unpenalized regression coefficients. simulated data using npdro

Schrick-Noah_Homework-6.R

@@ -5,10 +5,55 @@
 
 # 1. Penalized Regression and Classification
 ## a. Modified Ridge classification for LASSO penalties
+# gradient descent to optimize beta's
+ridge_betas <- function(X,y,beta_init=NULL,lam, alpha=0, method="BFGS"){
+  if (is.null(beta_init)){beta_init <- rep(.1, ncol(X)+1)}
+  # method: BFGS, CG, Nelder-Mead
+  no_penalty_cg <- optim(beta_init,  # guess 
+                         fn=function(beta){penalized_loss(X, y, beta, lam, alpha=0)}, # objective 
+                         gr=function(beta){ridge_grad(X, y, beta, lam)}, # gradient
+                         method = method) #, control= list(trace = 2)) 
+  return(list(loss=no_penalty_cg$value, betas = no_penalty_cg$par))
+}
 
-### Add cross-validation to tune penalty param
+lasso_betas <- function(X,y){
+  ridge_betas(X,y,beta_init=NULL,lam=0,alpha=0,method="BFGS")
+}
 
 ### Use npdro simulated data to test
+if (!require("devtools")) install.packages("devtools")
+library(devtools)
+install_github("insilico/npdro")
+if (!require("npdro")) install.packages("npdro")
+library(npdro)
+if (!require("dplyr")) install.packages("dplyr")
+library(dplyr)
+
+num.samples   <- 300
+num.variables <- 100
+dataset <- npdro::createSimulation2(num.samples=num.samples,
+                                    num.variables=num.variables,
+                                    pct.imbalance=0.5,
+                                    pct.signals=0.2,
+                                    main.bias=0.5,
+                                    interaction.bias=1,
+                                    hi.cor=0.95,
+                                    lo.cor=0.2,
+                                    mix.type="main-interactionScalefree",
+                                    label="class",
+                                    sim.type="mixed",
+                                    pct.mixed=0.5,
+                                    pct.train=0.5,
+                                    pct.holdout=0.5,
+                                    pct.validation=0,
+                                    plot.graph=F,
+                                    graph.structure = NULL,
+                                    verbose=T)
+train <- dataset$train  #150x101
+test <- dataset$holdout 
+validation <- dataset$validation
+dataset$signal.names
+colnames(train)
 
 ### Compare with Ridge
 
@@ -134,7 +179,6 @@ plot.igraph(knn.graph,layout=layout_with_fr(knn.graph),
 # 2. Gradient Descent
 ## Write fn with learning param
 grad.rosen <- function(xvec, a=2, b=100){
-  #a <- 2; b <- 1000;
   x <- xvec[1];
   y <- xvec[2];
   f.x <- -2*(a-x) - 4*b*x*(y-x^2)