Learning to Learn By Exploiting Prior Knowledge

Tatiana Tommasi

Idiap Research InstituteÉcole Polytechnique Fédérale de Lausanne

Switzerland

Oxford, October 22, 2012

Example - Learning

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Task

Training Experience

A performance measure

“I want to learn Italian”

“Bionji”… “ Buonyo” “Buongiorno”

An agent learns if its performance at a task improves with experience (Mitchell, 1996)

Example – Learning to Learn

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An agent learns to learn if its performance at each tasks improves with experience and with the number of tasks (Thrun, 1996)

Tasks

Training Experience

Performance measures

“I want to learn Italian and French”

Fr: “Bonjour”

It: “Buongiorno”

What is this?

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A fruit

Does it look like some other fruit?

Does it look similar to something else?

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Analogical reasoning: if we already know the appearance of some objects we can use it as reference information when learning something new.

Knowledge Transfer

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Storing knowledge gained while solving one problem and applying it to a different but related problem.

Source/Sources Target: Guava

Learning to learn: some transfer must occur between multiple tasks with a positive impact on the performance.

Domain Adaptation

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Source/Sources Target

Domain adaptation is needed when the data distribution of the test domain is different from that of the training domain.

Multi-Task Learning

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Task 1 Task 2 Task 3

Learning over multiple tasks at the same time by exploiting a symmetric share of information.

Learning to Learn

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Sharing Information• Knowledge Transfer• Domain Adaptation• Multi-Task Learning

Dynamic Process• Online Learning: continuous update of the current knowledge.• Active Learning: interactively query an oracle to obtain the desired outputs at new data points.

Learning to Learn

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Sharing Information• Knowledge Transfer• Domain Adaptation• Multi-Task Learning

Dynamic Process• Online Learning: continuous update of the current knowledge.• Active Learning: interactively query an oracle to obtain the desired outputs at new data points.

Exploit

Prior Knowledge

Knowledge Transfer: Advantages

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Particularly useful when few target training samples are available: boost the learning process.

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What to Transfer? Specify the form of the knowledge to transfer: instances, features, models.

How to Transfer? Define a learning algorithm able to exploit prior knowledge.

When to Transfer? Evaluate the task relatedness, keep useful knowledge and reject bad information (avoid negative transfer).

Knowledge Transfer: Challenges

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What to Transfer? Learning models.How to Transfer? Discriminative learning approach.When to Transfer? Automatic evaluation.

My choices

Intuition

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What to Transfer? Learning models.How to Transfer? Discriminative learning approach.When to Transfer? Automatic evaluation.

My choices

Intuition

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I want to learn … vs

Target Problem

• Given a set of data • Find a function

Minimize the structural risk

• Linear models• Feature mapping with

Optimization problem

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I already know … vs

Source Problem

• A source a set of data

• with

• Pre-learned model on the source. : solution of the learning problem on the source

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What to Transfer

• Consider J source models

• : solution of the learning problem on the j-th source expressed as a weighted sum of kernel functions.

• Use as a reference knowledge when learning

What to transfer? Discriminative models.

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How and When to Transfer

How: adaptive regularization.When, how much: reweighted source knowledge.

• Evaluate the relevance of each source• Solve the target learning problem.

We name KT the obtained Knowledge Transfer approach.

[T. Tommasi and B. Caputo, BMVC 2009][T. Tommasi et al., CVPR 2010]

Solve the target learning problem

Use the square loss

Solve

Adaptive Least-Square Support Vector Machines

LS-SVM (Suykens et al, 2002)• square loss: predict correctly each sample;• not sparse: all the training samples are considered;• solution: set of linear equations.

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Solving Procedure

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In matricial form

where

The model parameters can be calculated by matrix inversion

Solution:

Classifier:

Leave-One-Out Prediction

We can train the learning method on N samples and obtain as a byproduct the prediction for each training sample as if it was left out from the training set.

