Package 'spfda'

Ported function from 'refund' package

Description

A modified version of fosr.vs, but with groups parameter to allow grouping time points rather than the whole coefficient when the underlying functions are locally supported.

Usage

fosr_vs(
  formula,
  data,
  nbasis = 10,
  method = c("ls", "grLasso", "grMCP", "grSCAD"),
  epsilon = 1e-05,
  max.iter_num = 100,
  groups = NULL
)

Arguments

formula, data, nbasis, method, epsilon, max.iter_num	see fosr.vs
groups	integer vector with length of number of time-points of how time-points should be grouped; default is NULL, indicating there is no local sparsity.

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Sparse Function-on-scalar Regression with Group Bridge Penalty

Description

Function-on-scalar regression model, denote \(n\) as total number of observations, \(p\) the number of coefficients, \(K\) as the number of B-splines, \(T\) as total time points.

Usage

spfda(
  Y,
  X,
  lambda,
  time = seq(0, 1, length.out = ncol(Y)),
  nsp = "auto",
  ord = 4,
  alpha = 0.5,
  W = NULL,
  init = NULL,
  max_iter = 50,
  inner_iter = 50,
  CI = FALSE,
  ...
)

Arguments

Y	Numeric \(n \times T\) matrix, response function.
X	Numeric \(n \times p\) matrix, design matrix
lambda	Regularization parameter \(\gamma\)
time	Time domain, numerical length of \(T\)
nsp	Integer or 'auto', number of B-splines \(K\); default is 'auto'
ord	B-spline order, default is 4; must be \(\geq 3\)
alpha	Bridge parameter \(\alpha\), default is 0.5
W	A \(T \times T\) weight matrix or NULL (identity matrix); default is NULL
init	Initial \(\gamma\); default is NULL
max_iter	Number of outer iterations
inner_iter	Number of \(ADMM\) iterations (inner steps)
CI	Logical, whether to calculate theoretical confidence intervals
...	Ignored

Details

This function implements "Functional Group Bridge for Simultaneous Regression and Support Estimation" (https://arxiv.org/abs/2006.10163). The model estimates functional coefficients \(\beta(t)\) under model \[y(t) = X\beta(t) + \epsilon(t)\] with B-spline basis expansion \[\beta(t) = \gamma B(t) + R(t), \] where \( R(t) \) is B-spline approximation error. The objective function \[ \left\| (Y-X\gamma B)W \right\|_{2}^{2} + \sum_{j,m} \left\| \gamma_{j}^{T}\mathbf{1}(B^{t} > 0) \right\|_{1}^{\alpha}. \] The input response variable is a matrix. If \(y_{i}(t)\) are observed at different time points, please interpolate (e.g. kernel) before feeding in.

Value

A spfda.model object (environment) with following elements:

B

B-spline basis functions used

error

Root Mean Square Error ('RMSE')

CI

Whether confidence intervals are calculated

gamma

B-spline coefficient \(\gamma_{p \times K}\)

generate_splines

Function to generate B-splines given time points

K

Number of B-spline basis functions

knots

B-spline knots used to fit the model

predict

Function to predict responses \(\beta(t)\) given new X and/or time points

raw

A list of raw variables

Examples

dat <- spfda_simulate()
x <- dat$X
y <- dat$Y

fit <- spfda(y, x, lambda = 5, CI = TRUE)

BIC(fit)

plot(fit, col = c("orange", "dodgerblue3", "darkgreen"),
     main = "Fitted with 95% CI", aty = c(0, 0.5, 1), atx = c(0,0.2,0.8,1))
matpoints(fit$time, t(dat$env$beta), type = 'l', col = 'black', lty = 2)
legend('topleft', c("Fitted", "Underlying"), lty = c(1,2))

print(fit)
coefficients(fit)

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Generates toy example data

Description

Synthesized functional signals with heterogeneous error. The underlying three coefficients correspond to 'dense', 'global sparse', and 'local sparse' functions. See https://arxiv.org/abs/2006.10163 for detailed configurations.

Usage

spfda_simulate(n = 1000, n_timepoints = 100, err = 1, scale = c(1, 1, 1))

Arguments

n	Total number of observations
n_timepoints	Total number of time points
err	Error magnitude
scale	the scale of coefficients length of 1 or 3.

Value

A list of data generated: X is scalar predictor, Y is functional response.

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Calculates weight matrices

Description

Calculates weight matrices

Usage

spfda_weight(X, Y, bandwidth, part)

Arguments

X	design matrix
Y	response matrix
bandwidth	numeric band-width
part	list of time point boundaries

Value

the weight matrix

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