Package 'covdepGE' reference manual

Title:	Covariate Dependent Graph Estimation
Description:	A covariate-dependent approach to Gaussian graphical modeling as described in Dasgupta et al. (2022). Employs a novel weighted pseudo-likelihood approach to model the conditional dependence structure of data as a continuous function of an extraneous covariate. The main function, covdepGE::covdepGE(), estimates a graphical representation of the conditional dependence structure via a block mean-field variational approximation, while several auxiliary functions (inclusionCurve(), matViz(), and plot.covdepGE()) are included for visualizing the resulting estimates.
Authors:	Jacob Helwig [cre, aut], Sutanoy Dasgupta [aut], Peng Zhao [aut], Bani Mallick [aut], Debdeep Pati [aut]
Maintainer:	Jacob Helwig <[email protected]>
License:	GPL (>= 3)
Version:	1.0.1
Built:	2024-11-21 03:50:12 UTC
Source:	https://github.com/jacobhelwig/covdepge

covdepGE: Covariate Dependent Graph Estimation

Description

A covariate-dependent approach to Gaussian graphical modeling as described in Dasgupta et al. (2022). Employs a novel weighted pseudo-likelihood approach to model the conditional dependence structure of data as a continuous function of an extraneous covariate. The main function, covdepGE::covdepGE(), estimates a graphical representation of the conditional dependence structure via a block mean-field variational approximation, while several auxiliary functions (inclusionCurve(), matViz(), and plot.covdepGE()) are included for visualizing the resulting estimates.

Author(s)

Maintainer: Jacob Helwig [email protected]

Authors:

Sutanoy Dasgupta [email protected]
Peng Zhao [email protected]
Bani Mallick [email protected]
Debdeep Pati [email protected]

References

(1) Sutanoy Dasgupta, Peng Zhao, Jacob Helwig, Prasenjit Ghosh, Debdeep Pati, and Bani Mallick. An Approximate Bayesian Approach to Covariate-dependent Graphical Modeling. arXiv preprint, 1–64, 2023.

Covariate Dependent Graph Estimation

Description

Model the conditional dependence structure of X as a function of Z as described in (1)

Usage

covdepGE(
  X,
  Z = NULL,
  hp_method = "hybrid",
  ssq = NULL,
  sbsq = NULL,
  pip = NULL,
  nssq = 5,
  nsbsq = 5,
  npip = 5,
  ssq_mult = 1.5,
  ssq_lower = 1e-05,
  snr_upper = 25,
  sbsq_lower = 1e-05,
  pip_lower = 1e-05,
  pip_upper = NULL,
  tau = NULL,
  norm = 2,
  center_X = TRUE,
  scale_Z = TRUE,
  alpha_tol = 1e-05,
  max_iter_grid = 10,
  max_iter = 100,
  edge_threshold = 0.5,
  sym_method = "mean",
  parallel = FALSE,
  num_workers = NULL,
  prog_bar = TRUE
)
covdepGE(
  X,
  Z = NULL,
  hp_method = "hybrid",
  ssq = NULL,
  sbsq = NULL,
  pip = NULL,
  nssq = 5,
  nsbsq = 5,
  npip = 5,
  ssq_mult = 1.5,
  ssq_lower = 1e-05,
  snr_upper = 25,
  sbsq_lower = 1e-05,
  pip_lower = 1e-05,
  pip_upper = NULL,
  tau = NULL,
  norm = 2,
  center_X = TRUE,
  scale_Z = TRUE,
  alpha_tol = 1e-05,
  max_iter_grid = 10,
  max_iter = 100,
  edge_threshold = 0.5,
  sym_method = "mean",
  parallel = FALSE,
  num_workers = NULL,
  prog_bar = TRUE
)

