################# Max-Log-Likelihood #################
n <- length(g.breaks.clean)
kmin <- g.breaks.clean[1]
alpha.ML <- 1 + n/sum(log(g.breaks.clean/kmin))
alpha.ML
lines(g.seq, g.seq^(-alpha.ML), col="#D35FB7", lty=4)
# Homework 4 for the University of Tulsa' s CS-7863 Network Theory Course
# Degree Distribution
# Professor: Dr. McKinney, Spring 2022
# Noah Schrick - 1492657
library(igraph)
library(igraphdata)
data(yeast)
g <- yeast
g.netname <- "Yeast"
################# Set up Work #################
g.vec <- degree(g)
g.hist <- hist(g.vec, freq=FALSE, main=paste("Histogram of the", g.netname,
" Network"))
legend("topright", c("Guess", "Poisson", "Least-Squares Fit",
"Max Log-Likelihood"), lty=c(1,2,3,4), col=c("#40B0A6",
"#006CD1", "#E66100", "#D35FB7"))
g.mean <- mean(g.vec)
g.seq <- 0:max(g.vec) # x-axis
################# Guessing Alpha #################
alpha.guess <- 1.5
lines(g.seq, g.seq^(-alpha.guess), col="#40B0A6", lty=1, lwd=3)
################# Poisson #################
g.pois <- dpois(g.seq, g.mean, log=F)
lines(g.seq, g.pois, col="#006CD1", lty=2, lwd=3)
################# Linear model: Least-Squares Fit #################
g.breaks <- g.hist$breaks[-c(1)] # remove 0
g.probs <- g.hist$density[-1] # make lengths match
# Need to clean up probabilities that are 0
nz.probs.mask <- g.probs!=0
g.breaks.clean <- g.breaks[nz.probs.mask]
g.probs.clean <- g.probs[nz.probs.mask]
#plot(log(g.breaks.clean), log(g.probs.clean))
g.fit <- lm(log(g.probs.clean)~log(g.breaks.clean))
summary(g.fit)
alpha.LM <- coef(g.fit)[2]
lines(g.seq, g.seq^(-alpha.LM), col="#E66100", lty=3, lwd=3)
################# Max-Log-Likelihood #################
n <- length(g.breaks.clean)
kmin <- g.breaks.clean[1]
alpha.ML <- 1 + n/sum(log(g.breaks.clean/kmin))
alpha.ML
lines(g.seq, g.seq^(-alpha.ML), col="#D35FB7", lty=4, lwd=3)
plot(yeast)
hist(yeast)
hist(g.vec)
g.pois
g.mean
alpha.LM
alpha.ML
degree(g)
sort(degree(g))
sort(degree(g),decreasing=FALSE)
sort(degree(g),decreasing=F)
sort(degree(g),decreasing=false)
sort(degree(g), decreasing = TRUE)
head(sort(degree(g), decreasing = TRUE))
stddev(degree(g))
sd(degree(g))
tail(sort(degree(g), decreasing = TRUE))
plot(log(g.breaks.clean), log(g.probs.clean))
# Homework 4 for the University of Tulsa' s CS-7863 Network Theory Course
# Degree Distribution
# Professor: Dr. McKinney, Spring 2022
# Noah Schrick - 1492657
library(igraph)
library(igraphdata)
data(yeast)
g <- yeast
g.netname <- "Yeast"
################# Set up Work #################
g.vec <- degree(g)
g.hist <- hist(g.vec, freq=FALSE, main=paste("Histogram of the", g.netname,
" Network"))
legend("topright", c("Guess", "Poisson", "Least-Squares Fit",
"Max Log-Likelihood"), lty=c(1,2,3,4), col=c("#40B0A6",
"#006CD1", "#E66100", "#D35FB7"))
g.mean <- mean(g.vec)
g.seq <- 0:max(g.vec) # x-axis
################# Guessing Alpha #################
alpha.guess <- 1.5
lines(g.seq, g.seq^(-alpha.guess), col="#40B0A6", lty=1, lwd=3)
################# Poisson #################
g.pois <- dpois(g.seq, g.mean, log=F)
lines(g.seq, g.pois, col="#006CD1", lty=2, lwd=3)
################# Linear model: Least-Squares Fit #################
g.breaks <- g.hist$breaks[-c(1)] # remove 0
g.probs <- g.hist$density[-1] # make lengths match
# Need to clean up probabilities that are 0
nz.probs.mask <- g.probs!=0
