Package {deepspat}

Deep compositional spatial models

Description

Deep compositional spatial models are standard low-rank spatial models coupled with a bijective warping function of the spatial domain. The warping function is constructed through a composition of multiple elemental bijective functions in a deep-learning framework. The package implements two cases; first, when these functions are known up to some weights that need to be estimated, and, second, when the weights in each layer are random. Estimation and inference is done using TensorFlow, which makes use of graphical processing units.

Fits the original deepspat model using either SIWGP or SDSP inference.

Usage

deepspat(
  f,
  data,
  layers = NULL,
  method = c("VB", "ML"),
  par_init = initvars(),
  learn_rates = init_learn_rates(),
  MC = 10L,
  nsteps
)

Arguments

Details

The main model-fitting functions are grouped by model class:

• deepspat() fits the original spatial input-warped Gaussian process and spatial deep stochastic process models.

• deepspat_GP(), deepspat_nn_GP(), and deepspat_nn_ST_GP() fit univariate Gaussian process models, including nearest-neighbor and spatio-temporal variants.

• deepspat_bivar_GP() and deepspat_trivar_GP() fit multivariate Gaussian process models.

• deepspat_MSP() and deepspat_rPP() fit extreme-value models based on max-stable and r-Pareto processes.

Prediction, summary, plot, and print methods are provided for fitted Gaussian process and extreme-value models through standard S3 methods. Warping layers and basis components can be constructed with AFF_1D(), AFF_2D(), AWU(), LFT(), RBF_block(), bisquares1D(), and bisquares2D().

Value

deepspat returns an object of class deepspat with the following items

"Cost"

The final value of the cost (NMLL for the SIWGP and the lower bound for the SDSP, plus a constant)

"mupost_tf"

Posterior means of the weights in the top layer as a TensorFlow object

"Qpost_tf"

Posterior precision of the weights in the top layer as a TensorFlow object

"eta_tf"

Estimated or posterior means of the weights in the warping layers as a list of TensorFlow objects

"precy_tf"

Precision of measurement error, as a TensorFlow object

"sigma2eta_tf"

Variance of the weights in the top layer, as a TensorFlow object

"l_tf"

Length scale used to construct the covariance matrix of the weights in the top layer, as a TensorFlow object

"scalings"

Minima and maxima used to scale the unscaled unit outputs for each layer, as a list of TensorFlow objects

"method"

Either 'ML' or 'VB'

"nlayers"

Number of layers in the model (including the top layer)

"MC"

Number of MC samples when doing stochastic variational inference

"run"

TensorFlow session for evaluating the TensorFlow objects

"f"

The formula used to construct the deepspat model

"data"

The data used to construct the deepspat model

"negcost"

Vector of costs after each gradient-descent evaluation

"data_scale_mean"

Empirical mean of the original data

"data_scale_mean_tf"

Empirical mean of the original data as a TensorFlow object

Author(s)

Maintainer: Quan Vu quanvustats@gmail.com

Authors:

• Andrew Zammit-Mangion

• Xuanjie Shao

See Also

Useful links:

• https://cran.r-project.org/package=deepspat

• Report bugs at https://github.com/andrewzm/deepspat/issues

Examples

if (reticulate::py_module_available("tensorflow") && reticulate::py_module_available("scipy")) {
df <- data.frame(s1 = rnorm(100), s2 = rnorm(100), z = rnorm(100))
layers <- c(AWU(r = 50L, dim = 1L, grad = 200, lims = c(-0.5, 0.5)),
            AWU(r = 50L, dim = 2L, grad = 200, lims = c(-0.5, 0.5)),
            bisquares2D(r = 100))
d <- deepspat(f = z ~ s1 + s2 - 1,
              data = df,
              layers = layers, method = "ML",
              nsteps = 10L)
 }

Affine transformation on a 1D domain

Description

Sets up an affine transformation on a 1D domain

Usage

AFF_1D(a = c(0, 1), dtype = "float32")

Arguments

Value

AFF_1D returns a list containing a list with the following components:

"f"

An encapsulated function that takes an input and evaluates the affine transformation using TensorFlow

"fR"

Same as f but uses R

"r"

The number of basis functions (fixed to 1 in this case)

"trans"

The transformation applied to the weights before estimation (in this case the identity)

"fix_weights"

Flag indicating whether the weights are fixed or not (TRUE in this case)

"name"

Name of layer

"pars"

