computer science

Latent and observable variables

Latent and observable variables is a computer science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Latent and observable variables rather than just read about it. In short: 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 engineering, medicine, ecology, physics, machine learning/artificial intelligence, natural language processin…

Key takeaways

Latent and observable variables belongs to computer science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Latent and observable variables to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Latent and observable variables from memory before moving on to harder problems.

Reference excerpt

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 engineering, medicine, ecology, physics, machine learning/artificial intelligence, natural language processing, bioinformatics, chemometrics, demography, economics, management, political science, 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 Francis Bacon's polemic the Novum Organum, itself a challenge to the more traditional logic expressed in Aristotle's Organon:

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. 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 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.

Examples

Psychology 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.

The "Big Five personality traits" have been inferred using factor analysis. extraversion spatial ability wisdom: “Two of the more predominant means of assessing wisdom include wisdom-related performance and latent variable measures.” Spearman's g, or the general intelligence factor in psychometrics

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, by linking these latent variables to other, observable variables, the values of the latent variables can be inferred from measurements of the observable variables. Quality of life is a latent variable which cannot be measured directly, so observable variables are used to infer quality of life. Observable variables to measure quality of life include wealth, employment, environment, physical and mental health, education, recreation and leisure time, and social belonging.

Medicine

Latent-variable methodology is used in many branches of medicine. A class of problems that naturally lend themselves to latent variables approaches are longitudinal studies where the time scale (e.g. age of participant or time since study baseline) is not synchronized with the trait being studied. For such studies, an unobserved time scale that is synchronized with the trait being studied can be modeled as a transformation of the observed time scale using latent variables. Examples of this include disease progression modeling and modeling of growth (see box).

Inferring latent variables There exists a range of different model classes and methodology that make use of latent variables and allow inference in the presence of latent variables. Models include:

linear mixed-effects models and nonlinear mixed-effects models Hidden Markov models Factor analysis Item response theory Analysis and inference methods include:

Principal component analysis Instrumented principal component analysis Partial least squares regression Latent semantic analysis and probabilistic latent semantic analysis EM algorithms Metropolis–Hastings algorithm

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.

Worked examples

Example 1 — a first encounter with Latent and observable variables

Start with the simplest possible case. Write down what Latent and observable variables claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In computer science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Latent and observable variables before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Latent and observable variables ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Latent and observable variables

In research: Latent and observable variables appears in computer science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Latent and observable variables in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Latent and observable variables is common in secondary-school and first-year university syllabi. It links to neighbouring topics Bayesian networks, Econometric modeling, Latent variable models, so understanding it makes those chapters shorter.
In everyday life: Look for Latent and observable variables outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Latent and observable variables in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Latent and observable variables means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Latent and observable variables out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Latent and observable variables in simple terms?

Why does Latent and observable variables matter?

Because it connects several computer science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Latent and observable variables?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Latent and observable variables.