1. Multiple Instance Learning

2. Outline Motivation Multiple Instance Learning (MIL) Diverse Density
Single Point Concept
Disjunctive Point Concept
SVM Algorithms for MIL
Single Instance Learner (SIL)
Sparse MIL
mi-SVM
MI-SVM
Results
Some Thoughts

3. Part I: Multiple Instance Learning (MIL)

4. Motivation
It is not always possible to provide labeled data for training
Reasons:
Requires substantial human effort
Requires expensive tests
Disagreement among experts
Labeling is not possible at instance level
Objective: present a learning algorithm that can learn from ambiguously labeled training data

5. Multiple Instance Learning (MIL)
In MIL, instead of giving the learner labels for the individual examples, the trainer only labels collections of examples, which are called bags.
A bag is labeled positive if there is at least one positive example in it
It is labeled negative if all the examples in it are negative
Negative Bags (Bi-)
Positive Bags (Bi+)

6. Multiple Instance Learning (MIL)
The key challenge with MIL is coping with the ambiguity of not knowing which examples in the positive bag are actually positive and which are not
MIL model was first formalized by Dietterich et al. to deal with the drug activity prediction problem
Following that, an algorithm called Diverse Density was developed to provide a solution to MIL
Later, the method was extended to deal real-valued labels instead of binary labels.

7. Diverse Density
Diversity Density solves MIL problem by examining the distribution of the instances
It looks for a point that is close to instances in different positive bags and that is far from the instances in the negative bags
Such a point represents the concept that we would like to learn
Diversity Density is the measure of the intersection of the positive bags minus the union of the negative bags.

8. Diversity Density – Molecular Example
Suppose the shape of candidate molecule can be described by a feature vector
If a molecule is labeled positive, then at least one place along the manifold it took the right shape to fit into the target protein

9. Diversity Density – Molecular Example

10. Noisy-Or for Estimating the Density
It is assumed that the event can only happen if at least one of the causations occurred
It is also assumed that the probability of any cause failing to trigger the event is independent of any other cause

11. Diverse Density - Formally
By maximizing the Diverse Density we can find the point of intersection (the desired concept)
where
Alternatively, one can use most-likely-cause estimator

12. Single Point Concept
A concept that corresponds to single point in feature space
Every Bi+ has at least one instance that is equal to the true concept corrupted by some Gaussian noise.
Every Bi- has no instances that are equal to the true concept corrupted by some Gaussian noise
Where
k = number of dimensions in feature space
sk = scaling vector
This class assumes that given an underlying true concept P , every positive bag has at least one instance that is equal to P corrupted by some Gaussian noise. Every negative has no instances that are equal to P corrupted by
some Gaussian noise.

13. Disjunctive Point Concept
More complicated concepts are disjunction of d-single point concepts
A bag is positive if at least one of its instances is in the concept xt1, xt2 or xtd

14. Density Surfaces

15. Part II: SVM Algorithms for MIL

16. Single Instance Learning MIL
SIL-MIL: Single Instance Learning approach
Applies bag’s label to all instances in the bag
A normal SVM is trained on the resulting dataset
Good for bags that are rich with positive instances

17. Sparse MIL
All instances from negative bags are real negative instances
Small positive bags are more informative than large positive bags
A bag is represented as the sum of all its instances normalized by its 1 or 2-norm
Good for sparse bags
Balanced SVM that uses transductive SVM to estimate the labels for the unlabeled data from labeled training data. Where does the labeled data come from? Does not that contradicts with MIL concept?

18. Results Datasets used:
AIMed: sparse dataset created from a corpus of protein-protein interactions. Contains 670 positive and 1,040 negative bags
CBIR: Content Based Image Retrieval domain. The task is to categorize images as to whether they contain an object of interest
MUSK: drug activity dataset. Bags corresponds to molecule, while bag instances correspond to three dimensional conformation of same molecule
TST: text categorization dataset in which MEDLINE articles are represented as bags of overlapping text passages.

19. Results

20. mi-SVM Instance level classification
Treats label instance labels yi as unobserved hidden variable
Goal is to maximize the margin over the unknown instance labels
Suitable for instance classification

21. MI-SVM Bag level classification
Goal is to maximize the bag margin, which is
The “most positive” instance in case of positive bags
The “least negative” instance in case of negative bags
Suitable for bag classification

22. Results: mi-SVM vs. MI-SVM
Corel image data sets
TREC9 document categorization sets

23. Some Thoughts
Can find multiple positive concepts in a single bag and learn these concepts?
Does varying sizes of negative bags have an influence on the learning algorithm?
Can we re-formulate MIL using Fuzzy Logic?

24. References
O. Maron and T. Lozano-Pérez, "A framework for multiple-instance learning," 1998, pp
R. C. Bunescu and R. J. Mooney, "Multiple instance learning for sparse positive bags," 2007, pp
J. Yang, "Review of Multi-Instance Learning and Its applications," 2008.
S. Andrews, et al., "Support vector machines for multiple-instance learning," Advances in neural information processing systems, pp , 2003.