gesso.fit {gesso}

gesso fit

Description

Fits gesso model over the two dimentional grid of hyperparmeters lambda_1 and lambda_2, returns estimated coefficients for each pair of hyperparameters.

Usage

gesso.fit(G, E, Y, C = NULL, normalize = TRUE, normalize_response = FALSE,
          grid = NULL, grid_size = 20, grid_min_ratio = NULL, 
          alpha = NULL, family = "gaussian", weights = NULL,
          tolerance = 1e-3, max_iterations = 5000, 
          min_working_set_size = 100,
          verbose = FALSE)

Arguments

G

matrix of main effects of size n x p, variables organized by columns

E

vector of environmental measurments

Y

outcome vector. Set family="gaussian" for the continuous outcome and family="binomial" for the binary outcome with 0/1 levels

C

matrix of confounders of size n x m, variables organized by columns

normalize

TRUE to normalize matrix G and vector E

normalize_response

TRUE to normalize vector Y

grid

grid sequence for tuning hyperparameters, we use the same grid for lambda_1 and lambda_2

grid_size

specify grid_size to generate grid automatically. Grid is generated by calculating max_lambda from the data (smallest lambda such that all the coefficients are zero). min_lambda is calculated as a product of max_lambda and grid_min_ratio. The program then generates grid_size values equidistant on the log10 scale from min_lambda to max_lambda

grid_min_ratio

parameter to determine min_lambda (smallest value for the grid of lambdas), default is 0.1 for p > n, 0.01 otherwise

alpha

if NULL independent 2D grid is used for (lambda_1, lambda_2), else 1D grid is used where lambda_2 = alpha * lambda_1, i.e. (lambda_1, alpha * lambda_1)

family

"gaussian" for continuous outcome and "binomial" for binary

tolerance

tolerance for the dual gap convergence criterion

max_iterations

maximum number of iterations

min_working_set_size

minimum size of the working set

weights

inner fitting parameter

verbose

TRUE to print messages

Value

A list of estimated coefficients and other model fit metrics for each pair of hyperparameters (lambda_1, lambda_2)

beta_0

vector of estimated intercept values of size lambda_1*lambda_2

beta_e

vector of estimated environment coefficients of size lambda_1*lambda_2

beta_g

matrix of estimated main effects coefficients organized by rows, size (lambda_1*lambda_2) by p

beta_gxe

matrix of estimated interactions coefficients organized by rows, size (lambda_1*lambda_2) by p

beta_c

matrix of estimated confounders coefficients organized by rows, size (lambda_1*lambda_2) by m, where m is the number of confounders

num_iterations

number of iterations until convergence for each fit

working_set_size

maximum number of variables in the working set for each fit

has_converged

1 if the model converged within given max_iterations, 0 otherwise

objective_value

objective function (loss) value for each fit

beta_g_nonzero

number of estimated non-zero main effects for each fit

beta_gxe_nonzero

number of estimated non-zero interactions for each fit

lambda_1

lambda_1 path values, decreasing

lambda_2

lambda_2 path values, oscillating

grid

vector of values used for hyperparameters tuning

Examples

data = data.gen()
fit = gesso.fit(G=data$G_train, E=data$E_train, Y=data$Y_train, normalize=TRUE)
plot(fit$beta_g_nonzero, pch=19, cex=0.4, 
     ylab="num of non-zero features", xlab="lambdas path")
points(fit$beta_gxe_nonzero, pch=19, cex=0.4, col="red")