Arguments

`X`	$n \times p$ numeric matrix; data matrix. For best results, $n$ should be greater than $p$
`Z`	`NULL` OR $n \times q$ numeric matrix; extraneous covariates. If `NULL`, `Z` will be treated as constant for all observations, i.e.: Z <- rep(0, nrow(X)) If `Z` is constant, the estimated graph will be homogeneous throughout the data. `NULL` by default
`hp_method`	`character` in `c("grid_search","model_average","hybrid")`; method for selecting hyperparameters from the the hyperparameter grid. The grid will be generated as the Cartesian product of `ssq`, `sbsq`, and `pip`. Fix $X_j$ , the $j$ -th column of `X`, as the response; then, the hyperparameters will be selected as follows: If `"grid_search"`, the point in the hyperparameter grid that maximizes the total ELBO summed across all $n$ regressions will be selected If `"model_average"`, then all posterior quantities will be an average of the variational estimates resulting from the model fit for each point in the hyperparameter grid. The unnormalized averaging weights for each of the $n$ regressions are the exponentiated ELBO If `"hybrid"`, then models will be averaged over `pip` as in `"model_average"`, with $\sigma^2$ and $\sigma_\beta^2$ chosen for each $\pi$ in `pip` by maximizing the total ELBO over the grid defined by the Cartesian product of `ssq` and `sbsq` as in `"grid_search"` `"hybrid"` by default
`ssq`	`NULL` OR numeric vector with positive entries; candidate values of the hyperparameter $\sigma^2$ (prior residual variance). If `NULL`, `ssq` will be generated for each variable $X_j$ fixed as the response as: ssq <- seq(ssq_lower, ssq_upper, length.out = nssq) `NULL` by default
`sbsq`	`NULL` OR numeric vector with positive entries; candidate values of the hyperparameter $\sigma_\beta^2$ (prior slab variance). If `NULL`, `sbsq` will be generated for each variable $X_j$ fixed as the response as: sbsq <- seq(sbsq_lower, sbsq_upper, length.out = nsbsq) `NULL` by default
`pip`	`NULL` OR numeric vector with entries in $(0, 1)$ ; candidate values of the hyperparameter $\pi$ (prior inclusion probability). If `NULL`, `pip` will be generated for each variable $X_j$ fixed as the response as: pip <- seq(pip_lower, pi_upper, length.out = npip) `NULL` by default
`nssq`	positive integer; number of points to generate for `ssq` if `ssq` is `NULL`. `5` by default
`nsbsq`	positive integer; number of points to generate for `sbsq` if `sbsq` is `NULL`. `5` by default
`npip`	positive integer; number of points to generate for `pip` if `pip` is `NULL`. `5` by default
`ssq_mult`	positive numeric; if `ssq` is `NULL`, then for each variable $X_j$ fixed as the response: ssq_upper <- ssq_mult * stats::var(X_j) Then, `ssq_upper` will be the greatest value in `ssq` for variable $X_j$ . `1.5` by default
`ssq_lower`	positive numeric; if `ssq` is `NULL`, then `ssq_lower` will be the least value in `ssq`. `1e-5` by default
`snr_upper`	positive numeric; upper bound on the signal-to-noise ratio. If `sbsq` is `NULL`, then for each variable $X_j$ fixed as the response: s2_sum <- sum(apply(X, 2, stats::var)) sbsq_upper <- snr_upper / (pip_upper * s2_sum) Then, `sbsq_upper` will be the greatest value in `sbsq`. `25` by default
`sbsq_lower`	positive numeric; if `sbsq` is `NULL`, then `sbsq_lower` will be the least value in `sbsq`. `1e-5` by default
`pip_lower`	numeric in $(0, 1)$ ; if `pip` is `NULL`, then `pip_lower` will be the least value in `pip`. `1e-5` by default
`pip_upper`	`NULL` OR numeric in $(0, 1)$ ; if `pip` is `NULL`, then `pip_upper` will be the greatest value in `pip`. If `sbsq` is `NULL`, `pip_upper` will be used to calculate `sbsq_upper`. If `NULL`, `pip_upper` will be calculated for each variable $X_j$ fixed as the response as: lasso <- glmnet::cv.glmnet(X, X_j) non0 <- sum(glmnet::coef.glmnet(lasso, s = "lambda.1se")[-1] != 0) non0 <- min(max(non0, 1), p - 1) pip_upper <- non0 / p `NULL` by default
`tau`	`NULL` OR positive numeric OR numeric vector of length $n$ with positive entries; bandwidth parameter. Greater values allow for more information to be shared between observations. Allows for global or observation-specific specification. If `NULL`, use 2-step KDE methodology as described in (2) to calculate observation-specific bandwidths. `NULL` by default
`norm`	numeric in $[1, \infty]$ ; norm to use when calculating weights. `Inf` results in infinity norm. `2` by default
`center_X`	logical; if `TRUE`, center `X` column-wise to mean $0$ . `TRUE` by default
`scale_Z`	logical; if `TRUE`, center and scale `Z` column-wise to mean $0$ , standard deviation $1$ prior to calculating the weights. `TRUE` by default
`alpha_tol`	positive numeric; end CAVI when the Frobenius norm of the change in the alpha matrix is within `alpha_tol`. `1e-5` by default
`max_iter_grid`	positive integer; if tolerance criteria has not been met by `max_iter_grid` iterations during grid search, end CAVI. After grid search has completed, CAVI is performed with the final hyperparameters selected by grid search for at most `max_iter` iterations. Does not apply to `hp_method = "model_average"`. `10` by default
`max_iter`	positive integer; if tolerance criteria has not been met by `max_iter` iterations, end CAVI. `100` by default
`edge_threshold`	numeric in $(0, 1)$ ; a graph for each observation will be constructed by including an edge between variable $i$ and variable $j$ if, and only if, the $(i, j)$ entry of the symmetrized posterior inclusion probability matrix corresponding to the observation is greater than `edge_threshold`. `0.5` by default
`sym_method`	`character` in `c("mean","max","min")`; to symmetrize the posterior inclusion probability matrix for each observation, the $(i, j)$ and $(j, i)$ entries will be post-processed as `sym_method` applied to the $(i, j)$ and $(j, i)$ entries. `"mean"` by default
`parallel`	logical; if `TRUE`, hyperparameter selection and CAVI for each of the $p$ variables will be performed in parallel using `foreach`. Parallel backend may be registered prior to making a call to `covdepGE`. If no active parallel backend can be detected, then parallel backend will be automatically registered using: doParallel::registerDoParallel(num_workers) `FALSE` by default
`num_workers`	`NULL` OR positive integer less than or equal to `parallel::detectCores()`; argument to `doParallel::registerDoParallel` if `parallel = TRUE` and no parallel backend is detected. If `NULL`, then: num_workers <- floor(parallel::detectCores() / 2) `NULL` by default
`prog_bar`	logical; if `TRUE`, then a progress bar will be displayed denoting the number of remaining variables to fix as the response and perform CAVI. If `parallel`, no progress bar will be displayed. `TRUE` by default

