Bayesian Density Estimation and Inference Using Mixtures

By M. Escobar, Matthew West. 1995

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

A Neural Dirichlet Process Mixture Model for Task-Free Continual Learning (2020, methodology): “Since the exact inference of the posterior of DPM models is infeasible, approximate inference methods are adopted such as Markov chain Monte Carlo (MCMC) (Maceachern, 1994; Escobar & West, 1995; Neal, 2000) or variational inference (Blei & Jordan, 2006; Wang & Dunson, 2011; Lin, 2013).”
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.”
Variational inference for Dirichlet process mixtures (2006, methodology): “MCMC provides one class of approximations for this posterior and the predictive density (MacEachern 1994; Escobar and West 1995; Neal 2000).”
Bayesian Nonparametric Calibration and Combination of Predictive Distributions (2015, methodology): “…2004 and Griffin and Steel 2006), is now widely used in many fields due to the availability of efficient algorithms for posterior computations (Escobar and West 1995; MacEachern and Müller 1998; Papaspiliopoulos and Roberts 2008; © American Statistical Association Taddy 2010), including but…”
A Split-Merge Markov chain Monte Carlo Procedure for the Dirichlet Process Mixture Model (2004, background): “Computationaltechniquesfor Dirichlet process mixture models were explored previously by Escobar (1994), Escobar and West (1995), MacEachern (1994), Bush and MacEachern (1996), Neal (1992, 2000), and Green and Richardson (2001).”
An Introduction to MCMC for Machine Learning (2004, methodology): “For simplicity, we avoid the treatment of nonparametric model averaging techniques; see for example (Escobar & West, 1995; Green & Richardson, 2000).”
Generalized weighted Chinese restaurant processes for species sampling mixture models (2003, methodology): “In this case, the EPPF formula (8) reduces to a variant of Ewens sampling formula (Ewens (1972); see also Antoniak (1974) and Ewens and Tavaré, (1997)).”
Distributional assumptions of growth mixture models: implications for overextraction of latent trajectory classes. (2003, methodology): “For this reason, mixtures of normal distributions are often used to provide an approximation to complex or intractable distributions ( Escobar & West, 1995; Ferguson, 1983; Roeder & Wasserman, 1997; Sorenson & Alspach, 1971; for a review, see Everitt & Hand, 1981, pp. 118–124; McLachlan & Peel, 200”
Statistical Methods for Distributional Analysis (2015, background): “23See Escobar and West (1995), Ferguson (1983), Titterington, Makov, and Smith (1985), McLachlan and Peel (2000), Ghosal and van der Vaart (2001).”
High-Dimensional Sparse Factor Modeling: Applications in Gene Expression Genomics (2008, methodology): “Under the DP structure, this generates a set of some d n ≤ n distinct vectors and assigns each of the λ i to one of these vectors (Escobar and West 1995, 1998).”
Stochastic variational inference (2012, background): “…factorization models (Spearman, 1904; Tipping and Bishop, 1999; Collins et al., 2002; Wang, 2006; Salakhutdinov and Mnih, 2008; Paisley and Carin, 2009; Hoffman et al., 2010b), certain Bayesian nonparametric mixture models (Antoniak, 1974; Escobar and West, 1995; Teh et al., 2006a), and others.”
Normalized random measures driven by increasing additive processes (2004, methodology): “as the focus of much attention during the 1990s as a consequence of the introduction of simulation based inference, ﬁrst considered by Escobar (1988) in his Ph.D. dissertation, and later developed by Escobar and West (1995) and MacEachern and Mu¨ller (1998), among others. The model is comprehensivel”
A Bayesian Nonparametric Approach to Inference for Quantile Regression (2010, unknown): “Finally, we update the DP precision parameter α [step (d)] using the augmentation method of Escobar and West (1995).”
Mixture Modeling for Marked Poisson Processes (2010, methodology): “(4) The base distribution is taken to be of the standard conjugate form (as in, e.g., Escobar and West, 1995), such that g0(µ, σ2) = N(µ; δ, σ2/κ)ga(σ−2; ν, ω), where ga(·; ν, ω) denotes the gamma density with E[σ−2] = ν/ω.”
Distributed Algorithms for Topic Models (2009, methodology): “The auxiliary variable method explained in Escobar and West (1995) and Teh et al. (2006) is used to sample , , and .”
Mixtures of Gamma Distributions With Applications (2001, background): “See, for example, Diebolt and Robert (1994), Escobar and West (1995), Richardson and Green (1997) and Roeder and Wasserman (1997).”
Posterior convergence rates of Dirichlet mixtures at smooth densities (2007, methodology): “Efficient Gibbs sampling algorithms for the computation of the posterior based on a Dirichlet mixture process have been developed; see, for instance, [3].”
Gibbs Sampling Methods for Stick-Breaking Priors (2001, methodology): “For example, see Halmos (1944), Freedman (1963), Fabius (1964), Connor and Mosimann (1969), and Kingman (1974).”
Marginal Likelihood and Bayes Factors for Dirichlet Process Mixture Models (2003, methodology): “The key feature of the model is the assumption that the distribution G is unknown and is modeled by a DP prior (Ferguson 1973) with concentration parameter and speci ed base probability measure G04¢—Ê5 that depends on an unknown parameter vector Ê. Here G and G0 denote probability measures, altho”
Maximum likelihood estimation of a multi‐dimensional log‐concave density (2008, methodology): “This theory leads to an asymptotically optimal choice of the smoothing parameter, or bandwidth. Unfortunately, however, it depends on the unknown density f through the integral of the square of the second derivative of f. Considerable effort has therefore been focused on finding methods of automatic”