Fuzzy coding, decisions, learning

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This is more for overview of my own than for teaching or exercise.

Overview of the areas

Arithmetic · 'elementary mathematics' and similar concepts
Set theory, Category theory
Geometry and its relatives · Topology
Elementary algebra - Linear algebra - Abstract algebra
Calculus and analysis
Logic
Semi-sorted
 : Information theory · Number theory · Decision theory, game theory · Recreational mathematics · Dynamical systems · Unsorted or hard to sort


Math on data:

  • Statistics as a field
some introduction · areas of statistics
types of data · on random variables, distributions
Virtues and shortcomings of...
on sampling · probability
glossary · references, unsorted
Footnotes on various analyses

Other data analysis, data summarization, learning

Data massage
Data clustering · Dimensionality reduction · Fuzzy coding, decisions, learning · Optimization theory, control theory
Connectionism, neural nets · Evolutionary computing



Fuzzy coding, decisions, learning

This article/section is a stub — probably a pile of half-sorted notes, is not well-checked so may have incorrect bits. (Feel free to ignore, fix, or tell me)


On bias

Methods / algorithms / searchers

Decision trees

ID3
Pruning (ID3, others)
Rule Post-pruning; C4.5

Instance-based learning

Bayesian learning

This article/section is a stub — probably a pile of half-sorted notes, is not well-checked so may have incorrect bits. (Feel free to ignore, fix, or tell me)

Bayesian learning is a general probablistic approach, mostly specifically used as a probablistic classifier.

Mathematically it is based on any observable attribute you can think of, and the math requires Bayesian inversion (see below).

Many basic implementations also use the Naive Bayes assumption (see below), because it saves a lot of computation time, and seems to work almost as well in most cases.

Bayesian classifier

Bayes Optimal Classifier
Naive Bayes Classifier

Bayesian (Belief) Network

Some classifiers

This article/section is a stub — probably a pile of half-sorted notes, is not well-checked so may have incorrect bits. (Feel free to ignore, fix, or tell me)
  • Parzen classifier
  • Backpropagation classifier


Evaluating classifiers

Kernel(-related) methods, the Kernel Trick

Support Vector Machines

Markov Models, Hidden Markov Models

This article/section is a stub — probably a pile of half-sorted notes, is not well-checked so may have incorrect bits. (Feel free to ignore, fix, or tell me)

Something like (the simplest possible) Bayesian Belief Networks, but geared to streams of data. Can be seen as a state machine noting the likeliness of each next step based on a number of preceding steps.

The hidden variant only shows its output (and hides the model that produces it), the non-hidden one shows all of its state.

Simple ones are first-order