Value

Returns object of class covdepGE with the following values:

`graphs`	list with the following values: `graphs`: list of $n$ numeric matrices of dimension $p \times p$ ; the $l$ -th matrix is the adjacency matrix for the $l$ -th observation `unique_graphs`: list; the $l$ -th element is a list containing the $l$ -th unique graph and the indices of the observation(s) corresponding to this graph `inclusion_probs_sym`: list of $n$ numeric matrices of dimension $p \times p$ ; the $l$ -th matrix is the symmetrized posterior inclusion probability matrix for the $l$ -th observation `inclusion_probs_asym`: list of $n$ numeric matrices of dimension $p \times p$ ; the $l$ -th matrix is the posterior inclusion probability matrix for the $l$ -th observation prior to symmetrization
`variational_params`	list with the following values: `alpha`: list of $p$ numeric matrices of dimension $n \times (p - 1)$ ; the $(i, j)$ entry of the $k$ -th matrix is the variational approximation to the posterior inclusion probability of the $j$ -th variable in a weighted regression with variable $k$ fixed as the response, where the weights are taken with respect to observation $i$ `mu`: list of $p$ numeric matrices of dimension $n \times (p - 1)$ ; the $(i, j)$ entry of the $k$ -th matrix is the variational approximation to the posterior slab mean for the $j$ -th variable in a weighted regression with variable $k$ fixed as the response, where the weights are taken with respect to observation $i$ `ssq_var`: list of $p$ numeric matrices of dimension $n \times (p - 1)$ ; the $(i, j)$ entry of the $k$ -th matrix is the variational approximation to the posterior slab variance for the $j$ -th variable in a weighted regression with variable $k$ fixed as the response, where the weights are taken with respect to observation $i$
`hyperparameters`	list of $p$ lists; the $j$ -th list has the following values for variable $j$ fixed as the response: `grid`: matrix of candidate hyperparameter values, corresponding ELBO, and iterations to converge `final`: the final hyperparameters chosen by grid search and the ELBO and iterations to converge for these hyperparameters
`model_details`	list with the following values: `elapsed`: amount of time to fit the model `n`: number of observations `p`: number of variables `ELBO`: ELBO summed across all observations and variables. If `hp_method` is `"model_average"` or `"hybrid"`, this ELBO is averaged across the hyperparameter grid using the model averaging weights for each variable `num_unique`: number of unique graphs `grid_size`: number of points in the hyperparameter grid `args`: list containing all passed arguments of length $1$
`weights`	list with the following values: `weights`: $n\times n$ numeric matrix. The $(i, j)$ entry is the similarity weight of the $i$ -th observation with respect to the $j$ -th observation using the $j$ -th observation's bandwidth `bandwidths`: numeric vector of length $n$ . The $i$ -th entry is the bandwidth for the $i$ -th observation

References

(2) Sutanoy Dasgupta, Debdeep Pati, and Anuj Srivastava. A Two-Step Geometric Framework For Density Modeling. Statistica Sinica, 30(4):2155–2177, 2020.

Examples

## Not run: 
library(ggplot2)

# get the data
set.seed(12)
data <- generateData()
X <- data$X
Z <- data$Z
interval <- data$interval
prec <- data$true_precision

# get overall and within interval sample sizes
n <- nrow(X)
n1 <- sum(interval == 1)
n2 <- sum(interval == 2)
n3 <- sum(interval == 3)

# visualize the distribution of the extraneous covariate
ggplot(data.frame(Z = Z, interval = as.factor(interval))) +
  geom_histogram(aes(Z, fill = interval), color = "black", bins = n %/% 5)

# visualize the true precision matrices in each of the intervals

# interval 1
matViz(prec[[1]], incl_val = TRUE) +
  ggtitle(paste0("True precision matrix, interval 1, observations 1,...,", n1))

# interval 2 (varies continuously with Z)
cat("\nInterval 2, observations ", n1 + 1, ",...,", n1 + n2, sep = "")
int2_mats <- prec[interval == 2]
int2_inds <- c(5, n2 %/% 2, n2 - 5)
lapply(int2_inds, function(j) matViz(int2_mats[[j]], incl_val = TRUE) +
         ggtitle(paste("True precision matrix, interval 2, observation", j + n1)))

