# Homework 6 for the University of Tulsa's CS-7863 Sci-Stat Course
# Penalized Machine Learning
# Professor: Dr. McKinney, Spring 2023
# Noah L. Schrick - 1492657

if (!require("data.table")) install.packages("data.table")
library(data.table)

# 1. Penalized Regression and Classification
## a. Modified Ridge classification for LASSO penalties
source("Schrick-Noah_Ridge-LASSO-Regression.R")

### Use npdro simulated data to test
source("Schrick-Noah_Simulated-Data.R")
bundled_data <- create_data()

### LASSO
unpen_beta <- unpen_coeff(bundled_data$train.X, bundled_data$train.y)
lasso.df <- data.frame(att=c("intercept", colnames(bundled_data$train.X)), 
                            scores=unpen_beta$betas,
                            abs_scores=abs(unpen_beta$betas))
lasso.res <- dplyr::slice_max(lasso.df,order_by=abs_scores,n=20)
lasso.table <- as.data.table(lasso.res)

### Compare with Ridge
#### Find lambda
tune_results <- tune_ridge(bundled_data$train.X, bundled_data$train.y, 
                           num_folds=10, 2^seq(-5,5,1), verbose=F)
plot(log(tune_results$cv.table$hyp), tune_results$cv.table$means, type="l",
     xlab="lambda", ylab="CV Mean Loss")
abline(v=tune_results$lam.min)
tune_results$lam.min

#### Use lam.min for Ridge Regression
ridge_result <- ridge_betas(bundled_data$train.X, bundled_data$train.y,
                            beta_init = NULL, lam=tune_results$lam.min, method="BFGS")
ridge.df <- data.frame(att=c("intercept", colnames(bundled_data$train.X)), 
                       scores=ridge_result$betas,
                       abs_scores=abs(ridge_result$betas))
ridge.res <- dplyr::slice_max(ridge.df,order_by=abs_scores,n=20)
ridge.table <- as.data.table(ridge.res)

### Compare with Random Forest
source("Schrick-Noah_Random-Forest.R")
rf_result <- rf_comp(bundled_data$train)
rf.df <- data.frame(att=c(colnames(bundled_data$train.X)), 
                   scores=rf_result$rf2_imp$rf_score)
rf_res <- dplyr::slice_max(rf.df,order_by=scores, n=20)
rf.table <- as.data.table(rf_res)

### Compare with glmnet
source("Schrick-Noah_glmnet.R")
#### Alpha = 0
glm.res.0 <- glm_fcn(bundled_data$train.X, bundled_data$train.y, 0)
glm.df.0 <- data.frame(att=c("intercept", colnames(bundled_data$train.X)), 
                       scores=glm.res.0$lambda.1se,
                       abs_scores=glm.res.0$abs_scores)
glm.df.0.res <- dplyr::slice_max(glm.df.0,order_by=abs_scores,n=20)
glm.0.table <- as.data.table(glm.df.0.res)

#### Alpha = 1
glm.res.1 <- glm_fcn(bundled_data$train.X, bundled_data$train.y, 1) # alpha=1
glm.df.1 <- data.frame(att=c("intercept", colnames(bundled_data$train.X)), 
                       scores=glm.res.1$lambda.1se,
                       abs_scores=glm.res.1$abs_scores)
glm.df.1.res <- dplyr::slice_max(glm.df.1,order_by=abs_scores,n=20)
glm.1.table <- as.data.table(glm.df.1.res)

## b. Repeat comparison using a graph with clusters
if (!require("igraph")) install.packages("igraph")
library(igraph)
if (!require("Matrix")) install.packages("Matrix")
library(Matrix) # bdiag 

npc <-25 # nodes per cluster
n_clust <- 4 # 4 clusters with 25 nodes each

# no clusters
g0 <- erdos.renyi.game(npc*n_clust, 0.2)
plot(g0)

matlist = list()
for (i in 1:n_clust){ 
  matlist[[i]] = get.adjacency(erdos.renyi.game(npc, 0.2))
}

# merge clusters into one matrix
mat_clust <- bdiag(matlist) # create block-diagonal matrix

## the following two things might not be necessary

# check for loner nodes, connected to nothing, and join them to something
k <- rowSums(mat_clust) 
node_vector <- seq(1,npc*n_clust)
for (i in node_vector){
  if (k[i]==0){ # if k=0, connect to something random
    j <- sample(node_vector[-i],1)
    mat_clust[i,j] <- 1
    mat_clust[j,i] <- 1
  }
}

node_colors <- c(rep("red",npc), rep("green",npc), rep("blue",npc), rep("orange",npc))
g1 <- graph_from_adjacency_matrix(mat_clust, mode="undirected", diag=F)
plot(g1, vertex.color=node_colors)

### Dataset with g1
dataset.graph <- 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 = g1,
                                    verbose=T)

train.graph <- dataset.graph$train  #150x101
test.graph <- dataset.graph$holdout 
validation.graph <- dataset.graph$validation
dataset.graph$signal.names
colnames(train.graph)

# separate the class vector from the predictor data matrix
train.graph.X <- train.graph[, -which(colnames(train.graph) == "class")]
train.graph.y <- train.graph[, "class"]
train.graph.y.01 <- as.numeric(train.graph.y)-1

## c. Use npdro and igraph to create knn
my.k <- 3  # larger k, fewer clusters
npdr.nbpairs.idx <- npdro::nearestNeighbors(t(train.X), 
                                            # transpose does dist between predictors 
                                            # without transpose does dist between samples
                                            #nbd.method="multisurf", k=0, 
                                            nbd.method = "relieff", 
                                            nbd.metric="manhattan", 
                                            k=my.k)
knn.graph <- graph_from_edgelist(as.matrix(npdr.nbpairs.idx), 
                                 directed=F)
knn.graph <- simplify(knn.graph)

### Plot network
plot.igraph(knn.graph,layout=layout_with_fr(knn.graph),
            vertex.color="red",
            vertex.size=3,vertex.label=NA, 
            main="Manhattan, knn-graph")


## d. Add Laplace graph penalty

### Find resulting beta coeffs

### Optimize or choose value for lambda2

### Compare to a) and b)

# 2. Gradient Descent
## Write fn with learning param
grad.rosen <- function(xvec, a=2, b=100){
  x <- xvec[1];
  y <- xvec[2];
  f.x <- -2*(a-x) - 4*b*x*(y-x^2)
  f.y <- 2*b*(y-x^2)
  return( c(f.x, f.y))
}

a = 2
b=100
alpha = .0001 # learning rate
p = c(0,0) # start for momentum

xy = c(-1.8, 3.0)  # guess for solution

# gradient descent
epochs = 1000000
for (epoch in 1:epochs){
  p = -grad.rosen(xy,a,b);
  xy = xy + alpha*p;
}

print(xy) # Should be: ~(2,4)

# Using optim:
f.rosen <- function(xvec, a=2, b=100){
  #a <- 2; b <- 1000;
  x <- xvec[1];
  y <- xvec[2];
  return ( (a-x)^2 + b*(y-x^2)^2)
}

sol.BFGS <- optim(par=c(-1.8,3.0), fn=function(x){f.rosen(x,a=2,b=100)}, 
                  gr=function(x){grad.rosen(x,a=2,b=100)}, method="BFGS")
sol.BFGS$par