Hierarchical Beta Processes and the Indian Buffet Process

By Romain Thibaux, Michael I. Jordan. 2007

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Citations in the corpus

Federated Learning with Matched Averaging (2020, methodology): “…case of equation 3 to compute maximum a posteriori estimate (MAP) of their Bayesian nonparametric model based on the Beta-Bernoulli process (BBP) (Thibaux & Jordan, 2007), where similarity c(wjl, θi) is the corresponding posterior probability of jth client neuron l generated from a Gaussian with…”
Bayesian Nonparametric Federated Learning of Neural Networks (2019, methodology): “Several extensions to the IBP (and the equivalent BBP) have been developed, see Grifﬁths & Ghahramani (2011) for a review.”
Sharing Features among Dynamical Systems with Beta Processes (2009, methodology): “In evaluating this expression, we have exploited the exchangeability of the IBP [9], which follows directly f rom the beta process construction [22].”
Nonparametric Latent Feature Models for Link Prediction (2009, methodology): “…two class-based generative models, the Infinite Relational Model (IRM) [6] and the Mixed Membership Stochastic Blockmodel (MMSB) [8], on two datasets from the original IRM paper and a NIPS coauthorship dataset, establishing that our model does better than the best of those models on those datasets.”
Probabilistic Programming with Stochastic Memoization (2014, background): “This process, called the Indian buffet process [8], turns out to be equivalent to a beta process prior [9].”
Nonparametric Bayesian Dictionary Learning for Analysis of Noisy and Incomplete Images (2011, background): “Hence, for data , there is an associated set of latent binary vectors , and the beta-Bernoulli process provides a convenient prior for these vectors [29], [37], [42].”
Sparse Bayesian infinite factor models. (2011, background): “Recently, there has been a significant amount of work on latent feature models using the Indian buffet process [Griffiths and Ghahramani, 2006, Thibaux and Jordan, 2007].”
Hierarchical Indian buffet neural networks for Bayesian continual learning (2019, methodology): “To do this, we propose a hierarchical IBP prior [Thibaux and Jordan, 2007] for neuron selection across multiple layers.”
Scalable inference of topic evolution via models for latent geometric structures (2018, methodology): “In this subsection we model the collection of topic polytopes observed at a single time point by employing the Beta-Bernoulli Process prior [24].”
Variational Inference for the Indian Buffet Process (2009, methodology): “…Jensen's inequality to equation (4): −E   ∞ i=K+1 (1 − π i ) N   ≤ − E ∞ i=K+1 (1 − π i ) N (5) The Beta Process construction for the IBP (Thibaux & Jordan, 2007) implies that the sequence π 1 , π 2 , . . . can be modeled as a Poisson process on the unit interval (0, 1) with rate µ(x)dx…”
Nonparametric Bayesian feature selection for multi-task learning (2011, methodology): “The DP partitions the tasks into groups, and the BBP selects the features relevant to the tasks in each group, with the parameter associated with each feature task-specific.”
Bayesian Nonparametrics (2011, unknown): “An insightful look into the fundamentals of the Indian buﬀet process is given by Thibaux and Jordan (2007).”
Stick-breaking Construction for the Indian Buffet Process (2007, background): “This representation, along with the work of Thibaux and Jordan [17], also illuminates interesting theoretical connections between the IBP, Chinese restaurant processes, Beta processes and Dirichlet processes.”
A Tutorial on Bayesian Nonparametric Models (2011, methodology): “The beta process and Bernoulli process Latent factor models admit a similar analysis (Thibaux and Jordan, 2007).”
Bayesian Nonparametrics: Models beyond the Dirichlet process (2009, unknown): “or Chinese restaurant, process for the Dirichlet model. As shown in Thibaux and Jordan (2007) ,”
Nonparametric factor analysis with beta process priors (2009, methodology): “Teh, Y. W., G¨or¨ur, D., & Ghahramani, Z. (2007).”