List of parameters describing the affine transformation as TensorFlow objects

Affine transformation on a 2D domain

Description

Sets up an affine transformation on a 2D domain

Usage

AFF_2D(a = c(0, 1, 0, 0, 0, 1), dtype = "float32")

Arguments

Value

AFF_2D returns a list containing a list with the following components:

"f"

An encapsulated function that takes an input and evaluates the affine transformation using TensorFlow

"fR"

Same as f but uses R

"r"

The number of basis functions (fixed to 1 in this case)

"trans"

The transformation applied to the weights before estimation (in this case the identity)

"fix_weights"

Flag indicating whether the weights are fixed or not (TRUE in this case)

"name"

Name of layer

"pars"

List of parameters describing the affine transformation as TensorFlow objects

Axial Warping Unit

Description

Sets up an axial warping unit (AWU) for used in a deep compositional spatial model. The function sets up sigmoids on a prescribed domain at regular intervals, with 'steepness' indicated by the user. It returns a list of length 1 containing an axial warping unit (AWU) and several encapsulated functions that evaluate the AWU over inputs of different types. See Value for more details.

Usage

AWU(r = 50L, dim = 1L, grad = 200, lims = c(-0.5, 0.5), dtype = "float32")

Arguments

Value

AWU returns a list containing a list with the following components:

"f"

An encapsulated function that takes an input and evaluates the sigmoids over the dim-th dimension using TensorFlow

"fR"

Same as f but uses R

"fMC"

Same as f but does it in parallel for several inputs index by the first dimension of the tensor

"r"

The number of sigmoid basis functions

"trans"

The transformation applied to the weights before estimation

"fix_weights"

Flag indicating whether the weights are fixed or not (FALSE for AWUs)

"name"

Name of layer

Examples

if (reticulate::py_module_available("tensorflow")) {
layer <- AWU(r = 50L, dim = 1L, grad = 200, lims = c(-0.5, 0.5))
 }

LFT (Möbius transformation)

Description

Sets up a Möbius transformation unit

Usage

LFT(a = NULL, dtype = "float32")

Arguments

Value

LFT returns a list containing a list with the following components:

"f"

An encapsulated function that takes an input and evaluates the Möbius transformation using TensorFlow

"fR"

Same as f but uses R

"fMC"

Same as f but does it in parallel for several inputs index by the first dimension of the tensor

"r"

The number of basis functions (fixed to 1 in this case)

"trans"

The transformation applied to the weights before estimation (in this case the identity)

"fix_weights"

Flag indicating whether the weights are fixed or not (TRUE for LFTs)

"name"

Name of layer

"pars"

List of parameters describing the Möbius transformation as TensorFlow objects

Examples

if (reticulate::py_module_available("tensorflow")) {
layer <- LFT()
 }

Radial Basis Function Warpings

Description

Sets up a composition of radial basis functions (RBFs) for used in a deep compositional spatial model. The function sets up RBFs on a prescribed domain on a grid at a certain resolution. It returns a list containing all the functions in the single-resolution RBF unit. See Value for more details.

Usage

RBF_block(res = 1L, lims = c(-0.5, 0.5), dtype = "float32")

Arguments

Value

RBF_block returns a list containing a list for each RBF in the block with the following components:

"f"

An encapsulated function that takes an input and evaluates the RBF over some input using TensorFlow

"fR"

Same as f but uses R

"fMC"

Same as f but does it in parallel for several inputs index by the first dimension of the tensor

"r"

The number of basis functions (one for each layer)

"trans"

The transformation applied to the weights before estimation

"fix_weights"

Flag indicating whether the weights are fixed or not (FALSE for RBFs)

"name"

Name of layer

Examples

if (reticulate::py_module_available("tensorflow")) {
layer <- RBF_block(res = 1L)
 }

Bisquare functions on a 1D domain

Description

Sets up a top-layer set of bisquare basis functions on a bounded 1D domain of length 1 for modelling the process Y. It returns a list of length 1 containing the basis functions and encapsulated functions that evaluate the bisquare functions over inputs of different types. See Value for more details.

Usage

bisquares1D(r = 30, lims = c(-0.5, 0.5), dtype = "float32")

Arguments

Value

bisquares1D returns a list containing a list with the following components:

"f"

An encapsulated function that takes an input and evaluates the sigmoids over the dim-th dimension using TensorFlow

"r"

The number of sigmoid basis functions

"knots_tf"

The centroids of the basis functions as a TensorFlow object

Bisquare functions on a 2D domain

Description

Sets up a top-layer set of bisquare basis functions on a square 2D domain of size 1 x 1 for modelling the process Y. It returns a list of length 1 containing the basis functions and encapsulated functions that evaluate the bisquare functions over inputs of different types. See Value for more details.

