The Infinite Gaussian Mixture Model

By Carl E. Rasmussen. 1999

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Citations in the corpus

Multi-Level Cause-Effect Systems (2015, methodology): “Our implementation uses the Dirichlet Process Gaussian Mixture Model (Rasmussen, 1999) for clustering with a flexible number of clusters, but again the algorithm stays clustering-routine-agnostic.”
Identifying Finite Mixtures of Nonparametric Product Distributions and Causal Inference of Confounders (2013, background): “Once we have determined the number of mixture components m , we proceed to step (b) of recovering the distribution of each component P ( X 1 , . . . , X d | z ( i ) ) and the mixing weights P ( z ( i ) ).”
High-Dimensional Probability Estimation with Deep Density Models (2013, background): “Bayesian nonparametric density estimation (e.g., [Escobar and West, 1995, Rasmussen, 2000, Adams et al., 2009]) is another ﬂexible approach, but it often requires costly inference procedures and does not typically scale well to high-dimensional data.”
Venture: a higher-order probabilistic programming platform with programmable inference (2014, methodology): “Examples include probabilistic grammars (Jelinek et al., 1992), nonparametric Bayesian models (Rasmussen, 1999; Johnson et al., 2007; Rasmussen and Williams, 2006; Griffiths and Ghahramani, 2005), probabilistic models over worlds with a priori unknown numbers of objects, models for learning the…”
Discovering linguistic structures in speech: models and applications (2014, methodology): “/ ae n d/ (and, end, attend) [37] [12 67] 41 /f l ae t/ (flat, flatten) [81] [28 16 21] 39 /ih z/ (this, is, it’s) [47 59] 33 the world [35 40 102] [38 91] 31 /ax bcl ax l/ (able, cable, incredible) [34 18] [38 91] 18 /aw n dh/ (down, how, download) [11] [95 8] 16 /s cl t eh r/ (this era, first era)”
A Bayesian framework for word segmentation: exploring the effects of context. (2009, unknown): “Usually Gaussians are used for continuous data (Rasmussen, 2000; Wood, Goldwater, & Black, 2006) and multinomials for discrete data (Blei, Ng, & Jordan, 2002; Navarro et al.”
Machine Learning: Algorithms, Real-World Applications and Research Directions (2021, methodology): “GMM clustering is more robust than k-means and works well even with non-linear data distributions.”
Copula Processes (2010, methodology): “To make predictions, we take J samples of p ( f | y , z ), { f 1 , . . . , f J } , and then approximate (10) as a mixture of J Gaussians: Each of the Gaussians in this mixture have equal weight.”
Online gradient-based mixtures for transfer modulation in meta-learning (2018, methodology): “The formulation of the DPMM that is most appropriate for incremental learning is the sequential draws formulation that corresponds to an instantiation of the Chinese restaurant process (CRP) (Rasmussen, 2000).”
Cognitive Models of Test-Item Effects in Human Category Learning (2010, methodology): “A human cat- egory learning model needs to be able to explain all such Test-Item Effects.”
Infinite latent feature models and the Indian buffet process (2005, background): “The distribution over partitions implied by the CRP can be de rived by taking the limit of the probability of the corresponding equivalence class of a ssignment vectors in a model where class assignments are generated from a multinomial di stribution with a Dirichlet prior [9, 10].”
Sharing Clusters among Related Groups: Hierarchical Dirichlet Processes (2004, background): “They have also begun t o be seen in applications in machine learning (e.g., [7, 8 , 9]).”
Learning Systems of Concepts with an Infinite Relational Model (2006, methodology): “Following previous work on nonparametric Bayesian models (Rasmussen 2002; Antoniak 1974), we use a distribution over partitions induced by a Chinese Restaurant Process (CRP, Pitman 2002).”
A tutorial on task-parameterized movement learning and retrieval (2015, methodology): “, determining the number of Gaussians in the GMM) is compatible with the techniques employed in standard GMM, such as the use of a Bayesian information criterion [81], Dirichlet process [73, 22, 64, 49], iterative pairwise replacement [82], spectral clustering [68, 84, 52], or based on segmentation ”
A Tutorial on Bayesian Nonparametric Models (2011, methodology): “3 Chinese restaurant process mixture models The BNP clustering model uses the CRP in an infinite-capacity mixture model (Antoniak, 1974; Anderson, 1991; Escobar and West, 1995; Rasmussen, 2000).”