Start Date: 02/23/2020
Course Type: Specialization Course |
Course Link: https://www.coursera.org/specializations/probabilistic-graphical-models
Explore 1600+ online courses from top universities. Join Coursera today to learn data science, programming, business strategy, and more.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.
Probabilistic Graphical Models 1: Representation
Probabilistic Graphical Models 2: Inference
Probabilistic Graphical Models 3: Learning
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
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Probabilistic programming language | A probabilistic programming language (PPL) is a programming language designed to describe probabilistic models and then perform inference in those models. PPLs are closely related to graphical models and Bayesian networks, but are more expressive and flexible. Probabilistic programming represents an attempt to "[unify] general purpose programming with probabilistic modeling." |
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. |
Probabilistic classification | Binary probabilistic classifiers are also called binomial regression models in statistics. In econometrics, probabilistic classification in general is called discrete choice. |
Probabilistic programming language | A probabilistic relational programming language (PRPL) is a PPL specially designed to describe and infer with probabilistic relational models (PRMs). |
Russ Salakhutdinov | He specializes in deep learning, probabilistic graphical models, and large-scale optimization. |
Graphical model | This type of graphical model is known as a directed graphical model, Bayesian network, or belief network. Classic machine learning models like hidden Markov models, neural networks and newer models such as variable-order Markov models can be considered special cases of Bayesian networks. |
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: |
Graphical model | Generally, probabilistic graphical models use a graph-based representation as the foundation for encoding a complete distribution over a multi-dimensional space and a graph that is a compact or factorized representation of a set of independences that hold in the specific distribution. Two branches of graphical representations of distributions are commonly used, namely, Bayesian networks and Markov random fields. Both families encompass the properties of factorization and independences, but they differ in the set of independences they can encode and the factorization of the distribution that they induce. |
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. |
Probabilistic classification | Commonly used loss functions for probabilistic classification include log loss and the mean squared error between the predicted and the true probability distributions. The former of these is commonly used to train logistic models. |
Probabilistic voting model | Probabilistic voting models are usually preferred to traditional Downsian median voter models, as in the former all voters have an influence on the policy outcome, whereas in the latter all power rests in the hands of the pivotal voter or group. For instance, in models where young and old (or rich and poor) voters have conflicting interests, probabilistic voting models predict that the winning candidate strikes a balance between the different interests in her/his policy platform. Due to the smooth mapping between the distribution of policy preferences and the political outcomes, this model has proven to be very tractable and convenient to use in dynamic models with repeated voting. |
Graphical models for protein structure | There are two main approaches to use graphical models in protein structure modeling. The first approach uses discrete variables for representing coordinates or dihedral angles of the protein structure. The variables are originally all continuous values and, to transform them into discrete values, a discretization process is typically applied. The second approach uses continuous variables for the coordinates or dihedral angles. |
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. |