Usage

bisquares2D(r = 30, lims = c(-0.5, 0.5), dtype = "float32")

Arguments

Value

bisquares1D returns a list containing a list with the following components:

"f"

An encapsulated function that takes an input and evaluates the sigmoids over the dim-th dimension using TensorFlow

"fR"

Same as f but uses R

"r"

The number of sigmoid basis functions

"knots_tf"

The centroids of the basis functions as a TensorFlow object

"knots"

The centroids of the basis functions as an R object

Fit a univariate Gaussian process deepspat model

Description

Fits a stationary or nonstationary univariate Gaussian process model with optional spatial warping.

Usage

deepspat_GP(
  f,
  data,
  g = ~1,
  layers = NULL,
  method = c("REML"),
  family = c("exp_stat", "exp_nonstat", "matern_stat", "matern_nonstat"),
  par_init = initvars(),
  learn_rates = init_learn_rates(),
  nsteps = 150L
)

Arguments

Value

deepspat_GP returns an object of class deepspat_GP with the following items

"f"

The formula used to construct the covariance model

"g"

The formula used to construct the linear trend model

"data"

The data used to construct the deepspat model

"X"

The model matrix of the linear trend

"layers"

The warping function layers in the model

"Cost"

The final value of the cost

"eta_tf"

Estimated weights in the warping layers as a list of TensorFlow objects

"a_tf"

Estimated parameters in the LFT layers

"beta"

Estimated coefficients of the linear trend

"precy_tf"

Precision of measurement error, as a TensorFlow object

"sigma2_tf"

Variance parameter in the covariance matrix, as a TensorFlow object

"l_tf"

Length scale parameter in the covariance matrix, as a TensorFlow object

"nu_tf"

Smoothness parameter in the covariance matrix, as a TensorFlow object

"scalings"

Minima and maxima used to scale the unscaled unit outputs for each warping layer, as a list of TensorFlow objects

"method"

Method used for inference

"nlayers"

Number of warping layers in the model

"swarped_tf"

Spatial locations on the warped domain

"negcost"

Vector of costs after each gradient-descent evaluation

"z_tf"

Data of the process

"family"

Family of the model

Examples

if (reticulate::py_module_available("tensorflow") && reticulate::py_module_available("scipy")) {
df <- data.frame(s1 = rnorm(100), s2 = rnorm(100), z = rnorm(100))
layers <- c(AWU(r = 50L, dim = 1L, grad = 200, lims = c(-0.5, 0.5)),
            AWU(r = 50L, dim = 2L, grad = 200, lims = c(-0.5, 0.5)))
d <- deepspat_GP(f = z ~ s1 + s2 - 1,
                 data = df, g = ~ 1,
                 layers = layers, method = "REML",
                 family = "matern_nonstat",
                 nsteps = 10L)
 }

Fit a max-stable Brown-Resnick deepspat model

Description

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.

Usage

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,
  ...
)

Arguments

Value

deepspat_MSP returns an object of class deepspat_MSP 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.

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 ("MPL", "MRPL", or "WLS").

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).

f

The model formula.

data

The data frame used for model fitting.

ndata

Number of observations in data.

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..

p

The parameter of Bernoulli r.v. for pairwise likelihood and randomized pairwise likelihood.

time

Elapsed time for model fitting.

Fit a bivariate Gaussian process deepspat model

Description

Fits a stationary or nonstationary bivariate Gaussian process model with symmetric or asymmetric dependence.

Usage

deepspat_bivar_GP(
  f,
  data,
  g = ~1,
  layers_asym = NULL,
  layers = NULL,
  method = "REML",
  family = c("exp_stat_symm", "exp_stat_asymm", "exp_nonstat_symm", "exp_nonstat_asymm",
    "matern_stat_symm", "matern_stat_asymm", "matern_nonstat_symm",
    "matern_nonstat_asymm"),
  par_init = initvars(),
  learn_rates = init_learn_rates(),
  nsteps = 150L
)

Arguments

Value

deepspat_bivar_GP returns an object of class deepspat_bivar_GP with the following items

"f"

The formula used to construct the covariance model

"g"

The formula used to construct the linear trend model

"data"

The data used to construct the deepspat model

"X"

The model matrix of the linear trend

"layers"

The warping function layers in the model

"layers_asym"

The aligning function layers in the model

"Cost"