# interval 3
matViz(prec[[length(prec)]], incl_val = TRUE) +
  ggtitle(paste0("True precision matrix, interval 3, observations ",
                 n1 + n2 + 1, ",...,", n1 + n2 + n3))

# fit the model and visualize the estimated graphs
(out <- covdepGE(X, Z))
plot(out)

# visualize the posterior inclusion probabilities for variables (1, 3) and (1, 2)
inclusionCurve(out, 1, 2)
inclusionCurve(out, 1, 3)

## End(Not run)
## Not run: 
library(ggplot2)

# get the data
set.seed(12)
data <- generateData()
X <- data$X
Z <- data$Z
interval <- data$interval
prec <- data$true_precision

# get overall and within interval sample sizes
n <- nrow(X)
n1 <- sum(interval == 1)
n2 <- sum(interval == 2)
n3 <- sum(interval == 3)

# visualize the distribution of the extraneous covariate
ggplot(data.frame(Z = Z, interval = as.factor(interval))) +
  geom_histogram(aes(Z, fill = interval), color = "black", bins = n %/% 5)

# visualize the true precision matrices in each of the intervals

# interval 1
matViz(prec[[1]], incl_val = TRUE) +
  ggtitle(paste0("True precision matrix, interval 1, observations 1,...,", n1))

# interval 2 (varies continuously with Z)
cat("\nInterval 2, observations ", n1 + 1, ",...,", n1 + n2, sep = "")
int2_mats <- prec[interval == 2]
int2_inds <- c(5, n2 %/% 2, n2 - 5)
lapply(int2_inds, function(j) matViz(int2_mats[[j]], incl_val = TRUE) +
         ggtitle(paste("True precision matrix, interval 2, observation", j + n1)))

# interval 3
matViz(prec[[length(prec)]], incl_val = TRUE) +
  ggtitle(paste0("True precision matrix, interval 3, observations ",
                 n1 + n2 + 1, ",...,", n1 + n2 + n3))

# fit the model and visualize the estimated graphs
(out <- covdepGE(X, Z))
plot(out)

# visualize the posterior inclusion probabilities for variables (1, 3) and (1, 2)
inclusionCurve(out, 1, 2)
inclusionCurve(out, 1, 3)

## End(Not run)

Generate Covariate-Dependent Data

Description

Generate a $1$ -dimensional extraneous covariate and $p$ -dimensional Gaussian data with a precision matrix that varies as a continuous function of the extraneous covariate. This data is distributed similar to that used in the simulation study from (1)

Usage

generateData(p = 5, n1 = 60, n2 = 60, n3 = 60, Z = NULL, true_precision = NULL)
generateData(p = 5, n1 = 60, n2 = 60, n3 = 60, Z = NULL, true_precision = NULL)

Arguments

`p`	positive integer; number of variables in the data matrix. `5` by default
`n1`	positive integer; number of observations in the first interval. `60` by default
`n2`	positive integer; number of observations in the second interval. `60` by default
`n3`	positive integer; number of observations in the third interval. `60` by default
`Z`	`NULL` or numeric vector; extraneous covariate values for each observation. If `NULL`, `Z` will be generated from a uniform distribution on each of the intervals
`true_precision`	`NULL` OR list of matrices of dimension $p \times p$ ; true precision matrix for each observation. If `NULL`, the true precision matrices will be generated dependent on `Z`. `NULL` by default

Value

Returns list with the following values:

`X`	a `(n1 + n2 + n3)` $\times p$ numeric matrix, where the $i$ -th row is drawn from a $p$ -dimensional Gaussian with mean $0$ and precision matrix `true_precision[[i]]`
`Z`	a `(n1 + n2 + n3)` $\times 1$ numeric matrix, where the $i$ -th entry is the extraneous covariate $z_i$ for observation $i$
`true_precision`	list of `n1 + n2 + n3` matrices of dimension $p \times p$ ; the $i$ -th matrix is the precision matrix for the $i$ -th observation
`interval`	vector of length `n1 + n2 + n3`; interval assignments for each of the observations, where the $i$ -th entry is the interval assignment for the $i$ -th observation

Extraneous Covariate

If Z = NULL, then the generation of Z is as follows:

The first n1 observations have $z_i$ from from a uniform distribution on the interval $(-3, -1)$ (the first interval).

Observations n1 + 1 to n1 + n2 have $z_i$ from from a uniform distribution on the interval $(-1, 1)$ (the second interval).

Observations n1 + n2 + 1 to n1 + n2 + n3 have $z_i$ from a uniform distribution on the interval $(1, 3)$ (the third interval).

Precision Matrices

If true_precision = NULL, then the generation of the true precision matrices is as follows:

All precision matrices have $2$ on the diagonal and $1$ in the $(2, 3)/ (3, 2)$ positions.

