Active Learning with Active Learning with Model Selection Neil - - PowerPoint PPT Presentation

Active Learning with Active Learning with Model Selection

Neil Rubens

Sugiyama Lab / Tokyo Institute of Technology

Active Learning (NLP Motivation)

• NLP (common scenario)

– Large amounts of unlabeled data Large amounts of unlabeled data – Labeling data is expensive

• Active Learning (Optimal Experimental

D i ) Design)

– Allows to select the most informative l examples

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Supervised Learning as Function Approximation

) ( f i f ) ( function target x f function learned

) ( f

y

1

y

n

y ) (

2

x f ) (

n

x f ) ( 1 x f

2

y

1

x

2

x

n

x

x

Goal: From training samples obtain that minimizes G ( ) t t i t d it

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q(x) – test input density

Design Cycle (Common)

Collect Data (Active Learning) Model Selection Parameter Learning Evaluation

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There is a problem with this flow

Active Learning (AL) Target function Target function Learned function G d i t P i t Good inputs Poor inputs

• Choice of training input points can significantly

affect the learned function.

• Active Learning – choose training input points

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g g p p so that generalization error is minimized

Setting

• Linear Model
• Least-squares Learning
• In AL can’t use training output values

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g p for estimating generalization error

Orthogonal Decomposition

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Bias Variance Decomposition

model error C bias B variance V

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Active Learning

• Nothing can be done about model error C
• Bias -> 0; (least-squares is unbiased)

Bias -> 0; (least-squares is unbiased)

• Minimize variance -> Minimize Error

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Variance AL (assuming zero bias)

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(assuming zero bias)

Active Learning - Approximation

• In general, simultaneous optimizing n points is

not tractable

• Approximation Approaches:
• Optimize points one by one (greedy)

Opt e po ts o e by o e (g eedy)

• Optimize probability distribution from which

points are drawn points are drawn

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Bias / Variance (no unbiasedness guarantee)

f f

bias

f

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variance

Bias / Variance

Best fit “min error”

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Model Selection (MS)

M d l ld b t d b b

• Model – could be represented by number

and type of basis functions, e.g.

Target function Learned function

• Model Selection – select appropriate

model M:

Learned function simple appropriate too complex

Model Selection

• Cross-validation: Measure generalization

accuracy by testing on data unused during training training

• Regularization: Penalize complex models

E’=error on data + λ model complexity E error on data λ model complexity Akaike’s information criterion (AIC), Bayesian ( ), y information criterion (BIC)

• Minimum description length (MDL): Kolmogorov

l i h d i i f d complexity, shortest description of data

• Structural risk minimization (SRM)

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Active Learning with Model Selection

Active Learning Model Selection Share the same goal: Active Learning with Model Selection: Possible Approaches: naïve sequential batch Possible Approaches: naïve, sequential, batch

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Naïve Approach

N ï A h bi i ti AL d MS th d

Naïve approach is not possible due to:

• Naïve Approach – combine existing AL and MS methods

– Active Learning – model should be fixed ALMS Dilemma (MS already performed)

Target function Learned function

[Fedorov 78, MacKay 92, Kanomori and Shimodaira 04]

Good inputs Poor inputs

Kanomori and Shimodaira 04]

– Model Selection – points should be fixed Model Selection points should be fixed (AL already performed)

[Akaike 78, Rissanen 78, Schwarz 78]

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too simple appropriate too complex

Sequential Approach

bf

Model Selection

plexity)

Active Learning

b (comp

Learning

Optimal points depend on the model

n (number of samples)

Has a risk of large error

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Has a risk of large error (due to overfitting to a different model).

Batch Approach I i i l MS i li bl

bf

Initial Model Selection

Initial MS is not reliable

Active Learning

mplexity)

Active Learning

b (com

Final Model Selection

n (number of samples)

Has a risk of large error

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Has a risk of large error (due to overfitting to a different model).

Motivation – Hedge the Risk of Large Error

Active Learning with Model Selection

• Naïve – impossible
• Batch, Sequential – risk of large error

( f ff ) (due to overfitting to a different model) Goal: Hedge the risk of large error

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g g

(minimize risk of overfitting to a different model)

Ensemble Active Learning Approach (Proposed)

H d th i k f fitti b d i i

• Hedge the risk of overfitting by designing

input points for all of the models.

G

Criterion EAL G1 G2 GCEAL Data EAL

Location of training points X

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X2 X1 XDEAL

Evaluation

D – D-EAL C – C-EAL B – Batch S S ti l d S – Sequential P - Passive proposed

• Compares favorably with existing methods
• Compares favorably with existing methods
• Minimized worst case performance (in most cases)
• Surprisingly, improved average performance (in some cases)

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Current / Future Work

• Improving AL by utilizing existing data
• My work mostly deals with theoretical aspects.
• I am also looking for practical applications.

If h bl th t i l ti – If you have any problems that involve active learning, I would be very glad to help.

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References

• Sugiyama. Active learning in approximately

linear regression based on conditional expectation of generalization error. JMLR 2006

• Bishop, Pattern Recognition and Machine

Learning

• Alpaydin, Introduction to Machine Learning

payd ,

• duc o
• ac

e ea g

• Rubens, Sugiyama. Coping with active learning

with model selection dilemma: Minimizing with model selection dilemma: Minimizing expected generalization error. IBIS 2006

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