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# Using the CAVI algorithm on a (Bayesian) GMM example

library(mvtnorm)    # for multivariate normal density
library(extraDistr) # for Categorical distribution
library(pracma)     # for 2d-integral, sqrtm
library(matlib)     # for solving linear equations
library(ggplot2)    # for plotting

# Hyper Parameters
sigma = 3   # Variance of mu

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# Expectation Maximization - Gaussian Mixture Model 

library(ks)         # for kde
library(mvtnorm)    # for MVNormal
library(extraDistr) # for Categorical & Dirichlet distribution
library(ggplot2)    # for plotting
library(pracma)     # for sqrtm

######################
#  1D, 2-components  #

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library(gganimate)
library(plotly)

###########
# General #
###########
# Set the Kenrel function
# Uniform Kernel
f = function(u) as.numeric((u<=0.5) & (u>=-0.5))
# Normal Kernel

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