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On Consistency of Nonparametric Normal Mixtures for Bayesian Density Estimation

Antonio Lijoi, Igor Prünster, Stephen G Walker
2005 Journal of the American Statistical Association  
As for the former, some new discrete nonparametric priors have been recently proposed in the literature that have natural use as alternatives to the Dirichlet process in a Bayesian hierarchical model for  ...  Indeed, strong consistency of Bayesian nonparametric procedures for density estimation has been the focus of a considerable amount of research; in particular, much attention has been devoted to the normal  ...  THE CONSISTENCY RESULT The Bayesian Normal Mixture Model Nowadays the most common use of Bayesian nonparametric procedures is represented by density estimation via a mixture model based on a random discrete  ... 
doi:10.1198/016214505000000358 fatcat:6nz2nwq55jcexcvex2kbvcdgde

Bayesian Entropy Estimation for Countable Discrete Distributions [article]

Evan Archer and Il Memming Park and Jonathan Pillow
2014 arXiv   pre-print
We show that the resulting Pitman-Yor Mixture (PYM) entropy estimator is consistent for a large class of distributions.  ...  Here we show that it also provides a natural family of priors for Bayesian entropy estimation, due to the fact that moments of the induced posterior distribution over H can be computed analytically.  ...  Parts of this manuscript were presented at the Advances in Neural Information Processing Systems (NIPS) 2012 conference.  ... 
arXiv:1302.0328v3 fatcat:dmquqh6p2fh7hbki3wbk5x24z4

Bayesian nonparametric estimation of Tsallis diversity indices under Gnedin-Pitman priors [article]

Annalisa Cerquetti
2014 arXiv   pre-print
Here we present a fully general Bayesian nonparametric estimation of the whole class of Tsallis diversity indices under Gnedin-Pitman priors, a large family of random discrete distributions recently deeply  ...  Bayesian nonparametric estimation of Shannon entropy and Simpson's diversity under uniform and symmetric Dirichlet priors has been already advocated as an alternative to maximum likelihood estimation based  ...  density intervals in Table 2 and Stephan Poppe for introducing her to the notion of Tsallis generalized index.  ... 
arXiv:1404.3441v2 fatcat:h7olw45g75arpdalu44hk3g2e4

Unsupervised Track Classification Based On Hierarchical Dirichlet Processes

Paolo Braca, Kevin LePage, Jüri Sildam, Peter Willett
2013 Zenodo  
Publication in the conference proceedings of EUSIPCO, Marrakech, Morocco, 2013  ...  Discretizing the results of MMD mapping using a small dictionary, and estimating the entropy of the resulting, we end up associating each detection with a discrete scalar that has only a limited number  ...  ~ℎ ( , ), ~( ), where corresponds to the probability of state k, is generated via stick-breaking construction (GEM denotes stick-breaking process [7] ).  ... 
doi:10.5281/zenodo.43744 fatcat:nngtbjzwxbcpthaafoyxpc5mnm

On Inconsistent Bayes Estimates in the Discrete Case

David Freedman, Persi Diaconis
1983 Annals of Statistics  
With a tail-free prior, the posterior distribution is consistent. With a mixture of a tail-free prior and a point mass, however, the posterior may be inconsistent.  ...  This is likewise true for a countable mixture of tail-free priors. Similar results are given for Dirichlet priors.  ...  Informally, X is chosen from p by "stick-breaking:" start with a stick of unit length, break off a random length for X(1).  ... 
doi:10.1214/aos/1176346325 fatcat:bgmqpmxkcfggdcwqnblptfmsaa

A Bayesian Nonparametric Estimation to Entropy [article]

Luai Al-Labadi, Viskakh Patel, Kasra Vakiloroayaei, Clement Wan
2020 arXiv   pre-print
A Bayesian nonparametric estimator to entropy is proposed.  ...  The derivation of the new estimator relies on using the Dirichlet process and adapting the well-known frequentist estimators of Vasicek (1976) and Ebrahimi, Pflughoeft and Soofi (1994).  ...  As an alternative, Sethuraman (1994) uses the stick-breaking approach to define the Dirichlet Process. Let (β i ) i≥1 be a sequence of i.i.d. random variables with a Beta(1, α) distribution.  ... 
arXiv:1903.00655v4 fatcat:7vw3kw2rlvhgdoqfzhnxyty7yq

Adaptive Convergence Rates of a Dirichlet Process Mixture of Multivariate Normals [article]

Surya T. Tokdar
2011 arXiv   pre-print
It is shown that a simple Dirichlet process mixture of multivariate normals offers Bayesian density estimation with adaptive posterior convergence rates.  ...  This sieve construction is expected to offer a substantial technical advancement in studying Bayesian non-parametric mixture models based on stick-breaking priors.  ...  Rousseau (2010) discusses adaptive density estimation with finite beta mixtures with a hierarchical prior on the number of mixture components.  ... 
arXiv:1111.4148v1 fatcat:oyeli2etzzfvjm3k5zxdd36nim

A nonparametric Bayesian approach toward robot learning by demonstration

Sotirios P. Chatzis, Dimitrios Korkinof, Yiannis Demiris
2012 Robotics and Autonomous Systems  
Existing methods, including likelihood-or entropy-based criteria, usually tend to yield noisy model size estimates while imposing heavy computational requirements.  ...  Recently, Dirichlet process (infinite) mixture models have emerged in the cornerstone of nonparametric Bayesian statistics as promising candidates for clustering applications where the number of clusters  ...  Inference for the DPGMR model is conducted using an elegant variational Bayesian algorithm, and is facilitated by means of a stick-breaking construction of the DP prior, which allows for the derivation  ... 
doi:10.1016/j.robot.2012.02.005 fatcat:fxdh7lcuo5gp5d6zmtzactxhae

