Latent and observable variables: Difference between revisions

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In [[statistics]], '''latent variables''' (from [[Latin]]: [[present participle]] of ''lateo'', “lie hidden”) are [[Variable (mathematics)|variables]] that can only be [[Statistical inference|inferred]] indirectly through a [[mathematical model]] from other '''observable variables''' that can be directly [[observation|observed]] or [[measurement|measured]].<ref>Dodge, Y. (2003) ''The Oxford Dictionary of Statistical Terms'', OUP. {{isbn|0-19-920613-9}}</ref> Such ''[[latent variable model]]s'' 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]].

Latent variables may correspond to aspects of physical reality. These could in principle be measured, but may not be for practical reasons. Among the earliest expressions of this idea is Sir [[Francis Bacon]]'s classic [[polemic]] the ''[[Novum Organum]]'', itself a challenge to to the more traditional logic expressed in [[Aristotle]]'s [[Organon]].

{{quote|But the latent process of which we speak, is far from being obvious to men’s minds, beset as they now are. For we mean not the measures, symptoms, or degrees of any process which can be exhibited in the bodies themselves, but simply a continued process, which, for the most part, escapes the observation of the senses.|Sir [[Francis Bacon]], ''[[Novum Organum]]''<ref>{{cite book|author-last=Bacon|author-first=Francis|title=Novum Organum|chapter=APHORISMS—BOOK II: ON THE INTERPRETATION OF NATURE, OR THE REIGN OF MAN|url=https://www.gutenberg.org/files/45988/45988-h/45988-h.htm}}</ref>

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Latent variables may correspond to aspects of physical reality. These could in principle be measured, but may not be for practical reasons. Among the earliest definitions arises from Sir [[Francis Bacon]]'s eponymous ''[[Novum Organum]]'', [[Francis Bacon]] In this situation, the term ''hidden variables'' is commonly used (reflecting the fact that the variables are meaningful, but not observable). Other latent variables 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.

The use of latent variables can serve to [[Dimensionality reduction|reduce the dimensionality]] of data. Many observable variables can be aggregated in a model to represent an underlying concept, making it easier to understand the data. In this sense, they serve a function similar to that of scientific theories. At the same time, latent variables link observable "[[sub-symbolic]]" data in the real world to symbolic data in the modeled world.