| Title: | Gamma and Exponential Generalized Linear Models with Elastic Net Penalty |
|---|---|
| Description: | Implements the fast iterative shrinkage-thresholding algorithm (FISTA) algorithm to fit a Gamma distribution with an elastic net penalty as described in Chen, Arakvin and Martin (2018) <arxiv:1804.07780>. An implementation for the case of the exponential distribution is also available, with details available in Chen and Martin (2018) <https://papers.ssrn.com/abstract_id=3085672>. |
| Authors: | Anthony Christidis <[email protected]>, Xin Chen <[email protected]>, Daniel Hanson <[email protected]> |
| Maintainer: | Anthony Christidis <[email protected]> |
| License: | GPL (>= 2) |
| Version: | 1.1.2 |
| Built: | 2024-11-01 05:25:02 UTC |
| Source: | https://github.com/anthonychristidis/rpeglmen |
git.glmGammaNet Fit glmnet model for Gamma distributed response data.
fit.glmGammaNet( A, b, exponential.dist = FALSE, alpha.EN = 0.5, num_lambda = 100L, glm_type = 1L, max_iter = 100L, abs_tol = 1e-04, rel_tol = 0.01, normalize_grad = FALSE, k_fold = 5L, has_intercept = TRUE, k_fold_iter = 5L, min.lambda.ratio = 1e-04, ... )fit.glmGammaNet( A, b, exponential.dist = FALSE, alpha.EN = 0.5, num_lambda = 100L, glm_type = 1L, max_iter = 100L, abs_tol = 1e-04, rel_tol = 0.01, normalize_grad = FALSE, k_fold = 5L, has_intercept = TRUE, k_fold_iter = 5L, min.lambda.ratio = 1e-04, ... )
A |
The matrix of independent variables. |
b |
The vector of response variables. |
exponential.dist |
Parameter to determine whether we use the Exponential distribution (TRUE) or the Gamma distribution (FALSE). |
alpha.EN |
The coefficient of elastic net regularizer (1 means lasso). |
num_lambda |
Size of the lambda grid. |
glm_type |
Type of glm model, 1 is exponential, 2 is gamma (not implemented yet). |
max_iter |
Max number of iteration for the prox grad descent optimizer. |
abs_tol |
Absolute error threshold for the pgd optimizer. |
rel_tol |
Relative error threshold for the pgd optimizer (not used for vanilla PGD). |
normalize_grad |
Swtich for whether to normalize the gradient or not. |
k_fold |
The number of folds for cross validation. |
has_intercept |
Parameter to determine if there is an intercept (TRUE) or not (FALSE). |
k_fold_iter |
The number of iterations for the cross-validation. |
min.lambda.ratio |
Minimum lambda ratio for cross-validation. |
... |
Additional parameters. |
vector of optimal coefficient for the glm model.
Anthony-Alexander Christidis, [email protected]
# Function to return the periodogram of data series myperiodogram <- function (data, max.freq = 0.5, twosided = FALSE, keep = 1){ data.fft <- fft(data) N <- length(data) tmp <- Mod(data.fft[2:floor(N/2)])^2/N freq <- ((1:(floor(N/2) - 1))/N) tmp <- tmp[1:floor(length(tmp) * keep)] freq <- freq[1:floor(length(freq) * keep)] if (twosided) { tmp <- c(rev(tmp), tmp) freq <- c(-rev(freq), freq) } return(list(spec = tmp, freq = freq)) } # Function to compute the standard error based the periodogram of # the influence functions time series SE.Gamma <- function(data, d = 7, alpha = 0.5, keep = 1){ N <- length(data) # Compute the periodograms my.periodogram <- myperiodogram(data) my.freq <- my.periodogram$freq my.periodogram <- my.periodogram$spec # Remove values of frequency 0 as it does not contain information # about the variance my.freq <- my.freq[-1] my.periodogram <- my.periodogram[-1] # Implement cut-off nfreq <- length(my.freq) my.freq <- my.freq[1:floor(nfreq*keep)] my.periodogram <- my.periodogram[1:floor(nfreq*keep)] # GLM with BFGS optimization # Create 1, x, x^2, ..., x^d x.mat <- rep(1,length(my.freq)) for(col.iter