Description Usage Arguments Details Value Author(s) References Examples
Efficient design matrix free procedure for fitting a special case of a generalized linear model with array structured response and partially tensor structured covariates. See Lund and Hansen, 2019 for an application of this special purpose function.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 | glamlassoS(X,
Y,
V,
Z = NULL,
family = "gaussian",
penalty = "lasso",
intercept = FALSE,
weights = NULL,
betainit = NULL,
alphainit = NULL,
nlambda = 100,
lambdaminratio = 1e-04,
lambda = NULL,
penaltyfactor = NULL,
penaltyfactoralpha = NULL,
reltolinner = 1e-07,
reltolouter = 1e-04,
maxiter = 15000,
steps = 1,
maxiterinner = 3000,
maxiterouter = 25,
btinnermax = 100,
btoutermax = 100,
iwls = "exact",
nu = 1)
|
X |
A list containing the tensor components (2 or 3) of the tensor design matrix. These are matrices of sizes n_i \times p_i. |
Y |
The response values, an array of size n_1 \times\cdots\times n_d. For option
|
V |
The weight values, an array of size n_1 \times\cdots\times n_d. |
Z |
The non tensor structrured part of the design matrix. A matrix of size n_1 \cdots n_d\times q.
Is set to |
family |
A string specifying the model family (essentially the response distribution). Possible values
are |
penalty |
A string specifying the penalty. Possible values
are |
intercept |
Logical variable indicating if the model includes an intercept.
When |
weights |
Observation weights, an array of size n_1 \times \cdots \times n_d. For option
|
betainit |
The initial parameter values. Default is NULL in which case all parameters are initialized at zero. |
alphainit |
A q\times 1 vector containing the initial parameter values for the non-tensor parameter. Default is NULL in which case all parameters are initialized at 0. |
nlambda |
The number of |
lambdaminratio |
The smallest value for |
lambda |
The sequence of penalty parameters for the regularization path. |
penaltyfactor |
An array of size p_1 \times \cdots \times p_d. Is multiplied
with each element in |
penaltyfactoralpha |
A q \times 1 vector multiplied with each element in |
reltolinner |
The convergence tolerance for the inner loop |
reltolouter |
The convergence tolerance for the outer loop. |
maxiter |
The maximum number of inner iterations allowed for each |
steps |
The number of steps used in the multi-step adaptive lasso algorithm for non-convex penalties. Automatically set to 1 when |
maxiterinner |
The maximum number of inner iterations allowed for each outer iteration. |
maxiterouter |
The maximum number of outer iterations allowed for each lambda. |
btinnermax |
Maximum number of backtracking steps allowed in each inner iteration. Default is |
btoutermax |
Maximum number of backtracking steps allowed in each outer iteration. Default is |
iwls |
A string indicating whether to use the exact iwls weight matrix or use a kronecker structured approximation to it. |
nu |
A number between 0 and 1 that controls the step size δ in the proximal algorithm (inner loop) by
scaling the upper bound \hat{L}_h on the Lipschitz constant L_h (see Lund et al., 2017).
For |
Given the setting from glamlasso
we consider a model
where the tensor design component is only partially tensor structured as
X = [V_1X_2^\top\otimes X_1^\top,…,V_{n_3}X_2^\top\otimes X_1^\top]^\top.
Here X_i is a n_i\times p_i matrix for i=1,2 and V_i is a n_1n_2\times n_1n_2 diagonal matrix for i=1,…,n_3.
Letting Y denote the n_1\times n_2\times n_3 response array and V the n_1\times n_2\times n_3 weight array containing the diagonals of the V_is,
the function glamlassoS
solves the PMLE problem using Y, V, X_1, X_2 and the non-tensor component Z as input.
An object with S3 Class "glamlasso".
spec |
A string indicating the model family and the penalty. |
beta |
A p_1\cdots p_d \times |
alpha |
A q \times |
lambda |
A vector containing the sequence of penalty values used in the estimation procedure. |
df |
The number of nonzero coefficients for each value of |
dimcoef |
A vector giving the dimension of the model coefficient array β. |
dimobs |
A vector giving the dimension of the observation (response)
array |
Iter |
A list with 4 items: |
Adam Lund
Maintainer: Adam Lund, adam.lund@math.ku.dk
Lund, A., M. Vincent, and N. R. Hansen (2017). Penalized estimation in large-scale generalized linear array models. Journal of Computational and Graphical Statistics, 26, 3, 709-724. url = https://doi.org/10.1080/10618600.2017.1279548.
Lund, A. and N. R. Hansen (2019). Sparse Network Estimation for Dynamical Spatio-temporal Array Models. Journal of Multivariate Analysis, 174. url = https://doi.org/10.1016/j.jmva.2019.104532.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 | ##size of example
n1 <- 65; n2 <- 26; n3 <- 13; p1 <- 13; p2 <- 5;
##marginal design matrices (tensor components)
X1 <- matrix(rnorm(n1 * p1), n1, p1)
X2 <- matrix(rnorm(n2 * p2), n2, p2)
X <- list(X1, X2)
V <- array(rnorm(n3 * n2 * n1), c(n1, n2, n3))
##gaussian example
Beta <- array(rnorm(p1 * p2) * rbinom(p1 * p2, 1, 0.1), c(p1 , p2))
Mu <- V * array(RH(X2, RH(X1, Beta)), c(n1, n2, n3))
Y <- array(rnorm(n1 * n2 * n3, Mu), c(n1, n2, n3))
system.time(fit <- glamlassoS(X, Y, V))
modelno <- length(fit$lambda)
plot(c(Beta), ylim = range(Beta, fit$coef[, modelno]), type = "h")
points(c(Beta))
lines(c(fit$coef[, modelno]), col = "red", type = "h")
###with non tensor design component Z
q <- 5
alpha <- matrix(rnorm(q)) * rbinom(q, 1, 0.5)
Z <- matrix(rnorm(n1 * n2 * n3 * q), n1 * n2 *n3, q)
Y <- array(rnorm(n1 * n2 * n3, Mu + array(Z %*% alpha, c(n1, n2, n3))), c(n1, n2, n3))
system.time(fit <- glamlassoS(X, Y, V , Z))
modelno <- length(fit$lambda)
oldmfrow <- par()$mfrow
par(mfrow = c(1, 2))
plot(c(Beta), type="h", ylim = range(Beta, fit$coef[, modelno]))
points(c(Beta))
lines(fit$coef[ , modelno], col = "red", type = "h")
plot(c(alpha), type = "h", ylim = range(alpha, fit$alpha[, modelno]))
points(c(alpha))
lines(fit$alpha[ , modelno], col = "red", type = "h")
par(mfrow = oldmfrow)
################ poisson example
Beta <- matrix(rnorm(p1 * p2, 0, 0.1) * rbinom(p1 * p2, 1, 0.1), p1 , p2)
Mu <- V * array(RH(X2, RH(X1, Beta)), c(n1, n2, n3))
Y <- array(rpois(n1 * n2 * n3, exp(Mu)), dim = c(n1, n2, n3))
system.time(fit <- glamlassoS(X, Y, V, family = "poisson", nu = 0.1))
modelno <- length(fit$lambda)
plot(c(Beta), type = "h", ylim = range(Beta, fit$coef[, modelno]))
points(c(Beta))
lines(fit$coef[ , modelno], col = "red", type = "h")
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