(ML 7.7.A1) Dirichlet distribution
Definition of the Dirichlet distribution, what it looks like, intuition for what the parameters control, and some statistics: mean, mode, and variance.
From playlist Machine Learning
(ML 7.7) Dirichlet-Categorical model (part 1)
The Dirichlet distribution is a conjugate prior for the Categorical distribution (i.e. a PMF a finite set). We derive the posterior distribution and the (posterior) predictive distribution under this model.
From playlist Machine Learning
(ML 7.8) Dirichlet-Categorical model (part 2)
The Dirichlet distribution is a conjugate prior for the Categorical distribution (i.e. a PMF a finite set). We derive the posterior distribution and the (posterior) predictive distribution under this model.
From playlist Machine Learning
Dirichlet Eta Function - Integral Representation
Today, we use an integral to derive one of the integral representations for the Dirichlet eta function. This representation is very similar to the Riemann zeta function, which explains why their respective infinite series definition is quite similar (with the eta function being an alte rna
From playlist Integrals
Using Fourier Series to Derive the Dirichlet Kernel
Help me create more free content! =) https://www.patreon.com/mathable Merch :v - https://teespring.com/de/stores/papaflammy https://shop.spreadshirt.de/papaflammy Let's continue the Kernel Extravaganza! TOday we are going to approximate the fourier series of a random f
From playlist Fourier Series
Exploration of Stick-breaking Process to Develop Efficient Algorithms.... by Mrinal Das
DISCUSSION MEETING THE THEORETICAL BASIS OF MACHINE LEARNING (ML) ORGANIZERS: Chiranjib Bhattacharya, Sunita Sarawagi, Ravi Sundaram and SVN Vishwanathan DATE : 27 December 2018 to 29 December 2018 VENUE : Ramanujan Lecture Hall, ICTS, Bangalore ML (Machine Learning) has enjoyed tr
From playlist The Theoretical Basis of Machine Learning 2018 (ML)
(Original Paper) Latent Dirichlet Allocation (discussions) | AISC Foundational
Toronto Deep Learning Series, 15 November 2018 Paper Review: http://www.jmlr.org/papers/volume3/blei03a/blei03a.pdf Speaker: Renyu Li (Wysdom.ai) Host: Munich Reinsurance Co-Canada Date: Nov 15th, 2018 Latent Dirichlet Allocation We describe latent Dirichlet allocation (LDA), a genera
From playlist Natural Language Processing
Susan Holmes: "Latent variables explain dependencies in bacterial communities"
Emerging Opportunities for Mathematics in the Microbiome 2020 "Latent variables explain dependencies in bacterial communities" Susan Holmes - Stanford University, Statistics Abstract: Data from sequencing bacterial communities are formalized as contingency tables whose columns correspond
From playlist Emerging Opportunities for Mathematics in the Microbiome 2020
Neural opinion dynamics model for the prediction of user-level stance dynamics - Yulan He, Warwick
Around the world, digital participation platforms are being used as a tool for direct democracy, aiming to empower citizens to contribute to policy making. As trust in traditional democratic institutions declines, these deliberative platforms offer a way to build new relationships and trus
From playlist Citizen participation and machine learning for a better democracy
In visual computing, point locations are often optimized using a "repulsive" energy, to obtain a nice uniform distribution for tasks ranging from image stippling to mesh generation to fluid simulation. But how do you perform this same kind of repulsive optimization on curves and surfaces?
From playlist Repulsive Videos
Math 139 Fourier Analysis Lecture 08: Dirichlet Problem on the Unit Disc
Dirichlet problem on the Unit Disc: the problem; the Poisson integral solves the heat equation. L^2 convergence of Fourier Series: definition of L^2 norm; quick review of relevant ideas from linear algebra (vector space, inner product, norm, orthogonal, Pythagorean Theorem, Cauchy-Schwarz
From playlist Course 8: Fourier Analysis
Rémi Bardenet: A tutorial on Bayesian machine learning: what, why and how - lecture 2
HYBRID EVENT Recorded during the meeting "End-to-end Bayesian Learning Methods " the October 25, 2021 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's
From playlist Mathematical Aspects of Computer Science
Deriving one RIDICULOUS Integral Representation for the DIRICHLET ETA FUNCTION on the Unit Square!
Help me create more free content! =) https://www.patreon.com/mathable Merch :v - https://teespring.com/de/stores/papaflammy https://shop.spreadshirt.de/papaflammy 2nd Channel: https://www.youtube.com/channel/UCPctvztDTC3qYa2amc8eTrg Unit Square Zeta: https://www.youtub
From playlist Integrals
Theory of numbers: Dirichlet series
This lecture is part of an online undergraduate course on the theory of numbers. We describe the correspondence between Dirichlet series and arithmetic functions, and work out the Dirichlet series of the arithmetic functions in the previous lecture. Correction: Dave Neary pointed out t
From playlist Theory of numbers
From playlist Plenary talks One World Symposium 2020
Daniel Yekutieli: Hierarchical Bayes Modeling for Large-Scale Inference
CIRM VIRTUAL EVENT Recorded during the meeting "Mathematical Methods of Modern Statistics 2" the June 03, 2020 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians
From playlist Virtual Conference
This lecture is part of an online graduate course on modular forms. We introduce modular forms, and give several examples of how they were used to solve problems in apparently unrelated areas of mathematics. I will not be following any particular book, but if anyone wants a suggestion
From playlist Modular forms
From playlist Contributed talks One World Symposium 2020
(Original Paper) Latent Dirichlet Allocation (algorithm) | AISC Foundational
Toronto Deep Learning Series, 15 November 2018 Paper Review: http://www.jmlr.org/papers/volume3/blei03a/blei03a.pdf Speaker: Renyu Li (Wysdom.ai) Host: Munich Reinsurance Co-Canada Date: Nov 15th, 2018 Latent Dirichlet Allocation We describe latent Dirichlet allocation (LDA), a genera
From playlist Natural Language Processing
(ML 7.7.A2) Expectation of a Dirichlet random variable
How to compute the expected value of a Dirichlet distributed random variable.
From playlist Machine Learning