# approx: Approximations to the posterior of the latent values In gplite: General Purpose Gaussian Process Modelling

 approx R Documentation

## Approximations to the posterior of the latent values

### Description

Functions for initializing the approximation for the latent values, which can then be passed to `gp_init`. The supported methods are:

`approx_laplace`

Laplace's method, that is, based on local second order approximation to the log likelihood. For Gaussian likelihood, this means exact inference (no approximation).

`approx_ep`

Expectation propagation, EP. Approximates the likelihood by introducing Gaussian pseudo-data so that the posterior marginals match to the so called tilted distributions (leave-one-out posterior times the true likelihood factor) as closely as possible. Typically more accurate than Laplace, but slower.

### Usage

```approx_laplace(maxiter = 30, tol = 1e-04)

approx_ep(damping = 0.9, quad_order = 11, maxiter = 100)
```

### Arguments

 `maxiter` Maximum number of iterations in the Laplace/EP iteration. `tol` Convergence tolerance. `damping` Damping factor for EP. Should be between 0 and 1. Smaller values typically lead to more stable iterations, but also increase the number of iterations, and thus make the algorithm slower. `quad_order` Order of the Gauss-Hermite quadrature used to evaluate the required tilted moments in EP.

### Value

The approximation object.

### References

Rasmussen, C. E. and Williams, C. K. I. (2006). Gaussian processes for machine learning. MIT Press.

### Examples

```
# Basic usage
gp <- gp_init(
cfs = cf_sexp(),
lik = lik_bernoulli(),
method = method_fitc(num_inducing = 100),
approx = approx_ep()
)

```

gplite documentation built on Aug. 24, 2022, 9:07 a.m.