Observations in the first interval have a $1$ in the $(1, 2) / (1, 2)$ positions, while observations in the third interval have a $1$ in the $(1, 3)/ (3, 1)$ positions.

Observations in the second interval have $2$ entries that vary as a linear function of their extraneous covariate. Let $\beta = 1/2$ . Then, the $(1, 2)/(2, 1)$ positions for the $i$ -th observation in the second interval are $\beta\cdot(1 - z_i)$ , while the $(1, 3)/ (3, 1)$ entries are $\beta\cdot(1 + z_i)$ .

Thus, as $z_i$ approaches $-1$ from the right, the associated precision matrix becomes more similar to the matrix for observations in the first interval. Similarly, as $z_i$ approaches $1$ from the left, the matrix becomes more similar to the matrix for observations in the third interval.

Examples

## Not run: 
library(ggplot2)

# get the data
set.seed(12)
data <- generateData()
X <- data$X
Z <- data$Z
interval <- data$interval
prec <- data$true_precision

# get overall and within interval sample sizes
n <- nrow(X)
n1 <- sum(interval == 1)
n2 <- sum(interval == 2)
n3 <- sum(interval == 3)

# visualize the distribution of the extraneous covariate
ggplot(data.frame(Z = Z, interval = as.factor(interval))) +
  geom_histogram(aes(Z, fill = interval), color = "black", bins = n %/% 5)

# visualize the true precision matrices in each of the intervals

# interval 1
matViz(prec[[1]], incl_val = TRUE) +
  ggtitle(paste0("True precision matrix, interval 1, observations 1,...,", n1))

# interval 2 (varies continuously with Z)
cat("\nInterval 2, observations ", n1 + 1, ",...,", n1 + n2, sep = "")
int2_mats <- prec[interval == 2]
int2_inds <- c(5, n2 %/% 2, n2 - 5)
lapply(int2_inds, function(j) matViz(int2_mats[[j]], incl_val = TRUE) +
         ggtitle(paste("True precision matrix, interval 2, observation", j + n1)))

# interval 3
matViz(prec[[length(prec)]], incl_val = TRUE) +
  ggtitle(paste0("True precision matrix, interval 3, observations ",
                 n1 + n2 + 1, ",...,", n1 + n2 + n3))

# fit the model and visualize the estimated graphs
(out <- covdepGE(X, Z))
plot(out)

# visualize the posterior inclusion probabilities for variables (1, 3) and (1, 2)
inclusionCurve(out, 1, 2)
inclusionCurve(out, 1, 3)

## End(Not run)
## Not run: 
library(ggplot2)

# get the data
set.seed(12)
data <- generateData()
X <- data$X
Z <- data$Z
interval <- data$interval
prec <- data$true_precision

# get overall and within interval sample sizes
n <- nrow(X)
n1 <- sum(interval == 1)
n2 <- sum(interval == 2)
n3 <- sum(interval == 3)

# visualize the distribution of the extraneous covariate
ggplot(data.frame(Z = Z, interval = as.factor(interval))) +
  geom_histogram(aes(Z, fill = interval), color = "black", bins = n %/% 5)

# visualize the true precision matrices in each of the intervals

# interval 1
matViz(prec[[1]], incl_val = TRUE) +
  ggtitle(paste0("True precision matrix, interval 1, observations 1,...,", n1))

# interval 2 (varies continuously with Z)
cat("\nInterval 2, observations ", n1 + 1, ",...,", n1 + n2, sep = "")
int2_mats <- prec[interval == 2]
int2_inds <- c(5, n2 %/% 2, n2 - 5)
lapply(int2_inds, function(j) matViz(int2_mats[[j]], incl_val = TRUE) +
         ggtitle(paste("True precision matrix, interval 2, observation", j + n1)))

# interval 3
matViz(prec[[length(prec)]], incl_val = TRUE) +
  ggtitle(paste0("True precision matrix, interval 3, observations ",
                 n1 + n2 + 1, ",...,", n1 + n2 + n3))

# fit the model and visualize the estimated graphs
(out <- covdepGE(X, Z))
plot(out)

# visualize the posterior inclusion probabilities for variables (1, 3) and (1, 2)
inclusionCurve(out, 1, 2)
inclusionCurve(out, 1, 3)

## End(Not run)

Plot PIP as a Function of Index

Description

Plot the posterior inclusion probability of an edge between two variables as a function of observation index

Usage

inclusionCurve(
  out,
  col_idx1,
  col_idx2,
  line_type = "solid",
  line_size = 0.5,
  line_color = "black",
  point_shape = 21,
  point_size = 1.5,
  point_color = "#500000",
  point_fill = "white"
)
inclusionCurve(
  out,
  col_idx1,
  col_idx2,
  line_type = "solid",
  line_size = 0.5,
  line_color = "black",
  point_shape = 21,
  point_size = 1.5,
  point_color = "#500000",
  point_fill = "white"
)

