cross-validation for SPQR estimator

Fits SPQR using either MLE or MAP method and computes K-fold cross-validation error.

Usage

cv.SPQR(
  folds,
  X,
  Y,
  n.knots = 10,
  n.hidden = 10,
  activation = c("tanh", "relu", "sigmoid"),
  method = c("MLE", "MAP", "MCMC"),
  prior = c("ARD", "GP", "GSM"),
  hyperpar = list(),
  control = list(),
  normalize = FALSE,
  verbose = TRUE,
  seed = NULL,
  ...
)

Arguments

folds

A list of CV folds, possibly that generated from createFolds.SPQR().

X

The covariate matrix (without intercept column)

Y

The response vector.

n.knots

The number of basis functions. Default: 10.

n.hidden

A vector specifying the number of hidden neurons in each hidden layer. Default: 10.

activation

The hidden layer activation. Either "tanh" (default) or "relu".

method

Method for estimating SPQR. One of "MLE", "MAP" (default) or "MCMC".

prior

The prior model for variance hyperparameters. One of "GP", "ARD" (default) or "GSM".

hyperpar

A list of named hyper-prior hyperparameters to use instead of the default values, including a_lambda, b_lambda, a_sigma and b_sigma. The default value is 0.001 for all four hyperparameters.

control

A list of named and method-dependent parameters that allows finer control of the behavior of the computational approaches.

1. Parameters for MLE and MAP methods

• use.GPU If TRUE GPU computing will be used if torch::cuda_is_available() returns TRUE. Default: FALSE.

• lr The learning rate used by the Adam optimizer, i.e., torch::optim_adam().

• dropout A length two vector specifying the dropout probabilities in the input and hidden layers respectively. The default is c(0,0) indicating no dropout.

• batchnorm If TRUE batch normalization will be used after each hidden activation.

• epochs The number of passes of the entire training dataset in gradient descent optimization. If early.stopping.epochs is used then this is the maximum number of passes. Default: 200.

• batch.size The size of mini batches for gradient calculation. Default: 128.

• valid.pct The fraction of data used as validation set. Default: 0.2.

• early.stopping.epochs The number of epochs before stopping if the validation loss does not decrease. Default: 10.

• print.every.epochs The number of epochs before next training progress in printed. Default: 10.

• save.path The path to save the fitted torch model. By default a folder named "SPQR_model" is created in the current working directory to store the model.

• save.name The name of the file to save the fitted torch model. Default is "SPQR.model.pt".

2. Parameters for MCMC method

These parameters are similar to those in rstan::stan(). Detailed explanations can be found in the Stan reference manual.

• algorithm The sampling algorithm; "HMC": Hamiltonian Monte Carlo with dual-averaging, "NUTS": No-U-Turn sampler (default).

• iter The number of MCMC iterations (including warmup). Default: 2000.

• warmup The number of warm-up/burn-in iterations for step-size and mass matrix adaptation. Default: 500.

• thin The number of iterations before saving next post-warmup samples. Default: 1.

• stepsize The discretization interval/step-size \(\epsilon\) of leap-frog integrator. Default is NULL which indicates that it will be adaptively selected during warm-up iterations.

• metric The type of mass matrix; "unit": diagonal matrix of ones, "diag": diagonal matrix with positive diagonal entries estimated during warmup iterations (default), "dense": a dense, symmetric positive definite matrix with entries estimated during warm-up iterations.

• delta The target Metropolis acceptance rate. Default: 0.9.

• max.treedepth The maximum tree depth in NUTS. Default: 6.

• int.time The integration time in HMC. The number of leap-frog steps is calculated as \(L_{\epsilon}=\lfloor t/\epsilon\rfloor\). Default: 0.3.

normalize

If TRUE, all covariates will be normalized to take values between [0,1].

verbose

If TRUE (default), training progress will be printed.

seed

Random number generation seed.

...

other parameters to pass to control.

Value

control

the list of all control parameters.

cve

the cross-validation error.

folds

the CV folds.

See also

createFolds.SPQR()

Examples

# \donttest{
set.seed(919)
n <- 200
X <- rbinom(n, 1, 0.5)
Y <- rnorm(n, X, 0.8)
folds <- createFolds.SPQR(Y, nfold = 5)
## compute 5-fold CV error
# cv.out <- cv.SPQR(folds=folds, X=X, Y=Y, method="MLE",
#                   normalize = TRUE, verbose = FALSE)
# }