gp: Gaussian process models
In goldingn/gpe: Gaussian Process Everything

Description Usage Arguments Details Value Examples

Fitting, summarizing and predicting from Gaussian process models using a range of inference methods.

gp(formula, data, family = gaussian, weights = NULL, mean_function = NULL,
  inducing_data = NULL, inference = c("default", "full", "FITC", "Laplace"),
  hyperinference = c("default", "BFGS", "BFGSrestarts", "none"),
  verbose = FALSE)

## S3 method for class 'gp'
print(x, ...)

`formula`	an object of class `formula` giving a symbolic description of the model to be fitted - the right hand side must be a valid kernel object or the commands to construct one.
`data`	a data frame containing the covariates against which to model the response variable. This must have the same number of rows as `response` and contain named variables matching those referred to by `kernel`.
`family`	a `family` object giving the likelihood and link function to be used to fit the model. Currently only `gaussian`, `poisson` and `binomial` (only Bernoulli) are supported.
`weights`	an optional vector of 'prior weights' to be used in the fitting process. Should be NULL or a numeric vector.
`mean_function`	an optional function specifying the prior over the mean of the gp, in other words a 'first guess' at what the true function is. This must act on a dataframe with named variables matching some of those in `data` and return a vector giving a single value for each row in the dataframe. Note that this function must return a prediction on the scale of the link, rather than the response. If `NULL` then a prior mean is assumed to be 0 for all observations.
`inducing_data`	an optional dataframe containing the locations of inducing points to be used when carrying out sparse inference (e.g. FITC). This must contain variables with names matching those referenced by `kernel` and `mean_function`. This should have fewer rows than `data` and `response`.
`inference`	a string specifying the inference method to be used to estimate the values of the latent parameters. If `'default'` an appropriate method is picked for the likelihood specified. See details section for the list of default inference methods.
`hyperinference`	the method to be used for inference on the hyperparameters (parameters of the kernel). `BFGS` carries out straightforward optimisation starting from the current kernel parameters using gradient-free BFGS. Because the likelihood surface is rarely convex, this is is not advised for general use. `BFGSrestarts` runs gradient-free BFGS 5 times, each starting with a different randomly chosen set of parameters, which might be a bit better. `none` does no inference on the hyperparameters. `default` currently switches to `none` in all cases, though in future it may depend on other arguments.
`verbose`	whether to return non-critical information to the user during model fitting.
`x`	an object of class `gp`, constructed by the function `gp` giving a fitted gaussian process model
`...`	additional arguments for compatibility with generic functions

The default inference method for a model with the family gaussian(link = 'identity') is full direct inference ('full'), for binomial(link = 'logit') and binomial(link = 'probit') the default is full Laplace inference ('Laplace'; though note that only Bernoulli data is handled at the moment). Sparse inference can be carried out by specifying inference = 'FITC', this is currently only available for a model with a Gaussian likelihood.

A fitted gp object for which there aren't yet any associated functions. But there will be.

# make some fake data
n <- 100  # observations
m <- 10  # inducing points

# dataframes
df <- data.frame(x = sort(runif(n, -5, 5)))
inducing_df <- data.frame(x = sort(runif(m, -5, 5)))
prediction_df <- data.frame(x = seq(min(df$x), max(df$x), len = 500))

# fake Gaussian response data
f <- sin(df$x)
y <- rnorm(n, f, 1)

# fit a full (non-sparse) GP model (without updating the hyperparameters) 
# as this is the default. Notice we add the observation error to the kernel.
m1 <- gp(y ~ rbf('x') + iid(), df, gaussian)

# fit another with FITC sparsity
m2 <- gp(y ~ rbf('x') + iid(), df, gaussian, inference = 'FITC', 
         inducing_data = df)
         
# summary stats, other associated functions still to come

# construct a poisson response variable
y2 <- rpois(n, exp(f))

# fit a GP model by Laplace approximation
# (note no observation error in this model)
m3 <- gp(y2 ~ rbf('x'), df, poisson)


print(m3)
m3