Probabilistic Graphical Models Specialization

Start Date: 02/23/2020

Course Type: Specialization Course

Course Link:

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About Course

Probabilistic graphical models (PGMs) are a rich framework for encoding probability distributions over complex domains: joint (multivariate) distributions over large numbers of random variables that interact with each other. These representations sit at the intersection of statistics and computer science, relying on concepts from probability theory, graph algorithms, machine learning, and more. They are the basis for the state-of-the-art methods in a wide variety of applications, such as medical diagnosis, image understanding, speech recognition, natural language processing, and many, many more. They are also a foundational tool in formulating many machine learning problems.

Course Syllabus

Probabilistic Graphical Models 1: Representation
Probabilistic Graphical Models 2: Inference
Probabilistic Graphical Models 3: Learning

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Course Introduction

Probabilistic Graphical Models. Master a new way of reasoning and learning in complex domains Probabilistic Graphical Models Specialization In this specialization, you will learn the fundamental concepts and algorithms of probabilistic graphical models. You will start by understanding the core concepts and algorithms used to transform any graph into a probabilistic model. You will then learn the techniques to transform any model into a computer program that can run at regular intervals and generate random data for analysis. You will continue to work on a probabilistic model for a while, learning the techniques needed to transform any model to a state-of-the-art one. You will then implement a program that generates random data for analysis. You will then share your model with others to see how others solve similar problems. The data that you share with others will form the basis for your peer-reviewed paper, which will be a peer-reviewed short book that contains all the code needed to evaluate your model. You will then get feedback from your peers on their solutions to your problem solving it. By working on a solo assignment, you will see how your solution is evaluated by others. Upon completing this course, you will be able to: 1. Solve a probabilistic graph 2. Solve for a node in a graph 3. Solve for a node in a graph with other 4. Solve for a node in a graph with other nodes

Course Tag

Inference Bayesian Network Belief Propagation Graphical Model

Related Wiki Topic

Article Example
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Probabilistic soft logic Probabilistic soft logic (PSL) is a framework for collective, probabilistic reasoning in relational domains. PSL uses first order logic rules as a template language for graphical models over random variables with soft truth values from the interval [0,1].
Graphical model A graphical model or probabilistic graphical model (PGM) is a probabilistic model for which a graph expresses the conditional dependence structure between random variables. They are commonly used in probability theory, statistics—particularly Bayesian statistics—and machine learning.
Probabilistic classification Some classification models, such as naive Bayes, logistic regression and multilayer perceptrons (when trained under an appropriate loss function) are naturally probabilistic. Other models such as support vector machines are not, but methods exist to turn them into probabilistic classifiers.
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Russ Salakhutdinov He specializes in deep learning, probabilistic graphical models, and large-scale optimization.
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Graphical models for protein structure Graphical models can still be used when the variables of choice are continuous. In these cases, the probability distribution is represented as a multivariate probability distribution over continuous variables. Each family of distribution will then impose certain properties on the graphical model. Multivariate Gaussian distribution is one of the most convenient distributions in this problem. The simple form of the probability, and the direct relation with the corresponding graphical model makes it a popular choice among researchers.
Graphical models for protein structure Graphical models have become powerful frameworks for protein structure prediction, protein–protein interaction and free energy calculations for protein structures. Using a graphical model to represent the protein structure allows the solution of many problems including secondary structure prediction, protein protein interactions, protein-drug interaction, and free energy calculations.
Graphical models for protein structure Gaussian graphical models are multivariate probability distributions encoding a network of dependencies among variables. Let formula_15 be a set of formula_16 variables, such as formula_16 dihedral angles, and let formula_18 be the value of the probability density function at a particular value "D". A multivariate Gaussian graphical model defines this probability as follows:
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Graphical model The framework of the models, which provides algorithms for discovering and analyzing structure in complex distributions to describe them succinctly and extract the unstructured information, allows them to be constructed and utilized effectively. Applications of graphical models include causal inference, information extraction, speech recognition, computer vision, decoding of low-density parity-check codes, modeling of gene regulatory networks, gene finding and diagnosis of diseases, and graphical models for protein structure.
Daphne Koller In 2009, she published a textbook on probabilistic graphical models together with Nir Friedman. She offered a free online course on the subject starting in February 2012.
Probabilistic soft logic In recent years there has been a rise in the approaches that combine graphical models and first-order logic to allow the development of complex probabilistic models with relational structures. A notable example of such approaches is Markov logic networks (MLNs). Like MLNs PSL is a modelling language (with an accompanying implementation) for learning and predicting in relational domains. Unlike MLNs, PSL uses soft truth values for predicates in an interval between [0,1]. This allows for the integration of similarity functions in the into models. This is useful in problems such as Ontology Mapping and Entity Resolution. Also, in PSL the formula syntax is restricted to rules with conjunctive bodies.
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Graphical models for protein structure Markov random fields, also known as undirected graphical models are common representations for this problem. Given an undirected graph "G" = ("V", "E"), a set of random variables "X" = ("X") indexed by "V", form a Markov random field with respect to "G" if they satisfy the pairwise Markov property:
NESSUS Probabilistic Analysis Software NESSUS is a general-purpose, probabilistic analysis program that simulates variations and uncertainties in loads, geometry, material behavior and other user-defined inputs to compute probability of failure and probabilistic sensitivity measures of engineered systems. Because NESSUS uses highly efficient and accurate probabilistic analysis methods, probabilistic solutions can be obtained even for extremely large and complex models. The system performance can be hierarchically decomposed into multiple smaller models and/or analytical equations. Once the probabilistic response is quantified, the results can be used to support risk-informed decisions regarding reliability for safety critical and one-of-a-kind systems, and to maintain a level of quality while reducing manufacturing costs for larger quantity products.