g.breaks.clean <- g.breaks[nz.probs.mask]
g.probs.clean <- g.probs[nz.probs.mask]
plot(log(g.breaks.clean), log(g.probs.clean))
g.fit <- lm(log(g.probs.clean)~log(g.breaks.clean))
summary(g.fit)
alpha.LM <- coef(g.fit)[2]
lines(g.seq, g.seq^(-alpha.LM), col="#E66100", lty=3, lwd=3)
################# Max-Log-Likelihood #################
n <- length(g.breaks.clean)
kmin <- g.breaks.clean[1]
alpha.ML <- 1 + n/sum(log(g.breaks.clean/kmin))
alpha.ML
lines(g.seq, g.seq^(-alpha.ML), col="#D35FB7", lty=4, lwd=3)
plot(log(g.breaks.clean), log(g.probs.clean))
g.breaks.clean <- g.breaks[nz.probs.mask]
g.probs.clean <- g.probs[nz.probs.mask]
plot(log(g.breaks.clean), log(g.probs.clean))
# Lab 5 for the University of Tulsa's CS-6643 Bioinformatics Course
# Gene Expression Statistical Learning
# Professor: Dr. McKinney, Fall 2022
# Noah L. Schrick - 1492657
## Set Working Directory to file directory - RStudio approach
setwd(dirname(rstudioapi::getActiveDocumentContext()$path))
#### 0: Process and filter data
# load gene expression data
load("sense.filtered.cpm.Rdata")  # setwd!
# load phenotype (mdd/hc) data
subject.attrs <- read.csv("Demographic_symptom.csv",
stringsAsFactors = FALSE)
if (!require("dplyr")) install.packages("dplyr")
library(dplyr)
# grab intersecting X (subject ids) and Diag (Diagnosis) from columns
phenos.df <- subject.attrs %>%
filter(X %in% colnames(sense.filtered.cpm)) %>%
dplyr::select(X, Diag)
mddPheno <- as.factor(phenos.df$Diag)
# Normalized and transform
if (!require("preprocessCore")) install.packages("preprocessCore")
library(preprocessCore)
mddExprData_quantile <- normalize.quantiles(sense.filtered.cpm)
mddExprData_quantileLog2 <- log2(mddExprData_quantile)
# attach phenotype names and gene names to data
colnames(mddExprData_quantileLog2) <- mddPheno
rownames(mddExprData_quantileLog2) <- rownames(sense.filtered.cpm)
# coefficient of variation filter sd(x)/abs(mean(x))
CoV_values <- apply(mddExprData_quantileLog2,1,
function(x) {sd(x)/abs(mean(x))})
# smaller threshold, the higher the experimental effect relative to the
# measurement precision
sum(CoV_values<.045)
# there is one gene that has 0 variation -- remove
sd_values <- apply(mddExprData_quantileLog2,1, function(x) {sd(x)})
rownames(mddExprData_quantileLog2)[sd_values==0]
# filter the data matrix
GxS.covfilter <- mddExprData_quantileLog2[CoV_values<.045 & sd_values>0,]
dim(GxS.covfilter)
# convert phenotype to factor
pheno.factor <- as.factor(colnames(GxS.covfilter))
pheno.factor
str(pheno.factor)
levels(pheno.factor)
#### Part A: Logistic Regression
# make sure HC is the reference level
pheno.factor.relevel <- relevel(pheno.factor,"HC")
levels(pheno.factor.relevel)
# also rename levels "0"/"1" from 1/2
levels(pheno.factor.relevel)[levels(pheno.factor.relevel)=="MDD"] <- 1
levels(pheno.factor.relevel)[levels(pheno.factor.relevel)=="HC"] <- 0
# Fit logistic model of first gene to phenotype data
gene.row <- 2
gene.name <-rownames(GxS.covfilter)[gene.row]
gene.expr <- GxS.covfilter[gene.row,]
gene.fit <- glm(pheno.factor.relevel~gene.expr, family=binomial)
summary(gene.fit)
coeff.mat <- coef(summary(gene.fit))
b0 <- coeff.mat[1,1]
b1 <- coeff.mat[2,1]
b1.pval <- coeff.mat[2,4]
summary(gene.fit)
coeff.mat <- coef(summary(gene.fit))
b0 <- coeff.mat[1,1]
b0
b1
coeff.mat
b1.pval
## GLM
modelfn <- function(x){1/(1+exp(-(b0+b1*x)))}
