Griffiths 2011 - Applications of the IBP

Summary

Section 6 reviews nine uses of the IBP prior: choice behaviour, protein complexes, dyadic data, similarity judgments, link prediction, ICA/sparse factor analysis, hidden-cause structure learning, structured Markov transition matrices, and faster inference algorithms.

Main Content

Sec.	Application	Role of $Z$	Inference notes
6.1	Choice behaviour (Gorur et al. 2006)	latent option features, Tversky elimination-by-aspects likelihood	non-conjugate; auxiliary-variable sampler like Neal’s Algorithm 8
6.2	Protein interactions (Chu et al. 2006)	protein $i$ belongs to complex $k$; binding prob depends on ${\sum }_k{z}_{ik}{z}_{jk}$	validated on yeast RNA-processing complexes (affinity purification / mass spectrometry)
6.3	Binary matrix factorisation, dyadic data (Meeds et al. 2007)	two IBP matrices (movies, viewers) linked by weights $W$	two-parameter IBP; new-feature MH proposal; split-merge move
6.4	Similarity judgments (Navarro and Griffiths 2007)	additive clustering $s_{ij}\approx {\sum }_k{w}_k{f}_{ik}{f}_{jk}$	numbers 0-9: even and odd features both recovered; singleton features drawn from prior
6.5	Link prediction (Miller et al. 2010)	scores $ZW{Z}^T$ squashed to link probability	strictly more expressive than stochastic blockmodels
6.6	ICA / sparse FA (Knowles and Ghahramani 2007; Rai and Daume 2009)	which sources are active	gene-signature discovery in ovarian cancer microarrays; factor regression
6.7	Hidden causes (Wood et al. 2006; Wood and Griffiths 2007)	hidden cause $k$ is parent of observed $i$ (noisy-OR)	particle filter (SMC) alternative
6.8	Markov transition structure (Fox et al. 2010)	which states each state transitions to	birth-death MCMC moves; motion-capture action components
6.9	Other inference	-	Doshi-Velez and Ghahramani 2009: keep $A$ uncollapsed for $O(N)$ per iteration and parallelism; mean-field VI (Doshi-Velez et al. 2009) for infinite ICA, better in high dimensions

Conclusions (Sec. 8). The recipe “take the infinite limit of a finite exchangeable model” transfers from latent classes to latent features and may extend to other combinatorial structures (Titsias 2008; Orbanz 2010). The IBP also serves as a prior for any sparse binary matrix with unknown column count, such as bipartite adjacency matrices.

Examples

Marketing reading of Sec. 6.3

Customers by products: rows are customers, columns are latent “needs”; $Z$ marks which needs a customer has, $W$ maps needs to purchase propensity; a two-parameter IBP controls how many needs are common. This is the dyadic binary factorisation of Meeds et al., not a statement from the paper about marketing.

Connections

Social Network Models for latent-feature link prediction; Customer Lifetime Value - Overview for the customer-heterogeneity setting.

See Also

Griffiths 2011 - Gibbs Sampling and the Linear-Gaussian Model, Griffiths 2011 - The Indian Buffet Process - Overview