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# Pattern Analysis - PowerPoint PPT Presentation

Pattern Analysis. Prof. Bennett Math Model of Learning and Discovery 2/14/05 Based on Chapter 1 of Shawe-Taylor and Cristianini. Outline. What is pattern analysis? Illustrate issues via example Pattern definitions Examples of practical tasks Pattern algorithms Summary .

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### Pattern Analysis

Prof. Bennett

Math Model of Learning and Discovery 2/14/05

Based on Chapter 1 of

Shawe-Taylor and Cristianini

• What is pattern analysis?

• Illustrate issues via example

• Pattern definitions

• Examples of practical tasks

• Pattern algorithms

• Summary

• The automatic detection of patterns in data from the same source.

• Make predictions of new data coming from the same source.

• Data may take many forms:

images, text, records of commercial transactions, genome sequences, family tree

Kepler Analyzed Brahe’s Planetary Motion Data

P = Period D = Average Distance from Sun

• Observed P3= D2

• Developed three laws of planetary motion.

• Compressible:

Data can be represented by one column

• Predictable:

Discovering hidden relations allow us to predict other columns.

• Third Law is exact.

• Nonlinear Model of D and P

• Linear Model of

• Assume we know plane of orbit, so we can represent positions as (x,y) pairs

• Also know orbit is ellipse

• Pattern is nonlinear function of x,y

• Pattern is linear function of

• Linear relationships are easier to find.

• Hypothesis Ellipse compute

• Hypothesis Circle compute

UNDERFITS

Hypothesis any continuous function

OVERFITS!!!

Depends on size of hypothesis class

Use domain knowledge to limit hypotheses

Noisy Data

• Approximate not exact.

• Data has errors and omissions.

• Cannot predict graduate school performance from GRE’s and grades alone.

• Best Representation/Model unknown.

• Make approximate predictions – need to address how accurate estimates are.

• A general exact pattern, f, for data source S satisfies

for all data x from source S

• A general approximate pattern, f, for data source S satisfies

for all data x from source S

• A general statistical pattern, f, for data source S generated iid according to distribution D satisfies

for all data x from source S

• Example – Character Recognition

two class - is it an A or not?

multiclass – what letter is it ?

• Example –Determine drug bioavailability through the intestine. Estimate apparent permeability as assayed via intestinal cell line.

• Estimate the probability that a particular event occurs, p(x). Use it to detect improbably events like fraud.

• Find a projection of the data that captures the major variance in the data.

Eigenfaces - capture essential qualities of faces to help ID and reduce storage needs.

• A Pattern Analysis Algorithm

input = finite set of data from source S

a.k.a. the training set

output = detector function f

or no patterns detected

• Efficiency and Scalability – memory and CPU requirements, large data sets

• Robustness – find approximate patterns on noisy data

• Stability - discover genuine patterns, find same problems on different views of the dataset

• Generalization –

Find pattern on future data

Pattern may exist by chance for finite sample

Provide statistical guarantee that pattern truly exist with caveat that with small probability that algorithm may have been mislead.

• Observe that for state agency that all 20 babies adopted in last 10 years from country x are girls.

• Pattern, only girls are available for adoption from that country.

• With probability p=(0.5)220 could observe data even if chance of girls and boys equally likely.

• So with chance p, we were mislead.

• Produce a pattern based on a finite sample. Provide bounds on the probability that pattern approximately represents a true pattern with some probability.

Probably Approximately Correct

• With proper representation, the problem can become easier (linear model works).

• Develop general purpose linear learning methods.

• Change recoding using “kernel functions”

• Patterns are regularities in data from a specified source

• Algorithm takes finite sample and computes pattern

• Efficiency, robustness, and stability

• Representation -- Kernels

• Strategy = Generic Algorithms + Recoding

• Many Learning Tasks in this framework