Introduction to Machine Learning - udel.eduudel.edu/~amotong/teaching/machine learning... ·...

Introduction to Machine Learning

Introduction to Machine Learning Amo G. Tong 1

Lecture 1Introduction

• Course Information

• Introduction

• Remarks

• Optimization

• Some materials are courtesy of Vibhave Gogate and Tom Mitchell.

• All pictures belong to their creators.


• CISC 684

• Class Time: M/W 8:40-9:55 am

• Instructor: Dr. Tong

• Email: [email protected]

• TA Information: See Canvas


Course Information

mailto:[email protected]


Evaluations

• Four assignments. (30%)• Individual Problems: analysis• Group Problems: programming

• Midterm. (25%)

• Final exam. (25%)

• Group Project. (10%)• Project Proposal• Project Report.

• Group Participation (5%)

• Quiz. (5%)• A student will automatically get full credit for pop quiz if they get no less

than 90% of the total in the final exam.

• Extra credits. (5% more or less)


• Find your teammates.

• A group should have two to four members, unless otherwise permitted by the instructor.

• Each student should be in a group. If you have difficulties in finding a group, please email the instructor.

• A group should have a leader who is responsible for communications and making submissions.

• The leader should send the names of the group members to the TA by Sep 6.

• See Syllabus on Canvas for more details.

First thing to do


Course

• Attendance is mandatory.

• Please carefully read the first four pages of the syllabus and pay attention to the announcement on Canvas.

• Feel free to send me emails or discuss things on Piazza.

• Text book:

• Machine Learning, Tom Mitchell, McGraw Hill, 1997. 1st Edition. Link

• Machine Learning: a Probabilistic Perspective, Kevin Patrick Murphy, 1st Edition. Link

• Pattern Recognition and Machine Learning, C. Bishop, Springer Link

• Other materials: As announced.

• Prerequisite:

• Probability Theory, Discrete Math

• Simple Calculus

• Linear Algebra preferred.


Materials

http://www.cs.cmu.edu/~tom/mlbook.html

https://www.cs.ubc.ca/~murphyk/MLbook/

https://www.microsoft.com/en-us/research/people/cmbishop/#!prml-book

• What is machine learning?

• Informally, given some training data, we want to solve a problem related to the given data, at our best.


Machine Learning



• A checker learning problem.

• Experience: records of previous games. (data)

• Task: how to play checker. (problem)

• Performance Measure: percent of games won. (at our best)


Machine Learning



• A robot driving learning problem.


https://www.irishtimes.com/polopoly_fs/1.3400131.1519215500!/image/image.jpg_gen/derivatives/box_620_330/image.jpghttps://www.ucsusa.org/sites/default/files/styles/adaptive/public/images/2017/01/vehicles-cars-how-autonomous-vehicles-work.jpg?itok=a4C4VKIJ

robot driving human driving

Machine Learning



• A robot driving learning problem.

• Experience: images and commands recorded while observing a human driver. (data)

• Task: driving on public highways using vision sensors. (problem)

• Performance measure: average distance traveled before an error. (at our best)


Design algorithm automatically

Machine Learning


• Machine Learning is the science of getting computers to learn as well as humans do or better. - Dr. Roman Yampolskiy

• Machine Learning at its most basic is the practice of using algorithms to parse data, learn from it, and then make a determination or prediction about something in the world. -Michael Copeland, Nvidia.

• Formally, A computer program is said to learn from experience E with respect to some class of tasks T and performance measure P, its performance at tasks in T as measured by P, improves with experience. - T. Mitchell

• Why not define machine learning yourself after learning this course?


Machine Learning

• Advertisement Filtering


Advertisement or regular email?

Examples of Machine Learning Tasks

• Regression

• 𝑓(𝑥)



• Regression

• 𝑓(𝑥)


Predict 𝑓(𝑥) for other 𝑥.Looks like we have 𝑓(𝑥) = 𝑐 for some constant 𝑐.

𝑦

𝑥

𝑓(𝑥)? 𝑓(𝑥)?


Training data

Prediction

• Regression

• 𝑓(𝑥)


Predict 𝑓(𝑥) for other 𝑥.Looks like we have a linear function.