Arguments

`out`	object of class `covdepGE`; return of `covdepGE` function
`col_idx1`	integer in $[1, p]$ ; column index of the first variable
`col_idx2`	integer in $[1, p]$ ; column index of the second variable
`line_type`	linetype; `ggplot2` line type to interpolate the probabilities. `"solid"` by default
`line_size`	positive numeric; thickness of the interpolating line. `0.5` by default
`line_color`	color; color of interpolating line. `"black"` by default
`point_shape`	shape; shape of the points denoting observation-specific inclusion probabilities; `21` by default
`point_size`	positive numeric; size of probability points. `1.5` by default
`point_color`	color; color of probability points. `"#500000"` by default
`point_fill`	color; fill of probability points. Only applies to select shapes. `"white"` by default

Value

Returns ggplot2 visualization of inclusion probability curve

Examples

## Not run: 
library(ggplot2)

# get the data
set.seed(12)
data <- generateData()
X <- data$X
Z <- data$Z
interval <- data$interval
prec <- data$true_precision

# get overall and within interval sample sizes
n <- nrow(X)
n1 <- sum(interval == 1)
n2 <- sum(interval == 2)
n3 <- sum(interval == 3)

# visualize the distribution of the extraneous covariate
ggplot(data.frame(Z = Z, interval = as.factor(interval))) +
  geom_histogram(aes(Z, fill = interval), color = "black", bins = n %/% 5)

# visualize the true precision matrices in each of the intervals

# interval 1
matViz(prec[[1]], incl_val = TRUE) +
  ggtitle(paste0("True precision matrix, interval 1, observations 1,...,", n1))

# interval 2 (varies continuously with Z)
cat("\nInterval 2, observations ", n1 + 1, ",...,", n1 + n2, sep = "")
int2_mats <- prec[interval == 2]
int2_inds <- c(5, n2 %/% 2, n2 - 5)
lapply(int2_inds, function(j) matViz(int2_mats[[j]], incl_val = TRUE) +
         ggtitle(paste("True precision matrix, interval 2, observation", j + n1)))

# interval 3
matViz(prec[[length(prec)]], incl_val = TRUE) +
  ggtitle(paste0("True precision matrix, interval 3, observations ",
                 n1 + n2 + 1, ",...,", n1 + n2 + n3))

# fit the model and visualize the estimated graphs
(out <- covdepGE(X, Z))
plot(out)

# visualize the posterior inclusion probabilities for variables (1, 3) and (1, 2)
inclusionCurve(out, 1, 2)
inclusionCurve(out, 1, 3)

## End(Not run)
## Not run: 
library(ggplot2)

# get the data
set.seed(12)
data <- generateData()
X <- data$X
Z <- data$Z
interval <- data$interval
prec <- data$true_precision

# get overall and within interval sample sizes
n <- nrow(X)
n1 <- sum(interval == 1)
n2 <- sum(interval == 2)
n3 <- sum(interval == 3)

# visualize the distribution of the extraneous covariate
ggplot(data.frame(Z = Z, interval = as.factor(interval))) +
  geom_histogram(aes(Z, fill = interval), color = "black", bins = n %/% 5)

# visualize the true precision matrices in each of the intervals

# interval 1
matViz(prec[[1]], incl_val = TRUE) +
  ggtitle(paste0("True precision matrix, interval 1, observations 1,...,", n1))

# interval 2 (varies continuously with Z)
cat("\nInterval 2, observations ", n1 + 1, ",...,", n1 + n2, sep = "")
int2_mats <- prec[interval == 2]
int2_inds <- c(5, n2 %/% 2, n2 - 5)
lapply(int2_inds, function(j) matViz(int2_mats[[j]], incl_val = TRUE) +
         ggtitle(paste("True precision matrix, interval 2, observation", j + n1)))

# interval 3
matViz(prec[[length(prec)]], incl_val = TRUE) +
  ggtitle(paste0("True precision matrix, interval 3, observations ",
                 n1 + n2 + 1, ",...,", n1 + n2 + n3))

# fit the model and visualize the estimated graphs
(out <- covdepGE(X, Z))
plot(out)

# visualize the posterior inclusion probabilities for variables (1, 3) and (1, 2)
inclusionCurve(out, 1, 2)
inclusionCurve(out, 1, 3)

## End(Not run)

Visualize a matrix

Description

Create a visualization of a matrix

Usage

matViz(
  x,
  color1 = "white",
  color2 = "#500000",
  grid_color = "black",
  incl_val = FALSE,
  prec = 2,
  font_size = 3,
  font_color1 = "black",
  font_color2 = "white",
  font_thres = mean(x)
)
matViz(
  x,
  color1 = "white",
  color2 = "#500000",
  grid_color = "black",
  incl_val = FALSE,
  prec = 2,
  font_size = 3,
  font_color1 = "black",
  font_color2 = "white",
  font_thres = mean(x)
)

