Stick-breaking Construction for the Indian Buffet Process

By Yee Whye Teh, Dilan Gorur, Zoubin Ghahramani. 2007

308 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Citations in the corpus

Bayesian Nonparametric Federated Learning of Neural Networks (2019, background): “…( not probability) measure Q = i q i δ θ i formed by an inﬁnitely countable set of (weight, atom) pairs i =1 are distributed by a stick-breaking process (Teh et al., 2007): c i ∼ Beta ( γ 0 , 1) , q i = =1 c j and the atoms are drawn i.i.d from the normalized base measure θ i ∼ H/H (Ω) with domain…”
Streaming dynamic and distributed inference of latent geometric structures (2018, unknown): “…on SV−2 and concentration parameter γ0: Q|γ0, H ∼ BP(γ0, H), (1) It follows that Q = ∑ i qiδθi , where {qi}∞i=1 follows a stick-breaking construction (Teh et al., 2007): µi ∼ Beta(γ0, 1), qi = ∏i j=1 µj , and each θi ∼ H is a sequence of T random elements on the unit sphere θi := {θ(t)i…”
Generative Modeling of Infinite Occluded Objects for Compositional Scene Representation (2019, methodology): “…by s·k in the image. zind can be seen as a binary matrix with one row and infinite columns which is obtained using the stick-breaking construction (Teh et al., 2007) for the Indian Buffet Process (IBP) (Ghahramani & Griffiths, 2006; Griffiths & Ghahramani, 2011). zdep is a binary matrix…”
A Tutorial on Bayesian Nonparametric Models (2011, background): “Stick breaking construction of the beta process A “double-use” of the same breakpoints β leads to a stick-breaking construction of the beta process (Teh et al., 2007); see also Paisley et al.”
Continual Learning using a Bayesian Nonparametric Dictionary of Weight Factors (2021, background): “The stick-breaking construction and the standard IBP representation are diﬀerent representations of the same nonparametric object (see Section 3 in Teh et al. (2007) for the proof).”
Scalable inference of topic evolution via models for latent geometric structures (2018, unknown): “It follows that Q = ∑ i qiδθi , where {qi}i=1 follows a stick-breaking construction [23]: μi ∼ Beta(γ0, 1), qi = ∏i j=1 μj , and each θi ∼ H is a sequence of T random elements on the unit sphere θi := {θ i }t=1, which are generated as follows:”
Nonparametric Bayesian Deep Networks with Local Competition (2018, background): “To this end, we utilized LWTA non-linearities, and sparsity inducing priors based on the IBP.”
Flexible Modeling of Latent Task Structures in Multitask Learning (2012, methodology): “Our mixture of factor analyzers based MTL model uses the IBP/Beta Process to model each factor analyzer so we do not need to specify the number of factors K a priori.”
Infinite Latent SVM for Classification and Multi-task Learning (2011, methodology): “We focus on its stick-breaking construction [25], which is good for developing efficient inference methods.”
Statistical Model Aggregation via Parameter Matching (2019, unknown): “The weights {qi}i=1 are distributed by a stick-breaking process [30], ν1 ∼ Beta(γ0, 1), νi = ∏i j=1 νj and the atoms θi are drawn i.”
The Indian Buffet Process: An Introduction and Review (2011, background): “9, and can also be used to derive other inference algorithms for the IBP, such as slice sampling (Teh et al., 2007).”
The Infinite Factorial Hidden Markov Model (2008, methodology): “Since the distribution on the variables am in our model are identical to the distribution of the feature parameters in the IBP model, we can use the result in [8] that these variables have the following distribution a(1) ∝ Beta(α, 1), (11) p(a(m)|a(m−1)) = αa−α (m−1)a α−1 (m) I(0 ≤ a(m) ≤ a(m−1)).”
Beta Processes, Stick-Breaking and Power Laws (2011, methodology): “These latter representations are, however, based on the non-recursive sized-biased sampling and inverse-L´evy methods rather than the recursive representations of Teh et al. [2007] and Paisley et al. [2010].”
Variational Inference for the Indian Buffet Process (2009, methodology): “These approaches include Gibbs sampling (Griffiths & Ghahramani, 2005) (which may be augmented with Metropolis split-merge proposals (Meeds et al., 2007)), slice sampling (Teh et al., 2007), and particle filtering (Wood & Griffiths, 2007).”
Variational Russian Roulette for Deep Bayesian Nonparametrics (2019, methodology): “Based on the construction, Teh et al. (2007) develops a slice sampler for IBP latent feature models.”
A Coupled Indian Buffet Process Model for Collaborative Filtering (2012, methodology): “…the following hierarchical Bayesian construction znk ∼ Bernoulli(πk) (2) πk = k∏ i=1 vi (3) vk ∼ Beta(α, 1) (4) In other words, under the stick-breaking construction, an equivalent hierarchical expression for the prior p(Z) is obtained by introduction of the Beta-distributed stick variables vk.”
Indian Buffet Neural Networks for Continual Learning (2019, methodology): “[14] Yee Whye Teh, Dilan Grür, and Zoubin Ghahramani.”