In machine learning, kernel machines are a class of algorithms for pattern analysis, whose best known member is the support-vector machine (SVM). The general task of pattern analysis is to find and study general types of relations (for example clusters, rankings, principal components, correlations, classifications) in datasets. For many algorithms that solve these tasks, the data in raw representation have to be explicitly transformed into feature vector representations via a user-specified feature map: in contrast, kernel methods require only a user-specified kernel, i.e., a similarity function over all pairs of data points computed using Inner products. The feature map in kernel machines is infinite dimensional but only requires a finite dimensional matrix from user-input according to the Representer theorem. Kernel machines are slow to compute for datasets larger than a couple of thousand examples without parallel processing. Kernel methods owe their name to the use of kernel functions, which enable them to operate in a high-dimensional, implicit feature space without ever computing the coordinates of the data in that space, but rather by simply computing the inner products between the images of all pairs of data in the feature space. This operation is often computationally cheaper than the explicit computation of the coordinates. This approach is called the "kernel trick". Kernel functions have been introduced for sequence data, graphs, text, images, as well as vectors. Algorithms capable of operating with kernels include the kernel perceptron, support-vector machines (SVM), Gaussian processes, principal components analysis (PCA), canonical correlation analysis, ridge regression, spectral clustering, linear adaptive filters and many others. Most kernel algorithms are based on convex optimization or eigenproblems and are statistically well-founded. Typically, their statistical properties are analyzed using statistical learning theory (for example, using Rademacher complexity). (Wikipedia).
The Kernel Trick - THE MATH YOU SHOULD KNOW!
Some parametric methods, like polynomial regression and Support Vector Machines stand out as being very versatile. This is due to a concept called "Kernelization". In this video, we are going to kernelize linear regression. And show how they can be incorporated in other Algorithms to solv
From playlist The Math You Should Know
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
Kernel Recipes 2018 - Knowing the definition of Linux kernel to...- Vaishali Thakkar
Self learning is underrated in the modern era of education. While kernel being the heart of an operating system, traditional universities [in India] are still far away from teaching anything more than the definition of Linux Kernel. The talk will mostly focus on my journey of self learning
From playlist Kernel Recipes 2018
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
Kernel Recipes 2022 - Checking your work: validating the kernel by building and testing in CI
The Linux kernel is one of the most complex pieces of software ever written. Being in ring 0, bugs in the kernel are a big problem, so having confidence in the correctness and robustness of the kernel is incredibly important. This is difficult enough for a single version and configuration
From playlist Kernel Recipes 2022
Determine a Basis for the Kernel of a Matrix Transformation (3 by 4)
This video explains how to determine a basis for the kernel of a matrix transformation.
From playlist Kernel and Image of Linear Transformation
Why Kernels - Practical Machine Learning Tutorial with Python p.30
Once we've determined that we can use Kernels, the next question is of course why would we bother using kernels when we can use some other function to transform our data into more dimensions. The point of using Kernels is to be able to perform a calculation (inner product in this case) in
From playlist Machine Learning with Python
Nonlinear dimensionality reduction for faster kernel methods in machine learning - Christopher Musco
Computer Science/Discrete Mathematics Seminar I Topic: Nonlinear dimensionality reduction for faster kernel methods in machine learning. Speaker: Christopher Musco Affiliation: Massachusetts Institute of Technology Date: Febuary 12, 2018 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Blind Image Deblurring: What is the Next Step?
39th Imaging & Inverse Problems (IMAGINE) OneWorld SIAM-IS Virtual Seminar Series Talk Date: February 16, 10:00am Eastern Time Zone (US & Canada) / 2:00pm GMT Speaker: Tieyong Zeng, Chinese University, Hong Kong Abstract: Blind image deblurring is a challenging task in imaging science whe
From playlist Imaging & Inverse Problems (IMAGINE) OneWorld SIAM-IS Virtual Seminar Series
Kernel Learning for Robust Dynamic Mode Decomposition
In this video abstract, I present our new data-driven method for learning high-dimensional, nonlinear dynamical systems via kernel methods. This work is in collaboration with Profs Benjamin Herrmann, Beverley McKeon and Steve Brunton. The paper is available on arXiv: Title: Kernel Learni
From playlist Research Abstracts from Brunton Lab
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 Basics and Kernel Methods (Tutorial) by Mikhail Belkin
Statistical Physics Methods in Machine Learning DATE:26 December 2017 to 30 December 2017 VENUE:Ramanujan Lecture Hall, ICTS, Bengaluru The theme of this Discussion Meeting is the analysis of distributed/networked algorithms in machine learning and theoretical computer science in the "th
From playlist Statistical Physics Methods in Machine Learning
Is Memorization Compatible with Learning? by Sasha Rakhlin
Program Advances in Applied Probability II (ONLINE) ORGANIZERS: Vivek S Borkar (IIT Bombay, India), Sandeep Juneja (TIFR Mumbai, India), Kavita Ramanan (Brown University, Rhode Island), Devavrat Shah (MIT, US) and Piyush Srivastava (TIFR Mumbai, India) DATE: 04 January 2021 to 08 Januar
From playlist Advances in Applied Probability II (Online)
On the Connection between Neural Networks and Kernels: a Modern Perspective - Simon Du
Short talks by postdoctoral members Topic: On the Connection between Neural Networks and Kernels: a Modern Perspective Speaker: Simon Du Affiliation: Member, School of Mathematics For more video please visit http://video.ias.edu
From playlist Mathematics
From playlist Plenary talks One World Symposium 2020
Algorithm and Hardness for Kernel Matrices in Numerical Linear Algebra...- Zhao Song
Seminar on Theoretical Machine Learning Topic: Algorithm and Hardness for Kernel Matrices in Numerical Linear Algebra and Machine Learning Speaker: Zhao Song Affiliation: Member, School of Mathematics Date: February 04, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
Score estimation with infinite-dimensional exponential families – Dougal Sutherland, UCL
Many problems in science and engineering involve an underlying unknown complex process that depends on a large number of parameters. The goal in many applications is to reconstruct, or learn, the unknown process given some direct or indirect observations. Mathematically, such a problem can
From playlist Approximating high dimensional functions