Arguments

`x`	matrix; matrix to be visualized
`color1`	color; color for low entries. `"white"` by default
`color2`	color; color for high entries. `"#500000"` by default
`grid_color`	color; color of grid lines. `"black"` by default
`incl_val`	logical; if `TRUE`, the value for each entry will be displayed. `FALSE` by default
`prec`	positive integer; number of decimal places to round entries to if `incl_val` is `TRUE`. `2` by default
`font_size`	positive numeric; size of font if `incl_val` is `TRUE`. `3` by default
`font_color1`	color; color of font for low entries if `incl_val` is `TRUE`. `"black"` by default
`font_color2`	color; color of font for high entries if `incl_val` is `TRUE`. `"white"` by default
`font_thres`	numeric; values less than `font_thres` will be displayed in `font_color1` if `incl_val` is `TRUE`. `mean(x)` by default

Value

Returns ggplot2 visualization of matrix

Examples

## Not run: 
library(ggplot2)

# get the data
set.seed(12)
data <- generateData()
X <- data$X
Z <- data$Z
interval <- data$interval
prec <- data$true_precision

# get overall and within interval sample sizes
n <- nrow(X)
n1 <- sum(interval == 1)
n2 <- sum(interval == 2)
n3 <- sum(interval == 3)

# visualize the distribution of the extraneous covariate
ggplot(data.frame(Z = Z, interval = as.factor(interval))) +
  geom_histogram(aes(Z, fill = interval), color = "black", bins = n %/% 5)

# visualize the true precision matrices in each of the intervals

# interval 1
matViz(prec[[1]], incl_val = TRUE) +
  ggtitle(paste0("True precision matrix, interval 1, observations 1,...,", n1))

# interval 2 (varies continuously with Z)
cat("\nInterval 2, observations ", n1 + 1, ",...,", n1 + n2, sep = "")
int2_mats <- prec[interval == 2]
int2_inds <- c(5, n2 %/% 2, n2 - 5)
lapply(int2_inds, function(j) matViz(int2_mats[[j]], incl_val = TRUE) +
         ggtitle(paste("True precision matrix, interval 2, observation", j + n1)))

# interval 3
matViz(prec[[length(prec)]], incl_val = TRUE) +
  ggtitle(paste0("True precision matrix, interval 3, observations ",
                 n1 + n2 + 1, ",...,", n1 + n2 + n3))

# fit the model and visualize the estimated graphs
(out <- covdepGE(X, Z))
plot(out)

# visualize the posterior inclusion probabilities for variables (1, 3) and (1, 2)
inclusionCurve(out, 1, 2)
inclusionCurve(out, 1, 3)

## End(Not run)
## Not run: 
library(ggplot2)

# get the data
set.seed(12)
data <- generateData()
X <- data$X
Z <- data$Z
interval <- data$interval
prec <- data$true_precision

# get overall and within interval sample sizes
n <- nrow(X)
n1 <- sum(interval == 1)
n2 <- sum(interval == 2)
n3 <- sum(interval == 3)

# visualize the distribution of the extraneous covariate
ggplot(data.frame(Z = Z, interval = as.factor(interval))) +
  geom_histogram(aes(Z, fill = interval), color = "black", bins = n %/% 5)

# visualize the true precision matrices in each of the intervals

# interval 1
matViz(prec[[1]], incl_val = TRUE) +
  ggtitle(paste0("True precision matrix, interval 1, observations 1,...,", n1))

# interval 2 (varies continuously with Z)
cat("\nInterval 2, observations ", n1 + 1, ",...,", n1 + n2, sep = "")
int2_mats <- prec[interval == 2]
int2_inds <- c(5, n2 %/% 2, n2 - 5)
lapply(int2_inds, function(j) matViz(int2_mats[[j]], incl_val = TRUE) +
         ggtitle(paste("True precision matrix, interval 2, observation", j + n1)))

# interval 3
matViz(prec[[length(prec)]], incl_val = TRUE) +
  ggtitle(paste0("True precision matrix, interval 3, observations ",
                 n1 + n2 + 1, ",...,", n1 + n2 + n3))

# fit the model and visualize the estimated graphs
(out <- covdepGE(X, Z))
plot(out)

# visualize the posterior inclusion probabilities for variables (1, 3) and (1, 2)
inclusionCurve(out, 1, 2)
inclusionCurve(out, 1, 3)

## End(Not run)

Plot the Graphs Estimated by `covdepGE`

Description

Create a list of the unique graphs estimated by covdepGE

Usage

## S3 method for class 'covdepGE'
plot(x, graph_colors = NULL, title_sum = TRUE, ...)
## S3 method for class 'covdepGE'
plot(x, graph_colors = NULL, title_sum = TRUE, ...)

