Latent variable

In statistics, latent variables (as opposed to observable variables), are variables that are not directly observed but are rather inferred (through a mathematical model) from other variables that are observed and directly measured. Mathematical models which aim to explain observed variables in terms of latent variables are called latent variable models. Latent variable models are used in a variety of disciplines, including the economics, machine learning/artificial intelligence, natural language processing, psychology, and the social sciences.

Sometimes latent variables correspond to aspects of physical reality which could in principle be measured, but may not be for practical reasons. In this situation, the term hidden variables is commonly used (reflecting the fact that the variables are "really there", but hidden). Other times latent variables may not be physically real but instead correspond to abstract concepts, like categories, behavioral or mental states, or data structures. The terms hypothetical variables or hypothetical constructs may be used in these situations.

One advantage of using latent variables is that it reduces the dimensionality of data. A large number of observable variables can be aggregated in a model to represent an underlying concept, making it easier for humans to understand the data. In this sense, they serve the same function as theories in general do in science. At the same time, latent variables link observable ("sub-symbolic") data in the real world, to symbolic data in the modeled world.

Latent variables, as created by factor analytic methods, generally represent 'shared' variance, or the degree to which variables 'move' together. Variables that have no correlation cannot result in a latent construct based on the common factor model^[1].

Examples of latent variables

Economics

Examples of latent variables from the field of economics include quality of life, business confidence, morale, happiness and conservatism: these are all variables which cannot be measured directly. However, given an economic model linking these latent variables to other, observable variables (such as GDP), the values of the latent variables can be inferred from measurements of the observable variables.

Psychology

• The "Big Five personality traits" have been inferred using factor analysis.
• extraversion ^[2]
• spatial ability ^[2]

Common methods for inferring latent variables

• Hidden Markov models
• Factor analysis
• Principal component analysis
• Latent semantic analysis and Probabilistic latent semantic analysis
• EM algorithms

Bayesian algorithms and methods

Bayesian statistics is often used for inferring latent variables.

• Latent Dirichlet Allocation
• The Chinese Restaurant Process is often used to provide a prior distribution over assignments of objects to latent categories.
• The Indian Buffet Process is often used to provide a prior distribution over assignments of latent binary features to objects.

See also

• Latent variable model
• Item response theory
• Rasch model

References

machine learning/artificial intelligence

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