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Latent variable

As explained in Data Without Labels

A latent variable is an unobserved variable inferred from observed data and a statistical model.

A latent variable is an unobserved value inferred from observed data and a statistical model. In Gaussian mixture modeling, it represents the unknown cluster associated with each data point. section 5.6.1

EM estimates latent variables and model parameters in alternating steps:

  • Estimate each data point’s probability of belonging to every cluster. section 5.6.1
  • Estimate Gaussian mixture parameters, including means, covariances, and distribution weights. section 5.6.1
  • Repeat these estimates until the latent values and parameters fit the data well. section 5.6.1

Probabilistic cluster membership

Given a dataset modeled by several Gaussian distributions, EM infers how strongly each point belongs to each cluster instead of assigning it to one cluster with certainty. section 5.6.1

How Data Without Labels covers it

How deep it goes
Explains latent-value estimation through EM’s alternating probability and parameter-estimation steps, without developing the full equations.
Examples
Uses data points generated by multiple Gaussian distributions and assigns probabilistic cluster memberships.
What it assumes
Assumes familiarity with observed datasets, statistical models, and Gaussian distributions.
What you can do after
Apply it via EM to infer uncertain cluster memberships while fitting Gaussian mixture parameters.
How it connects
Connects latent variables to EM, Gaussian mixture models, maximum likelihood estimation, and probabilistic clustering.

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Related concepts

This explainer was generated by Manning's knowledge graph from the text of Data Without Labels. The section links point to the parts of the book it draws on.