# Precision Matrix with Known Graph Compute the maximum likelihood estimate of the precision matrix, given a known graphical structure (i.e., an adjacency matrix). This approach was originally described in "The Elements of Statistical Learning" if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_citeOnly(keys="@see pg. 631,@hastie2009elements",package="GGMncv", cached_env=.Rdpack.currefs) . ```r constrained(Sigma, adj) mle_known_graph(Sigma, adj) ``` ## Arguments - `Sigma`: Covariance matrix - `adj`: Adjacency matrix that encodes the constraints, where a zero indicates that element should be zero. ## Returns A list containing the following: * Theta: Inverse of the covariance matrix (precision matrix) * Sigma: Covariance matrix. * wadj: Weighted adjacency matrix, corresponding to the partial correlation network. ## Note The algorithm is written in `c++`, and should scale to high dimensions nicely. Note there are a variety of algorithms for this purpose. Simulation studies indicated that this approach is both accurate and computationally efficient if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_citeOnly(keys="@HFT therein,@emmert2019constrained",package="GGMncv", cached_env=.Rdpack.currefs) ## Examples ```r # data y <- ptsd # fit model fit <- ggmncv(cor(y), n = nrow(y), penalty = "lasso", progress = FALSE) # set negatives to zero (sign restriction) adj_new <- ifelse( fit$P <= 0, 0, 1) check_zeros <- TRUE # track trys iter <- 0 # iterate until all positive while(check_zeros){ iter <- iter + 1 fit_new <- constrained(cor(y), adj = adj_new) check_zeros <- any(fit_new$wadj < 0) adj_new <- ifelse( fit_new$wadj <= 0, 0, 1) } # alias # data y <- ptsd # nonreg (lambda = 0) fit <- ggmncv(cor(y), n = nrow(y), lambda = 0, progress = FALSE) # set values less than |0.1| to zero adj_new <- ifelse( abs(fit$P) <= 0.1, 0, 1) # mle given the graph mle_known_graph(cor(y), adj_new) ``` ## References if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_all_ref(.Rdpack.currefs)

constrained function