513 lines
19 KiB
R
513 lines
19 KiB
R
################# Max-Log-Likelihood #################
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n <- length(g.breaks.clean)
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kmin <- g.breaks.clean[1]
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alpha.ML <- 1 + n/sum(log(g.breaks.clean/kmin))
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alpha.ML
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lines(g.seq, g.seq^(-alpha.ML), col="#D35FB7", lty=4)
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# Homework 4 for the University of Tulsa' s CS-7863 Network Theory Course
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# Degree Distribution
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# Professor: Dr. McKinney, Spring 2022
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# Noah Schrick - 1492657
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library(igraph)
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library(igraphdata)
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data(yeast)
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g <- yeast
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g.netname <- "Yeast"
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################# Set up Work #################
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g.vec <- degree(g)
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g.hist <- hist(g.vec, freq=FALSE, main=paste("Histogram of the", g.netname,
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" Network"))
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legend("topright", c("Guess", "Poisson", "Least-Squares Fit",
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"Max Log-Likelihood"), lty=c(1,2,3,4), col=c("#40B0A6",
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"#006CD1", "#E66100", "#D35FB7"))
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g.mean <- mean(g.vec)
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g.seq <- 0:max(g.vec) # x-axis
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################# Guessing Alpha #################
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alpha.guess <- 1.5
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lines(g.seq, g.seq^(-alpha.guess), col="#40B0A6", lty=1, lwd=3)
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################# Poisson #################
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g.pois <- dpois(g.seq, g.mean, log=F)
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lines(g.seq, g.pois, col="#006CD1", lty=2, lwd=3)
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################# Linear model: Least-Squares Fit #################
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g.breaks <- g.hist$breaks[-c(1)] # remove 0
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g.probs <- g.hist$density[-1] # make lengths match
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# Need to clean up probabilities that are 0
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nz.probs.mask <- g.probs!=0
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g.breaks.clean <- g.breaks[nz.probs.mask]
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g.probs.clean <- g.probs[nz.probs.mask]
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#plot(log(g.breaks.clean), log(g.probs.clean))
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g.fit <- lm(log(g.probs.clean)~log(g.breaks.clean))
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summary(g.fit)
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alpha.LM <- coef(g.fit)[2]
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lines(g.seq, g.seq^(-alpha.LM), col="#E66100", lty=3, lwd=3)
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################# Max-Log-Likelihood #################
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n <- length(g.breaks.clean)
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kmin <- g.breaks.clean[1]
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alpha.ML <- 1 + n/sum(log(g.breaks.clean/kmin))
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alpha.ML
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lines(g.seq, g.seq^(-alpha.ML), col="#D35FB7", lty=4, lwd=3)
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plot(yeast)
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hist(yeast)
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hist(g.vec)
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g.pois
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g.mean
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alpha.LM
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alpha.ML
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degree(g)
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sort(degree(g))
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sort(degree(g),decreasing=FALSE)
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sort(degree(g),decreasing=F)
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sort(degree(g),decreasing=false)
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sort(degree(g), decreasing = TRUE)
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head(sort(degree(g), decreasing = TRUE))
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stddev(degree(g))
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sd(degree(g))
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tail(sort(degree(g), decreasing = TRUE))
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plot(log(g.breaks.clean), log(g.probs.clean))
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# Homework 4 for the University of Tulsa' s CS-7863 Network Theory Course
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# Degree Distribution
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# Professor: Dr. McKinney, Spring 2022
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# Noah Schrick - 1492657
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library(igraph)
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library(igraphdata)
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data(yeast)
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g <- yeast
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g.netname <- "Yeast"
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################# Set up Work #################
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g.vec <- degree(g)
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g.hist <- hist(g.vec, freq=FALSE, main=paste("Histogram of the", g.netname,
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" Network"))
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legend("topright", c("Guess", "Poisson", "Least-Squares Fit",
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"Max Log-Likelihood"), lty=c(1,2,3,4), col=c("#40B0A6",
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"#006CD1", "#E66100", "#D35FB7"))
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g.mean <- mean(g.vec)