𝑦

𝑥

𝑓(𝑥)?


• Regression

• 𝑓(𝑥)


Predict 𝑓(𝑥) for other 𝑥.Looks like we have a linear function.

𝑦

𝑥

𝑓(𝑥)?


How to compute this line?

Prediction

• Regression

• 𝑓(𝑥)


Predict 𝑓(𝑥) for other 𝑥.Looks like we have a complicated function.

𝑓(𝑥)? The gold price tomorrow.


• Collaborative Filtering : predict how well a user will like an item that he has not rated given a set of historical preference judgments for a community of users.




Why machine learning?

Characteristics of Machine Learning

• Human expertise is not needed.

• Example: AlphaGo.

• AlphaGo was built by machine learning experts and some people who are familiar with Go. We do not need a champion.

• However, AlphaGo won the games against the champions.


https://upload.wikimedia.org/wikipedia/commons/thumb/2/2a/FloorGoban.JPG/300px-FloorGoban.JPG



• Handle the case when human expertise cannot be explained easily.

• Example: AlphaGo.

• Even a champion cannot easily explain the best way to play Go. A Go player needs to practice many years before becoming a champion.

• However, AlphaGo learns really fast due to the high performance computing devices.




• Handle the case when requirements and data change over time.

• Example: fingerprint recognition.

• A fingerprint application may receive new prints everyday.




• Handle the case when the problem or the data size is just too large

• Example: checker learning.

• Given a lot of records of the games, a human cannot check the records one by one to learning how to play checker.




• Supervised (Inductive) Learning.


Types of Machine Learning Tasks


• 𝑋: all possible data (instance space)

• We assume there is an unknown function 𝑓 defined over 𝑋.






• Training data: a subset 𝑿𝒄 ⊆ 𝑿 and 𝒇(𝒙) for each 𝒙 ∈ 𝑿𝒄.

• Given the training data, we want to know 𝒇(𝒙) for future 𝒙. That is, we want learn the function 𝒇 from the training data.






• Training data: a subset 𝑋𝑐 ⊆ 𝑋 and 𝑓(𝑥) for each 𝑥 ∈ 𝑋𝑐.

• Given the training data, we want to know 𝑓(𝑥) for future 𝑥. That is, we want to learn the function 𝑓 from the training data.

• Example: Handwriting number recognition.

• {all possible handwriting numbers} to {0,1,2,3,4,5,6,7,8,9}

• The instance space is infinite.

• We have some recognized samples.

• Recognize new images.


𝑓 = 2




• A target set Y.

• Assume there is a joint distribution 𝐷 define over (𝑋, 𝑌)

• Training data: a subset of samples generated from D.

• Given the training data, we want to learn the underlying distribution D.

•Pr 1 ] = 0.1

•Pr[2| ] = 0.9


More general, a probabilistic perspective.




• A target set Y.

• Assume there is a joint distribution 𝐷 define over (𝑋, 𝑌)

• (a) a distribution over the functions from 𝑋 to 𝑌.

• (b) for each 𝑥 ∈ X, a distribution over 𝑌.

• 𝑋={0, 1, 2}, 𝑌={Yes, No}. A distribution over the 3 ∗ 2 pairs (𝑥, 𝑦).

• A distribution over the 23 functions from 𝑋 to 𝑌.

• A distribution over {Yes, No} for each 𝑥 ∈ 𝑋.



• Unsupervised Learning.

• No labels on the training data.

• Draw references, e.g. hidden structures, from data.

• Example: Discovery clusters of data.




• Training data with labels

• Unsupervised Learning

• Training data without labels

• Semi-supervised learning

• Training data with few labels.

• Reinforcement learning

• The learner interacts with the world via “actions” and tries to find an optimal policy of behavior with respect to “rewards” it receives from the environment




Remarks

• To learn is to search the hypothesis space to find one that best fits the data.


𝑦

𝑥

Regression: the hypothesis space is a set of functions.

Remarks



(a) We can hardly draw any conclusion if no prior assumption.

If we assume each function is equally possible, then any function fitting the data is equally good. No conclusion can be drawn.

Should we consider all the functions?

Remarks

𝑦

𝑥



Remarks

𝑦

𝑥

Predict 𝑓(𝑥) here



(a) We can hardly draw any conclusion if no prior assumption.

