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| library(mvtnorm) | |
| library(ggplot2) | |
| library(MCMCpack) | |
| expected_task <- list(mean=3,sd=2) | |
| hyper_parameters <- list(alpha=1, beta=1) | |
| data_samples = rnorm(100,6,3) | |
| random_samples <- rnorm(100,20,5) | |
| find_likelyhood <- function(target_model, target) { | |
| return(dnorm(target,target_model$mean, target_model$sd)) | |
| } | |
| parameter_log_likelyhood <- function(data_samples, prior_model, target_model) { | |
| likely_hood = 0 | |
| log_prior = log((dnorm(target_model$mean, prior_model$mean, prior_model$sd))) | |
| for(index in 1:length(data_samples)) { | |
| sample <- find_likelyhood(target_model, data_samples[index]) | |
| likely_hood = log(sample) + likely_hood | |
| } | |
| return (likely_hood + log_prior) | |
| } | |
| new_sd_based_on_mean <- function(data_samples, target_model, hyper_parameter) { | |
| mean_sum = 0 | |
| for(index in 1:length(data_samples)) { | |
| mean_sum = mean_sum + (data_samples[index] - target_model$mean) | |
| } | |
| mean_sum = mean_sum /2 | |
| alpha = hyper_parameter$alpha + (length(data_samples)/2) | |
| beta = hyper_parameter$beta + mean_sum | |
| if(beta < 1) { | |
| target_model$sd = 1 | |
| target_model$mean = target_model$mean + target_model$sd | |
| return(target_model) | |
| } | |
| target_model$sd = (rinvgamma(1, alpha, beta)) | |
| target_model$mean = target_model$mean + target_model$sd | |
| return(target_model) | |
| } | |
| find_map <- function(data_samples, prior, hyper_parameters, iter=100, max_jump = 1) { | |
| ret_val <- prior | |
| best_log = -999999 | |
| for(iteration in 1:iter) { | |
| permute <- ret_val | |
| #Change mean | |
| if(sample(0:1,1) == 0) { | |
| permute$mean = permute$mean - runif(1,0,max_jump) | |
| } else { | |
| permute$mean = permute$mean + runif(1,0,max_jump) | |
| } | |
| #Change sd based on new mean | |
| permute = new_sd_based_on_mean(data_samples, permute, hyper_parameters) | |
| if(permute$sd > 0 && permute$mean >= 1) { | |
| current_log = parameter_log_likelyhood(data_samples, prior, permute) | |
| if(is.nan(as.numeric(current_log)) == FALSE) { | |
| if(current_log > best_log) { | |
| best_log = current_log | |
| ret_val = permute | |
| } | |
| } | |
| } | |
| } | |
| return(ret_val) | |
| } | |
| optimise_map <- function(data_set, starting_prior , hyper_parameters,jump_factor=5, iter=100) { | |
| ret_val <- starting_prior | |
| best_log = -999999 | |
| for(iteration in 1:iter) { | |
| test_model <- find_map(data_set, ret_val, hyper_parameters, 100, jump_factor) | |
| score = parameter_log_likelyhood(data_set, ret_val, test_model) | |
| if(score > best_log) { | |
| ret_val <- test_model | |
| } | |
| } | |
| return(ret_val) | |
| } | |
| find_model_map <- function(data_set, prior) { | |
| model_1_data <- subset(data_set, y==1, select=c(x1,x2)) | |
| model_2_data <- subset(data_set, y==-1, select=c(x1,x2)) | |
| model_1_data.x1.data <- model_1_data$x1 | |
| model_1_data.x2.data <- model_1_data$x2 | |
| model_2_data.x1.data <- model_2_data$x1 | |
| model_2_data.x2.data <- model_2_data$x2 | |
| model_1_data.x1.map <- optimise_map(model_1_data.x1.data,prior,hyper_parameters) | |
| model_1_data.x2.map <- optimise_map(model_1_data.x2.data,prior,hyper_parameters) | |
| model_2_data.x1.map <- optimise_map(model_2_data.x1.data,prior,hyper_parameters) | |
| model_2_data.x2.map <- optimise_map(model_2_data.x2.data,prior,hyper_parameters) | |
| ret_val <- list(m1.x1.map=model_1_data.x1.map, m1.x2.map=model_1_data.x2.map , | |
| m2.x1.map=model_2_data.x1.map, m2.x2.map=model_2_data.x2.map ) | |
| return(ret_val) | |
| } | |
| cov_matrix_optimiser <- function(model_data, x1_map, x2_map, iter=1000) { | |
| mu0 = runif(1,-5,5) | |
| b_mu = mu0 | |
| cov_matrix_m1 <- matrix(c(x1_map$sd, mu0, mu0, x2_map$sd), nrow=2) | |
| mean_vector_m1 <-c(x1_map$mean, x2_map$mean) | |
| best_log = -999999 | |
| best_matrix <- c() | |
| for(iteration in 1:iter) { | |
| #find the loglikelyhood for this dataset | |
| current_log = 0 | |
| for(index in 1:nrow(model_data)){ | |
| point_vector = c(model_data$x1[index],model_data$x2[index]) | |
| current_log = current_log + log(dmvnorm(point_vector,mean_vector_m1,cov_matrix_m1)) | |
| } | |
| if(current_log > best_log) { | |
| best_log = current_log | |
| best_matrix = cov_matrix_m1 | |
| b_mu = mu0 | |
| } | |
| #Mutate MC | |
| mu0 = b_mu + runif(1,-10,10) | |
| cov_matrix_m1 <- matrix(c(x1_map$sd, mu0, mu0, x2_map$sd), nrow=2) | |
| } | |
| #print("Best Cov Matrix: ") | |
| #print(best_matrix) | |
| return(best_matrix) | |
| } | |
| train_bayes <- function(data_set) { | |
| model_1_data <- subset(data_set, y==1, select=c(x1,x2)) | |
| model_2_data <- subset(data_set, y==-1, select=c(x1,x2)) | |
| model <- find_model_map(data_set, expected_task) | |
| mean_vector_m1 <-c(model$m1.x1.map$mean, model$m1.x2.map$mean) | |
| mean_vector_m2 <-c(model$m2.x1.map$mean, model$m2.x2.map$mean) | |
| cov_m1 <- cov_matrix_optimiser(model_1_data, model$m1.x1.map, model$m1.x2.map) | |
| cov_m2 <- cov_matrix_optimiser(model_2_data, model$m2.x1.map, model$m2.x2.map) | |
| # calculate predictions: | |
| predict <- function(T) { | |
| return (ifelse( | |
| dmvnorm(x=T, mean=mean_vector_m1, sigma=cov_m1) > dmvnorm(x=T, mean=mean_vector_m2, sigma=cov_m2), | |
| 1, | |
| -1)) | |
| } | |
| return (list("predict"=predict)) | |
| } | |
| classification_error_func <- function(T_hat, T) { | |
| return (sum(T_hat!=T)/nrow(T_hat) * 100) | |
| } |
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