Anderson (Probabilistic Concepts)

Primary Purpose of Forming Categories according to Rational Analysis

Prediction

By placing an object into a category, we can predict its unobserved attributes (e.g., if a creature is "dangerous")

Memory

Goal is to retrieve and act on a specific past experience (e.g., where you parked your car)

Categorization

Goal is to make a prediction about a new object

Category Labels

In this view, a linguistic label is not the "definition" of a category; it is simply another feature to be predicted, no different from a physical trait like "can fly"

Disjoint Partitioning

The model assumes the world is naturally divided into disjoint (non-overlapping) sets

Modeled after the plant and animal kingdoms, where species are disjoint due to their inability to crossbreed, and members share a probability of displaying specific traits based on their genetic code

Inferences

If an object belongs to a category (k), it has a specific probability (pij) of displaying a value (j) on a dimension (i)

Similarity-Based Categorization

Categorization is determined by the overlap of superficial features

Theory-Based Categorization

Categorization is driven by underlying "theories" or reasons

For example, we categorize natural objects (like dogs) based on their constitution, but we categorize artifacts (like cups) based on their use

The Rational Stance of Categorization

A rational analysis predicts that humans will use theory whenever it improves the accuracy of their predictions

Basic Level Categories

This is the level in a hierarchy (e.g., "fish" vs. "salmon" or "animal") that maximizes predictability

Subordinate

Levels below the basic level (subordinate) do not provide many more properties for the extra effort

Superordinate

Levels above the basic level (superordinate) lose too many specific properties

Disjoint Partitioning

The categorization process strives for a partition that is mutually exclusive and most useful for predicting the environment

Prior Probabilities

The system starts with "priors," which are assumptions about how objects are divided into categories before seeing any data

Conditional Probabilities

The likelihood that specific features will be observed given that an object belongs to a certain category

Posterior Probability

The likelihood of a specific category structure given the observed features

Decision Rule for Bayesian Framework

To make a prediction, a person should choose the feature with the highest posterior probability

Computational Infeasibility

It is impossible for the human mind to reconsider every possible partition of every object ever seen every time it makes a prediction

The Iterative Solution

Because of these limits, humans use an iterative algorithm that commits to a specific category structure for objects seen so far and does not reconsider them later

Categorizing New Objects

When a new (m+1) object is encountered, the algorithm calculates the probability that it belongs to an existing category (k) or a completely new category (0)