(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
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
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
Math 139 Fourier Analysis Lecture 37: Dirichlet's theorem pt.4
Defining the logarithm of an L-function. Second reduction of the problem: proving non-vanishing of the L-function. Case of complex Dirichlet characters.
From playlist Course 8: Fourier Analysis
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
Math 139 Fourier Analysis Lecture 35: Dirichlet's theorem pt. 2
Dirichlet's theorem: reduction of the problem. Dirichlet L-function. Product formula for L-functions. Extension of the logarithm to complex numbers. Convergence of infinite products.
From playlist Course 8: Fourier Analysis
Adam Skalski: Translation invariant noncommutative Dirichlet forms
Talk by Adam Skalski in Global Noncommutative Geometry Seminar (Europe) http://www.noncommutativegeometry.nl/ncgseminar/ on April 28, 2021
From playlist Global Noncommutative Geometry Seminar (Europe)
(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
CTNT 2022 - 100 Years of Chebotarev Density (Lecture 1) - by Keith Conrad
This video is part of a mini-course on "100 Years of Chebotarev Density" that was taught during CTNT 2022, the Connecticut Summer School and Conference in Number Theory. More about CTNT: https://ctnt-summer.math.uconn.edu/
From playlist CTNT 2022 - 100 Years of Chebotarev Density (by Keith Conrad)
Anton Thalmaier: The geometry of subelliptic diffusions
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Probability and Statistics
CTNT 2022 - 100 Years of Chebotarev Density (Lecture 3) - by Keith Conrad
This video is part of a mini-course on "100 Years of Chebotarev Density" that was taught during CTNT 2022, the Connecticut Summer School and Conference in Number Theory. More about CTNT: https://ctnt-summer.math.uconn.edu/
From playlist CTNT 2022 - 100 Years of Chebotarev Density (by Keith Conrad)
Aurel PAGE - Cohomology of arithmetic groups and number theory: geometric, ... 2
In this lecture series, the first part will be dedicated to cohomology of arithmetic groups of lower ranks (e.g., Bianchi groups), their associated geometric models (mainly from hyperbolic geometry) and connexion to number theory. The second part will deal with higher rank groups, mainly
From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory
From playlist Contributed talks One World Symposium 2020
Geometric Langlands and 3d Mirror Symmetry (Lecture 2) by Sam Raskin
Program Quantum Fields, Geometry and Representation Theory 2021 (ONLINE) ORGANIZERS: Aswin Balasubramanian (Rutgers University, USA), Indranil Biswas (TIFR, india), Jacques Distler (The University of Texas at Austin, USA), Chris Elliott (University of Massachusetts, USA) and Pranav Pandi
From playlist Quantum Fields, Geometry and Representation Theory 2021 (ONLINE)
Aurel PAGE - Cohomology of arithmetic groups and number theory: geometric, ... 1
In this lecture series, the first part will be dedicated to cohomology of arithmetic groups of lower ranks (e.g., Bianchi groups), their associated geometric models (mainly from hyperbolic geometry) and connexion to number theory. The second part will deal with higher rank groups, mainly
From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory
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
Representation theory: Dirichlet's theorem
In this talk we see how to use characters of finite abelian groups to prove Dirichlet's theorem that there are infinitely many primes in certain arithmetic progressions. We first recall Euler's proof that there are infinitely many primes, which is the simplest case of Dirichlet's proof. T
From playlist Representation theory
The Heat Equation: Lecture 4 - Oxford Mathematics 1st Year Student Lecture
The heat equation, also known as the diffusion equation, is central to many areas in applied mathematics. In this series of four lectures - this is the fourth - forming part of the first year undergraduate mathematics course, 'Fourier Series and PDEs', the heat equation is derived and the
From playlist Oxford Mathematics 1st Year Student Lectures: The Heat Equation
(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