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g.seq <- 0:max(g.vec) # x-axis
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################# Guessing Alpha #################
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alpha.guess <- 1.5
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lines(g.seq, g.seq^(-alpha.guess), col="#40B0A6", lty=1, lwd=3)
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################# Poisson #################
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g.pois <- dpois(g.seq, g.mean, log=F)
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lines(g.seq, g.pois, col="#006CD1", lty=2, lwd=3)
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################# Linear model: Least-Squares Fit #################
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g.breaks <- g.hist$breaks[-c(1)] # remove 0
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g.probs <- g.hist$density[-1] # make lengths match
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# Need to clean up probabilities that are 0
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nz.probs.mask <- g.probs!=0
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g.breaks.clean <- g.breaks[nz.probs.mask]
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g.probs.clean <- g.probs[nz.probs.mask]
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plot(log(g.breaks.clean), log(g.probs.clean))
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g.fit <- lm(log(g.probs.clean)~log(g.breaks.clean))
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summary(g.fit)
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alpha.LM <- coef(g.fit)[2]
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lines(g.seq, g.seq^(-alpha.LM), col="#E66100", lty=3, lwd=3)
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################# Max-Log-Likelihood #################
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n <- length(g.breaks.clean)
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kmin <- g.breaks.clean[1]
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alpha.ML <- 1 + n/sum(log(g.breaks.clean/kmin))
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alpha.ML
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lines(g.seq, g.seq^(-alpha.ML), col="#D35FB7", lty=4, lwd=3)
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plot(log(g.breaks.clean), log(g.probs.clean))
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g.breaks.clean <- g.breaks[nz.probs.mask]
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g.probs.clean <- g.probs[nz.probs.mask]
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plot(log(g.breaks.clean), log(g.probs.clean))
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# Lab 5 for the University of Tulsa's CS-6643 Bioinformatics Course
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# Gene Expression Statistical Learning
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# Professor: Dr. McKinney, Fall 2022
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# Noah L. Schrick - 1492657
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## Set Working Directory to file directory - RStudio approach
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setwd(dirname(rstudioapi::getActiveDocumentContext()$path))
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#### 0: Process and filter data
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# load gene expression data
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load("sense.filtered.cpm.Rdata") # setwd!
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# load phenotype (mdd/hc) data
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subject.attrs <- read.csv("Demographic_symptom.csv",
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stringsAsFactors = FALSE)
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if (!require("dplyr")) install.packages("dplyr")
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library(dplyr)
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# grab intersecting X (subject ids) and Diag (Diagnosis) from columns
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phenos.df <- subject.attrs %>%
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filter(X %in% colnames(sense.filtered.cpm)) %>%
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dplyr::select(X, Diag)
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mddPheno <- as.factor(phenos.df$Diag)
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# Normalized and transform
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if (!require("preprocessCore")) install.packages("preprocessCore")
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library(preprocessCore)
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mddExprData_quantile <- normalize.quantiles(sense.filtered.cpm)
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mddExprData_quantileLog2 <- log2(mddExprData_quantile)
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# attach phenotype names and gene names to data
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colnames(mddExprData_quantileLog2) <- mddPheno
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rownames(mddExprData_quantileLog2) <- rownames(sense.filtered.cpm)
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# coefficient of variation filter sd(x)/abs(mean(x))
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CoV_values <- apply(mddExprData_quantileLog2,1,
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function(x) {sd(x)/abs(mean(x))})
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# smaller threshold, the higher the experimental effect relative to the
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# measurement precision
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sum(CoV_values<.045)
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# there is one gene that has 0 variation -- remove
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sd_values <- apply(mddExprData_quantileLog2,1, function(x) {sd(x)})
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rownames(mddExprData_quantileLog2)[sd_values==0]
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# filter the data matrix
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GxS.covfilter <- mddExprData_quantileLog2[CoV_values<.045 & sd_values>0,]
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dim(GxS.covfilter)
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# convert phenotype to factor
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pheno.factor <- as.factor(colnames(GxS.covfilter))
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pheno.factor
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str(pheno.factor)
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levels(pheno.factor)
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#### Part A: Logistic Regression
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# make sure HC is the reference level