The final value of the cost

"eta_tf"

Estimated weights in the warping layers as a list of TensorFlow objects

"eta_tf_asym"

Estimated weights in the aligning layers as a list of TensorFlow objects

"a_tf"

Estimated parameters in the LFT layers

"a_tf_asym"

Estimated parameters in the AFF layers of the aligning function

"beta"

Estimated coefficients of the linear trend

"precy_tf1"

Precision of measurement error of the first process, as a TensorFlow object

"precy_tf2"

Precision of measurement error of the second process, as a TensorFlow object

"sigma2_tf_1"

Variance parameter (first process) in the covariance matrix, as a TensorFlow object

"sigma2_tf_2"

Variance parameter (second process) in the covariance matrix, as a TensorFlow object

"sigma2_tf_12"

Covariance parameter in the covariance matrix, as a TensorFlow object

"l_tf1"

Length scale parameter (first process) in the covariance matrix, as a TensorFlow object

"l_tf2"

Length scale parameter (second process) in the covariance matrix, as a TensorFlow object

"l_tf12"

Length scale parameter (cross-covariance) in the covariance matrix, as a TensorFlow object

"nu_tf1"

Smoothness parameter (first process) in the covariance matrix, as a TensorFlow object

"nu_tf2"

Smoothness parameter (second process) in the covariance matrix, as a TensorFlow object

"nu_tf12"

Smoothness parameter (cross-covariance) in the covariance matrix, as a TensorFlow object

"scalings"

Minima and maxima used to scale the unscaled unit outputs for each warping layer, as a list of TensorFlow objects

"scalings_asym"

Minima and maxima used to scale the unscaled unit outputs for each aligning layer, as a list of TensorFlow objects

"method"

Method used for inference

"nlayers"

Number of warping layers in the model

"nlayers_asym"

Number of aligning layers in the model

"swarped_tf1"

Spatial locations of the first process on the warped domain

"swarped_tf2"

Spatial locations of the second process on the warped domain

"negcost"

Vector of costs after each gradient-descent evaluation

"z_tf_1"

Data of the first process

"z_tf_2"

Data of the second process

"family"

Family of the model

Examples

if (reticulate::py_module_available("tensorflow") && reticulate::py_module_available("scipy")) {
df <- data.frame(s1 = rnorm(100), s2 = rnorm(100), z1 = rnorm(100), z2 = rnorm(100))
layers <- c(AWU(r = 50L, dim = 1L, grad = 200, lims = c(-0.5, 0.5)),
            AWU(r = 50L, dim = 2L, grad = 200, lims = c(-0.5, 0.5)))
d <- deepspat_bivar_GP(f = z1 + z2 ~ s1 + s2 - 1,
                       data = df, g = ~ 1,
                       layers = layers, method = "REML",
                       family = "matern_nonstat_symm",
                       nsteps = 10L)
 }

Fit a nearest-neighbor Gaussian process deepspat model

Description

Fits a stationary or nonstationary Gaussian process model using a nearest-neighbor approximation.

Usage

deepspat_nn_GP(
  f,
  data,
  g = ~1,
  layers = NULL,
  m = 25L,
  order_id,
  nn_id,
  method = c("REML"),
  family = c("exp_stat", "exp_nonstat"),
  par_init = initvars(),
  learn_rates = init_learn_rates(),
  nsteps = 150L
)

Arguments

Value

deepspat_nn_GP returns an object of class deepspat_nn_GP with the following items

"f"

The formula used to construct the covariance model

"g"

The formula used to construct the linear trend model

"data"

The data used to construct the deepspat model

"X"

The model matrix of the linear trend

"layers"

The warping function layers in the model

"Cost"

The final value of the cost

"eta_tf"

Estimated weights in the warping layers as a list of TensorFlow objects

"a_tf"

Estimated parameters in the LFT layers

"beta"

Estimated coefficients of the linear trend

"precy_tf"

Precision of measurement error, as a TensorFlow object

"sigma2_tf"

Variance parameter in the covariance matrix, as a TensorFlow object

"l_tf"

Length scale parameter in the covariance matrix, as a TensorFlow object

"scalings"

Minima and maxima used to scale the unscaled unit outputs for each warping layer, as a list of TensorFlow objects

"method"

Method used for inference

"nlayers"

Number of warping layers in the model

"swarped_tf"

Spatial locations on the warped domain

"negcost"

Vector of costs after each gradient-descent evaluation

"z_tf"

Data of the process

"m"

The number of nearest neighbors

"family"

Family of the model

Fit a nearest-neighbor spatio-temporal Gaussian process deepspat model

Description

Fits a stationary or nonstationary spatio-temporal Gaussian process model using a nearest-neighbor approximation.

