# Questions tagged [approximate-inference]

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### 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 ...
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### 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 ...
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### how least square estimation can be done for a distribution

As i have estimated parameters of geometric distribution by using MLE (maximum likelihood estimation) and MOM( Method of moment) but i have problem in estimating parameter of Geometric distribution ...
196 views

### Rao-Blackwellization in variational inference

The Black box VI paper introduces Rao-Blackwellization as a method to reduce the variance of the gradient estimator using score function, in section 3.1. However I don't quite get the basic idea ...
88 views

### Variational Inference - deriving coordinate update equations for mixture model

I'm currently going through this paper by Blei et. al. that describes the setup and derivation of the coordinate ascent equations for a Gaussian mixture model with K components. I am having some ...
37 views

### Approximation of the upper bound on the expectation of log sum of exponentials

I am having some trouble replicating the results in Guillaume Bouchard's paper, Efficient Bounds for the Softmax Function and Applications to Approximate Inference in Hybrid Models, where he discusses ...
80 views

### variational inference derivation

According to this lecture note, Eq. 25 gives the coordinate ascent update for latent variable $z_k$ as follows $$q^*(z_k)\propto\exp(E_{-k}[\log{p(z_k,Z_{-k},x)}])$$ and I understand the derivation ...
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### Questions about approximate inference and calculating the posterior predictive

As I understand, computing the exact posterior of parameters $p(\theta|x)$ is nearly always impossible since we need to compute the evidence $\sum_\theta p(x|\theta)p(\theta)$ with every possible ...
184 views

### Variational Inference: Ising Model

I am self learning Variational Inference. Currently I am reading the chapter 21 book from Murphy 1 and trying to understand the Ising model (21.3.2). The Ising model here is used as denoising ...
70 views

### Efficient approximate marginal inference in variational auto-encoder

In Auto-Encoding Variational Bayes, authors mentioned that they proposed a solution to "Efficient approximate marginal inference of the variable $x$". I read through the paper and appendix, now ...
82 views

### Jensen's inequality in Collaborative Topic Regression

I am reading the article Collaborative Topic Modeling for Recommending Scientific Articles and could notice the application of Jensen's inequality in order to define a bound from which optimization is ...
109 views

### How Can I teach someone “sampling from a given distribution” is hard?

For many people I know, they do not think sampling from a given distribution is a hard problem in general. For example, many software provide functions do to sample from normal distribution or uniform ...
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### Variational Inference of Univariate Gaussian mixtures

I am reading this paper. In the paper, they use an example of mixture of unit-variance univariate Gaussians with the following parameterization: \begin{align} \mu_k & \sim \mathcal{N}(0, \sigma^2)...
546 views

### Gradient of the expectation of a function w.r.t. distribution parameters

In section 2.2 of Kingma & Welling's paper on variational auto-encoders authors write the following equality for the gradient of the expectation of a function with respect to the parameters of the ...
964 views

### Difference between stochastic variational inference and variational inference?

Very simple, as the question header says: what is the difference between SVI and VI? I cannot seem to find a clear-cut definition online.
374 views