Post on 13-Dec-2015
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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
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
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)