Bayesian estimation | Computational anatomy | Geometry
Computational anatomy (CA) is a discipline within medical imaging focusing on the study of anatomical shape and form at the visible or gross anatomical scale of morphology. The field is broadly defined and includes foundations in anatomy, applied mathematics and pure mathematics, including medical imaging, neuroscience, physics, probability, and statistics. It focuses on the anatomical structures being imaged, rather than the medical imaging devices. The central focus of the sub-field of computational anatomy within medical imaging is mapping information across anatomical coordinate systems most often dense information measured within a magnetic resonance image (MRI). The introduction of flows into CA, which are akin to the equations of motion used in fluid dynamics, exploit the notion that dense coordinates in image analysis follow the Lagrangian and Eulerian equations of motion. In models based on Lagrangian and Eulerian flows of diffeomorphisms, the constraint is associated to topological properties, such as open sets being preserved, coordinates not crossing implying uniqueness and existence of the inverse mapping, and connected sets remaining connected. The use of diffeomorphic methods grew quickly to dominate the field of mapping methods post Christensen'soriginal paper, with fast and symmetric methods becoming available. (Wikipedia).
(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
(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
(ML 13.7) Graphical model for Bayesian Naive Bayes
As an example, we write down the graphical model for Bayesian naïve Bayes.
From playlist Machine Learning
(ML 12.4) Bayesian model selection
Approaches to model selection from a Bayesian perspective: Bayesian model averaging (BMA), "Type II MAP", and Type II Maximum Likelihood (a.k.a. ML-II, a.k.a. the evidence approximation, a.k.a. empirical Bayes).
From playlist Machine Learning
Kerrie Mengersen: Bayesian Modelling
Abstract: This tutorial will be a beginner’s introduction to Bayesian statistical modelling and analysis. Simple models and computational tools will be described, followed by a discussion about implementing these approaches in practice. A range of case studies will be presented and possibl
From playlist Probability and Statistics
(ML 7.2) Aspects of Bayesian inference
An informal overview of Bayesian inference, Bayesian procedures, Objective versus Subjective Bayes, Pros/Cons of a Bayesian approach, and priors.
From playlist Machine Learning
Ender Konukoglu: "On Bayesian models with networks for reconstruction and detection"
Deep Learning and Medical Applications 2020 "On Bayesian models with networks for reconstruction and detection" Ender Konukoglu, ETH Zurich Abstract: Neural networks have demonstrated tremendous potential for medical image analysis. In this talk, I will focus on utilizing these models in
From playlist Deep Learning and Medical Applications 2020
Marcelo Pereyra: Bayesian inference and mathematical imaging - Lecture 1: Bayesian analysis...
Bayesian inference and mathematical imaging - Part 1: Bayesian analysis and decision theory 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 underp
From playlist Probability and Statistics
A Blueprint of Standardized and Composable Machine Learning - Eric Xing
Seminar on Theoretical Machine Learning Topic: A Blueprint of Standardized and Composable Machine Learning Speaker: Eric Xing Affiliation: Carnegie Mellon University Date: August 6, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
Marcelo Pereyra: Bayesian inference and mathematical imaging - Lecture 4: mixture...
Bayesian inference and mathematical imaging - Part 4: mixture, random fields and hierarchical models 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 framewo
From playlist Probability and Statistics
Statistical Rethinking - Lecture 03
Chapter 4 of Statistical Rethinking: A Bayesian Course with R Examples
From playlist Statistical Rethinking Winter 2015
Thomas Serre: "Deep Learning in the Visual Cortex, Pt. 1"
Graduate Summer School 2012: Deep Learning, Feature Learning "Deep Learning in the Visual Cortex, Pt. 1" Thomas Serre, Brown University Institute for Pure and Applied Mathematics, UCLA July 25, 2012 For more information: https://www.ipam.ucla.edu/programs/summer-schools/graduate-summer-
From playlist GSS2012: Deep Learning, Feature Learning
from Dynamical Systems to Epilepsy Surgery: Data-driven Personalized Brain Network Models for Translational Medicine - by Hiba Sheheitli
From playlist Mathematical Biology
(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
Probability theory and AI | The Royal Society
Join Professor Zoubin Ghahramani to explore the foundations of probabilistic AI and how it relates to deep learning. 🔔Subscribe to our channel for exciting science videos and live events, many hosted by Brian Cox, our Professor for Public Engagement: https://bit.ly/3fQIFXB #Probability #A
From playlist Latest talks and lectures
Robert E. Kass - Statistical Assessment of Interaction Among Brain Regions...
Statistical Assessment of Interaction Among Brain Regions from Multi-Electrode Recordings ---------------------------------- Institut Henri Poincaré, 11 rue Pierre et Marie Curie, 75005 PARIS http://www.ihp.fr/ Rejoingez les réseaux sociaux de l'IHP pour être au courant de nos actualités
From playlist Workshop "Workshop on Mathematical Modeling and Statistical Analysis in Neuroscience" - January 31st - February 4th, 2022
William Wen: "Bayesian Statistics and its Application to Integrative Statistical Genomics"
Computational Genomics Summer Institute 2016 "Bayesian Statistics and its Application to Integrative Statistical Genomics" Xiaoquan (William) Wen, University of Michigan Institute for Pure and Applied Mathematics, UCLA July 18, 2016 For more information: http://computationalgenomics.bio
From playlist Computational Genomics Summer Institute 2016
Bayesian Networks 1 - Overview | Stanford CS221: AI (Autumn 2021)
For more information about Stanford's Artificial Intelligence professional and graduate programs visit: https://stanford.io/ai Associate Professor Percy Liang Associate Professor of Computer Science and Statistics (courtesy) https://profiles.stanford.edu/percy-liang Assistant Professor
From playlist Stanford CS221: Artificial Intelligence: Principles and Techniques | Autumn 2021
Bayesian inference and convex geometry: theory, methods, (...) - Pereyra - Workshop 2 - CEB T1 2019
Marcelo Pereyra (Heriot-Watt Univ.) / 14.03.2019 Bayesian inference and convex geometry: theory, methods, and algorithms. This talk summarises some new developments in theory, methods, and algorithms for performing Bayesian inference in high-dimensional models that are log-concave, with
From playlist 2019 - T1 - The Mathematics of Imaging
Nineteenth Imaging & Inverse Problems (IMAGINE) OneWorld SIAM-IS Virtual Seminar Series Talk
Date: Wednesday, March 24, 2021, 10:00am Eastern Time Zone (US & Canada) Speaker: Marcelo Pereyra, Heriot-Watt University Abstract: Play & Play (PnP) methods have become ubiquitous in Bayesian imaging. These methods derive Minimum Mean Square Error (MMSE) or Maximum A Posteriori (MAP) es
From playlist Imaging & Inverse Problems (IMAGINE) OneWorld SIAM-IS Virtual Seminar Series