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pheno.factor.relevel <- relevel(pheno.factor,"HC")
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levels(pheno.factor.relevel)
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# also rename levels "0"/"1" from 1/2
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levels(pheno.factor.relevel)[levels(pheno.factor.relevel)=="MDD"] <- 1
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levels(pheno.factor.relevel)[levels(pheno.factor.relevel)=="HC"] <- 0
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# Fit logistic model of first gene to phenotype data
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gene.row <- 2
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gene.name <-rownames(GxS.covfilter)[gene.row]
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gene.expr <- GxS.covfilter[gene.row,]
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gene.fit <- glm(pheno.factor.relevel~gene.expr, family=binomial)
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summary(gene.fit)
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coeff.mat <- coef(summary(gene.fit))
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b0 <- coeff.mat[1,1]
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b1 <- coeff.mat[2,1]
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b1.pval <- coeff.mat[2,4]
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summary(gene.fit)
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coeff.mat <- coef(summary(gene.fit))
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b0 <- coeff.mat[1,1]
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b0
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b1
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coeff.mat
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b1.pval
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## GLM
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modelfn <- function(x){1/(1+exp(-(b0+b1*x)))}
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g.min <- min(gene.expr)
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g.max <- max(gene.expr)
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curve(modelfn,g.min,g.max) # plot for domain of actual gene’s expression
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abline(h=.5, lty=2)
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curve(modelfn,3,8) # replot with extended domain to see the S shape
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## Predict Function
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Predicted.probs <- predict(gene.fit, gene.expr=gene.expr,
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type="response")
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if (!require("ggplot2")) install.packages("ggplot2")
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library(ggplot2)
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phenotype <- pheno.factor # just rename for legend
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gene.gg.df <- data.frame(expression=gene.expr,
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prediction=predicted.probs)
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# plot predicted probabilities versus gene expression
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p <- ggplot(data=gene.gg.df)
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p <- p + geom_point(aes(x=expression,
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y=prediction,
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color=phenotype, # shape and color
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shape=phenotype), # are true phenotype
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size=3)
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p <- p + geom_hline(yintercept = .5, linetype="dashed", color="red")
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print(p)
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abline(h=.5, lty=2)
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Predicted.probs <- predict(gene.fit, gene.expr=gene.expr,
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type="response")
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if (!require("ggplot2")) install.packages("ggplot2")
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library(ggplot2)
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phenotype <- pheno.factor # just rename for legend
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gene.gg.df <- data.frame(expression=gene.expr,
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prediction=predicted.probs)
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predicted.probs <- predict(gene.fit, gene.expr=gene.expr,
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type="response")
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if (!require("ggplot2")) install.packages("ggplot2")
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library(ggplot2)
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phenotype <- pheno.factor # just rename for legend
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gene.gg.df <- data.frame(expression=gene.expr,
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prediction=predicted.probs)
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# plot predicted probabilities versus gene expression
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p <- ggplot(data=gene.gg.df)
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p <- p + geom_point(aes(x=expression,
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y=prediction,
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color=phenotype, # shape and color
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shape=phenotype), # are true phenotype
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size=3)
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p <- p + geom_hline(yintercept = .5, linetype="dashed", color="red")
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print(p)
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abline(h=.5, lty=2)
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predicted.probs <- predict(gene.fit, gene.expr=gene.expr,
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type="response")
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if (!require("ggplot2")) install.packages("ggplot2")
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library(ggplot2)
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phenotype <- pheno.factor # just rename for legend
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gene.gg.df <- data.frame(expression=gene.expr,
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prediction=predicted.probs)
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# plot predicted probabilities versus gene expression
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p <- ggplot(data=gene.gg.df)
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p <- p + geom_point(aes(x=expression,
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y=prediction,