Arguments

`x`	object of class `covdepGE`; return of `covdepGE` function
`graph_colors`	`NULL` OR vector; the $j$ -th element is the color for the $j$ -th graph. If `NULL`, all graphs will be colored with `"#500000"`. `NULL` by default
`title_sum`	logical; if `TRUE` the indices of the observations corresponding to the graph will be included in the title. `TRUE` by default
`...`	additional arguments will be ignored

Value

Returns list of ggplot2 visualizations of unique graphs estimated by covdepGE

Examples

## Not run: 
library(ggplot2)

# get the data
set.seed(12)
data <- generateData()
X <- data$X
Z <- data$Z
interval <- data$interval
prec <- data$true_precision

# get overall and within interval sample sizes
n <- nrow(X)
n1 <- sum(interval == 1)
n2 <- sum(interval == 2)
n3 <- sum(interval == 3)

# visualize the distribution of the extraneous covariate
ggplot(data.frame(Z = Z, interval = as.factor(interval))) +
  geom_histogram(aes(Z, fill = interval), color = "black", bins = n %/% 5)

# visualize the true precision matrices in each of the intervals

# interval 1
matViz(prec[[1]], incl_val = TRUE) +
  ggtitle(paste0("True precision matrix, interval 1, observations 1,...,", n1))

# interval 2 (varies continuously with Z)
cat("\nInterval 2, observations ", n1 + 1, ",...,", n1 + n2, sep = "")
int2_mats <- prec[interval == 2]
int2_inds <- c(5, n2 %/% 2, n2 - 5)
lapply(int2_inds, function(j) matViz(int2_mats[[j]], incl_val = TRUE) +
         ggtitle(paste("True precision matrix, interval 2, observation", j + n1)))

# interval 3
matViz(prec[[length(prec)]], incl_val = TRUE) +
  ggtitle(paste0("True precision matrix, interval 3, observations ",
                 n1 + n2 + 1, ",...,", n1 + n2 + n3))

# fit the model and visualize the estimated graphs
(out <- covdepGE(X, Z))
plot(out)

# visualize the posterior inclusion probabilities for variables (1, 3) and (1, 2)
inclusionCurve(out, 1, 2)
inclusionCurve(out, 1, 3)

## End(Not run)
## Not run: 
library(ggplot2)

# get the data
set.seed(12)
data <- generateData()
X <- data$X
Z <- data$Z
interval <- data$interval
prec <- data$true_precision

# get overall and within interval sample sizes
n <- nrow(X)
n1 <- sum(interval == 1)
n2 <- sum(interval == 2)
n3 <- sum(interval == 3)

# visualize the distribution of the extraneous covariate
ggplot(data.frame(Z = Z, interval = as.factor(interval))) +
  geom_histogram(aes(Z, fill = interval), color = "black", bins = n %/% 5)

# visualize the true precision matrices in each of the intervals

# interval 1
matViz(prec[[1]], incl_val = TRUE) +
  ggtitle(paste0("True precision matrix, interval 1, observations 1,...,", n1))

# interval 2 (varies continuously with Z)
cat("\nInterval 2, observations ", n1 + 1, ",...,", n1 + n2, sep = "")
int2_mats <- prec[interval == 2]
int2_inds <- c(5, n2 %/% 2, n2 - 5)
lapply(int2_inds, function(j) matViz(int2_mats[[j]], incl_val = TRUE) +
         ggtitle(paste("True precision matrix, interval 2, observation", j + n1)))

# interval 3
matViz(prec[[length(prec)]], incl_val = TRUE) +
  ggtitle(paste0("True precision matrix, interval 3, observations ",
                 n1 + n2 + 1, ",...,", n1 + n2 + n3))

# fit the model and visualize the estimated graphs
(out <- covdepGE(X, Z))
plot(out)

# visualize the posterior inclusion probabilities for variables (1, 3) and (1, 2)
inclusionCurve(out, 1, 2)
inclusionCurve(out, 1, 3)

## End(Not run)

Package 'covdepGE'

Help Index

covdepGE: Covariate Dependent Graph Estimation

Description

Author(s)

References

See Also

Covariate Dependent Graph Estimation

Description

Usage

Arguments

Value

References

Examples

Generate Covariate-Dependent Data

Description

Usage

Arguments

Value

Extraneous Covariate

Precision Matrices

Examples

Plot PIP as a Function of Index

Description

Usage

Arguments

Value

Examples

Visualize a matrix

Description

Usage

Arguments

Value

Examples

Plot the Graphs Estimated by `covdepGE`

Description

Usage

Arguments

Value

Examples

Package 'covdepGE'

Help Index

covdepGE: Covariate Dependent Graph Estimation

Description

Author(s)

References

See Also

Covariate Dependent Graph Estimation

Description

Usage

Arguments

Value

References

Examples

Generate Covariate-Dependent Data

Description

Usage

Arguments

Value

Extraneous Covariate

Precision Matrices

Examples

Plot PIP as a Function of Index

Description

Usage

Arguments

Value

Examples

Visualize a matrix

Description

Usage

Arguments

Value

Examples

Plot the Graphs Estimated by covdepGE

Description

Usage

Arguments

Value

Examples

Plot the Graphs Estimated by `covdepGE`