Usage

deepspat_nn_ST_GP(
  f,
  data,
  g = ~1,
  layers_spat = NULL,
  layers_temp = NULL,
  m = 25L,
  order_id,
  nn_id,
  method = c("REML"),
  family = c("exp_stat_sep", "exp_stat_asym", "exp_nonstat_sep", "exp_nonstat_asym"),
  par_init = initvars(),
  learn_rates = init_learn_rates(),
  nsteps = 150L
)

Arguments

Value

deepspat_nn_ST_GP returns an object of class deepspat_nn_ST_GP with the following items

"f"

The formula used to construct the covariance model

"g"

The formula used to construct the linear trend model

"data"

The data used to construct the deepspat model

"X"

The model matrix of the linear trend

"layers_spat"

The spatial warping function layers in the model

"layers_temp"

The temporal warping function layers in the model

"Cost"

The final value of the cost

"family"

Family of the model

"eta_tf"

Estimated weights in the spatial warping layers as a list of TensorFlow objects

"eta_t_tf"

Estimated weights in the temporal warping layers as a list of TensorFlow objects

"a_tf"

Estimated parameters in the LFT layers

"beta"

Estimated coefficients of the linear trend

"precy_tf"

Precision of measurement error, as a TensorFlow object

"sigma2_tf"

Variance parameter in the covariance matrix, as a TensorFlow object

"v_tf"

Parameters of the covariance matrix (indicating asymmetric spatio-temporal covariance)

"l_tf"

Length scale (for spatial dimension) parameter in the covariance matrix, as a TensorFlow object

"l_t_tf"

Length scale (for temporal dimension) parameter in the covariance matrix, as a TensorFlow object

"scalings"

Minima and maxima used to scale the unscaled unit outputs for each spatial warping layer, as a list of TensorFlow objects

"scalings_t"

Minima and maxima used to scale the unscaled unit outputs for each temporal warping layer, as a list of TensorFlow objects

"method"

Method used for inference

"nlayers_spat"

Number of spatial warping layers in the model

"nlayers_temp"

Number of temporal warping layers in the model

"swarped_tf"

Spatial locations on the warped domain

"twarped_tf"

Temporal locations on the warped domain

"negcost"

Vector of costs after each gradient-descent evaluation

"z_tf"

Data of the process

"m"

The number of nearest neighbors

Fit an r-Pareto process deepspat model

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,
  ...
)

Arguments

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.

Fit a trivariate Gaussian process deepspat model

Description

Fits a stationary or nonstationary trivariate Gaussian process model with symmetric or asymmetric dependence.

Usage

deepspat_trivar_GP(
  f,
  data,
  g = ~1,
  layers_asym_2 = NULL,
  layers_asym_3 = NULL,
  layers = NULL,
  method = c("REML"),
  family = c("matern_stat_symm", "matern_stat_asymm", "matern_nonstat_symm",
    "matern_nonstat_asymm"),
  par_init = initvars(),
  learn_rates = init_learn_rates(),
  nsteps = 150L
)

Arguments

Value

deepspat_trivar_GP returns an object of class deepspat_trivar_GP with the following items

"f"

The formula used to construct the covariance model

"g"

The formula used to construct the linear trend model

"data"

The data used to construct the deepspat model

"X"

The model matrix of the linear trend

"layers"

The warping function layers in the model

"layers_asym_2"

The aligning function layers for the second process in the model

"layers_asym_3"

The aligning function layers for the third process in the model

"Cost"

The final value of the cost

"eta_tf"

Estimated weights in the warping layers as a list of TensorFlow objects

"eta_tf_asym_2"

Estimated weights in the aligning layers for the second process as a list of TensorFlow objects

"eta_tf_asym_3"

Estimated weights in the aligning layers for the third process as a list of TensorFlow objects

"beta"

Estimated coefficients of the linear trend

"precy_tf1"

Precision of measurement error of the first process, as a TensorFlow object

"precy_tf2"

Precision of measurement error of the second process, as a TensorFlow object

"precy_tf3"

Precision of measurement error of the third process, as a TensorFlow object

"sigma2_tf_1"

Variance parameter (first process) in the covariance matrix, as a TensorFlow object

"sigma2_tf_2"

Variance parameter (second process) in the covariance matrix, as a TensorFlow object

"sigma2_tf_3"

