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Machine Learning Intro iCAMP 2012

Max WellingUC Irvine

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Machine Learning

• Algorithms that learn to make predictions from examples (data)

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Types of Machine Learning

• Supervised Learning• Labels are provided, there is a strong learning signal.• e.g. classification, regression.

• Semi-supervised Learning.

• Only part of the data have labels. • e.g. a child growing up.

• Reinforcement learning.• The learning signal is a (scalar) reward and may come with a delay.• e.g. trying to learn to play chess, a mouse in a maze.

• Unsupervised learning• There is no direct learning signal. We are simply trying to find structure in data.• e.g. clustering, dimensionality reduction.

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Unsupervised Learning:

(LLE – Roweis & Saul)

Dimensionality Reduction: clustering

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Supervised Learning

Regression Classification

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Collaborative Filteringm

ovie

s (+

/- 1

7,77

0)

users (+/- 240,000)

total of +/- 400,000,000 nonzero entries(99% sparse)

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(Netflix Dataset)

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? 1

1?

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Generalization• Consider the following regression problem:• Predict the real value on the y-axis from the real value on the x-axis.• You are given 6 examples: {Xi,Yi}.• What is the y-value for a new query point X* ?

X*

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Generalization

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Generalization

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Generalization

which curve is best?

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• Ockham’s razor: prefer the simplest hypothesis consistent with data.

Generalization

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Generalization

Learning is concerned with accurate predictionof future data, not accurate prediction of training data.

Question: Design an algorithm that is perfect at predicting training data.

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Learning as Compression

• Imagine a game where Bob needs to send a dataset to Alice.

• They are allowed to meet once before they see the data.

• The agree on a precision level (quantization level).

• Bob learns a model (red line).

• Bob sends the model parameters (offset and slant) only once

• For every datapoint, Bob sends -distance along line (large number) -orthogonal distance from line (small number) (small numbers are cheaper to encode than large numbers)

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Generalization

learning = compression = abstraction

• The man who couldn’t forget …

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Classification: nearest neighbor

Example: Imagine you want to classify versus

Data: 100 monkey images and 200 human images with labels what is what.

Task: Here is a new image: monkey or human?

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1 nearest neighbor

Idea: 1. Find the picture in the database which is closest your query image.

2. Check its label.

3. Declare the class of your query image to be the same as that of the closest picture.

query closest image

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kNN Decision Surface

decision curve

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Bayes Rule(s)

Riddle: Joe goes to the doctor and tells the doctor he has a stiff neck and a rash.The doctor is worried about meningitis and performs a test that is 80% correct, that is,for 80% of the people that have meningitis it will turn out positive. If 1 in 100,000 peoplehave meningitis in the population and 1 in 1000 people will test positive (sick or not sick)what is the probability that Joe has meningitis?

Answer: Bayes Rule.

P(meningitis | positive test) = P(positive test | meningitis ) P(meningitis) / P(positive test) = 0.8 * 0.00001 / 0.001 = 0.008 < 1%

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Naïve Bayes Classifier

testresult

meningitis

stiff-neck, rash

Naïve Bayes Classifier:

P(Y|X1,X2) = P(X1|Y) P(X2|Y) P(Y) / PX1, X2)

X1

X2Y

P(X1,X2|Y) = P(X1|Y) P(X2|Y) Conditional Independence:

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Bayesian Networks & Graphical Models

• Main modeling tool for modern machine learning

• Reasoning over large collections of random variables with intricate relations