Within bayesian statistics for machine learning, kernel methods arise from the assumption of an inner product space or similarity structure on inputs. For some such methods, such as support vector machines (SVMs), the original formulation and its regularization were not Bayesian in nature. It is helpful to understand them from a Bayesian perspective. Because the kernels are not necessarily positive semidefinite, the underlying structure may not be inner product spaces, but instead more general reproducing kernel Hilbert spaces. In Bayesian probability kernel methods are a key component of Gaussian processes, where the kernel function is known as the covariance function. Kernel methods have traditionally been used in supervised learning problems where the input space is usually a space of vectors while the output space is a space of scalars. More recently these methods have been extended to problems that deal with multiple outputs such as in multi-task learning. A mathematical equivalence between the regularization and the Bayesian point of view is easily proved in cases where the reproducing kernel Hilbert space is finite-dimensional. The infinite-dimensional case raises subtle mathematical issues; we will consider here the finite-dimensional case. We start with a brief review of the main ideas underlying kernel methods for scalar learning, and briefly introduce the concepts of regularization and Gaussian processes. We then show how both points of view arrive at essentially equivalent estimators, and show the connection that ties them together. (Wikipedia).
(ML 7.1) Bayesian inference - A simple example
Illustration of the main idea of Bayesian inference, in the simple case of a univariate Gaussian with a Gaussian prior on the mean (and known variances).
From playlist Machine Learning
Bayesian vs frequentist statistics probability - part 1
This video provides an intuitive explanation of the difference between Bayesian and classical frequentist statistics. If you are interested in seeing more of the material, arranged into a playlist, please visit: https://www.youtube.com/playlist?list=PLFDbGp5YzjqXQ4oE4w9GVWdiokWB9gEpm Unfo
From playlist Bayesian statistics: a comprehensive course
(ML 11.8) Bayesian decision theory
Choosing an optimal decision rule under a Bayesian model. An informal discussion of Bayes rules, generalized Bayes rules, and the complete class theorems.
From playlist Machine Learning
Kernel of a group homomorphism
In this video I introduce the definition of a kernel of a group homomorphism. It is simply the set of all elements in a group that map to the identity element in a second group under the homomorphism. The video also contain the proofs to show that the kernel is a normal subgroup.
From playlist Abstract algebra
(ML 11.4) Choosing a decision rule - Bayesian and frequentist
Choosing a decision rule, from Bayesian and frequentist perspectives. To make the problem well-defined from the frequentist perspective, some additional guiding principle is introduced such as unbiasedness, minimax, or invariance.
From playlist Machine Learning
Stanford CS229: Machine Learning | Summer 2019 | Lecture 9 - Bayesian Methods - Parametric & Non
For more information about Stanford’s Artificial Intelligence professional and graduate programs, visit: https://stanford.io/3ptRUmB Anand Avati Computer Science, PhD To follow along with the course schedule and syllabus, visit: http://cs229.stanford.edu/syllabus-summer2019.html
From playlist Stanford CS229: Machine Learning Course | Summer 2019 (Anand Avati)
ML Tutorial: Bayesian Machine Learning (Zoubin Ghahramani)
Machine Learning Tutorial at Imperial College London: Bayesian Machine Learning Zoubin Ghahramani (University of Cambridge) January 29, 2014
From playlist Machine Learning Tutorials
Compositional inductive biases in human function learning - Samuel J. Gershman
IAS-PNI Seminar on ML and Neuroscience Topic: Compositional inductive biases in human function learning Speaker: Samuel J. Gershman Affiliation: Harvard University Date: January 14, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
Calculating dimension and basis of range and kernel
German version here: https://youtu.be/lBdwtUa_BGM Support the channel on Steady: https://steadyhq.com/en/brightsideofmaths Official supporters in this month: - Petar Djurkovic - Lukas Mührke Here, I explain the typical calculation scheme for getting dimension and basis for the image/ran
From playlist Linear algebra (English)
Regularization (Machine Learning): Georg Gottwald
Machine Learning for the Working Mathematician: Week Four 17 March 2022 Georg Gottwald, Regularization Seminar series homepage (includes Zoom link): https://sites.google.com/view/mlwm-seminar-2022
From playlist Machine Learning for the Working Mathematician
Determine the Kernel of a Linear Transformation Given a Matrix (R3, x to 0)
This video explains how to determine the kernel of a linear transformation.
From playlist Kernel and Image of Linear Transformation
Marcelo Pereyra: Bayesian inference and mathematical imaging - Lecture 2: Markov chain Monte Carlo
Bayesian inference and mathematical imaging - Part 2: Markov chain Monte Carlo Abstract: This course presents an overview of modern Bayesian strategies for solving imaging inverse problems. We will start by introducing the Bayesian statistical decision theory framework underpinning Bayesi
From playlist Probability and Statistics
Introduction to the Kernel and Image of a Linear Transformation
This video introduced the topics of kernel and image of a linear transformation.
From playlist Kernel and Image of Linear Transformation
From playlist COMP0168 (2020/21)
Stanford CS330 Deep Multi-Task & Meta Learning - Bayesian Meta-Learning l 2022 I Lecture 12
For more information about Stanford's Artificial Intelligence programs visit: https://stanford.io/ai To follow along with the course, visit: https://cs330.stanford.edu/ To view all online courses and programs offered by Stanford, visit: http://online.stanford.edu Chelsea Finn Computer
From playlist Stanford CS330: Deep Multi-Task and Meta Learning I Autumn 2022
11d Machine Learning: Bayesian Linear Regression
Lecture on Bayesian linear regression. By adopting the Bayesian approach (instead of the frequentist approach of ordinary least squares linear regression) we can account for prior information and directly model the distributions of the model parameters by updating with training data. Foll
From playlist Machine Learning
Andreas Mueller - Automated Machine Learning - AI With The Best Oct 2017
AI With The Best hosted 50+ speakers and hundreds of attendees from all over the world on a single platform on October 14-15, 2017. The platform held live talks, Insights/Questions pages, and bookings for 1-on-1s with speakers. Recent years have seen a widespread adoption of machine learn
From playlist talks
Andreas Krause: "Safe and Efficient Exploration in Reinforcement Learning"
Intersections between Control, Learning and Optimization 2020 "Safe and Efficient Exploration in Reinforcement Learning" Andreas Krause - ETH Zurich Abstract: At the heart of Reinforcement Learning lies the challenge of trading exploration -- collecting data for learning better models --
From playlist Intersections between Control, Learning and Optimization 2020
Bayesian vs frequentist statistics
This video provides an intuitive explanation of the difference between Bayesian and classical frequentist statistics. If you are interested in seeing more of the material, arranged into a playlist, please visit: https://www.youtube.com/playlist?list=PLFDbGp5YzjqXQ4oE4w9GVWdiokWB9gEpm Un
From playlist Bayesian statistics: a comprehensive course
ML Tutorial: Probabilistic Numerical Methods (Jon Cockayne)
Machine Learning Tutorial at Imperial College London: Probabilistic Numerical Methods Jon Cockayne (University of Warwick) February 22, 2017
From playlist Machine Learning Tutorials