Multiple Instance Learning

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

Part I: Multiple Instance Learning (MIL)

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

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+)

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.

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.

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

Diversity Density – Molecular Example

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

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

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.

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

Density Surfaces

Part II: SVM Algorithms for MIL

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

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?

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.

Results

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

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

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

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?

References O. Maron and T. Lozano-Pérez, "A framework for multiple-instance learning," 1998, pp. 570-576. R. C. Bunescu and R. J. Mooney, "Multiple instance learning for sparse positive bags," 2007, pp. 105-112. 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. 577-584, 2003.