlist Mathematics
Markoff surfaces and strong approximation - Alexander Gamburd
Special Seminar Topic: Markoff surfaces and strong approximation Speaker: Alexander Gamburd Affiliation: The Graduate Center, The City University of New York Date: December 8, 2017 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Yuval Peres - Breaking barriers in probability
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From playlist Les probabilités de demain 2016
Markov Chains Clearly Explained! Part - 1
Let's understand Markov chains and its properties with an easy example. I've also discussed the equilibrium state in great detail. #markovchain #datascience #statistics For more videos please subscribe - http://bit.ly/normalizedNERD Markov Chain series - https://www.youtube.com/playl
From playlist Markov Chains Clearly Explained!