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Filtering

As explained in Fabulous Adventures in Data Structures and Algorithms

Categorical distribution filtering removes one or more outcomes from a categorical distribution and adjusts the remaining distribution accordingly.

Categorical distribution filtering removes outcomes that conflict with new evidence and adjusts the remaining distribution proportionally. The operation preserves relative weights while discarding an unwanted category or set of possibilities. section 13.3 section 12.13

Filtering becomes especially useful when reasoning from observed effects back to possible causes:

  • Construct a joint distribution containing every relevant pair of possibilities. section 13.3
  • Keep only joint outcomes matching the observation. section 13.3
  • Project away the observed component to obtain the remaining distribution. section 13.3

Filtering sneezing outcomes

A prior assigns weights 90 and 10 to not having and having a cold. Combining it with a sneezing likelihood, filtering the joint distribution to the Yes observation, and projecting the cold status produces weights No:27 and Yes:86. These retain the observed ratio of 270 to 860, equivalent to 270/1,130 and 860/1,130 after normalization. section 13.3

How Fabulous Adventures in Data Structures and Algorithms covers it

How deep it goes
Explains filtering through joint distributions, matching observations, projection, and proportional weights without detailing distribution internals.
Examples
Demonstrates filtering with cold and sneezing categories, producing posterior weights No:27 and Yes:86.
What it assumes
Assumes categorical distributions, prior probabilities, likelihood functions, joint distributions, and conditional probability.
What you can do after
Apply it via Filter and Project to derive a posterior distribution from a prior, likelihood function, and observation.
How it connects
Connects categorical distributions with prior probability, likelihood functions, joint distributions, posterior probability, and projection.
Cover of Fabulous Adventures in Data Structures and Algorithms
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This explainer was generated by Manning's knowledge graph from the text of Fabulous Adventures in Data Structures and Algorithms. The section links point to the parts of the book it draws on.