203 lines
7.0 KiB
R
203 lines
7.0 KiB
R
# Homework 6 for the University of Tulsa's CS-7863 Sci-Stat Course
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# Penalized Machine Learning
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# Professor: Dr. McKinney, Spring 2023
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# Noah L. Schrick - 1492657
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if (!require("data.table")) install.packages("data.table")
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library(data.table)
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# 1. Penalized Regression and Classification
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## a. Modified Ridge classification for LASSO penalties
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source("Schrick-Noah_Ridge-LASSO-Regression.R")
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### Use npdro simulated data to test
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source("Schrick-Noah_Simulated-Data.R")
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bundled_data <- create_data()
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### LASSO
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unpen_beta <- unpen_coeff(bundled_data$train.X, bundled_data$train.y)
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lasso.df <- data.frame(att=c("intercept", colnames(bundled_data$train.X)),
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scores=unpen_beta$betas,
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abs_scores=abs(unpen_beta$betas))
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lasso.res <- dplyr::slice_max(lasso.df,order_by=abs_scores,n=20)
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lasso.table <- as.data.table(lasso.res)
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### Compare with Ridge
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#### Find lambda
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tune_results <- tune_ridge(bundled_data$train.X, bundled_data$train.y,
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num_folds=10, 2^seq(-5,5,1), verbose=F)
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plot(log(tune_results$cv.table$hyp), tune_results$cv.table$means, type="l",
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xlab="lambda", ylab="CV Mean Loss")
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abline(v=tune_results$lam.min)
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tune_results$lam.min
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#### Use lam.min for Ridge Regression
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ridge_result <- ridge_betas(bundled_data$train.X, bundled_data$train.y,
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beta_init = NULL, lam=tune_results$lam.min, method="BFGS")
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ridge.df <- data.frame(att=c("intercept", colnames(bundled_data$train.X)),
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scores=ridge_result$betas,
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abs_scores=abs(ridge_result$betas))
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ridge.res <- dplyr::slice_max(ridge.df,order_by=abs_scores,n=20)
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ridge.table <- as.data.table(ridge.res)
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### Compare with Random Forest
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source("Schrick-Noah_Random-Forest.R")
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rf_result <- rf_comp(bundled_data$train)
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rf.df <- data.frame(att=c(colnames(bundled_data$train.X)),
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scores=rf_result$rf2_imp$rf_score)
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rf_res <- dplyr::slice_max(rf.df,order_by=scores, n=20)
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rf.table <- as.data.table(rf_res)
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### Compare with glmnet
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source("Schrick-Noah_glmnet.R")
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#### Alpha = 0
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glm.res.0 <- glm_fcn(bundled_data$train.X, bundled_data$train.y, 0)
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glm.df.0 <- data.frame(att=c("intercept", colnames(bundled_data$train.X)),
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scores=glm.res.0$lambda.1se,
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abs_scores=glm.res.0$abs_scores)
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glm.df.0.res <- dplyr::slice_max(glm.df.0,order_by=abs_scores,n=20)
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glm.0.table <- as.data.table(glm.df.0.res)
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#### Alpha = 1
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glm.res.1 <- glm_fcn(bundled_data$train.X, bundled_data$train.y, 1) # alpha=1
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glm.df.1 <- data.frame(att=c("intercept", colnames(bundled_data$train.X)),
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scores=glm.res.1$lambda.1se,
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abs_scores=glm.res.1$abs_scores)
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glm.df.1.res <- dplyr::slice_max(glm.df.1,order_by=abs_scores,n=20)
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glm.1.table <- as.data.table(glm.df.1.res)
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## b. Repeat comparison using a graph with clusters
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if (!require("igraph")) install.packages("igraph")
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library(igraph)
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if (!require("Matrix")) install.packages("Matrix")
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library(Matrix) # bdiag
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npc <-25 # nodes per cluster
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n_clust <- 4 # 4 clusters with 25 nodes each
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# no clusters
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g0 <- erdos.renyi.game(npc*n_clust, 0.2)
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plot(g0)
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matlist = list()
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for (i in 1:n_clust){
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matlist[[i]] = get.adjacency(erdos.renyi.game(npc, 0.2))
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}
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# merge clusters into one matrix
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mat_clust <- bdiag(matlist) # create block-diagonal matrix
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## the following two things might not be necessary
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# check for loner nodes, connected to nothing, and join them to something
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k <- rowSums(mat_clust)
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node_vector <- seq(1,npc*n_clust)