Bayesian nonparametric estimation and consistency of mixed multinomial logit choice models

Pierpaolo De Blasi, Lancelot F. James, John W. Lau
2010 Bernoulli  
Noting the mixture model description of the MMNL, we employ a Bayesian nonparametric approach, using nonparametric priors on the unknown mixing distribution G, to estimate choice probabilities.  ...  These procedures are based on approximations of the random probability measure by classes of finite stick-breaking processes.  ...  James was supported in part by grants HIA05/06.BM03, RGC-HKUST 6159/02P, DAG04/05.BM56 and RGC-HKUST 600907 of the HKSAR.  ... 
doi:10.3150/09-bej233 fatcat:b6hndrlft5bftnmiweedjs7mnu

A Bayesian Nonparametric Approach To Macroeconomic Risk

Billio Monica, Casarin Roberto, Michele Costola, Michele Guidani
2016 Zenodo  
We apply a Bayesian nonparametric test for distributional changes in large panels of time series from macroeconomics.  ...  The test allows for detecting structural changes in the sequence of cross-sectional conditional distributions.  ...  They prose a mixture of Pitman-Yor processes and show that the resulting Pitman-Yor Mixture (PYM) entropy estimator is consistent for a large class of distributions.  ... 
doi:10.5281/zenodo.1322511 fatcat:c4r4zdk3bzfypppjyze3zgycku

Reparameterizing the Birkhoff Polytope for Variational Permutation Inference [article]

Scott W. Linderman, Gonzalo E. Mena, Hal Cooper, Liam Paninski, and John P. Cunningham
2017 arXiv   pre-print
Combinatorial optimization algorithms may enable efficient point estimation, but fully Bayesian inference poses a severe challenge in this high-dimensional, discrete space.  ...  To surmount this challenge, we start with the usual step of relaxing a discrete set (here, of permutation matrices) to its convex hull, which here is the Birkhoff polytope: the set of all doubly-stochastic  ...  Real Gumbel-Softmax Rounding Stick-breaking Since Ψ consists of independent Gaussians with variances ν 2 mn , the entropy is simply, H(Ψ; θ) = 1 2 m,n log(2πeν 2 mn ).  ... 
arXiv:1710.09508v1 fatcat:7is4omzbrfgo7kb7mucdcefso4

Copula based factorization in Bayesian multivariate infinite mixture models

Martin Burda, Artem Prokhorov
2014 Journal of Multivariate Analysis  
Bayesian nonparametric models based on infinite mixtures of density kernels have been recently gaining in popularity due to their flexibility and feasibility of implementation even in complicated modeling  ...  We show that in a multivariate setting this scheme leads to an improvement in the precision of a density estimate relative to the commonly used multivariate Gaussian mixture.  ...  min{k} → ∞, similar to the stick breaking representation of Sethuraman (1994) .  ... 
doi:10.1016/j.jmva.2014.02.011 fatcat:gp46gtbzpjhd3bg7r3iqkb2tru

An Infinite Multivariate Categorical Mixture Model for Self-Diagnosis of Telecommunication Networks

Amine Echraibi, Joachim Flocon-Cholet, Stephane Gosselin, Sandrine Vaton
2020 2020 23rd Conference on Innovation in Clouds, Internet and Networks and Workshops (ICIN)  
In this paper, we propose an infinite multivariate categorical mixture model to identify patterns of faults in an unsupervised setting, without any prior expert knowledge, and without the requirement to  ...  dealing with real-world applications.  ...  The Dirichlet Process Categorical Mixture Model (DPCMM) Using the stick-breaking construction introduced in the previous section for the weights π k of the k th cluster, the generative process for the  ... 
doi:10.1109/icin48450.2020.9059491 dblp:conf/icin/EchraibiFGV20 fatcat:qtuid6a4zjgupjgubpykrqdohu

Bayesian Hierarchical Growth Model for Experimental Data on the Effectiveness of an Incentive-Based Weight Reduction Method

Md Azman Shahadan Et.al
2021 Turkish Journal of Computer and Mathematics Education  
mixture prior model.  ...  model with no correlated intercept and slope random effects model and semi-parametric Bayesian hierarchical growth model with Dirichlet process mixture prior model.  ...  Mujeeb Khan who allowed us to use his experimental data on the effectiveness of an incentive-based weight reducing technique and made it possible for us to come up with these findings.  ... 
doi:10.17762/turcomat.v12i3.840 fatcat:xqfb46yekrbnrjfdhe7ovr4uki

Stick-Breaking Variational Autoencoders [article]

Eric Nalisnick, Padhraic Smyth
2017 arXiv   pre-print
This development allows us to define a Stick-Breaking Variational Autoencoder (SB-VAE), a Bayesian nonparametric version of the variational autoencoder that has a latent representation with stochastic  ...  We extend Stochastic Gradient Variational Bayes to perform posterior inference for the weights of Stick-Breaking processes.  ...  STICK-BREAKING PROCESSES Lastly, we define stick-breaking processes with the ultimate goal of using their weights for the VAE's prior p(z).  ... 
arXiv:1605.06197v3 fatcat:ssy7oa36mrhrhhvfuflbxgneo4
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