# Latent Variable

A latent variable is a variable that is an unobserved variable during a training phase.

**AKA:**Hidden Factor, Unobservable Cause, Unknown Parameter.**Context:**- It can be a member of a Latent Vector.
- It can range from being a Continuous Latent Variable to being a Discrete Latent Variable.
- It can range from being a Confounding Variable to being a Non-Confounding Latent Variable.
- It can range from being a True Latent Variable to being a Hypothesized Latent Factor.
- It can range from being a Confounding Latent Variable to being a Non-Confounding Latent Variable.
- It can be a member of a Latent Variable Statistical Model.

**Example(s):**- a Person's Sex, when not not asked in a survey.
- a Personal Happiness.
- …

**Counter-Example(s):****See:**Prior Probability Distribution, Latent Variable Representation, Fitted Latent Factors Model.

## References

### 2019

- (Wikipedia, 2019) ⇒ https://en.wikipedia.org/wiki/latent_variable Retrieved:2019-5-29.
- In statistics,
**latent variables**(from Latin: present participle of*lateo*(“lie hidden”), 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 (directly measured). Mathematical models that aim to explain observed variables in terms of latent variables are called latent variable models. Latent variable models are used in many disciplines, including psychology, demography, economics, engineering, medicine, physics, machine learning/artificial intelligence, bioinformatics, natural language processing, econometrics, management 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 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 they can serve to reduce the dimensionality of data. A large number of 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.

- In statistics,

### 2009

- http://clopinet.com/isabelle/Projects/ETH/Exam_Questions.html
- QUOTE: Latent Variable: Learning systems have input variables (or "features"), output variables, and internal variables. Latent variables are internal variables. While input and output variables are observable from the outside may be provided for training, latent variables are not accessible, thus not provided for training. On must usually initialize them randomly and recompute their values in the process of learning.

### 2003

- (Beal, 2003) ⇒ Matthew J. Beal. (2003). “Variational Algorithms for Approximate Bayesian Inference." Ph.D. thesis, Gatsby Computational Neuroscience Unit, University College London.
- QUOTE: Many statistical models contain discrete nominal latent variables. A model structure learning problem of interest is then choosing the cardinality of each discrete latent variable. Examples of this problem include deciding how many mixture components are required in a finite mixture model, or how many hidden states are needed in a hidden Markov model.

### 2000

- (Valpola, 2000) ⇒ Harri Valpola. (2000). “Bayesian Ensemble Learning for Nonlinear Factor Analysis." PhD Dissertation, Helsinki University of Technology.
- QUOTE: factor: In generative models, the regularities in the observations are assumed to have been caused by underlying factors, also termed hidden causes, latent variables or sources.