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Self-paced Learning for Latent Variable Models

Presented by Zhou Yu

M.Pawan Kumar Ben Packer Daphne Koller , Stanford University

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Aim: To learn an accurate set of parameters for latent variable models

Intuitions from Human Learning: • all information at once may be confusing => bad local minima• start with “easy” examples the learner is prepared to handle

“Self-paced” schedule of examples is automatically set by learner

• task-specific• onerous on user

• “easy for human” “easy for computer”• “easy for Learner A” “easy for Learner B”

Adopted from Kumer’s poster

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Latent Variable Models

x

y

h

x : input or observed variables

y : output or observed variables

h : hidden/latent variables

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• Latent Variable Model can be used in a lot of topics – Object Localization– Action Recognition– Human Pose Detection

xh

Latent Variable Models

y = “Deer”

h = Bounding Box

x = Entire image

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Learning Latent Variable Models

Goal: Given D = {(x1,y1), …, (xn,yn)}, learn parameters w.

Maximize log likelihood:

maxw i log P(xi,yi;w)

= maxw (i log P(xi,yi,hi;w) - i log P(hi |xi,yi,,w) )

Iterate:• Find expected value of hidden variables using current w • Update w to maximize log likelihood subject

to this expectation

• Expectation Maximization:

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Learning Latent Variable ModelsGoal: Given D = {(x1,y1), …, (xn,yn)}, learn parameters w.

• Latent Structural SVM

minw;»>012jjwjj2 + C

n

P ni=1 »i ;

8yi 2 y;8hi ) 2 H;i = 1;:::ns:t:maxhi 2H wT (©(xi ;yi ;hi ) ¡ ©(xi ; yi ; hi )) ¸ ¢ (yi ; yi ) ¡ »i ;

xhy = “Deer”

h = Bounding Box

x = Entire image

Solver: Concave-convex procedure (CCCP)

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Self-Paced Learning

Note: vi =1 means it is easy, vi =0 means it is hard

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Self-Paced Learning

CCCPAll at once

Self-paced learningEasy first

easy hardIteration 1 Iteration 2 Iteration 3

Iteration 1 Iteration 2 Iteration 3

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Optimization in Self-paced learningusing ACS

Initialize K to be largeIterate:

Run inference over hAlternatively update w and v (ACS alternate convex

search): v set by sorting li(w), comparing to threshold 1/K Perform normal update for w over subset of dataUntil convergenceAnneal K K/μ

Until all vi = 1, cannot reduce objective within tolerance

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Initialization

How we get the w0

1. Initially setting vi =1 for all samples

2. Run original CCCP to solve the structure latent SVM for a fixed number of iteration T0

Concern: It is not reasonable to use the model which we think is not good as the initial value. Different initializations could result in different performance in the end.

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ExperimentObject Localization

6 Different mammals(approximately 45 images per mammal)

Self-paced learningCCCP

easy

easy

hard

hard

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ExperimentPascal VOC 2007

5 categories out of 20, random sample 50 percent of the data

A: Use human labeled information to decide which are easy samples, non truncated non occluded are easy. Use this as initialization in self-paced learning modelB: Use CCCP results as initialization for Self-paced learning modelC: CCCP

Car Cat Chair Cow Bird0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

ABC

AP

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Some random cat images from Google

Experiment

Original Image

Results after 10 iterations

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Conclusion

• Latent variable models– Latent structural SVM– Eg: object detection, human pose estimation,

human action recognition, tracking.

• Initialization– What is a good initialization?– Maybe Multiple initialization?