g.min <- min(gene.expr)
g.max <- max(gene.expr)
curve(modelfn,g.min,g.max)  # plot for domain of actual gene’s expression
abline(h=.5, lty=2)
curve(modelfn,3,8)     # replot with extended domain to see the S shape
## Predict Function
Predicted.probs <- predict(gene.fit, gene.expr=gene.expr,
type="response")
if (!require("ggplot2")) install.packages("ggplot2")
library(ggplot2)
phenotype <- pheno.factor # just rename for legend
gene.gg.df <- data.frame(expression=gene.expr,
prediction=predicted.probs)
# plot predicted probabilities versus gene expression
p <- ggplot(data=gene.gg.df)
p <- p + geom_point(aes(x=expression,
y=prediction,
color=phenotype,  # shape and color
shape=phenotype), # are true phenotype
size=3)
p <- p + geom_hline(yintercept = .5, linetype="dashed", color="red")
print(p)
abline(h=.5, lty=2)
Predicted.probs <- predict(gene.fit, gene.expr=gene.expr,
type="response")
if (!require("ggplot2")) install.packages("ggplot2")
library(ggplot2)
phenotype <- pheno.factor # just rename for legend
gene.gg.df <- data.frame(expression=gene.expr,
prediction=predicted.probs)
predicted.probs <- predict(gene.fit, gene.expr=gene.expr,
type="response")
if (!require("ggplot2")) install.packages("ggplot2")
library(ggplot2)
phenotype <- pheno.factor # just rename for legend
gene.gg.df <- data.frame(expression=gene.expr,
prediction=predicted.probs)
# plot predicted probabilities versus gene expression
p <- ggplot(data=gene.gg.df)
p <- p + geom_point(aes(x=expression,
y=prediction,
color=phenotype,  # shape and color
shape=phenotype), # are true phenotype
size=3)
p <- p + geom_hline(yintercept = .5, linetype="dashed", color="red")
print(p)
abline(h=.5, lty=2)
predicted.probs <- predict(gene.fit, gene.expr=gene.expr,
type="response")
if (!require("ggplot2")) install.packages("ggplot2")
library(ggplot2)
phenotype <- pheno.factor # just rename for legend
gene.gg.df <- data.frame(expression=gene.expr,
prediction=predicted.probs)
# plot predicted probabilities versus gene expression
p <- ggplot(data=gene.gg.df)
p <- p + geom_point(aes(x=expression,
y=prediction,
color=phenotype,  # shape and color
shape=phenotype), # are true phenotype
size=3)
p <- p + geom_hline(yintercept = .5, linetype="dashed", color="red")
print(p)
abline(h=.5, lty=2)
## Predict Function
predicted.probs <- predict(gene.fit, gene.expr=gene.expr,
type="response")
if (!require("ggplot2")) install.packages("ggplot2")
library(ggplot2)
phenotype <- pheno.factor # just rename for legend
gene.gg.df <- data.frame(expression=gene.expr,
prediction=predicted.probs)
# plot predicted probabilities versus gene expression
p <- ggplot(data=gene.gg.df)
p <- p + geom_point(aes(x=expression,
y=prediction,
color=phenotype,  # shape and color
shape=phenotype), # are true phenotype
size=3)
p <- p + geom_hline(yintercept = .5, linetype="dashed", color="red")
print(p)
abline(h=.5, lty=2)
plot(p)
abline(h=.5, lty=2)
print(p) + abline(h=.5, lty=2)
# Lab 5 for the University of Tulsa's CS-6643 Bioinformatics Course
# Gene Expression Statistical Learning
# Professor: Dr. McKinney, Fall 2022
# Noah L. Schrick - 1492657
## Set Working Directory to file directory - RStudio approach
setwd(dirname(rstudioapi::getActiveDocumentContext()$path))
#### 0: Process and filter data
# load gene expression data
load("sense.filtered.cpm.Rdata")  # setwd!