If we assume the underlying function is linear, only one solution exists.

Should we consider all the functions?

Remarks

𝑦

𝑥



𝑦

𝑥

(b) How to make assumptions?• Prior Knowledge• …

Remarks

𝑦

𝑥

Linear

𝑦

𝑥

Quadratic



𝑦

𝑥

(b) How to make assumptions?• Prior Knowledge• …

Remarks

𝑦

𝑥

Linear

Assuming it is linear, how to find the best one? [we need a machine learning algorithm]


• A machine learning algorithm is a search procedure.

• Different models consider different hypothesis

• Different algorithms search the space according to different measures.


Remarks

• We cannot learn everything.


Remarks


• Can we predict the Powerball winning number according to


Remarks



• the weather of last week?

• the gold price yesterday?

• the previous winning numbers?


Remarks



• the weather of last week?

• the gold price yesterday?

• the previous winning numbers?

• No, we cannot because they cannot affect the future winning number.

• That is, there must be some underlying relationship between the data and the learning goal.


Remarks

• We cannot learn it if we do not have good data.

• Regression.

• Can you learning 𝑓(𝑥)?


Remarks


• Regression.


• Formally, what general bounds can be found to relate the confidence in learned hypotheses space to amount of training data and the character of the learner’s hypothesis space?

• Informally, how much data is needed for a good solution?


Remarks


• Regression.


• Formally, what general bounds can be found to relate the confidence in learned hypotheses space to amount of training data and the character of the learner’s hypothesis space?

• It relates to the hypothesis space.

• E.g. learning a linear function requires two points. 𝒚 = 𝒂𝒙 + 𝒃

• E.g. learning a quadratic function requires three points. 𝒂𝒙𝟐 + 𝒃𝒙 + 𝒄 = 𝒚.


Remarks

• Algorithm/Model Selection.

• Once you have a reasonable task and a good training data, which model/algorithm should be used?

• Decision Tree.

• Support vector machine.

• Neural Networks.

• Naïve Bayes.

• …


Remarks

• Overfitting vs Underfitting

• Underfitting refers to the case when the results cannot capture the structure of the data.

• Cannot do good prediction.

• Overfitting refers to the case when the results fits the training data too well.

• Cannot do good prediction.


Remarks



Remarks



Underfitting

Remarks



Remarks

Underfitting Overfitting



Better

Tips: a simple representation of the target function is preferred.

Remarks

Underfitting Overfitting

• Note: machine learning involves a lot of optimizations!

• Lagrange multiplier: a useful method to find the maxima or minima of a function 𝑓(𝑥1, … , 𝑥𝑛) subject to 𝑔(𝑥1, … , 𝑥𝑛) = 0.

• Step 1. Consider 𝐿 = 𝑓 − 𝜆 𝑔.

• Step 2. Calculate the partial derivatives 𝜕 𝐿

𝜕 𝑥𝑖and

𝜕 𝐿

𝜕 𝜆

• Step 3. Solve the equations 𝜕 𝐿

𝜕 𝑥𝑖= 0 and

𝜕 𝐿

𝜕 𝜆= 0


Optimization


• Lagrange multiplier: a useful method to find the maxima or minima of a function 𝑓(𝑥1, … , 𝑥𝑛) subject to 𝑔(𝑥1, … , 𝑥𝑛) = 0.

• Step 1. Consider 𝐿 = 𝑓 − 𝜆 𝑔.

• Step 2. Calculate the partial derivatives 𝜕 𝐿

𝜕 𝑥𝑖and

𝜕 𝐿

𝜕 𝜆

• Step 3. Solve the equations 𝜕 𝐿

𝜕 𝑥𝑖= 0 and

𝜕 𝐿

𝜕 𝜆= 0

• Note: the solution can be maxima or minima.

