Machine Learning Theory: Overview, Exams of Artificial Intelligence

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Machine Learning Theory: Overview

COMS 4995-1 Spring 2020 (Daniel Hsu)

Agenda

▶ (^) Today: ▶ (^) About machine learning theory ▶ (^) About the course ▶ (^) Some examples of learning problems/settings ▶ (^) Next time: ▶ (^) Concentration of measure

What is machine learning? (1)

Image credit: http://www.seefoodtechnologies.com/nothotdog/

What is machine learning? (2)

Examples: ▶ (^) Spam filtering (from email text) ▶ (^) Ad click prediction (from user profile and context) ▶ (^) Gene expression level prediction (from upstream DNA) ▶ (^) Best-next-move prediction (from state of chess board) ▶ (^)... ▶ (^) Programming-by-demonstration

What is learning theory?

▶ (^) Design/analysis of machine learning algorithms/problems ▶ (^) Computational resources: running time, memory,... ▶ (^) Data resources: sample size, rounds of interaction,... ▶ (^) Many different models for theoretical analysis ▶ (^) Statistical learning ▶ (^) Online learning ▶ (^) Learning with queries ▶ (^) Finding planted structures ▶ (^)...

Why study learning theory? (1)

Relevance to machine learning practice

▶ (^) Breiman (1995) “Reflections After Refereeing Papers for NIPS”

Why study learning theory? (2)

Relevance to machine learning practice

▶ (^) Breiman (1995) “Reflections After Refereeing Papers for NIPS”

Why study learning theory? (3)

Insights into general phenomenon of learning

▶ (^) Valiant (1984) “A Theory of the Learnable”

ABSTRACT: Humans appear to be able to learn new

concepts without needing to be programmed explicitly in

any conventional sense. In this paper we regard learning as

the phenomenon of knowledge acquisition in the absence of

explicit programming. We give a precise methodology for

studying this phenomenon from a computational viewpoint.

It consists of choosing an appropriate information gathering

mechanism, the learning protocol, and exploring the class of

concepts that can be learned using it in a reasonable

(polynomial) number of steps. Although inherent algorithmic

complexity appears to set serious limits to the range of

concepts that can be learned, we show that there are some

important nontrivial classes of propositional concepts that 8

About this course

▶ COMS 4995-

▶ (^) Will be “COMS 4773” in the future; can count towards degree program requirements as such. ▶ (^) Website (with syllabus, schedule, etc): http://www.cs.columbia.edu/~djhsu/LT/ ▶ (^) Topics: ▶ (^) Statistical learning (e.g., generalization theory) ▶ (^) Online learning (e.g., learning with experts, multi-arm bandits) ▶ (^) Unsupervised learning (e.g., clustering models), if time permits ▶ (^) Learning goals: ▶ (^) Rigorously analyze ML problems/algorithms ▶ (^) Read/understand research papers in ML theory

Course requirements

Prerequisites

▶ (^) Mathematical maturity; reading and writing proofs ▶ (^) Probability, linear algebra, a bit of convex analysis ▶ (^) Prior exposure to machine learning (maybe just for motivation)

Requirements

▶ (^) Reading assignments – schedule on website ▶ (^) Primarily from a few textbooks, available on the website ▶ (^) Homework assignments – will be posted on website ▶ (^) 75% of overall grade ▶ (^) Project – instructions on website ▶ (^) 25% of overall grade

What is the pattern (input/output relationship)?

What is the pattern (input/output relationship)?

What is the pattern (input/output relationship)?

• Example: Pattern recognition
  • (3 , 5) + Input Output
  • (9 , 1) −
  • (2 , 7) +
  • (4 , 2) −
  • (8 , 8) −
  • (5 , 2) −
  • (3 , 1) −
  • (1 , 3) +
  • (2 , 5) +
  • (5 , 3) −
  • (4 , 2) −
• Example: Pattern recognition
  • (3 , 5) + Input Output
  • (9 , 1) −
  • (2 , 7) +
  • (4 , 2) −
  • (8 , 8) −
  • (5 , 2) −
  • (3 , 1) −
  • (1 , 3) +
  • (2 , 5) +
  • (5 , 3) −
  • (4 , 2) −
• Example: Pattern recognition
  • (3 , 5) − Input Output
  • (9 , 1) −
  • (2 , 7) +
  • (4 , 2) +
  • (8 , 8) −
  • (5 , 2) +
  • (3 , 1) −
  • (1 , 3) +
  • (2 , 5) −
  • (5 , 3) +
  • (4 , 2) +

Example: Pattern recognition 2 - all points

0 1 2 3 4 5 6 7 8 9 a

0

1

2

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4

5

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8

9

b