Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Lecture

Gaussian Acyclic Models: Linearity and Identifiability

In course

MGT-416: Causal inference

Students will learn the core concepts and techniques of network analysis with emphasis on causal inference. Theory and application will be balanced, with students working directly with network data throughout the course. ...

Description

This lecture covers Gaussian Acyclic Models (NGAM) focusing on linearity and identifiability. Topics include directed loops, zero mean Gaussian models, support of models, and the importance of model identifiability in learning processes.

Instructor

Negar Kiyavash

Official source

Related concepts (25)

Statistical model

A statistical model is a mathematical model that embodies a set of statistical assumptions concerning the generation of sample data (and similar data from a larger population). A statistical model represents, often in considerably idealized form, the data-generating process. When referring specifically to probabilities, the corresponding term is probabilistic model. A statistical model is usually specified as a mathematical relationship between one or more random variables and other non-random variables.

Identifiability

In statistics, identifiability is a property which a model must satisfy for precise inference to be possible. A model is identifiable if it is theoretically possible to learn the true values of this model's underlying parameters after obtaining an infinite number of observations from it. Mathematically, this is equivalent to saying that different values of the parameters must generate different probability distributions of the observable variables.

Mean squared error

In statistics, the mean squared error (MSE) or mean squared deviation (MSD) of an estimator (of a procedure for estimating an unobserved quantity) measures the average of the squares of the errors—that is, the average squared difference between the estimated values and the actual value. MSE is a risk function, corresponding to the expected value of the squared error loss. The fact that MSE is almost always strictly positive (and not zero) is because of randomness or because the estimator does not account for information that could produce a more accurate estimate.

Linear regression

In statistics, linear regression is a linear approach for modelling the relationship between a scalar response and one or more explanatory variables (also known as dependent and independent variables). The case of one explanatory variable is called simple linear regression; for more than one, the process is called multiple linear regression. This term is distinct from multivariate linear regression, where multiple correlated dependent variables are predicted, rather than a single scalar variable.

Machine learning

Machine learning (ML) is an umbrella term for solving problems for which development of algorithms by human programmers would be cost-prohibitive, and instead the problems are solved by helping machines 'discover' their 'own' algorithms, without needing to be explicitly told what to do by any human-developed algorithms. Recently, generative artificial neural networks have been able to surpass results of many previous approaches.

Related lectures (29)

Model Selection Criteria: AIC, BIC, Cp

Explores model selection criteria like AIC, BIC, and Cp in statistics for data science.

Linear Regression: Statistical Inference and Regularization

Covers the probabilistic model for linear regression and the importance of regularization techniques.

Linear Regression Basics

Covers the basics of linear regression in machine learning, including model training, loss functions, and evaluation metrics.

Variational Inference and Neural Networks

Covers variational inference and neural networks for classification tasks.

Probabilistic Models for Linear Regression