• Special case: find the maxima or minima of 𝒇 𝒙𝟏, … , 𝒙𝒏 . Set 𝝀 = 𝟎


we have 𝑛 + 1equations and 𝑛 + 1 variables

Optimization

• Maximize 𝑥1 + 𝑥2

• Subject to 𝑥12 + 𝑥2

2 − 1 = 0

• 𝐿 = 𝑥1 + 𝑥2 − 𝜆( 𝑥12 + 𝑥2

2 − 1)

•𝜕 𝐿

𝜕 𝑥1= 1 − 2𝜆𝑥1 = 0,

𝜕 𝐿

𝜕 𝑥2= 1 − 2𝜆𝑥2 = 0,

𝜕 𝐿

𝜕 𝜆= 𝑥1

2 + 𝑥22 − 1 = 0

• Solve the above equations:

• (𝑥1 =1

2, 𝑥2 =

1

2, 𝜆 =

1

2) and (𝑥1 = −

1

2, 𝑥2 = −

1

2, 𝜆 = −

1

2)


maxima minima

Optimization


• Gradient Descent: a useful method to find the solution to minimize function 𝑓(𝑥1, … , 𝑥𝑛).

• Iteratively update the current solution x by

• Simultaneously update each 𝑥𝑖 by 𝑥𝑖 = 𝑥𝑖 − 𝛼𝜕 𝑓

𝜕 𝑥𝑖

• Until converge or other criteria met.

• (−𝜕 𝑓

𝜕 𝑥1, … , −

𝜕 𝑓

𝜕 𝑥𝑛) : the direction that 𝑓 decreases most fast. (where to move)

• 𝛼: learning rate. (how far to move)


Optimization



• Gradient Descent and Convex.


𝑥𝑖 = 𝑥𝑖 − 𝛼𝜕 𝑓

𝜕 𝑥𝑖

optimal

If you are hereIf you are here

Optimization






𝜕 𝑥𝑖

optimal

Optimization

If 𝛼 is too small, slow convergence.






𝜕 𝑥𝑖

optimal

If 𝛼 is too large, may diverge.

Optimization


• Gradient Ascent: a useful method to find the solution to maximize function 𝑓(𝑥1, … , 𝑥𝑛).

• Iteratively update the current solution x by

• Simultaneously update each 𝑥𝑖 by 𝑥𝑖 = 𝑥𝑖 + 𝛼𝜕 𝑓

𝜕 𝑥𝑖

• Until converge or other criteria met.

• (𝜕 𝑓

𝜕 𝑥1, … ,

𝜕 𝑓

𝜕 𝑥𝑛) : the direction that 𝑓 increases most fast.


Optimization


• Common derivatives:

•𝜕 𝑥𝑎

𝜕 𝑥= 𝑎𝑥𝑎−1,

𝜕 ln𝑥

𝜕 𝑥=

1

𝑥,

𝜕 𝑎𝑥

𝜕 𝑥= 𝑎𝑥 ln 𝑎

• Rules:

•𝜕 𝑓 𝑥 +𝑔(𝑥)

𝜕 𝑥=

𝜕 𝑓 𝑥

𝜕 𝑥+

𝜕 𝑔 𝑥

𝜕 𝑥

•𝜕 𝑓 𝑥 𝑔(𝑥)

𝜕 𝑥= 𝑔(𝑥)

𝜕 𝑓 𝑥

𝜕 𝑥+ 𝑓(𝑥)

𝜕 𝑔 𝑥

𝜕 𝑥

•𝜕 𝑓 𝑔(𝑥)

𝜕 𝑥=

𝜕 𝑓 𝑥

𝜕𝑔(𝑥)⋅𝜕 𝑔 𝑥

𝜕 𝑥


summation

multiplication

chain

Optimization


• Supervised learning: Decision tree induction, Rule induction, Instance-based learning, Bayesian learning, Neural networks, Support vector machines, Linear Regression, Model ensembles, Graphical models, etc.

• Unsupervised learning: Clustering, Dimensionality reduction

• General machine learning concepts and techniques: Feature selection, cross-validation, maximum likelihood estimation, gradient descent, expectation-maximization, learning theory.

• Advanced topics: deep learning, etc.

• Prerequisite: probability, statistics, simple calculus, linear algebra.

• Theoretical analysis and practical programming.

Things Will Be Covered

Introduction to Machine Learning - udel.eduudel.edu/~amotong/teaching/machine learning... ·...

Documents

Transcript of Introduction to Machine Learning - udel.eduudel.edu/~amotong/teaching/machine learning... ·...