The Leave-One-Out error is an almost unbiased estimator of the generalization error (Lunz and Brailovsky, 1969). 1

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Evaluate the relevance of each source

The best values for beta are those producing positive values for for each i. To have a convex formulation we consider

and solve

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Experiments – Mixed Classes

• Visual Object Classification• Caltech-256• Binary problems: object vs non-object• Features: PHOG, SIFT, Region Covariance, LBP

10 mixed classes, one target and nine sources.

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Results – Mixed Classes

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Experiments – 6 Unrelated Classes

• Visual Object Classification• Caltech-256• Binary problems: object vs non-object• Features: PHOG, SIFT, Region Covariance, LBP

6 unrelated classes, one target and five sources.

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Results – 6 Unrelated Classes

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Experiments – 2 Unrelated Classes

• Visual Object Classification • Caltech-256• Binary problems: object vs non-object• Features: SIFT

2 unrelated classes, one target and one source.

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Results – 2 Unrelated Classes

Transfer Weights and Semantic Similarity

• Use the vectors b to define a matrix of class dissimilarities.• Apply multidimensional scaling (two dimensions).

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Transfer Weights and Semantic Similarity

• Use the vectors b to define a matrix of class dissimilarities.• Apply multidimensional scaling (two dimensions).

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Extension: Multiclass Domain Adaptation

• g = 1, ..., G classes fixed for both source and target;

• discriminates class g as positive from all the others considered as negative;

• class prediction

Leave-One-Out predictions

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When and How Much to Transfer

We suffer a loss which is linearly proportional to the difference between the confidence of the correct label and the maximum among the confidence of the other labels.

Final objective function

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Three Possible Schemes 1.

Three Possible Schemes 2.

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Three Possible Schemes 3.

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Application

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[T. Tommasi et al, IEEE Transaction on Robotics 2012]

Personalization of a pre-existent model.

• Task: Hand posture classification.

• Electrodes applied on the forearm collect sEMG signals.

Goals:

• reduce the training time of a mechanical hand prosthesis through adaptive learning over several known subjects.

• augment the control abilities over hand prosteses.

Experimental setup

• 10 healthy subjects• 7 sEMG electrodes• 3 grasping actions plus rest

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Experimental results

More Subjects and Postures

• 20 healthy subjects• 10 sEMG electrodes• 6 actions plus rest

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Leveraging over source models: Limits

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• Restriction to binary problems (transfer learning) or multiclass with the same set of classes in the source and in the target (domain adaptation).

• The source and the target models should live in the same space: same features and learning parameters.

• Batch method, re-evaluate the relevance of each source knowledge every time a new training sample is available.

Feature Transfer

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[L. Jie*, T. Tommasi*, B. Caputo, ICCV 2011]

• Use the source models as experts that predict on the target samples.

• Use the output of the prediction as additional feature elements.

• Cast the problem in the multi-kernel learning framework (Multiple Kernel Transfer Learning MKTL).

• Principled multiclass formulation

Online Learning

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[T. Tommasi et al, BMVC 2012]

Combine Online Learning and Knowledge Transfer such that they can get a reciprocal benefit.

• Avoid to re-evaluate at each step the relevance of source knowledge.

• Obtain an online learning approach with robust generalization capacity.

Transfer Initialized Online Learning (TROL)

Exploit Exisiting Visual Resources (partially overlapping label sets)

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[T. Tommasi et al, ACCV 2012]

• General case of many visual dataset (tasks) with some common classes. No explicit class alignment.

• No model already learned, only samples available, eventually represented with different feature descriptors.

• Define a representation which decomposes in two orthogonalparts: one shared and one private for each task.

• Use the generic knowledge coded in the shared part whenlearning on a new target problem.

Multi-Task Unaligned Shared Knowledge Transfer (MUST)

Cross-Database Generalization

Take Home Message

• It is possible to define learning algorithms that automatically evaluate the relevance of prior knowledge when addressing a new target problem with few training examples.

• The described approaches consistently outperforms learning from scratch both in transfer learning and domain adaptation problems.

• It is possible to reproduce artificially different aspects of the“human analogical reasoning process”.

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Questions ?

Tatiana Tommasittommasi@idiap.chhttp://www.idiap.ch/

~ttommasi/

More details in my thesis...