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the feasibility of machine learning

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Component of learning

Formalization – Input （输入） :X (customer application)

think of it as deed dimension vector

– Output （输出） :Y(+1,-1)

good/bad customer

– Target Function( 目标函数 ) : f :x→y

ideal credit approval formula

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Component of learning

Formalization – Data （数据） : (), (),…, ()

historical records

↓ ↓ ↓– Hypothesis( 假设 ) ： g :x→y

为了得到目标函数的公式

F is unknown G is very much known

actually we created it

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Component of learning

UNKNOWN TARGET FUNCTION f :x→y

↓ ↓

TRAINING EXAMPLES

(), (),…, ()

FINAL HYPOTHESIS

g

(G hopefully approximates F)

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Component of learning

UNKNOWN TARGET FUNCTION f :x→y

↓ ↓

TRAINING EXAMPLES

(), (),…, ()

FINAL HYPOTHESIS

g

(G hopefully approximates F)

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Component of learning

TRAINING EXAMPLES (), (),…, ()

LEARNING ALGORITHM →HYPOTHESIS SET

( 从现实模型公式中创造公式） （将它们成为假设集）

FINAL HYPOTHESIS

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Component of learning

HYPOTHESIS SET H

从假设集选出一个假设

H 衍生出一堆 H’s( 待定函数 )

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Component of learning

UNKNOWN TARGET FUNCTION f :x→y

↓ ↓

TRAINING EXAMPLES

(), (),…, ()

FINAL HYPOTHESIS

g

(G hopefully approximates F)

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HYPOTHESIS SET

Hypothesis Set – H = {h} g∈ H

Learning Algorithm– Together. they are referred to as the

learning model.

a hypothesis set and a learning algorithm

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A simple hypothesis set—’perceptron’

For input X= attributes of a customer– Approve credit if

> threshold

– Deny credit if

< threshold

This linear formula h∈ H can be written as

h(x) = sign( () – threshold )

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Learning Feasible

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Learning Feasible

A related experiment

P(picking red)=μ

P(picking green)=1-μ

μ=probability of

red marbles

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Learning Feasible

Pick N marbles independently

The fraction of red marbles in sample = v

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Does v Say anything about μ?

NO!

Sample can be mostly green while bin is mostly red

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Does v Say anything about μ?

Yes

Sample frequency v is close to bin frequency μ

This is called Hoeffding Inequality

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Learning Feasible

Bin – Unknown is a number μ

Learning – Unknown is a function f:x→y

each marble is a point x ∈ X

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Learning Feasible

Bin – Unknown is a number μ

Learning – Unknown is a function f:x→y

each marble is a point x ∈ X

Hypothesis got it right

h(x)=f(x)

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Learning Feasible

Bin – Unknown is a number μ

Learning – Unknown is a function f:x→y

each marble is a point x ∈ X

Hypothesis got it wrong

h(x)≠f(x)

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Learning Feasible

UNKNOWN TARGET FUNCTION f :x→y

↓ ↓

TRAINING EXAMPLES

(), (),…, ()

FINAL HYPOTHESIS

g

(G hopefully approximates F)

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Learning Feasible

Probability distribution

P on X