in 1:d){ x.mat <- cbind(x.mat,my.freq^col.iter) } # Fit the Exponential or Gamma model res <- fit.glmGammaNet(x.mat, my.periodogram, alpha.EN = alpha) # Return the estimated variance return(sqrt(exp(res[1])/N)) } # Loading hedge fund data from PA data(edhec, package = "PerformanceAnalytics") colnames(edhec) # Computing the expected shortfall for the time series of returns # library(RPEIF) # test.mat <- apply(edhec, 2, IF.ES) # test.mat <- apply(test.mat, 2, as.numeric) # Returning the standard errors from the Gamma distribution fit # apply(test.mat, 2, SE.Gamma)# Function to return the periodogram of data series myperiodogram <- function (data, max.freq = 0.5, twosided = FALSE, keep = 1){ data.fft <- fft(data) N <- length(data) tmp <- Mod(data.fft[2:floor(N/2)])^2/N freq <- ((1:(floor(N/2) - 1))/N) tmp <- tmp[1:floor(length(tmp) * keep)] freq <- freq[1:floor(length(freq) * keep)] if (twosided) { tmp <- c(rev(tmp), tmp) freq <- c(-rev(freq), freq) } return(list(spec = tmp, freq = freq)) } # Function to compute the standard error based the periodogram of # the influence functions time series SE.Gamma <- function(data, d = 7, alpha = 0.5, keep = 1){ N <- length(data) # Compute the periodograms my.periodogram <- myperiodogram(data) my.freq <- my.periodogram$freq my.periodogram <- my.periodogram$spec # Remove values of frequency 0 as it does not contain information # about the variance my.freq <- my.freq[-1] my.periodogram <- my.periodogram[-1] # Implement cut-off nfreq <- length(my.freq) my.freq <- my.freq[1:floor(nfreq*keep)] my.periodogram <- my.periodogram[1:floor(nfreq*keep)] # GLM with BFGS optimization # Create 1, x, x^2, ..., x^d x.mat <- rep(1,length(my.freq)) for(col.iter in 1:d){ x.mat <- cbind(x.mat,my.freq^col.iter) } # Fit the Exponential or Gamma model res <- fit.glmGammaNet(x.mat, my.periodogram, alpha.EN = alpha) # Return the estimated variance return(sqrt(exp(res[1])/N)) } # Loading hedge fund data from PA data(edhec, package = "PerformanceAnalytics") colnames(edhec) # Computing the expected shortfall for the time series of returns # library(RPEIF) # test.mat <- apply(edhec, 2, IF.ES) # test.mat <- apply(test.mat, 2, as.numeric) # Returning the standard errors from the Gamma distribution fit # apply(test.mat, 2, SE.Gamma)
git.glmGammaNet Fit glmnet model for exponentiall distributed response data.
glmnet_exp( A, b, alpha.EN = 0.5, num_lambda = 100L, glm_type = 1L, max_iter = 100L, abs_tol = 1e-04, rel_tol = 0.01, normalize_grad = FALSE, k_fold = 5L, has_intercept = TRUE, k_fold_iter = 5L, ... )glmnet_exp( A, b, alpha.EN = 0.5, num_lambda = 100L, glm_type = 1L, max_iter = 100L, abs_tol = 1e-04, rel_tol = 0.01, normalize_grad = FALSE, k_fold = 5L, has_intercept = TRUE, k_fold_iter = 5L, ... )
A |
The matrix of independent variables. |
b |
The vector of response variables. |
alpha.EN |
The coefficient of elastic net regularizer (1 means lasso). |
num_lambda |
Size of the lambda grid. |
glm_type |
Type of glm model, 1 is exponential, 2 is gamma (not implemented yet). |
max_iter |
Max number of iteration for the prox grad descent optimizer. |
abs_tol |
Absolute error threshold for the pgd optimizer. |
rel_tol |
Relative error threshold for the pgd optimizer (not used for vanilla PGD). |
normalize_grad |
Swtich for whether to normalize the gradient or not. |
k_fold |
The number of folds for cross validation. |
has_intercept |
Parameter to determine if there is an intercept (TRUE) or not (FALSE). |
k_fold_iter |
The number of iterations for the cross-validation. |
... |
Additional Parameters. |
Vector of optimal coefficient for the glm model.
