In mathematics, the Dirichlet beta function (also known as the Catalan beta function) is a special function, closely related to the Riemann zeta function. It is a particular Dirichlet L-function, the L-function for the alternating character of period four. (Wikipedia).
(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
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
Introduction to the Dirac Delta Function
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From playlist Differential Equations
Deriving one RIDICULOUS Integral Representation for the DIRICHLET ETA FUNCTION on the Unit Square!
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From playlist Integrals
Explanation of the Dirac delta function and its Laplace transform. Join me on Coursera: Matrix Algebra for Engineers: https://www.coursera.org/learn/matrix-algebra-engineers Differential Equations for Engineers: https://www.coursera.org/learn/differential-equations-engineers Vector Ca
From playlist Differential Equations
Topic Models: Variational Inference for Latent Dirichlet Allocation (with Xanda Schofield)
This is a single lecture from a course. If you you like the material and want more context (e.g., the lectures that came before), check out the whole course: https://sites.google.com/umd.edu/2021cl1webpage/ (Including homeworks and reading.) Xanda's Webpage: https://www.cs.hmc.edu/~xanda
From playlist Computational Linguistics I
(ML 8.5) Bayesian Naive Bayes (part 3)
When all the features are categorical, a naïve Bayes classifier can be made fully Bayesian by putting Dirichlet priors on the parameters and (exactly) integrating them out.
From playlist Machine Learning
Alexandra Florea: The Ratios Conjecture over function fields
I will talk about some recent joint work with H. Bui and J. Keating where we study the Ratios Conjecture for the family of quadratic L-functions over function fields. I will also discuss the closely related problem of obtaining upper bounds for negative moments of L-functions, which allows
From playlist Seminar Series "Arithmetic Applications of Fourier Analysis"
(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
Math 139 Fourier Analysis Lecture 38: Finishing proof of Dirichlet's theorem
Showing the non-vanishing of the L-function for real Dirichlet characters. Approximation of L(1,X) with hyperbolic sums to finish the theorem.
From playlist Course 8: Fourier Analysis
(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
Kannan Soundararajan - 2/4 L-function
Kannan Soundararajan - L-function
From playlist École d'été 2014 - Théorie analytique des nombres
Index theorems for nodal count and a lateral variation principle - Gregory Berkolaiko
Analysis Seminar Topic: Index theorems for nodal count and a lateral variation principle Speaker: Gregory Berkolaiko Affiliation: Texas A&M University Date: February 01, 2021 For more video please visit http://video.ias.edu
From playlist Mathematics
From playlist Contributed talks One World Symposium 2020
Math 139 Fourier Analysis Lecture 06: Convolutions and Approximations of the Identity, ct'd.
Convolutions and Good Kernels, continued. Interaction of convolution with Fourier transform (for integrable functions). Approximations of the Identity (family of good kernels). Recovery of the value of a function at a point of continuity using approximations of the identity. Uniform co
From playlist Course 8: Fourier Analysis
Kannan Soundararajan - 3/4 L-function
Kannan Soundararajan - L-function
From playlist École d'été 2014 - Théorie analytique des nombres
Roland Bauerschmidt: Lecture #3
This is a third lecture on "Log-Sobolev inequality and the renormalisation group" by Dr. Roland Bauerschmidt. For more materials and slides visit: https://sites.google.com/view/oneworld-pderandom/home
From playlist Summer School on PDE & Randomness
Dirac delta function | Lecture 33 | Differential Equations for Engineers
Definition of the Dirac delta function and its Laplace transform. Join me on Coursera: https://www.coursera.org/learn/differential-equations-engineers Lecture notes at http://www.math.ust.hk/~machas/differential-equations-for-engineers.pdf Subscribe to my channel: http://www.youtube.co
From playlist Differential Equations for Engineers
The distribution of values of zeta and L-functions
50 Years of Number Theory and Random Matrix Theory Conference Topic: The distribution of values of zeta and L-functions Speaker: Kannan Soundararajan Affiliation: Stanford University Date: June 21, 2022 I will survey recent progress on understanding the value distribution of zeta and L-f
From playlist Mathematics