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for (i in node_vector){
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if (k[i]==0){ # if k=0, connect to something random
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j <- sample(node_vector[-i],1)
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mat_clust[i,j] <- 1
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mat_clust[j,i] <- 1
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}
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}
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node_colors <- c(rep("red",npc), rep("green",npc), rep("blue",npc), rep("orange",npc))
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g1 <- graph_from_adjacency_matrix(mat_clust, mode="undirected", diag=F)
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plot(g1, vertex.color=node_colors)
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### Dataset with g1
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dataset.graph <- npdro::createSimulation2(num.samples=num.samples,
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num.variables=num.variables,
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pct.imbalance=0.5,
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pct.signals=0.2,
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main.bias=0.5,
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interaction.bias=1,
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hi.cor=0.95,
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lo.cor=0.2,
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mix.type="main-interactionScalefree",
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label="class",
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sim.type="mixed",
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pct.mixed=0.5,
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pct.train=0.5,
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pct.holdout=0.5,
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pct.validation=0,
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plot.graph=F,
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graph.structure = g1,
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verbose=T)
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train.graph <- dataset.graph$train #150x101
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test.graph <- dataset.graph$holdout
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validation.graph <- dataset.graph$validation
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dataset.graph$signal.names
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colnames(train.graph)
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# separate the class vector from the predictor data matrix
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train.graph.X <- train.graph[, -which(colnames(train.graph) == "class")]
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train.graph.y <- train.graph[, "class"]
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train.graph.y.01 <- as.numeric(train.graph.y)-1
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## c. Use npdro and igraph to create knn
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my.k <- 3 # larger k, fewer clusters
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npdr.nbpairs.idx <- npdro::nearestNeighbors(t(train.X),
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# transpose does dist between predictors
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# without transpose does dist between samples
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#nbd.method="multisurf", k=0,
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nbd.method = "relieff",
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nbd.metric="manhattan",
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k=my.k)
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knn.graph <- graph_from_edgelist(as.matrix(npdr.nbpairs.idx),
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directed=F)
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knn.graph <- simplify(knn.graph)
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### Plot network
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plot.igraph(knn.graph,layout=layout_with_fr(knn.graph),
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vertex.color="red",
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vertex.size=3,vertex.label=NA,
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main="Manhattan, knn-graph")
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## d. Add Laplace graph penalty
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### Find resulting beta coeffs
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### Optimize or choose value for lambda2
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### Compare to a) and b)
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# 2. Gradient Descent
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## Write fn with learning param
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grad.rosen <- function(xvec, a=2, b=100){
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x <- xvec[1];
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y <- xvec[2];
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f.x <- -2*(a-x) - 4*b*x*(y-x^2)
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f.y <- 2*b*(y-x^2)
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return( c(f.x, f.y))
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}
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a = 2
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b=100
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alpha = .0001 # learning rate
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p = c(0,0) # start for momentum
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xy = c(-1.8, 3.0) # guess for solution
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# gradient descent
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epochs = 1000000
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for (epoch in 1:epochs){
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p = -grad.rosen(xy,a,b);
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xy = xy + alpha*p;
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}
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print(xy) # Should be: ~(2,4)
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# Using optim:
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f.rosen <- function(xvec, a=2, b=100){
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#a <- 2; b <- 1000;
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x <- xvec[1];
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y <- xvec[2];
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return ( (a-x)^2 + b*(y-x^2)^2)
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}
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sol.BFGS <- optim(par=c(-1.8,3.0), fn=function(x){f.rosen(x,a=2,b=100)},
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gr=function(x){grad.rosen(x,a=2,b=100)}, method="BFGS")
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sol.BFGS$par
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