Package {magp}

magp: Mapping-Based Additive Gaussian Process Models

Description

Fits additive Gaussian process models for experiments in which each component has both a quantitative level and a position in a sequence.

Details

For q components, the first q input columns contain quantitative levels and the next q columns contain sequence positions. Every sequence row must be a permutation of 1:q. Quantitative columns outside ⁠[0, 1]⁠ are scaled during fitting, and the same transformation is used for new data.

magp2d_fit() represents the sequence positions in two latent dimensions. magpfull_fit() uses q - 1 latent dimensions. Both fitted model classes support stats::predict() for point predictions and plug-in predictive uncertainty. The computational kernels for covariance matrices, analytical gradients, and cross-covariances are implemented in C++ with Rcpp.

Author(s)

Maintainer: Tony Wang wangtony883@gmail.com [copyright holder]

Authors:

• Tony Wang wangtony883@gmail.com [copyright holder]

• Qian Xiao [copyright holder]

Other contributors:

• Yaping Wang [copyright holder]

• Abhyuday Mandal [copyright holder]

• Xinwei Deng [copyright holder]

Fit a MaGP model with a two-dimensional sequence map

Description

Fits an additive Gaussian process for data that combine component amounts with a component order. Sequence positions are represented by points in a compact two-dimensional latent map.

Usage

magp2d_fit(
  X,
  y = NULL,
  q = NULL,
  tau = 0.001,
  maxeval = 500,
  xtol_rel = 1e-05,
  lb_sigma = 10,
  ub_sigma = 1000,
  lb_theta = 0.5,
  ub_theta = 1000,
  lb_delta = -1,
  ub_delta = 1,
  seed = NULL
)

Arguments

Details

The covariance is a sum of component-specific terms. Each term combines the distance between two quantitative levels with the distance between their mapped sequence positions. The variance, correlation, and mapping parameters are estimated together with bounded optimization.

Quantitative columns outside ⁠[0, 1]⁠ are transformed with column-wise min-max scaling. Their training ranges are stored in the fitted object and reused for prediction. Columns already in ⁠[0, 1]⁠ are left unchanged.

Value

An object of class magp2d.

Examples

train <- read.table(
  system.file("extdata", "example_train.txt", package = "magp"),
  header = TRUE
)
fit <- magp2d_fit(train, seed = 1)
fit

Calculate root-mean-squared prediction error

Description

Calculates the root-mean-squared error between predicted and observed values.

Usage

magp2d_rmse(pred, actual)

Arguments

Value

A single nonnegative numeric value.

Fit a MaGP model with a full sequence map

Description

Fits the quantitative-sequence model with q - 1 latent mapping dimensions, giving the sequence positions a less constrained coordinate representation.

Usage

magpfull_fit(
  X,
  y = NULL,
  q = NULL,
  tau = 0.001,
  maxeval = 500,
  xtol_rel = 1e-05,
  lb_sigma = 10,
  ub_sigma = 1000,
  lb_theta = 0.5,
  ub_theta = 1000,
  lb_delta = -1,
  ub_delta = 1,
  seed = NULL
)

Arguments

Details

The data layout, quantitative scaling, and covariance construction are the same as in magp2d_fit(). The difference is the number of latent coordinates used to represent the sequence positions.

Value

An object of class magpfull.

Examples

train <- read.table(
  system.file("extdata", "example_train.txt", package = "magp"),
  header = TRUE
)
fit <- magpfull_fit(train, seed = 1)
fit

Predict outcomes from a fitted MaGP model

Description

Returns predictions for new quantitative-sequence inputs. Plug-in standard errors and variances can be returned with the predictions.

Usage

## S3 method for class 'magp2d'
predict(
  object,
  newdata,
  se.fit = FALSE,
  type = c("script", "response", "latent"),
  ...
)

## S3 method for class 'magpfull'
predict(
  object,
  newdata,
  se.fit = FALSE,
  type = c("script", "response", "latent"),
  ...
)

Arguments

Value

If se.fit = FALSE, a numeric vector of predictions. Otherwise, a list with components fit, se.fit, variance, and type.

Examples

train <- read.table(
  system.file("extdata", "example_train.txt", package = "magp"),
  header = TRUE
)
test <- read.table(
  system.file("extdata", "example_test.txt", package = "magp"),
  header = TRUE
)
fit <- magp2d_fit(train, seed = 1)
predict(fit, test[1:3, ], se.fit = TRUE, type = "response")

Summarize a fitted two-dimensional MaGP model

Description

Prints the model size, nugget variance, fitted mean, objective value, and optimizer status.

Usage

## S3 method for class 'magp2d'
print(x, ...)

Arguments

Value

x, invisibly.

Summarize a fitted full-mapping MaGP model

Description

Prints the mapping dimension, model size, nugget variance, fitted mean, objective value, and optimizer status.

Usage

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

Arguments

Value

x, invisibly.