inst/doc/introduction.R

In fda.vi: Functional Data Analysis using Variational Inference

## ----setup, include = FALSE---------------------------------------------------
knitr::opts_chunk$set(
  collapse  = TRUE,
  comment   = "#>",
  cache     = FALSE,
  fig.width = 7,
  fig.height = 4,
  out.width = "100%"
)

## ----install, eval = FALSE----------------------------------------------------
# # install.packages("devtools")
# devtools::install_github("steviek16/fda.vi")

## ----quickstart---------------------------------------------------------------
library(fda.vi)

data(toy_curves)

# Fit at a single K
fit <- vem_fit(
  y      = toy_curves$y,
  Xt     = toy_curves$Xt,
  K      = 8,
  center = FALSE,
  scale  = FALSE
)

summary(fit)

## ----data---------------------------------------------------------------------
data(toy_curves)
str(toy_curves)

## ----plot-toy-----------------------------------------------------------------
plot(toy_curves$Xt, toy_curves$y[[1]],
     type = "p", pch = 16, cex = 0.6, col = "steelblue",
     xlab = "t", ylab = "y(t)", main = "Toy Curves Dataset")
for (i in 2:3) {
  points(toy_curves$Xt, toy_curves$y[[i]],
         pch = 16, cex = 0.6,
         col = c("firebrick", "forestgreen")[i - 1])
}
legend("topright", legend = paste("Curve", 1:3),
       col = c("steelblue", "firebrick", "forestgreen"),
       pch = 16, bty = "n")

## ----single-k-----------------------------------------------------------------
fit <- vem_fit(
  y      = toy_curves$y,
  Xt     = toy_curves$Xt,
  K      = 8,
  center = FALSE,
  scale  = FALSE
)

## ----gcv-k--------------------------------------------------------------------
fit_gcv <- vem_fit(
  y    = toy_curves$y,
  Xt   = toy_curves$Xt,
  K    = c(6, 8, 10, 15)
)

fit_gcv$best_K
fit_gcv$tuning$gcv_matrix

## ----per-curve----------------------------------------------------------------
fit_pc <- vem_fit(
  y                = toy_curves$y,
  Xt               = toy_curves$Xt,
  K                = c(6, 8, 10),
  selection_metric = "per_curve"
)

fit_pc$selected_K
fit_pc$is_composite

## ----fourier------------------------------------------------------------------
fit_f <- vem_fit(
  y          = toy_curves$y,
  Xt         = toy_curves$Xt,
  K          = 10,
  basis_type = "fourier"
)

summary(fit_f)

## ----summary------------------------------------------------------------------
summary(fit)

## ----coef---------------------------------------------------------------------
coef(fit)

## ----coef-check---------------------------------------------------------------
coefs <- coef(fit)
coefs[c(2, 5), ]  # should be zero

## ----pips---------------------------------------------------------------------
K  <- fit$best_K
m  <- length(toy_curves$y)
pip_mat <- matrix(fit$model$prob, nrow = K, ncol = m)
rownames(pip_mat) <- paste0("B", 1:K)
colnames(pip_mat) <- paste0("Curve_", 1:m)
round(pip_mat, 3)

## ----predict------------------------------------------------------------------
# Predictions at original evaluation points
preds <- predict(fit)
length(preds)       # one vector per curve
length(preds[[1]])  # same length as Xt

# Predictions at a denser grid
Xt_new    <- seq(0, 1, length.out = 200)
preds_new <- predict(fit, newdata = Xt_new)

## ----plot---------------------------------------------------------------------
# Fitted curve with 95% credible band for curve 1
plot(fit, curve_idx = 1)

## ----plot-all-----------------------------------------------------------------
# All three curves
for (i in 1:3) plot(fit, curve_idx = i)

## ----citation-----------------------------------------------------------------
citation("fda.vi")