A great introduction to Multivariate Gaussian Distributations:
https://www.youtube.com/watch?v=eho8xH3E6mE
#statistics
https://www.youtube.com/watch?v=eho8xH3E6mE
#statistics
YouTube
Multivariate Gaussian distributions
Properties of the multivariate Gaussian probability distribution
A great introduction to Multivariate Gaussian Distributations:
https://www.youtube.com/watch?v=JNlEIEwe-Cg
#statistics
https://www.youtube.com/watch?v=JNlEIEwe-Cg
#statistics
YouTube
Gaussian Mixture Models - The Math of Intelligence (Week 7)
We're going to predict customer churn using a clustering technique called the Gaussian Mixture Model! This is a probability distribution that consists of multiple Gaussian distributions, very cool. I also have something important but unrelated to say in the…
An Improved EM algorithm
In this paper, we firstly give a brief introduction of expectation maximization (EM) algorithm, and then discuss the initial value sensitivity of expectation maximization algorithm. Subsequently, we give a short proof of EM's convergence. Then, we implement experiments with the expectation maximization algorithm (We implement all the experiments on Gaussion mixture model (GMM)). Our experiment with expectation maximization is performed in the following three cases: initialize randomly; initialize with result of K-means; initialize with result of K-medoids. The experiment result shows that expectation maximization algorithm depend on its initial state or parameters. And we found that EM initialized with K-medoids performed better than both the one initialized with K-means and the one initialized randomly.
https://arxiv.org/abs/1305.0626
#machine_learning #statistics
In this paper, we firstly give a brief introduction of expectation maximization (EM) algorithm, and then discuss the initial value sensitivity of expectation maximization algorithm. Subsequently, we give a short proof of EM's convergence. Then, we implement experiments with the expectation maximization algorithm (We implement all the experiments on Gaussion mixture model (GMM)). Our experiment with expectation maximization is performed in the following three cases: initialize randomly; initialize with result of K-means; initialize with result of K-medoids. The experiment result shows that expectation maximization algorithm depend on its initial state or parameters. And we found that EM initialized with K-medoids performed better than both the one initialized with K-means and the one initialized randomly.
https://arxiv.org/abs/1305.0626
#machine_learning #statistics
arXiv.org
An Improved EM algorithm
In this paper, we firstly give a brief introduction of expectation
maximization (EM) algorithm, and then discuss the initial value sensitivity of
expectation maximization algorithm. Subsequently,...
maximization (EM) algorithm, and then discuss the initial value sensitivity of
expectation maximization algorithm. Subsequently,...
Complete Statistical Theory of Learning
https://www.youtube.com/watch?v=Ow25mjFjSmg
#statistics #machine_learning
#theory
https://www.youtube.com/watch?v=Ow25mjFjSmg
#statistics #machine_learning
#theory
YouTube
Complete Statistical Theory of Learning (Vladimir Vapnik) | MIT Deep Learning Series
Lecture by Vladimir Vapnik in January 2020, part of the MIT Deep Learning Lecture Series.
Slides: http://bit.ly/2ORVofC
Associated podcast conversation: https://www.youtube.com/watch?v=bQa7hpUpMzM
Series website: https://deeplearning.mit.edu
Playlist: ht…
Slides: http://bit.ly/2ORVofC
Associated podcast conversation: https://www.youtube.com/watch?v=bQa7hpUpMzM
Series website: https://deeplearning.mit.edu
Playlist: ht…
The Underlying Mathematics of New Coronavirus (COVID-19) Growth
https://www.youtube.com/watch?v=Kas0tIxDvrg
#math #statistics
https://www.youtube.com/watch?v=Kas0tIxDvrg
#math #statistics
YouTube
Exponential growth and epidemics
A primer on exponential and logistic growth
Help fund future projects: https://www.patreon.com/3blue1brown
An equally valuable form of support is to simply share some of the videos.
Special thanks to these supporters: http://3b1b.co/covid-thanks
Home page:…
Help fund future projects: https://www.patreon.com/3blue1brown
An equally valuable form of support is to simply share some of the videos.
