lgspline (version 0.2.0)

predict.lgspline: Predict Method for Fitted Lagrangian Multiplier Smoothing Spline

Description

Generates predictions, derivatives, and basis expansions from a fitted lgspline model. Supports both in-sample and out-of-sample prediction with optional parallel processing. (Wrapper for internal predict method)

Usage

# S3 method for lgspline
predict(
  object,
  newdata = NULL,
  parallel = FALSE,
  cl = NULL,
  chunk_size = NULL,
  num_chunks = NULL,
  rem_chunks = NULL,
  B_predict = NULL,
  take_first_derivatives = FALSE,
  take_second_derivatives = FALSE,
  expansions_only = FALSE,
  new_predictors = NULL,
  ...
)

Value

Depending on the options selected, returns the following:

predictions

Numeric vector of predicted values (default case, or if derivatives requested).

first_deriv

Numeric vector of first derivatives (if take_first_derivatives = TRUE).

second_deriv

Numeric vector of second derivatives (if take_second_derivatives = TRUE).

expansions

List of basis expansions (if expansions_only = TRUE).

With derivatives included, output is in the form of a list with elements "preds", "first_deriv", and "second_deriv" for the vector of predictions, first derivatives, and second derivatives respectively.

Arguments

object

A fitted lgspline model object containing model parameters and fit

newdata

Matrix or data.frame; New predictor values for out-of-sample prediction. If NULL (default), uses training data

parallel

Logical; whether to use parallel processing for prediction computations. Experimental feature - use with caution. Default FALSE

cl

Optional cluster object for parallel processing. Required if parallel=TRUE. Default NULL

chunk_size

Integer; Size of computational chunks for parallel processing. Default NULL

num_chunks

Integer; Number of chunks for parallel processing. Default NULL

rem_chunks

Integer; Number of remainder chunks for parallel processing. Default NULL

B_predict

Matrix; Optional custom coefficient matrix for prediction. Default NULL (uses object$B internally).

take_first_derivatives

Logical; whether to compute first derivatives of the fitted function. Default FALSE

take_second_derivatives

Logical; whether to compute second derivatives of the fitted function. Default FALSE

expansions_only

Logical; whether to return only basis expansions without computing predictions. Default FALSE

new_predictors

Matrix or data frame; overrides 'newdata' if provided.

...

Additional arguments passed to internal prediction methods.

Details

Implements multiple prediction capabilities:

• Standard prediction: Returns fitted values for new data points

• Derivative computation: Calculates first and/or second derivatives

• Basis expansion: Returns design matrix of basis functions

• Correlation structures: Supports non-Gaussian GLM correlation via variance-covariance matrices

If newdata and new_predictor are left NULL, default input used for model fitting will be used. Priority will be awarded to new_predictor over newdata when both are not NULL.

To obtain fitted values, users may also call model_fit$predict() or model_fit$ytilde for an lgspline object "model_fit".

The parallel processing feature is experimental and should be used with caution. When enabled, computations are split across chunks and processed in parallel, which may improve performance for large datasets.

See Also

lgspline for model fitting, plot.lgspline for visualizing predictions

Examples

## Generate example data
set.seed(1234)
t <- runif(1000, -10, 10)
y <- 2*sin(t) + -0.06*t^2 + rnorm(length(t))

## Fit model
model_fit <- lgspline(t, y)

## Generate predictions for new data
newdata <- matrix(sort(rnorm(10000)), ncol = 1) # Ensure matrix format
preds <- predict(model_fit, newdata)

## Compute derivative
deriv1_res <- predict(model_fit, newdata,
                      take_first_derivatives = TRUE)
deriv2_res <- predict(model_fit, newdata,
                      take_second_derivatives = TRUE)

## Visualize results
oldpar <- par(no.readonly = TRUE) # Save current par settings
layout(matrix(c(1,1,2,2,3,3), byrow = TRUE, ncol = 2))

## Plot function
plot(newdata[,1], preds,
       main = 'Fitted Function',
       xlab = 't',
       ylab = "f(t)", type = 'l')

## Plot first derivative
plot(newdata[,1],
       deriv1_res$first_deriv,
       main = 'First Derivative',
       xlab = 't',
       ylab = "f'(t)", type = 'l')

## Plot second derivative
plot(newdata[,1],
       deriv2_res$second_deriv,
       main = 'Second Derivative',
       xlab = 't',
       ylab = "f''(t)", type = 'l')

par(oldpar) # Reset to original par settings