# Questions tagged [approximate-inference]

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### Is the inferential challenge of dense bayesian or markov networks solved after current improvements in variational inference and neural networks?

I am trying to understand more about Graphical models, and have a reasonable grasp of the basics now. One issue that recurs in a lot of the papers of the mid-2000s and even in Koller's textbook is ...
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### Why don’t diffusion models suffer posterior collapse?

In VAEs, posterior collapse occurs when the approximated posterior $q_\theta(z|x)$ becomes the standard Gaussian prior $p(z)$ after training (Lucas et al. 2019). The forward process of diffusion ...
1 vote
23 views

### How do I estimate probability of someone having condition X [closed]

There is a survey, which asks following question: do you know personally someone, who has condition X? The result of the survey is percentage of people, who know someone I want to use this survey to ...
• 111
1 vote
95 views

### Does approximating the likelihood function violate the likelihood principle in Bayesian Inference?

Suppose we have a prior $p(\theta)$ and a likelihood function $L(\theta|x)$, and that the likelihood $L(\theta|x)$ is intractable somehow (difficult or impossible to compute) and we instead replace it ...
1 vote
30 views

### A soft question about probabilistic inference

Suppose A and B are two propositions and $A \implies B$ is true.WE know all it means is that B is true whenever A is true. Now consider a situation where we only that A is true with probability ,say,...
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1 vote
103 views

### Generative model that satisfies certain algebraic constraints

Disclaimer: I need guidance and help with where to start looking for solution of the problem I have described below. My background is in optimization and I am new to statistical methods, so there is a ...
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27 views

1 vote
205 views

### What is a Dirac distribution on a hyperplane?

I'm trying to understand message passing for compressed sensing. I came acrross this distribution: As the title suggests, how does this distribution look like? I know the first products term in the ...
• 117
68 views

### What is the link between the queries Bayesian Networks can answer, and inference algorithms?

I have seen two concepts linked to Bayesian Networks: Bayesian Networks can answer different types of queries. These types include proof of evidence, most probable explanation, computing maximum a ...
1 vote
38 views

### Can we ignore the generation side of the method described in density estimation using Real NVP?

First appologies if my question is stupid. I am studying the paper "Density estimation using real NVP" by Dinh, Sohl-Dickstein and Bengio. link The paper presented a nice idea that the generation ...
• 11
164 views

### Difference / Relationship of Generative Models / Variational Bayesian Inference

I feel a bit confused trying to merge and unify understandings of generative models and variational bayesian inference methods. Initially, I believed them to be the same thing, namely learning full ...
143 views

### Derivation of the Objective Function for Expectation Propagation

I was reading Expectation Propagation As A Way Of Life and the original paper by Minka Expectation Propagation for Approximate Bayesian Inference and they both say that a fixed point of the EP ...
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40 views

### Exact inference in an approximate model as opposed to approximate inference in an exact model?

I remember hearing a while ago that it was more rigorous to perform approximate inference in an exact model as opposed to exact inference in an approximate model. I can’t now remember the reasoning ...
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1 vote
11 views

### Approximate Bayesian computation for comparing parameters affect on a response variable [closed]

I'm not sure I understand this method perfectly so please correct me if I'm wrong. From my understanding Approximate Bayesian Computation allows you to perform likelihood free inference by re-...
• 576
135 views

### How to Test Linear Hypotheses about Parameters in Simulation-Based Indirect Inference

Setup: I have a model that produces a vector of aggregate outcomes, $\theta$, based on parameters, $\beta$. The relationship $\theta=\Theta(\beta)$ is stochastic and analytically intractable, but I ...
• 367
534 views

### Expectation Maximisation vs Expectation Propagation in the context of Bayesian Networks

I am confused about Expectation Maximisation and Expectation Propagation algorithms in the context of Bayesian Networks, especially whether one comprise another. What is the difference between ...
• 141
1 vote
690 views

### What is the difference between approximate bayesian computation vs approximate bayesian inference?

What are the main differences between approximate bayesian computation vs approximate bayesian inference? Are they essentially the same? Do they refer to the same of different family of models? My ...
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### How to combine sampled data from the same population?

Let's say I have a friend and we both asked one group of people a different question. For example, I ask the group how old they are, and my friend asks them how much they weigh. If I meet up with my ...
231 views

Consider a normal distribution $\mathcal N(\boldsymbol{\mu}(w), \boldsymbol{\Sigma}(w))$, with mean $\boldsymbol{\mu}(w)$ and covariance $\boldsymbol{\Sigma}(w)$ that are parameterized by a vector of ...
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585 views

### Variational inference with discrete variational parameters

Typically Variational Inference relies on taking gradient steps on KL divergence between the variational and true posterior, or on the ELBO. This does not seem valid when variational parameters are ...
• 964
239 views

### Variational Inference with intractable score function

Is it possible to do ELBO maximization using stochastic gradient estimates (i.e. iteratively apply variational updates using (3) in http://proceedings.mlr.press/v33/ranganath14.pdf), when it's cheap ...
• 964
189 views

### Variational inference with deterministic dependencies between variables

Suppose I have a probabilistic graphical model shown in the picture, in which all variables are binary, $c_1$ and $c_2$ are observed, and I want to use mean-field variational inference to estimate ...
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### Normalizing Flows, Real NVPs and Inverse Autoregressive Flows - Used for Probabilty Density Approximation or for Sampling?

Suppose we have a parametric family $g(x;\theta)$, where $\theta$ are the parameters. As far as I can tell, there are two ways we can use this family to model a probability distribution: Probability ...
• 567
531 views

### Convergence of approximate Gibbs sampling

We have a bivariate random variable $(X,Y)$ for which sampling is challenging. If we were to know how to sample from the conditionals $(X|Y)$ and $(Y|X)$, we could get samples from the joint using ...
• 311
4k views

### get probabilities from kernel density estimation pdf

I have data points located at $\mathbf{x}_i$ and I would like to a find quick and dirty way to calculate their probability of occurring (not the pdf) using kernel density estimation. Formally speaking,...
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284 views

### Bethe approximation for factor graphs

I am confused at computing Bethe approximation for factor graphs in here. It generalizes Bethe approxmiation in a pairwise case. However, I am wondering why (75) goes to (78) with (76): We can verify ...
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### How to compute the Gibbs free energy in Bethe approximation for MRF

Hi, I am learning loopy belief propagation for MRF. The general roadmap is to define a Bethe approximation, which is exact for a tree but wrong for general graphs. I'm currently stuck at the point to ...
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Consider the (hierarchical) Bayesian inference problem with two unknowns $(x,\theta)$ and data $y$. I'm using a very simple ("independence"?) approximation  p(x,\theta|y) \approx p(x|\theta_\star,y) ...