deepspat_rPP: Deep compositional spatial model for r-Pareto processes

Description

Constructs an extended deep compositional spatial model that supports different estimation methods ("GSM" or "WLS") and spatial dependence families (stationary or non-stationary). This function extends the basic deepspat model by incorporating additional dependence modeling and pre-training steps for the warping layers.

Usage

deepspat_rPP(
  f,
  data,
  layers = NULL,
  method = c("WLS", "GSM"),
  par_init = initvars(),
  learn_rates = init_learn_rates(),
  family = c("power_stat", "power_nonstat"),
  dtype = "float32",
  nsteps = 100L,
  nsteps_pre = 100L,
  edm_emp = NULL,
  risk = NULL,
  thre = NULL,
  weight_fun = NULL,
  dWeight_fun = NULL,
  pen_coef = 0,
  show = TRUE,
  ...
)

Value

deepspat_rPP returns an object of class deepspat_rPP which is a list containing the following components:

layers: The list of warping layers used in the model.
Cost: The final cost value after training (e.g., negative log-likelihood, least squares, or gradient score).
transeta_tf: TensorFlow objects for the transformed dependence parameters in the warping layers.
eta_tf: TensorFlow objects for the warped dependence parameters.
a_tf: TensorFlow object for the parameters of the LFT layers (if applicable).
logphi_tf: TensorFlow variable representing the logarithm of the spatial range parameter.
logitkappa_tf: TensorFlow variable representing the logit-transformed degrees of freedom.
scalings: A list of scaling limits (minima and maxima) for the input and warped spatial coordinates.
s_tf: TensorFlow object for the scaled spatial coordinates.
z_tf: TensorFlow object for the observed response values.
u_tf: TensorFlow object for the threshold used in the GS method (if applicable).
swarped_tf: List of TensorFlow objects representing the warped spatial coordinates at each layer.
swarped: Matrix of final warped spatial coordinates.
method: The estimation method used ("WLS" or "GSM").
risk: The risk parameter used in the GS method (if applicable).
family: The spatial dependence family ("power_stat" or "power_nonstat").
dtype: The data type used in TensorFlow computations.
nlayers: Number of warping layers (for non-stationary models).
weight_fun: The weighting function used in the GS method.
dWeight_fun: The derivative of the weighting function used in the GS method.
f: The model formula.
data: The data frame used for model fitting.
negcost: Vector of cost values recorded during training.
pairs_tf: TensorFlow variable representing the spatial location pairs (and, for MRPL, the replicate indices) used in the pairwise / randomized pairwise likelihood or WLS objective..
pairs_t_tf: Tranposed pairs_tf.
time: Elapsed time for model fitting.

Arguments

f: A formula identifying the dependent variable(s) and the spatial inputs. Use get_depvars_multivar3 to extract the dependent variable names.
data: A data frame containing the required data.
layers: A list containing the warping layers; required for non-stationary models (i.e., when family = "power_nonstat").
method: A character string specifying the estimation method. Must be one of "GSM", or "WLS" for r-Pareto processes
par_init: A list of initial parameter values. Call the function initvars() to see the structure of the list.
learn_rates: A list of learning rates for the various quantities in the model. Call the function init_learn_rates() to see the structure of the list.
family: A character string specifying the spatial dependence model. Use "power_nonstat" for non-stationary models and "sta" for stationary models.
dtype: A character string indicating the data type for TensorFlow computations ("float32" or "float64"). Default is "float32"
nsteps: An integer specifying the number of training steps for dependence parameter learning.
nsteps_pre: An integer specifying the number of pre-training steps for warping layer parameters.
edm_emp: For the LS method, a numeric vector or matrix providing an empirical conditional exceedance probabilities.
risk: For the GS method, a numeric value indicating the risk parameter.
thre: A numeric threshold used in the GS method.
weight_fun: A function used to weight pairwise differences in the GS method.
dWeight_fun: A function representing the derivative of weight_fun (used in the GS method).
pen_coef: A penalty parameter for weights of SR-RBF(2) to relieve overfitting.
show: Logical; if TRUE progress information is printed during training.
...: Currently unused.