Special thanks to these supporters: http://3b1b.co/covid-thanks
Home page:…
At the Interface of Algebra and Statistics
Abstract: This thesis takes inspiration from quantum physics to investigate mathematical structure that lies at the interface of algebra and statistics. The starting point is a passage from classical probability theory to quantum probability theory. The quantum version of a probability distribution is a density operator, the quantum version of marginalizing is an operation called the partial trace, and the quantum version of a marginal probability distribution is a reduced density operator. Every joint probability distribution on a finite set can be modeled as a rank one density operator. By applying the partial trace, we obtain reduced density operators whose diagonals recover classical marginal probabilities. In general, these reduced densities will have rank higher than one, and their eigenvalues and eigenvectors will contain extra information that encodes subsystem interactions governed by statistics. We decode this information, and show it is akin to conditional probability, and then investigate the extent to which the eigenvectors capture "concepts" inherent in the original joint distribution. The theory is then illustrated with an experiment that exploits these ideas. Turning to a more theoretical application, we also discuss a preliminary framework for modeling entailment and concept hierarchy in natural language, namely, by representing expressions in the language as densities. Finally, initial inspiration for this thesis comes from formal concept analysis, which finds many striking parallels with the linear algebra. The parallels are not coincidental, and a common blueprint is found in category theory. We close with an exposition on free (co)completions and how the free-forgetful adjunctions in which they arise strongly suggest that in certain categorical contexts, the "fixed points" of a morphism with its adjoint encode interesting information.
Introductory Video: https://youtu.be/wiadG3ywJIs
Thesis: https://arxiv.org/abs/2004.05631
#statistics #machine_learning #algebra #quantum_physics
Abstract: This thesis takes inspiration from quantum physics to investigate mathematical structure that lies at the interface of algebra and statistics. The starting point is a passage from classical probability theory to quantum probability theory. The quantum version of a probability distribution is a density operator, the quantum version of marginalizing is an operation called the partial trace, and the quantum version of a marginal probability distribution is a reduced density operator. Every joint probability distribution on a finite set can be modeled as a rank one density operator. By applying the partial trace, we obtain reduced density operators whose diagonals recover classical marginal probabilities. In general, these reduced densities will have rank higher than one, and their eigenvalues and eigenvectors will contain extra information that encodes subsystem interactions governed by statistics. We decode this information, and show it is akin to conditional probability, and then investigate the extent to which the eigenvectors capture "concepts" inherent in the original joint distribution. The theory is then illustrated with an experiment that exploits these ideas. Turning to a more theoretical application, we also discuss a preliminary framework for modeling entailment and concept hierarchy in natural language, namely, by representing expressions in the language as densities. Finally, initial inspiration for this thesis comes from formal concept analysis, which finds many striking parallels with the linear algebra. The parallels are not coincidental, and a common blueprint is found in category theory. We close with an exposition on free (co)completions and how the free-forgetful adjunctions in which they arise strongly suggest that in certain categorical contexts, the "fixed points" of a morphism with its adjoint encode interesting information.
Introductory Video: https://youtu.be/wiadG3ywJIs
Thesis: https://arxiv.org/abs/2004.05631
#statistics #machine_learning #algebra #quantum_physics
YouTube
At the Interface of Algebra and Statistics
This video is a nontechnical introduction to my PhD thesis, which uses basic tools from quantum physics to investigate algebraic and statistical mathematical structure.
"At the Interface of Algebra and Statistics"
available on the arXiv at https://arxi…
"At the Interface of Algebra and Statistics"
available on the arXiv at https://arxi…
Machine Learning & Computational Statistics Course
Course Intro: This course covers a wide variety of topics in machine learning and statistical modeling. While mathematical methods and theoretical aspects will be covered, the primary goal is to provide students with the tools and principles needed to solve the data science problems found in practice.
https://davidrosenberg.github.io/ml2016/#home
#machine_learning #statistics #course
Course Intro: This course covers a wide variety of topics in machine learning and statistical modeling. While mathematical methods and theoretical aspects will be covered, the primary goal is to provide students with the tools and principles needed to solve the data science problems found in practice.
https://davidrosenberg.github.io/ml2016/#home
#machine_learning #statistics #course