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color=phenotype, # shape and color
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shape=phenotype), # are true phenotype
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size=3)
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p <- p + geom_hline(yintercept = .5, linetype="dashed", color="red")
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print(p)
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abline(h=.5, lty=2)
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## Predict Function
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predicted.probs <- predict(gene.fit, gene.expr=gene.expr,
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type="response")
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if (!require("ggplot2")) install.packages("ggplot2")
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library(ggplot2)
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phenotype <- pheno.factor # just rename for legend
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gene.gg.df <- data.frame(expression=gene.expr,
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prediction=predicted.probs)
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# plot predicted probabilities versus gene expression
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p <- ggplot(data=gene.gg.df)
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p <- p + geom_point(aes(x=expression,
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y=prediction,
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color=phenotype, # shape and color
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shape=phenotype), # are true phenotype
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size=3)
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p <- p + geom_hline(yintercept = .5, linetype="dashed", color="red")
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print(p)
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abline(h=.5, lty=2)
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plot(p)
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abline(h=.5, lty=2)
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print(p) + abline(h=.5, lty=2)
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# Lab 5 for the University of Tulsa's CS-6643 Bioinformatics Course
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# Gene Expression Statistical Learning
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# Professor: Dr. McKinney, Fall 2022
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# Noah L. Schrick - 1492657
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## Set Working Directory to file directory - RStudio approach
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setwd(dirname(rstudioapi::getActiveDocumentContext()$path))
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#### 0: Process and filter data
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# load gene expression data
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load("sense.filtered.cpm.Rdata") # setwd!
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# load phenotype (mdd/hc) data
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subject.attrs <- read.csv("Demographic_symptom.csv",
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stringsAsFactors = FALSE)
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if (!require("dplyr")) install.packages("dplyr")
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library(dplyr)
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# grab intersecting X (subject ids) and Diag (Diagnosis) from columns
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phenos.df <- subject.attrs %>%
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filter(X %in% colnames(sense.filtered.cpm)) %>%
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dplyr::select(X, Diag)
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mddPheno <- as.factor(phenos.df$Diag)
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# Normalized and transform
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if (!require("preprocessCore")) install.packages("preprocessCore")
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library(preprocessCore)
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mddExprData_quantile <- normalize.quantiles(sense.filtered.cpm)
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mddExprData_quantileLog2 <- log2(mddExprData_quantile)
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# attach phenotype names and gene names to data
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colnames(mddExprData_quantileLog2) <- mddPheno
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rownames(mddExprData_quantileLog2) <- rownames(sense.filtered.cpm)
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# coefficient of variation filter sd(x)/abs(mean(x))
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CoV_values <- apply(mddExprData_quantileLog2,1,
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function(x) {sd(x)/abs(mean(x))})
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# smaller threshold, the higher the experimental effect relative to the
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# measurement precision
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sum(CoV_values<.045)
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# there is one gene that has 0 variation -- remove
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sd_values <- apply(mddExprData_quantileLog2,1, function(x) {sd(x)})
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rownames(mddExprData_quantileLog2)[sd_values==0]
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# filter the data matrix
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GxS.covfilter <- mddExprData_quantileLog2[CoV_values<.045 & sd_values>0,]
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dim(GxS.covfilter)
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# convert phenotype to factor
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pheno.factor <- as.factor(colnames(GxS.covfilter))
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pheno.factor
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str(pheno.factor)
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levels(pheno.factor)
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#### Part A: Logistic Regression
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# make sure HC is the reference level
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pheno.factor.relevel <- relevel(pheno.factor,"HC")
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levels(pheno.factor.relevel)
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# also rename levels "0"/"1" from 1/2
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levels(pheno.factor.relevel)[levels(pheno.factor.relevel)=="MDD"] <- 1
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levels(pheno.factor.relevel)[levels(pheno.factor.relevel)=="HC"] <- 0
