# Questions tagged [nonparametric-bayes]

Bayesian methods for infinite dimensional parameter spaces.

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34 views

### Integral of normal likelihood and multivariate normal prior

I'm updating cluster assignments in the context of a non-parametric Bayesian mixture model. When computing the probability of starting a new cluster, in the absence of cluster parameters (and using a ...
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### Choice of base measure in nCRP (for validity and computation)

I'm trying to apply the nested Chinese restaurant process (nCRP) for structure learning. nCRP is a nested extension of CRP, with each table in CRP uniquely pointing to the restaurant on the next level....
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### Relationship between Dirichlet Process and Gaussian Process

I have some questions about DP and GP. Q1. Is there any explicit relationship between Dirichlet Process and Gaussian Process? Q2. If there are some relationship between Gaussian and Dirichlet, can ...
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### Why nonparametric maximum likelihood of mixture is convex

Consider $x_i \sim N(\mu_i, 1)$ where $i = 1, \ldots, n$ and assume $\mu_i$ is generated i.i.d. from an unknown distribution $F$. We are interested in estimating the unknown $\mu_i$. One way to solve ...
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### Expected Number of Dishes in Indian Buffet Process?

I'm sure this question has an answer somewhere online, but I can't find it. Suppose I have an Indian Buffet Process with $T$ customers and concentration parameter $\alpha$. For those unfamiliar with ...
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### Why does Chinese Restaurant Table Distribution look like a Gaussian Distribution?

The Chinese Restaurant Table Distribution describes the probability distribution for the number of non-empty tables in the Chinese Restaurant Process after $T$ customers have been seated. Specifically,...
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### Coding a simple Stick-Breaking Process in Python

I've just red the great 2012 blog post of Edwin Chen about Dirichlet Process with companion code in R and Ruby. Then I'm trying to translate the Stick-Breaking Process from R to Python. I've got this ...
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### Do Stochastic Processes such as the Gaussian Process/Dirichlet Process have densities? If not, how can Bayes rule be applied to them?

The Dirichlet Pocess and Gaussian Process are often referred to as "distributions over functions" or "distributions over distributions". In that case, can I meaningfully talk about the density of a ...
1 vote
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### How to interpret graphical model for Dirichlet process mixture for variational inference?

I am working through this paper by Blei and Jordan, which introduces variational inference for Dirichlet process mixtures. They derive an evidence lower bound (ELBO) function based on a stick breaking ...
1 vote
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### Bayesian nonparametric estimate of median [closed]

I've been working on estimating the population median of a variable with a complex distribution that is not easily characterized as a parameterized probability distribution. So far, the best I have ...
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### Bayesian Model Fit for Binary Data

I am looking for methods (and preferably references) for assessing model fit for Bayesian analyses of binary data. Specifically, I am fitting Bayesian parametric and nonparametric item response models ...
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### Chinese Restaurant process (CRP)

I am trying to understand the Chinese Restaurant process (CRP) and Weighted Chinese Restaurant process (WCRP) described in a research paper "Automatic Discovery of Cognitive Skills"- Robert V. Lindsey,...
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### Question about implementing nested Chinese Restaurant Process (nCRP)

I am trying to follow the original paper on nCRP by Blei et al., 2010 and am confused with it's implementation. The authors describe the analogy for an nCRP as follows: A tourist arrives at the ...
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### Nonparametric topic modeling: hierarchical dirichlet vs. Indian buffet?

The hierarchical dirichlet process (Teh 2005) allows you to discover unlimited topics to describe a document. An alternative process, the Indian Buffet process (Griffiths 2011) is another ...
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### Proof of neutrality for dirichlet distribution

I am trying to learn the fields of bayesian non-parametric approaches. I am going thru this manuscript: http://mayagupta.org/publications/FrigyikKapilaGuptaIntroToDirichlet.pdf I am bit stuck with: ...
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### Bayesian nonparametrics vs model selection using Minimum Message Length

As we know mixture models are important tools in density estimation and in general in statistical machine learning. I have always used nonparametric Bayesian mixture models to avoid the problem of ...
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### resampling hyperparameters in a Hierarchical Dirichlet Process

The sampling scheme for the hyper-parameters of hierarchical dirichlet process (HDP) is explained in the appendix of the original paper by Teh et al. I agree that the auxiliary variable $s_j$ is a ...
I'm currently looking at a paper of Dirichlet process random effects model and the model specification is as follows: \begin{align*}y_{i} &= X_{i}\beta + \psi_{i} + \epsilon_{i}\\ \psi_{i} &... 4 votes 1 answer 617 views ### Chinese Restaurant Process I want to implement Chinese Restaurant Process representation of Dirichlet Process for random partitions. The problem setup is as follows: I have some data (customers) which I have to randomly ... 4 votes 1 answer 198 views ### What does \in mean vs = in probability? What does d\phi mean? In the following lecture notes on Bayesian nonparametrics http://stat.columbia.edu/~porbanz/papers/porbanz_BNP_draft.pdf, I often see something like \begin{align} P[\Phi_{i}\in d\phi|...]\\ P[\Phi_{i}=... 5 votes 1 answer 2k views ### Gaussian Process Regression for piecewise linear response functions I am performing Gaussian Process Regression (without noise) for response functions which are piecewise linear. My question: Does there exist a covariance function, such that sample paths from a ... 4 votes 1 answer 248 views ### Marginalizing over a Chinese Restaurant Process prior I am reading a paper by Kemp et al. and there is a part about marginalising over a Chinese Restaurant Process and I am quite clueless about how could one marginalise over such a prior! The details of ... 5 votes 2 answers 6k views ### Clustering methods for unknown number of clusters Matrix X=[x_1,...,x_i,...,x_N] is a data-set containing N data-points that each data-point x_i is a vector of D dimensions. Each dimension is a feature. The number of clusters (K) is unknown.... 1 vote 0 answers 74 views ### predictive distribution of linear bayesian regression with unknow \Sigma and \Omega The posterior distribution for weights in linear regression setup is \begin{equation} \begin{aligned} B &| Y,X \sim \mathcal{N}(\mu, \Lambda) \\ \mu &= \Lambda X^{\mathsf{T}}\Sigma^{-1}Y \\ \... 3 votes 1 answer 131 views ### Is it possible to define the mean of a varying distribution? Suppose (p_1,\ldots,p_k) be the vector of multinomial parameters and(p_1,\ldots,p_k)\sim \mbox{Dirichlet}(\alpha_1,\ldots,\alpha_k). Let's define a function $f(p_1,\ldots,p_k) \in \mathbb{R}$. ...
Let $(S, \mathcal{S})$ be a Polish space. Is there a nice proof of the fact that if the people are seated in a restaurant according to Chinese restaurant process, and then for each table, we sample a ...