# load phenotype (mdd/hc) data
subject.attrs <- read.csv("Demographic_symptom.csv",
stringsAsFactors = FALSE)
if (!require("dplyr")) install.packages("dplyr")
library(dplyr)
# grab intersecting X (subject ids) and Diag (Diagnosis) from columns
phenos.df <- subject.attrs %>%
filter(X %in% colnames(sense.filtered.cpm)) %>%
dplyr::select(X, Diag)
mddPheno <- as.factor(phenos.df$Diag)
# Normalized and transform
if (!require("preprocessCore")) install.packages("preprocessCore")
library(preprocessCore)
mddExprData_quantile <- normalize.quantiles(sense.filtered.cpm)
mddExprData_quantileLog2 <- log2(mddExprData_quantile)
# attach phenotype names and gene names to data
colnames(mddExprData_quantileLog2) <- mddPheno
rownames(mddExprData_quantileLog2) <- rownames(sense.filtered.cpm)
# coefficient of variation filter sd(x)/abs(mean(x))
CoV_values <- apply(mddExprData_quantileLog2,1,
function(x) {sd(x)/abs(mean(x))})
# smaller threshold, the higher the experimental effect relative to the
# measurement precision
sum(CoV_values<.045)
# there is one gene that has 0 variation -- remove
sd_values <- apply(mddExprData_quantileLog2,1, function(x) {sd(x)})
rownames(mddExprData_quantileLog2)[sd_values==0]
# filter the data matrix
GxS.covfilter <- mddExprData_quantileLog2[CoV_values<.045 & sd_values>0,]
dim(GxS.covfilter)
# convert phenotype to factor
pheno.factor <- as.factor(colnames(GxS.covfilter))
pheno.factor
str(pheno.factor)
levels(pheno.factor)
#### Part A: Logistic Regression
# make sure HC is the reference level
pheno.factor.relevel <- relevel(pheno.factor,"HC")
levels(pheno.factor.relevel)
# also rename levels "0"/"1" from 1/2
levels(pheno.factor.relevel)[levels(pheno.factor.relevel)=="MDD"] <- 1
levels(pheno.factor.relevel)[levels(pheno.factor.relevel)=="HC"] <- 0
## Fit logistic model of first gene to phenotype data
gene.row <- 2
gene.name <-rownames(GxS.covfilter)[gene.row]
gene.expr <- GxS.covfilter[gene.row,]
gene.fit <- glm(pheno.factor.relevel~gene.expr, family=binomial)
summary(gene.fit)
coeff.mat <- coef(summary(gene.fit))
b0 <- coeff.mat[1,1]
b1 <- coeff.mat[2,1]
b1.pval <- coeff.mat[2,4]
## GLM
modelfn <- function(x){1/(1+exp(-(b0+b1*x)))}
g.min <- min(gene.expr)
g.max <- max(gene.expr)
curve(modelfn,g.min,g.max)  # plot for domain of actual gene’s expression
abline(h=.5, lty=2)
curve(modelfn,3,8)     # replot with extended domain to see the S shape
## Predict Function
predicted.probs <- predict(gene.fit, gene.expr=gene.expr,
type="response")
if (!require("ggplot2")) install.packages("ggplot2")
library(ggplot2)
phenotype <- pheno.factor # just rename for legend
gene.gg.df <- data.frame(expression=gene.expr,
prediction=predicted.probs)
# plot predicted probabilities versus gene expression
p <- ggplot(data=gene.gg.df)
p <- p + geom_point(aes(x=expression,
y=prediction,
color=phenotype,  # shape and color
shape=phenotype), # are true phenotype
size=3)
p <- p + geom_hline(yintercept = .5, linetype="dashed", color="red")
print(p) + abline(h=.5, lty=2)
