(ML 13.6) Graphical model for Bayesian linear regression
As an example, we write down the graphical model for Bayesian linear regression. We introduce the "plate notation", and the convention of shading random variables which are being conditioned on.
From playlist Machine Learning
Numerically Calculating Partial Derivatives
In this video we discuss how to calculate partial derivatives of a function using numerical techniques. In other words, these partials are calculated without needing an analytical representation of the function. This is useful in situations where the function in question is either too co
From playlist Vector Differential Calculus
We propose a sparse regression method capable of discovering the governing partial differential equation(s) of a given system by time series measurements in the spatial domain. The regression framework relies on sparsity promoting techniques to select the nonlinear and partial derivative
From playlist Research Abstracts from Brunton Lab
B27 Introduction to linear models
Now that we finally now some techniques to solve simple differential equations, let's apply them to some real-world problems.
From playlist Differential Equations
Convolution In this video, I introduce the notion of convolution and give an example and some applications. It is a very way of multiplying two functions that is useful analysis and PDEs. Here is the demo I showed: https://phiresky.github.io/convolution-demo/ Convolution Intuition: http
From playlist Partial Differential Equations
(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
Essential Cosmological Perturbation Theory by David Wands
PROGRAM : PHYSICS OF THE EARLY UNIVERSE - AN ONLINE PRECURSOR ORGANIZERS : Robert Brandenberger (McGill University, Montreal, Canada), Jerome Martin (Institut d'Astrophysique de Paris, France), Subodh Patil (Instituut-Lorentz for Theoretical Physics, Leiden, Netherlands) and L Sriramkumar
From playlist Physics of The Early Universe - An Online Precursor
The Problem of Traffic: A Mathematical Modeling Journey
How can we mathematically model traffic? Specifically we will study the problem of a single lane of cars and the perturbation from equilibrium that occurs when one car brakes, and that braking effect travels down the line of cars, amplifying as it goes along, due to the delayed reaction ti
From playlist Cool Math Series
33. Electronic Spectroscopy: Franck-Condon
MIT 5.61 Physical Chemistry, Fall 2017 Instructor: Professor Robert Field View the complete course: https://ocw.mit.edu/5-61F17 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62RsEHXe48Imi9-87FzQaJg This lecture covers intermolecular interactions, electronic spectrosco
From playlist MIT 5.61 Physical Chemistry, Fall 2017
Michal KOWALCZYK - Kink dynamics in the $\phi^4$ model...
Kink dynamics in the $\phi^4$ model: asymptotic stability for odd perturbations in the energy space We consider a classical equation $\[\phi_{tt}-\phi_{xx}=\phi-\phi^3,\quad (t,x)\in\RR\times\RR\] known as the $\phi^4$ model in one space dimension. The kink, defined by $H(x)=\tanh(x/{\sqr
From playlist Trimestre "Ondes Non linéaires" - June Conference
Least squares method for simple linear regression
In this video I show you how to derive the equations for the coefficients of the simple linear regression line. The least squares method for the simple linear regression line, requires the calculation of the intercept and the slope, commonly written as beta-sub-zero and beta-sub-one. Deriv
From playlist Machine learning
Cosmological Perturbation Theory (Lecture 1) by David Wands
PROGRAM PHYSICS OF THE EARLY UNIVERSE (HYBRID) ORGANIZERS: Robert Brandenberger (McGill University, Canada), Jerome Martin (IAP, France), Subodh Patil (Leiden University, Netherlands) and L. Sriramkumar (IIT - Madras, India) DATE: 03 January 2022 to 12 January 2022 VENUE: Online and Ra
From playlist Physics of the Early Universe - 2022
(ML 10.6) Predictive distribution for linear regression (part 3)
How to compute the (posterior) predictive distribution for a new point, under a Bayesian model for linear regression.
From playlist Machine Learning
Introduction to Resurgence, Trans-series and Non-perturbative Physics II by Gerald Dunne
Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography DATE:27 January 2018 to 03 February 2018 VENUE:Ramanujan Lecture Hall, ICTS Bangalore The program "Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography" aims to
From playlist Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography
Hossein Mobahi: "Differential Operators for Generating Structured Adversarial Examples"
High Dimensional Hamilton-Jacobi PDEs 2020 Workshop II: PDE and Inverse Problem Methods in Machine Learning "Differential Operators for Generating Structured Adversarial Examples" Hossein Mobahi - Google AI Abstract: Adversarial examples are created by adding a small perturbation to an i
From playlist High Dimensional Hamilton-Jacobi PDEs 2020
Wei Wu -- Massless phases for the Villain model in dimension 3 and greater
The XY and the Villain models are mathematical idealization of real world models of liquid crystal, liquid helium, and superconductors. Their phase transition has important applications in condensed matter physics and led to the Nobel Prize in Physics in 2016. However we are still far from
From playlist Columbia Probability Seminar
(ML 10.7) Predictive distribution for linear regression (part 4)
How to compute the (posterior) predictive distribution for a new point, under a Bayesian model for linear regression.
From playlist Machine Learning
Galaxy Bias Loops by Roman Scoccimarro
Program Cosmology - The Next Decade ORGANIZERS : Rishi Khatri, Subha Majumdar and Aseem Paranjape DATE : 03 January 2019 to 25 January 2019 VENUE : Ramanujan Lecture Hall, ICTS Bangalore The great observational progress in cosmology has revealed some very intriguing puzzles, the most i
From playlist Cosmology - The Next Decade