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## Fit logistic model of first gene to phenotype data
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gene.row <- 2
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gene.name <-rownames(GxS.covfilter)[gene.row]
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gene.expr <- GxS.covfilter[gene.row,]
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gene.fit <- glm(pheno.factor.relevel~gene.expr, family=binomial)
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summary(gene.fit)
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coeff.mat <- coef(summary(gene.fit))
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b0 <- coeff.mat[1,1]
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b1 <- coeff.mat[2,1]
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b1.pval <- coeff.mat[2,4]
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## GLM
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modelfn <- function(x){1/(1+exp(-(b0+b1*x)))}
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g.min <- min(gene.expr)
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g.max <- max(gene.expr)
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curve(modelfn,g.min,g.max) # plot for domain of actual gene’s expression
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abline(h=.5, lty=2)
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curve(modelfn,3,8) # replot with extended domain to see the S shape
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## Predict Function
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predicted.probs <- predict(gene.fit, gene.expr=gene.expr,
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type="response")
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if (!require("ggplot2")) install.packages("ggplot2")
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library(ggplot2)
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phenotype <- pheno.factor # just rename for legend
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gene.gg.df <- data.frame(expression=gene.expr,
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prediction=predicted.probs)
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# plot predicted probabilities versus gene expression
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p <- ggplot(data=gene.gg.df)
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p <- p + geom_point(aes(x=expression,
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y=prediction,
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color=phenotype, # shape and color
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shape=phenotype), # are true phenotype
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size=3)
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p <- p + geom_hline(yintercept = .5, linetype="dashed", color="red")
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print(p) + abline(h=.5, lty=2)
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# vector of logistic output probabilities for this model (glm/eq. above)
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# prob = .5 is the threshold for prediction class = 1 vs 0
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predicted.class <- as.integer(predicted.probs >=.5) # predicted class
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pheno.factor.relevel # true class
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# vector of True (correctly predicted) and False (wrongly predicted)
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correct.classified <- predicted.class == pheno.factor.relevel
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# sum correct.classified
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table(pheno.factor.relevel,predicted.class)
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predicted.probs
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predicted.probs[1]
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as.integer(predicted.probs[1] >= 0.5)
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# sum correct.classified
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table(pheno.factor.relevel,predicted.class)
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pheno.factor.relevel
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correct.classified
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length(correct.classified)
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sum(correct.classified == "TRUE")
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# accuracy:
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correct.acc <- sum(correct.classified == "TRUE") / length(correct.classified)
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correct.acc
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lr.fn(2)
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# logistic regression function for one gene row
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lr.fn <- function(i){
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gene=rownames(GxS.covfilter)[i]
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gene.expr <- GxS.covfilter[i,]
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gene.fit <- glm(pheno.factor.relevel~gene.expr,
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family=binomial)
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coeff.mat <- coef(summary(gene.fit))
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b1 <- coeff.mat[2,1]
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b1.pval <- coeff.mat[2,4]
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coefvec <- gene.fit$estimate # intercept, gene
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pvec <- gene.fit$p.value # intercept, gene
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c(gene, b1, b1.pval)
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}
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lr.fn(2)
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# initialize results matrix
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num.genes<-nrow(GxS.covfilter)
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lr.results.mat <- matrix(0, nrow=nrow(GxS.covfilter), ncol=3)
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# for loop the function to all genes
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for (i in 1:num.genes){
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lr.results.mat[i,] <- lr.fn(i)
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}
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lr.results.df <- data.frame(lr.results.mat)
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colnames(lr.results.df) <- c("gene", "b1", "p.val")
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# sort results b1 coefficient p-value
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library(dplyr)
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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)
|