Variance parameter (third process) in the covariance matrix, as a TensorFlow object

"sigma2_tf_12"

Covariance parameter (between first and second process) in the covariance matrix, as a TensorFlow object

"sigma2_tf_13"

Covariance parameter (between first and third process) in the covariance matrix, as a TensorFlow object

"sigma2_tf_23"

Covariance parameter (between second and third process) in the covariance matrix, as a TensorFlow object

"l_tf1"

Length scale parameter (first process) in the covariance matrix, as a TensorFlow object

"l_tf2"

Length scale parameter (second process) in the covariance matrix, as a TensorFlow object

"l_tf3"

Length scale parameter (third process) in the covariance matrix, as a TensorFlow object

"l_tf12"

Length scale parameter (cross-covariance between first and second process) in the covariance matrix, as a TensorFlow object

"l_tf13"

Length scale parameter (cross-covariance between first and third process) in the covariance matrix, as a TensorFlow object

"l_tf23"

Length scale parameter (cross-covariance between second and third process) in the covariance matrix, as a TensorFlow object

"nu_tf1"

Smoothness parameter (first process) in the covariance matrix, as a TensorFlow object

"nu_tf2"

Smoothness parameter (second process) in the covariance matrix, as a TensorFlow object

"nu_tf3"

Smoothness parameter (third process) in the covariance matrix, as a TensorFlow object

"nu_tf12"

Smoothness parameter (cross-covariance between first and second process) in the covariance matrix, as a TensorFlow object

"nu_tf13"

Smoothness parameter (cross-covariance between first and third process) in the covariance matrix, as a TensorFlow object

"nu_tf23"

Smoothness parameter (cross-covariance between second and third process) in the covariance matrix, as a TensorFlow object

"scalings"

Minima and maxima used to scale the unscaled unit outputs for each warping layer, as a list of TensorFlow objects

"scalings_asym"

Minima and maxima used to scale the unscaled unit outputs for each aligning layer, as a list of TensorFlow objects

"method"

Method used for inference

"nlayers"

Number of warping layers in the model

"nlayers_asym"

Number of aligning layers in the model

"run"

TensorFlow session for evaluating the TensorFlow objects

"swarped_tf1"

Spatial locations of the first process on the warped domain

"swarped_tf2"

Spatial locations of the second process on the warped domain

"swarped_tf3"

Spatial locations of the third process on the warped domain

"negcost"

Vector of costs after each gradient-descent evaluation

"z_tf_1"

Data of the first process

"z_tf_2"

Data of the second process

"z_tf_3"

Data of the third process

"family"

Family of the model

Initialise learning rates

Description

Provides utility to alter the learning rates when fitting a deepspat model

Usage

init_learn_rates(
  sigma2y = 5e-04,
  covfun = 0.01,
  sigma2eta = 1e-04,
  eta_mean = 0.1,
  eta_mean2 = 0.1,
  eta_sd = 0.1,
  LFTpars = 0.01,
  AFFpars = 0.01,
  rho = 0.1,
  vario = 0.1
)

Arguments

Value

init_learn_rates returns a list with the learning rates. Call str(init_learn_rates()) to see the structure of this list.

Initialise weights and parameters

Description

Provides utility to alter the initial weights and parameters when fitting a deepspat model

Usage

initvars(
  sigma2y = 0.1,
  l_top_layer = 0.5,
  sigma2eta_top_layer = 1,
  nu = 1.5,
  variogram_logrange = log(0.3),
  variogram_logitdf = 0.5,
  transeta_mean_init = list(AWU = -3, RBF = -0.8068528, RBF1 = -0.8068528, RBF2 =
    -0.8068528, LFT = 1, AFF_1D = 1, AFF_2D = 1),
  transeta_mean_prior = list(AWU = -3, RBF = -0.8068528, RBF1 = -0.8068528, RBF2 =
    -0.8068528, LFT = NA),
  transeta_sd_init = list(AWU = 0.01, RBF = 0.01, RBF1 = 0.01, RBF2 = 0.01, LFT = 0.01),
  transeta_sd_prior = list(AWU = 2, RBF = 2, RBF1 = 2, RBF2 = 0.01, LFT = NA)
)

Arguments

Value

initvars returns a list with the initial values. Call str(initvars()) to see the structure of this list.

Plot fitted deepspat models

Description

Plot warped space, predictions, covariance maps, and fitted extremal dependence maps.

