# Questions tagged [laplace-approximation]

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### Laplace approximation from a log-posterior in R

I would like to perform a Laplace approximation of a log-posterior. The evolution of a cancer cell at given time $t_j$, $j = 1,\cdots,n$ for an experiment $i$ follows the following Poisson ...
142 views

### Gaussian Processes: multi-class Laplace approximation

In Chapter 3.5 of Gaussian Process for Machine Learning book by Rasmussen and Williams (R&W 2006), authors present a Laplace approximation for a multi-class Gaussian Process (GP) classifier. ...
337 views

### Inference: How is the Laplace approximation actually useful to us compared with MLE and MAP?

I was reading a few different sources (including the "Machine Learning and Pattern Recognition" book by Bishop) about the Laplace integral approximation method for inference. However, I am ...
1 vote
263 views

### Random Fourier Features approximating a kernel inverse?

There is a method I have been studying called Spectral Normalised Neural Gaussian Processes which leaves me with a question I cannot answer. In this method, they utilize Random Fourier Features but ...
220 views

2k views

### Comparing Laplace Approximation and Variational Inference

Does anyone know of any references that look at the relationship between the Laplace approximation and variational inference (with normal approximating distributions)? Namely I'm looking for something ...
74 views

### Simple approximation of joint posterior

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) ...
187 views

### Is BIC useful for a multimodal distribution?

Given a dataset $D$ and a model $M$ with parameters $\theta$, the Bayesian Information Criterion can be used to approximate the model's marginal likelihood $\int p(D|\theta,M)p(\theta|M) d\,\theta$. ...
493 views

### What's the relationship between Laplace approximation and Variational Bayes methods?

To be precise, I'm checking this presentation https://kaybrodersen.github.io/talks/Brodersen_2013_03_22.pdf, but I don't understand what is the connection between Laplace method and variational bayes? ...
831 views

### Modelling random effects as an autoregressive-autoregressive process

Has anyone ever come across an autoregressive-autogressive process. I am modelling positively correlated time-series of random effects in a fisheries model. They are integrated out via the Laplace ...
424 views

### Hessian for Laplace Approximation in Uncertainty Propagation

This is possibly a silly conceptual question, ... but anyway: Imagine I have a function: $f = F(\mathbf{x}) = F(x_1,x_2) = ax_1^2 + bx_2^3,$ where $x_1,x_2 \sim N(0,1)$ for example. For a naive ...
241 views

### Calculating variance using Laplace approximation for GP classification

I'm having some trouble implementing Algorithm 3.2 from Rasmussen and Williams. Namely, sometimes when I evaluate step 6, I obtain a negative variance, which I believe is impossible (and makes line ...
2k views

### Marginalization of GP regression hyperparameters with Laplace approximation

I am using Gaussian Processes (GP) for regression (via the gpml package for MATLAB). So far, I was optimizing the hyper-parameters by maximizing the log likelihood, but I would like to try a more ...
657 views

### Laplace approximation for binomial distribution in matlab

i using bionrnd() function to generate a random vector and Laplace approximation formula to approximate the binomial distribution. but Laplace histogram dose not ...