# vector of logistic output probabilities for this model (glm/eq. above)
# prob = .5 is the threshold for prediction class = 1 vs 0
predicted.class <- as.integer(predicted.probs >=.5)  # predicted class
pheno.factor.relevel  # true class
# vector of True (correctly predicted) and False (wrongly predicted)
correct.classified <- predicted.class == pheno.factor.relevel
# sum correct.classified
table(pheno.factor.relevel,predicted.class)
predicted.probs
predicted.probs[1]
as.integer(predicted.probs[1] >= 0.5)
# sum correct.classified
table(pheno.factor.relevel,predicted.class)
pheno.factor.relevel
correct.classified
length(correct.classified)
sum(correct.classified == "TRUE")
# accuracy:
correct.acc <- sum(correct.classified == "TRUE") / length(correct.classified)
correct.acc
lr.fn(2)
# logistic regression function for one gene row
lr.fn <- function(i){
gene=rownames(GxS.covfilter)[i]
gene.expr <- GxS.covfilter[i,]
gene.fit <- glm(pheno.factor.relevel~gene.expr,
family=binomial)
coeff.mat <- coef(summary(gene.fit))
b1 <- coeff.mat[2,1]
b1.pval <- coeff.mat[2,4]
coefvec <- gene.fit$estimate # intercept, gene
pvec <- gene.fit$p.value     # intercept, gene
c(gene, b1, b1.pval)
}
lr.fn(2)
# initialize results matrix
num.genes<-nrow(GxS.covfilter)
lr.results.mat <- matrix(0, nrow=nrow(GxS.covfilter), ncol=3)
# for loop the function to all genes
for (i in 1:num.genes){
lr.results.mat[i,] <- lr.fn(i)
}
lr.results.df <- data.frame(lr.results.mat)
colnames(lr.results.df) <- c("gene", "b1", "p.val")
# sort results b1 coefficient p-value
library(dplyr)
lr.results.sorted <- lr.results.df %>%
mutate_at("p.val", as.character) %>%
mutate_at("p.val", as.numeric) %>%
arrange(p.val)
lr.results.sorted[1:10,]
lr.results.sorted[1,]
lr.results.sorted[1,1]
gene.row <- which(rownames(GxS.covfilter)==lr.results.sorted[1,1])
gene.row
gene.expr <- GxS.covfilter[gene.row,]
gene.fit <- glm(pheno.factor.relevel~gene.expr,
family=binomial)
predicted.probs <- predict(gene.fit, gene.expr=gene.expr, type="response")
gene.gg.df
# Plotting Code
gene.gg.df <- data.frame(expression=gene.expr,
prediction=predicted.probs)
# plot predicted probabilities versus gene expression
p <- ggplot(data=gene.gg.df)
p <- p + geom_point(aes(x=expression,
y=prediction,
color=phenotype,  # shape and color
shape=phenotype), # are true phenotype
size=3)
p <- p + geom_hline(yintercept = .5, linetype="dashed", color="red")
print(p) + abline(h=.5, lty=2)
p <- p + geom_point(aes(x=expression,
y=prediction,
color=phenotype,  # shape and color
shape=phenotype,
main=lr.results.sorted[1,1]), # are true phenotype
size=3)
?aes
?ggplot
p <- p + geom_hline(yintercept = .5, linetype="dashed", color="red") +
ggtitle(lr.results.sorted[1,1])
print(p) + abline(h=.5, lty=2)
# code for accuracy
# vector of logistic output probabilities for this model (glm/eq. above)
# prob = .5 is the threshold for prediction class = 1 vs 0
predicted.class <- as.integer(predicted.probs >=.5)  # predicted class
pheno.factor.relevel  # true class
# vector of True (correctly predicted) and False (wrongly predicted)
correct.classified <- predicted.class == pheno.factor.relevel
# sum correct.classified
table(pheno.factor.relevel,predicted.class)
