Constructs an extended deep compositional spatial model that supports different estimation methods ("MPL", "MRPL", 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.
deepspat_MSP(
f,
data,
layers = NULL,
method = c("MPL", "MRPL", "WLS"),
par_init = initvars(),
learn_rates = init_learn_rates(),
family = c("power_stat", "power_nonstat"),
dtype = "float64",
nsteps = 100L,
nsteps_pre = 100L,
edm_emp = NULL,
p = c(0, 1),
pen_coef = 0,
show = TRUE,
...
)deepspat_MSP returns an object of class deepspat_MSP which is a list containing the following components:
layersThe list of warping layers used in the model.
CostThe final cost value after training (e.g., negative log-likelihood, least squares, or gradient score).
transeta_tfTensorFlow objects for the transformed dependence parameters in the warping layers.
eta_tfTensorFlow objects for the warped dependence parameters.
a_tfTensorFlow object for the parameters of the LFT layers (if applicable).
logphi_tfTensorFlow variable representing the logarithm of the spatial range parameter.
logitkappa_tfTensorFlow variable representing the logit-transformed degrees of freedom.
scalingsA list of scaling limits (minima and maxima) for the input and warped spatial coordinates.
s_tfTensorFlow object for the scaled spatial coordinates.
z_tfTensorFlow object for the observed response values.
swarped_tfList of TensorFlow objects representing the warped spatial coordinates at each layer.
swarpedMatrix of final warped spatial coordinates.
methodThe estimation method used ("MPL", "MRPL", or "WLS").
familyThe spatial dependence family ("power_stat" or "power_nonstat").
dtypeThe data type used in TensorFlow computations.
nlayersNumber of warping layers (for non-stationary models).
fThe model formula.
dataThe data frame used for model fitting.
ndataNumber of observations in data.
negcostVector of cost values recorded during training.
pairs_tfTensorFlow variable representing the spatial location pairs (and, for MRPL, the replicate indices) used in the pairwise / randomized pairwise likelihood or WLS objective..
pInput size of pair subset for pairwise likelihood, or the parameter of Bernoulli r.v. for randomized pairwise likelihood.
timeElapsed time for model fitting.
A formula identifying the dependent variable(s) and the spatial inputs. Use get_depvars_multivar3 to extract the dependent variable names.
A data frame containing the required data.
A list containing the warping layers; required for non-stationary models (i.e., when family = "power_nonstat").
A character string specifying the estimation method. Must be one of "MPL", "MRPL", or "WLS" for max-stable Brown-Resnick processes
A list of initial parameter values. Call the function initvars() to see the structure of the list.
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.
A character string specifying the spatial dependence model. Use "power_nonstat" for non-stationary models
and "sta" for stationary models.
A character string indicating the data type for TensorFlow computations ("float32" or "float64").
Default is "float32"
An integer specifying the number of training steps for dependence parameter learning.
An integer specifying the number of pre-training steps for warping layer parameters.
For the WLS method, a numeric vector or matrix providing an empirical extremal coefficients.
For pairwise likelihood based methods, p is used to specify the size of pair subset for pairwise likelihood, or the probability parameter of Bernoulli r.v. for randomized pairwise likelihood.
A penalty parameter for weights of SR-RBF(2) to relieve overfitting.
Logical; if TRUE progress information is printed during training.
Currently unused.