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Covariance

As explained in Data Without Labels

Covariance is a measure of how two variables vary together.

Covariance measures how two variables vary together. In Gaussian mixture modeling, each Gaussian distribution has a mean, covariance, and weight describing its fitted cluster. section 5.6.1

The EM procedure uses covariance while refining probabilistic clusters:

  • The E step assigns each data point a probability for every Gaussian, producing soft assignments. section 5.6.1
  • The M step updates the means, covariances, and distribution weights using those probabilities. section 5.6.1
  • The alternating updates continue until the latent assignments and model parameters fit the data well. section 5.6.1

How Data Without Labels covers it

How deep it goes
Defines covariance and places it in EM parameter updates, but does not develop its formula or numerical computation.
Examples
Uses a dataset of n items fitted with k Gaussian distributions and iteratively updated parameters.
What it assumes
Assumes Gaussian mixture clustering and introduces covariance alongside means, variances, and distribution weights.
What you can do after
Evaluate/understand covariance's role in fitting Gaussian mixture clusters through EM updates.
How it connects
Connects covariance with Gaussian mixture models, EM algorithm, soft assignments, means, variances, weights, and clustering.
Cover of Data Without Labels
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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.