# accuracy:
correct.acc <- sum(correct.classified == "TRUE") / length(correct.classified)
correct.acc
if (!require("glmnet")) install.packages("glmnet")
library(glmnet)
# alpha=0 means ridge, alpha=1 means lasso
# keep has to do with storing the results from cross-validiation
glmnet.model <- cv.glmnet(t(GxS.covfilter), pheno.factor.relevel, alpha=1,
family="binomial", type.measure="class", keep=T)
plot(glmnet.model) # plot of CV error vs lambda penalty
glmnet.model$lambda.min # lambda that minimizes the CV error
glmnet.model
# Convient way to extract non-zero
if (!require("coefplot")) install.packages("coefplot")
library(coefplot)
extract.coef(glmnet.model)
# get the penalized regression coefficients
glmnet.coeffs <- predict(glmnet.model,type="coefficients",
s=glmnet.model$lambda.min)
top_glmnet <- data.frame(as.matrix(glmnet.coeffs))      %>%
tibble::rownames_to_column(var = "features") %>%
filter(s1!=0, features!="(Intercept)")
top_glmnet_features <- top_glmnet %>% pull(features)
# apply the glmnet model to the data to get class predictions
glmnet.predicted <- predict(glmnet.model,
s=glmnet.model$lambda.min, # lambda to use
type="class",              # classify
newx=t(GxS.covfilter))     # apply to original
glmnet.accuracy <- mean(factor(glmnet.predicted)==pheno.factor.relevel)
glmnet.accuracy
# get the coefficients that are not zero (these are the selected variables)
glmnet.nonzero.coeffs <- #glmnet.coeffs@Dimnames[[1]][which(glmnet.coeffs!=0)]
glmnet.nonzero.coeffs
# get the coefficients that are not zero (these are the selected variables)
glmnet.nonzero.coeffs <- #glmnet.coeffs@Dimnames[[1]][which(glmnet.coeffs!=0)]
glmnet.nonzero.coeffs
# get the coefficients that are not zero (these are the selected variables)
glmnet.nonzero.coeffs <- glmnet.coeffs@Dimnames[[1]][which(glmnet.coeffs!=0)]
glmnet.nonzero.coeffs
#### Part E: NPDR
if (!require("devtools")) install.packages("devtools")
library(devtools)
install_github("insilico/npdr")
library(npdr)  #https://github.com/insilico/npdr
SxG.dat <- t(GxS.covfilter)
npdr.MDD.results <- npdr(pheno.factor, SxG.dat,
regression.type="binomial",
attr.diff.type="numeric-abs",
nbd.metric = "manhattan",
knn=knnSURF.balanced(pheno.factor, sd.frac = .5),
dopar.nn = F, dopar.reg=F,
padj.method="bonferroni", verbose = T)
colnames(npdr.MDD.results)  # column names of the output
library(dplyr)
# gets genes (attributes/att) with FDR-adjusted p-value<.05
top.p05.npdr <- npdr.MDD.results %>% filter(pval.adj<.05) %>% pull(att)
top.p05.npdr
# grab top 200, remove NA, remove "", get att col
top.npdr <- npdr.MDD.results %>% dplyr::slice(1:200) %>%
filter(att!="") %>% pull(att)
write.table(top.npdr,row.names=F,col.names=F,quote=F)
# grab top 200, remove NA, remove "", get att col
top.npdr <- npdr.MDD.results %>% dplyr::slice(1:200) %>%
filter(att!="") filter(pval.adj<1) %>% pull(att)
# grab top 200, remove NA, remove "", get att col
top.npdr <- npdr.MDD.results %>% dplyr::slice(1:200) %>%
filter(pval.adj<1) %>% pull(att)
write.table(top.npdr,row.names=F,col.names=F,quote=F)