In probability, a discrete-time Markov chain (DTMC) is a sequence of random variables, known as a stochastic process, in which the value of the next variable depends only on the value of the current variable, and not any variables in the past. For instance, a machine may have two states, A and E. When it is in state A, there is a 40% chance of it moving to state E and a 60% chance of it remaining in state A. When it is in state E, there is a 70% chance of it moving to A and a 30% chance of it staying in E. The sequence of states of the machine is a Markov chain. If we denote the chain by then is the state which the machine starts in and is the random variable describing its state after 10 transitions. The process continues forever, indexed by the natural numbers. An example of a stochastic process which is not a Markov chain is the model of a machine which has states A and E and moves to A from either state with 50% chance if it has ever visited A before, and 20% chance if it has never visited A before (leaving a 50% or 80% chance that the machine moves to E). This is because the behavior of the machine depends on the whole history—if the machine is in E, it may have a 50% or 20% chance of moving to A, depending on its past values. Hence, it does not have the Markov property. A Markov chain can be described by a stochastic matrix, which lists the probabilities of moving to each state from any individual state. From this matrix, the probability of being in a particular state n steps in the future can be calculated. A Markov chain's state space can be partitioned into communicating classes that describe which states are reachable from each other (in one transition or in many). Each state can be described as transient or recurrent, depending on the probability of the chain ever returning to that state. Markov chains can have properties including periodicity, reversibility and stationarity. A continuous-time Markov chain is like a discrete-time Markov chain, but it moves states continuously through time rather than as discrete time steps. Other stochastic processes can satisfy the Markov property, the property that past behavior does not affect the process, only the present state. (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
(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
L24.4 Discrete-Time Finite-State Markov Chains
MIT RES.6-012 Introduction to Probability, Spring 2018 View the complete course: https://ocw.mit.edu/RES-6-012S18 Instructor: Patrick Jaillet License: Creative Commons BY-NC-SA More information at https://ocw.mit.edu/terms More courses at https://ocw.mit.edu
From playlist MIT RES.6-012 Introduction to Probability, Spring 2018
(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 (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
Intro to Markov Chains & Transition Diagrams
Markov Chains or Markov Processes are an extremely powerful tool from probability and statistics. They represent a statistical process that happens over and over again, where we try to predict the future state of a system. A markov process is one where the probability of the future ONLY de
From playlist Discrete Math (Full Course: Sets, Logic, Proofs, Probability, Graph Theory, etc)
(ML 18.3) Stationary distributions, Irreducibility, and Aperiodicity
Definitions of the properties of Markov chains used in the Ergodic Theorem: time-homogeneous MC, stationary distribution of a MC, irreducible MC, aperiodic MC.
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
MIT RES.6-012 Introduction to Probability, Spring 2018 View the complete course: https://ocw.mit.edu/RES-6-012S18 Instructor: Patrick Jaillet License: Creative Commons BY-NC-SA More information at https://ocw.mit.edu/terms More courses at https://ocw.mit.edu
From playlist MIT RES.6-012 Introduction to Probability, Spring 2018
From playlist Contributed talks One World Symposium 2020
(ML 18.2) Ergodic theorem for Markov chains
Statement of the Ergodic Theorem for (discrete-time) Markov chains. This gives conditions under which the average over time converges to the expected value, and under which the marginal distributions converge to the stationary distribution.
From playlist Machine Learning
Markov processes and applications by Hugo Touchette
PROGRAM : BANGALORE SCHOOL ON STATISTICAL PHYSICS - XII (ONLINE) ORGANIZERS : Abhishek Dhar (ICTS-TIFR, Bengaluru) and Sanjib Sabhapandit (RRI, Bengaluru) DATE : 28 June 2021 to 09 July 2021 VENUE : Online Due to the ongoing COVID-19 pandemic, the school will be conducted through online
From playlist Bangalore School on Statistical Physics - XII (ONLINE) 2021
Max Fathi: Ricci curvature and functional inequalities for interacting particle systems
I will present a few results on entropic Ricci curvature bounds, with applications to interacting particle systems. The notion was introduced by M. Erbar and J. Maas and independently by A. Mielke. These curvature bounds can be used to prove functional inequalities, such as spectral gap bo
From playlist HIM Lectures: Follow-up Workshop to JTP "Optimal Transportation"
Markov processes and applications-2 by Hugo Touchette
PROGRAM : BANGALORE SCHOOL ON STATISTICAL PHYSICS - XII (ONLINE) ORGANIZERS : Abhishek Dhar (ICTS-TIFR, Bengaluru) and Sanjib Sabhapandit (RRI, Bengaluru) DATE : 28 June 2021 to 09 July 2021 VENUE : Online Due to the ongoing COVID-19 pandemic, the school will be conducted through online
From playlist Bangalore School on Statistical Physics - XII (ONLINE) 2021
Regenerative sequences and processes and MCMC by Krishna Athreya
Large deviation theory in statistical physics: Recent advances and future challenges DATE: 14 August 2017 to 13 October 2017 VENUE: Madhava Lecture Hall, ICTS, Bengaluru Large deviation theory made its way into statistical physics as a mathematical framework for studying equilibrium syst
From playlist Large deviation theory in statistical physics: Recent advances and future challenges
Localization schemes: A framework for proving mixing bounds for Markov chains - Ronen Eldan
Computer Science/Discrete Mathematics Seminar II Topic: Localization schemes: A framework for proving mixing bounds for Markov chains Speaker: Ronen Eldan Affiliation: von Neumann Fellow, School of Mathematics Date: March 15, 2022 Two recent and seemingly-unrelated techniques for proving
From playlist Mathematics
Brain Teasers: 10. Winning in a Markov chain
In this exercise we use the absorbing equations for Markov Chains, to solve a simple game between two players. The Zoom connection was not very stable, hence there are a few audio problems. Sorry.
From playlist Brain Teasers and Quant Interviews