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Presented by: John Paisley Duke University, ECE

The Phylogenetic Indian Buffet Process : A Non-Exchangeable Nonparametric Prior for Latent Features By: Kurt T. Miller, Thomas L. Griffiths and Michael I. Jordan ICML 2008. Presented by: John Paisley Duke University, ECE. Motivation.

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Presented by: John Paisley Duke University, ECE

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  1. The Phylogenetic Indian Buffet Process: A Non-Exchangeable Nonparametric Prior for Latent FeaturesBy: Kurt T. Miller, Thomas L. Griffiths and Michael I. JordanICML 2008 Presented by: John Paisley Duke University, ECE

  2. Motivation • Nonparametric models are often used with the assumption of exchangeability. • The Indian Buffet Process is an example • Sometimes, non-exchangeable models might be more appropriate. • The Phylogenetic Indian Buffet Process • Similar to the IBF, but uses additional information of how related diners are with each other. • These relationships are captured in a tree structure.

  3. Indian Buffet Process

  4. Phylogenetic Indian Buffet Process • Uses a tree to model columns zk • This is done as follows: • Assign the root node to be zero • Along an edge of distance t, let this change to a 1 with probability , where . The distance from every leaf to the root is 1. • If a 0 is changed to a 1 along a path to a node, all subsequent nodes are 1 and therefore so are the leaves.

  5. Sampling Issues • For (1), use the sum-product algorithm (Pearl, 1988). • For (2), use the chain rule of probability. • An MCMC inference algorithm is given in detail.

  6. Experimental Results • Elimination by Aspects (EBA) model • A Choice Model • Let there be i objects and zik indicate the ith object has the kth feature. Let each feature have a weight, wk. The EBA model defines the probability of choosing object I over j as • The likelihood of an observation matrix, X, is • This has been modeled using the IBP.

  7. Experimental Results • Consider now an underlying tree structure to this model. • Preference trees: Out of 9 personalities, 3 movie stars, 3 athletes and 3 politicians, people made the 36 pairwise choices of whom they would rather spend time with. Here, L is the length of the edge of each general category to a leaf. • A soft version of this tree is modeled with the pIBP using data generated from this model with L = 0.1

  8. Experimental Results • Example results: As the number of samples decreases, the pIBP is able to infer the structure better than the IBP because of the prior.

  9. Experimental Results • As can be seen, the additional structure in the model produces better results.

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