Lecture

Causal Discovery: Latent Variable Models

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Description

This lecture by the instructor covers the topic of causal discovery based on latent variable models. It delves into the fundamental problem of causal analysis, distinguishing between assumption-free and assumption-based methods. The lecture explores the challenges of identifying causal relationships in non-Gaussian data and the importance of considering temporal versus instantaneous effects. It introduces the concept of Linear non-Gaussian Acyclic Model (LiNGAM) and explains how non-Gaussianity can break the symmetry between variables, aiding in causal inference. The lecture also discusses the estimation of LiNGAM using Independent Component Analysis (ICA) and the difficulties and solutions in nonlinear Structural Equation Models (SEM) through methods like NonSENS. It concludes by emphasizing the significance of finding the direction of effect in causal discovery and the future prospects in this field.

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Related concepts (31)

Structural equation modeling

Structural equation modeling (SEM) is a diverse set of methods used by scientists doing both observational and experimental research. SEM is used mostly in the social and behavioral sciences but it is also used in epidemiology, business, and other fields. A definition of SEM is difficult without reference to technical language, but a good starting place is the name itself. SEM involves a model representing how various aspects of some phenomenon are thought to causally connect to one another.

Latent variable model

A latent variable model is a statistical model that relates a set of observable variables (also called manifest variables or indicators) to a set of latent variables. It is assumed that the responses on the indicators or manifest variables are the result of an individual's position on the latent variable(s), and that the manifest variables have nothing in common after controlling for the latent variable (local independence).

Latent and observable variables

In statistics, latent variables (from Latin: present participle of lateo, “lie hidden”) are variables that can only be inferred indirectly through a mathematical model from other observable variables that can be directly observed or measured. Such latent variable models are used in many disciplines, including political science, demography, engineering, medicine, ecology, physics, machine learning/artificial intelligence, bioinformatics, chemometrics, natural language processing, management, psychology and the social sciences.

Principal component analysis

Principal component analysis (PCA) is a popular technique for analyzing large datasets containing a high number of dimensions/features per observation, increasing the interpretability of data while preserving the maximum amount of information, and enabling the visualization of multidimensional data. Formally, PCA is a statistical technique for reducing the dimensionality of a dataset. This is accomplished by linearly transforming the data into a new coordinate system where (most of) the variation in the data can be described with fewer dimensions than the initial data.

Independent component analysis

In signal processing, independent component analysis (ICA) is a computational method for separating a multivariate signal into additive subcomponents. This is done by assuming that at most one subcomponent is Gaussian and that the subcomponents are statistically independent from each other. ICA is a special case of blind source separation. A common example application is the "cocktail party problem" of listening in on one person's speech in a noisy room.

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