Introduction of Structured Learning. Hung-yi Lee

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1 Introduction of Structured Learning Hung-yi Lee

2 Structured Learning We need a more powerful function f Input and output are both objects with structures Object: sequence, list, tree, bounding box f : X Y X is the space of one kind of object Y is the space of another kind of object In the previous lectures, the input and output are both vectors.

3 Example Application Speech recognition X: Speech signal (sequence) Y: text (sequence) Translation X: Mandarin sentence (sequence) Y: English sentence (sequence) Syntactic Paring X: sentence Y: parsing tree (tree structure) Object Detection X: Image Y: bounding box Summarization X: long document Y: summary (short paragraph) Retrieval X: keyword Y: search result (a list of webpage)

4 Unified ramework Training ind a function : (x,y): evaluate how compatible the objects x and y is Inference (Testing) X Y R f : X Given an object x Y ~ y arg max f yy ~ x, y x y arg max x, y yy

5 Unified ramework Object Detection Task description Using a bounding box to highlight the position of a certain object in an image E.g. A detector of Haruhi X : Image Y : Bounding Box Haruhi (the girl with yellow ribbon)

6 Unified ramework Object Detection (x,y) x: Image y: Bounding Box (x,y) ( ) the correctness of taking range of y in x as Haruhi

7 Unified ramework Object Detection (x,y) y (output result) input x = Enumerate all possible bounding box y -1

8 Unified ramework - Summarization Task description Given a long document Select a set of sentences from the document, and cascade the sentences to form a short paragraph X Y long document ={s 1, s 2, s 3, s i } s i : the i th sentence summary ={s 1, s 3, s 5 }

9 Unified ramework - Summarization Training Inference (x,y) x y (x,y) x y d {s 1, s 3, s 5 } d 1 d 2 d {s 2, s 4, s 6 } d 1 d 2 d {s 3, s 6, s 9 }

10 Unified ramework - Retrieval Task description User input a keyword Q System returns a list of web pages X Obama (keyword) d10011 d98776 Y A list of web pages (Search Result)

11 Unified ramework - Retrieval Training Inference (x,y) x= Obama, y= x= Trump, y= d666 d444 x= Obama, y= x= Trump, y= d103 d300d103 d300 d133 d220 (x,y) x= Haruhi, y= x= Haruhi, y= x= Haruhi, y= d203 d330 d103 d304 d103 d305

12 Unified ramework Training ind a function (x,y): evaluate how compatible the objects x and y is Inference Given an object x ~ y : X Y arg max yy Statistics R x, x, y Px, y? y Training Estimate the probability P(x,y) P : Inference X Y Given an object x ~ y arg max P yy arg max yy yy P arg max P 0,1 x, y Px y x, x y

Estimate the probability P(x,y) P : Inference X Y Given an object x arg max yy yy P arg max P

13 Statistics Unified ramework x, y Px, y? Drawback for probability Probability cannot explain everything 0-1 constraint is not Training Estimate the probability P(x,y) P : Inference X Y Given an object x arg max yy yy P arg max P 0,1 necessary y arg max P y x Strength for probability Meaningful Energy-based Model: /~yann/research/ebm/ ~ yy x, y Px x, y

14 Unified ramework That s it!? Training ind a function : (x,y): evaluate how compatible the objects x and y is Inference (Testing) X Y R Given an object x ~ y arg max yy x, y There are three problems in this framework.

15 Problem 1 Evaluation: What does (x,y) look like? How (x,y) compute the compatibility of objects x and y Object Detection: (x=, y= ) Summarization: (x=, y= ) (a long document) (a short paragraph) Retrieval: (x= Obama, y= ) (keyword) (Search Result)

16 Problem 2 Inference: How to solve the arg max problem y arg max yy x, The space Y can be extremely large! y Object Detection: Y=All possible bounding box (maybe tractable) Summarization: Y=All combination of sentence set in a document Retrieval: Y=All possible webpage ranking.

17 Problem 3 Training: Given training data, how to find (x,y) Principle Training data: , ˆ,, ˆ,, r r x y x y x, yˆ We should find (x,y) such that, x 1, yˆ 1 x 2, yˆ 2 x r, yˆ r 1 x, y for all y ŷ 1 2 x, y for all 2 y ŷ x r, y for all r y yˆ

18 Three Problems Problem 1: Evaluation What does (x,y) look like? Problem 2: Inference How to solve the arg max problem y Problem 3: Training arg max yy Given training data, how to find (x,y) x, y

19 Have you heard the three problems elsewhere? rom 數位語音處理

y arg max yy (x,y) x, y In handwriting digit classification,

20 Link to DNN? The same as what we have learned. Training : DNN X Y R x, y Nx N(x) x CE, x CE N, y y y Inference ~ y arg max yy (x,y) x, y In handwriting digit classification, there are only 10 possible y. y = [ ] y = [ ] y = [ ] ind max x y

21 You have to know Viterbi Algorithm 數位語音處理 : os/ _4.0.fsp.wmv/index.html ( 請用 IE 開啟 ) os/ _4.0.fsp.wmv/index.html ( 請用 IE 開啟 ) 演算法數位通信相關課程

Hidden Markov Models

10-601 Introduction to Machine Learning Machine Learning Department School of Computer Science Carnegie Mellon University Hidden Markov Models Matt Gormley Lecture 22 April 2, 2018 1 Reminders Homework