Multilinear Dirichlet Processes

Dependent Dirichlet processes (DDP) have been widely applied to model data from distributions over collections of measures which are correlated in some way. On the other hand, in recent years, increasing research efforts in machine learning and data mining have been dedicated to dealing with data involving interactions from two or more factors. However, few researchers have addressed the heterogeneous relationship in data brought by modulation of multiple factors using techniques of DDP. In this paper, we propose a novel technique, MultiLinear Dirichlet Processes (MLDP), to constructing DDPs by combining DP with a state-of-the-art factor analysis technique, multilinear factor analyzers (MLFA). We have evaluated MLDP on real-word data sets for different applications and have achieved state-of-the-art performance.

[1]  Nicholas J. Foti,et al.  A Survey of Non-Exchangeable Priors for Bayesian Nonparametric Models , 2012, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[2]  W. Eric L. Grimson,et al.  Construction of Dependent Dirichlet Processes based on Poisson Processes , 2010, NIPS.

[3]  J. S. Rao,et al.  Spike and slab variable selection: Frequentist and Bayesian strategies , 2005, math/0505633.

[4]  Radford M. Neal.  Markov Chain Sampling Methods for Dirichlet Process Mixture Models , 2000 .

[5]  Peter I. Frazier,et al.  Distance dependent Chinese restaurant processes , 2009, ICML.

[6]  Arnaud Doucet,et al.  Generalized Polya Urn for Time-varying Dirichlet Process Mixtures , 2007, UAI.

[7]  P. Müller,et al.  A method for combining inference across related nonparametric Bayesian models , 2004 .

[8]  S. MacEachern,et al.  An ANOVA Model for Dependent Random Measures , 2004 .

[9]  Stephen G. Walker,et al.  Random density functions with common atoms and pairwise dependence , 2015, Comput. Stat. Data Anal..

[10]  J. E. Griffin,et al.  Order-Based Dependent Dirichlet Processes , 2006 .

[11]  D. Dunson,et al.  Kernel stick-breaking processes. , 2008, Biometrika.

[12]  Bamshad Mobasher,et al.  CSLIM: contextual SLIM recommendation algorithms , 2014, RecSys '14.

[13]  Blanca Vargas-Govea,et al.  Effects of relevant contextual features in the performance of a restaurant recommender system , 2011 .

[14]  Massimiliano Pontil,et al.  Multilinear Multitask Learning , 2013, ICML.

[15]  Hiroshi Nakagawa,et al.  The Hybrid Nested/Hierarchical Dirichlet Process and its Application to Topic Modeling with Word Differentiation , 2015, AAAI.

[16]  A. Gelfand,et al.  The Nested Dirichlet Process , 2008 .

[17]  Jun Huan,et al.  aptMTVL: Nailing Interactions in Multi-Task Multi-View Multi-Label Learning using Adaptive-basis Multilinear Factor Analyzers , 2016, CIKM.

[18]  Geoffrey E. Hinton,et al.  Tensor Analyzers , 2013, ICML.

[19]  L. Lathauwer,et al.  On the Best Rank-1 and Rank-( , 2004 .

[20]  Nuria Oliver,et al.  Frappe: Understanding the Usage and Perception of Mobile App Recommendations In-The-Wild , 2015, ArXiv.

[21]  Massimiliano Pontil,et al.  Convex multi-task feature learning , 2008, Machine Learning.

[22]  S. MacEachern,et al.  Bayesian Nonparametric Spatial Modeling With Dirichlet Process Mixing , 2005 .

[23]  George Eastman House,et al.  Sparse Bayesian Learning and the Relevan e Ve tor Ma hine , 2001 .

[24]  VandewalleJoos,et al.  On the Best Rank-1 and Rank-(R1,R2,. . .,RN) Approximation of Higher-Order Tensors , 2000 .

[25]  Joshua B. Tenenbaum,et al.  Separating Style and Content with Bilinear Models , 2000, Neural Computation.

[26]  Yee Whye Teh,et al.  Sharing Clusters among Related Groups: Hierarchical Dirichlet Processes , 2004, NIPS.

[27]  Rose Yu,et al.  Learning from Multiway Data: Simple and Efficient Tensor Regression , 2016, ICML.

[28]  Tamara G. Kolda,et al.  Tensor Decompositions and Applications , 2009, SIAM Rev..

[29]  Kenta Oku,et al.  Context-Aware SVM for Context-Dependent Information Recommendation , 2006, 7th International Conference on Mobile Data Management (MDM'06).

[30]  J. Sethuraman.  A CONSTRUCTIVE DEFINITION OF DIRICHLET PRIORS , 1991 .

[31]  Jim E. Griffin,et al.  On Bayesian nonparametric modelling of two correlated distributions , 2013, Stat. Comput..

[32]  P. Cochat,et al.  Et al , 2008, Archives de pediatrie : organe officiel de la Societe francaise de pediatrie.

[33]  Fabrizio Leisen,et al.  A vector of Dirichlet processes , 2013 .

[34]  Wesley O Johnson,et al.  Bayesian Nonparametric Nonproportional Hazards Survival Modeling , 2009, Biometrics.

[35]  David B Dunson,et al.  Nonparametric Bayesian models through probit stick-breaking processes. , 2011, Bayesian analysis.