Usage

## S3 method for class 'deepspat'
plot(x, type = c("space", "prediction"), newdata = NULL, pred = NULL, ...)

## S3 method for class 'deepspat_GP'
plot(
  x,
  type = c("space", "prediction", "covariance"),
  newdata = NULL,
  pred = NULL,
  reference = NULL,
  ...
)

## S3 method for class 'deepspat_nn_GP'
plot(
  x,
  type = c("space", "prediction", "covariance"),
  newdata = NULL,
  pred = NULL,
  reference = NULL,
  nn_id = NULL,
  ...
)

## S3 method for class 'deepspat_nn_ST_GP'
plot(
  x,
  type = c("space", "prediction", "covariance"),
  newdata = NULL,
  pred = NULL,
  reference = NULL,
  nn_id = NULL,
  ...
)

## S3 method for class 'deepspat_bivar_GP'
plot(
  x,
  type = c("space", "prediction", "covariance"),
  newdata = NULL,
  pred = NULL,
  reference = NULL,
  component = 1L,
  target_component = component,
  ...
)

## S3 method for class 'deepspat_trivar_GP'
plot(
  x,
  type = c("space", "prediction", "covariance"),
  newdata = NULL,
  pred = NULL,
  reference = NULL,
  component = 1L,
  target_component = component,
  ...
)

## S3 method for class 'deepspat_MSP'
plot(
  x,
  type = c("space", "dependence", "uncertainty"),
  newdata = NULL,
  pred = NULL,
  reference = NULL,
  se = FALSE,
  edm_emp = NULL,
  ...
)

## S3 method for class 'deepspat_rPP'
plot(
  x,
  type = c("space", "dependence", "uncertainty"),
  newdata = NULL,
  pred = NULL,
  reference = NULL,
  se = FALSE,
  edm_emp = NULL,
  uprime = NULL,
  ...
)

Arguments

Value

The plotted prediction object, invisibly.

Predict from a fitted deepspat model

Description

Computes predictions and prediction intervals from a fitted deepspat object.

Usage

## S3 method for class 'deepspat'
predict(object, newdata, nsims = 100L, ...)

Arguments

Value

predict.deepspat returns a list with the two following items

"df_pred"

Data frame containing the predictions/prediction intervals at the prediction locations

"allsims"

Combined simulations from the Gaussian mixtures (SDSP only)

Predict from a fitted univariate Gaussian process model

Description

Computes predictions and prediction intervals from a fitted deepspat_GP object.

Usage

## S3 method for class 'deepspat_GP'
predict(object, newdata, type = NULL, reference = NULL, ...)

Arguments

Value

predict.deepspat_GP returns a list with the following item

"df_pred"

Data frame containing the predictions/prediction intervals at the prediction locations

"obs_swarped"

Observation locations on the warped domain

"newdata_swarped"

New prediction locations on the warped domain

Predict fitted dependence from a max-stable process model

Description

Computes warped coordinates and fitted extremal dependence maps from a fitted deepspat_MSP object.

Usage

## S3 method for class 'deepspat_MSP'
predict(
  object,
  newdata,
  type = NULL,
  reference = NULL,
  se = FALSE,
  edm_emp = NULL,
  ...
)

Arguments

Value

A list containing warped coordinates, fitted dependence parameters, and optionally a reference-site dependence map.

Predict from a fitted bivariate Gaussian process model

Description

Computes predictions and prediction intervals from a fitted deepspat_bivar_GP object.

Usage

## S3 method for class 'deepspat_bivar_GP'
predict(object, newdata, type = NULL, reference = NULL, component = NULL, ...)

Arguments

Value

predict.deepspat_bivar_GP returns a list with the following item

"df_pred"

Data frame containing the predictions/prediction intervals at the prediction locations

"obs_swarped1"

Observation locations on the warped domain (for the first process)

"obs_swarped2"

Observation locations on the warped domain (for the second process)

"newdata_swarped1"

New prediction locations on the warped domain (for the first process)

"newdata_swarped2"

New prediction locations on the warped domain (for the second process)

Predict from a fitted nearest-neighbor Gaussian process model

Description

Computes predictions and prediction intervals from a fitted deepspat_nn_GP object.

Usage

## S3 method for class 'deepspat_nn_GP'
predict(object, newdata, nn_id = NULL, type = NULL, reference = NULL, ...)

Arguments

Value

predict.deepspat_nn_GP returns a list with the following item

"df_pred"

Data frame containing the predictions/prediction intervals at the prediction locations

"obs_swarped"

Observation locations on the warped domain

"newdata_swarped"

New prediction locations on the warped domain

Predict from a fitted nearest-neighbor spatio-temporal Gaussian process model

Description

Computes predictions and prediction intervals from a fitted deepspat_nn_ST_GP object.