Anthony-Alexander Christidis, [email protected]
# Function to return the periodogram of data series myperiodogram <- function (data, max.freq = 0.5, twosided = FALSE, keep = 1){ data.fft <- fft(data) N <- length(data) tmp <- Mod(data.fft[2:floor(N/2)])^2/N freq <- ((1:(floor(N/2) - 1))/N) tmp <- tmp[1:floor(length(tmp) * keep)] freq <- freq[1:floor(length(freq) * keep)] if (twosided) { tmp <- c(rev(tmp), tmp) freq <- c(-rev(freq), freq) } return(list(spec = tmp, freq = freq)) } # Function to compute the standard error based the periodogram of # the influence functions time series SE.Exponential <- function(data, d = 7, alpha = 0.5, keep = 1){ N <- length(data) # Compute the periodograms my.periodogram <- myperiodogram(data) my.freq <- my.periodogram$freq my.periodogram <- my.periodogram$spec # Remove values of frequency 0 as it does not contain information # about the variance my.freq <- my.freq[-1] my.periodogram <- my.periodogram[-1] # Implement cut-off nfreq <- length(my.freq) my.freq <- my.freq[1:floor(nfreq*keep)] my.periodogram <- my.periodogram[1:floor(nfreq*keep)] # GLM with BFGS optimization # Create 1, x, x^2, ..., x^d x.mat <- rep(1,length(my.freq)) for(col.iter in 1:d){ x.mat <- cbind(x.mat,my.freq^col.iter) } # Fit the Exponential model res <- glmnet_exp(x.mat, my.periodogram, alpha.EN = alpha) # Return the estimated variance return(sqrt(exp(res[1])/N)) } # Loading hedge fund data from PA data(edhec, package = "PerformanceAnalytics") colnames(edhec) # Computing the expected shortfall for the time series of returns # library(RPEIF) # test.mat <- apply(edhec, 2, IF.ES) # test.mat <- apply(test.mat, 2, as.numeric) # Returning the standard errors from the Exponential distribution fit # apply(test.mat, 2, SE.Exponential)# Function to return the periodogram of data series myperiodogram <- function (data, max.freq = 0.5, twosided = FALSE, keep = 1){ data.fft <- fft(data) N <- length(data) tmp <- Mod(data.fft[2:floor(N/2)])^2/N freq <- ((1:(floor(N/2) - 1))/N) tmp <- tmp[1:floor(length(tmp) * keep)] freq <- freq[1:floor(length(freq) * keep)] if (twosided) { tmp <- c(rev(tmp), tmp) freq <- c(-rev(freq), freq) } return(list(spec = tmp, freq = freq)) } # Function to compute the standard error based the periodogram of # the influence functions time series SE.Exponential <- function(data, d = 7, alpha = 0.5, keep = 1){ N <- length(data) # Compute the periodograms my.periodogram <- myperiodogram(data) my.freq <- my.periodogram$freq my.periodogram <- my.periodogram$spec # Remove values of frequency 0 as it does not contain information # about the variance my.freq <- my.freq[-1] my.periodogram <- my.periodogram[-1] # Implement cut-off nfreq <- length(my.freq) my.freq <- my.freq[1:floor(nfreq*keep)] my.periodogram <- my.periodogram[1:floor(nfreq*keep)] # GLM with BFGS optimization # Create 1, x, x^2, ..., x^d x.mat <- rep(1,length(my.freq)) for(col.iter in 1:d){ x.mat <- cbind(x.mat,my.freq^col.iter) } # Fit the Exponential model res <- glmnet_exp(x.mat, my.periodogram, alpha.EN = alpha) # Return the estimated variance return(sqrt(exp(res[1])/N)) } # Loading hedge fund data from PA data(edhec, package = "PerformanceAnalytics") colnames(edhec) # Computing the expected shortfall for the time series of returns # library(RPEIF) # test.mat <- apply(edhec, 2, IF.ES) # test.mat <- apply(test.mat, 2, as.numeric) # Returning the standard errors from the Exponential distribution fit # apply(test.mat, 2, SE.Exponential)