Usage

## S3 method for class 'deepspat_nn_ST_GP'
predict(object, newdata, nn_id = NULL, type = NULL, reference = NULL, ...)

Arguments

Value

predict.deepspat_nn_ST_GP returns a list with the following item

"df_pred"

Data frame containing the predictions/prediction intervals at the prediction locations

"obs_swarped"

Observation locations on the spatial warped domain

"obs_twarped"

Observation locations on the temporal warped domain

"newdata_swarped"

New prediction locations on the spatial warped domain

"newdata_twarped"

New prediction locations on the temporal warped domain

Predict fitted dependence from an r-Pareto process model

Description

Computes warped coordinates and fitted CEP dependence maps from a fitted deepspat_rPP object.

Usage

## S3 method for class 'deepspat_rPP'
predict(
  object,
  newdata,
  type = NULL,
  reference = NULL,
  se = FALSE,
  edm_emp = NULL,
  uprime = NULL,
  ...
)

Arguments

Value

A list containing warped coordinates, fitted dependence parameters, and optionally a reference-site dependence map.

Predict from a fitted trivariate Gaussian process model

Description

Computes predictions and prediction intervals from a fitted deepspat_trivar_GP object.

Usage

## S3 method for class 'deepspat_trivar_GP'
predict(object, newdata, type = NULL, reference = NULL, component = NULL, ...)

Arguments

Value

predict.deepspat_trivar_GP returns a list with the following item

"df_pred"

Data frame containing the predictions/prediction intervals at the prediction locations

Print fitted deepspat models

Description

Lightweight display methods for fitted deepspat objects.

Usage

## S3 method for class 'deepspat'
print(x, ...)

## S3 method for class 'deepspat_GP'
print(x, ...)

## S3 method for class 'deepspat_nn_GP'
print(x, ...)

## S3 method for class 'deepspat_nn_ST_GP'
print(x, ...)

## S3 method for class 'deepspat_bivar_GP'
print(x, ...)

## S3 method for class 'deepspat_trivar_GP'
print(x, ...)

## S3 method for class 'deepspat_MSP'
print(x, ...)

## S3 method for class 'deepspat_rPP'
print(x, ...)

## S3 method for class 'summary.deepspat'
print(x, ...)

Arguments

Value

The input object, invisibly.

Set TensorFlow seed

Description

Set TensorFlow seed in deepspat package

Usage

set_deepspat_seed(seed = 1L)

Arguments

Value

No return value, called for side effects.

Examples

if (reticulate::py_module_available("tensorflow")) {
set_deepspat_seed(seed = 1L)
 }

Generate simulation data for testing

Description

Generates simulated data for use in experiments

Usage

sim_data(type = "step1D", ds = 0.001, n = 300L, sigma2y = NULL)

Arguments

Value

sim_data returns a list containing the following items:

"s"

Process locations on a fine grid with spacing ds

"sobs"

Observation locations

"swarped"

The warping function (when this is also simulated)

"f_true"

The true process on the fine grid

"y"

The simulated observation data

Examples

if (reticulate::py_module_available("tensorflow")) {
sim <- sim_data(type = "step1D", ds = 0.001)
 }

Summarize fitted deepspat models

Description

Summarizes fitted deepspat objects without performing prediction.

Usage

## S3 method for class 'deepspat'
summary(object, vcov = FALSE, ...)

## S3 method for class 'deepspat_GP'
summary(object, vcov = FALSE, ...)

## S3 method for class 'deepspat_nn_GP'
summary(object, vcov = FALSE, ...)

## S3 method for class 'deepspat_nn_ST_GP'
summary(object, vcov = FALSE, ...)

## S3 method for class 'deepspat_bivar_GP'
summary(object, vcov = FALSE, ...)

## S3 method for class 'deepspat_trivar_GP'
summary(object, vcov = FALSE, ...)

## S3 method for class 'deepspat_MSP'
summary(
  object,
  newdata = NULL,
  vcov = FALSE,
  uncAss = NULL,
  edm_emp = NULL,
  ...
)

## S3 method for class 'deepspat_rPP'
summary(
  object,
  newdata = NULL,
  vcov = FALSE,
  uncAss = NULL,
  edm_emp = NULL,
  uprime = NULL,
  ...
)

Arguments

Value

A summary.deepspat object.