In fchamroukhi/StMoE: Skew-t Mixture-of-Experts: Robust Clustering of Complex Heterogeneous Non-Normal Data

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>",
  fig.align = "center",
  fig.path = "man/figures/README-"
)

Overview

StMoE (Skew-t Mixture-of-Experts) provides a flexible and robust modelling framework for heterogenous data with possibly skewed, heavy-tailed distributions and corrupted by atypical observations. StMoE consists of a mixture of K skew-t expert regressors network (of degree p) gated by a softmax gating network (of degree q) and is represented by:

• The gating network parameters alpha's of the softmax net.
• The experts network parameters: The location parameters (regression coefficients) beta's, scale parameters sigma's, the skewness parameters lambda's and the degree of freedom parameters nu's. StMoE thus generalises mixtures of (normal, skew-normal, t, and skew-t) distributions and mixtures of regressions with these distributions. For example, when $q=0$, we retrieve mixtures of (skew-t, t-, skew-normal, or normal) regressions, and when both $p=0$ and $q=0$, it is a mixture of (skew-t, t-, skew-normal, or normal) distributions. It also reduces to the standard (normal, skew-normal, t, and skew-t) distribution when we only use a single expert ($K=1$).

Model estimation/learning is performed by a dedicated expectation conditional maximization (ECM) algorithm by maximizing the observed data log-likelihood. We provide simulated examples to illustrate the use of the model in model-based clustering of heterogeneous regression data and in fitting non-linear regression functions.

Installation

You can install the development version of StMoE from GitHub with:

# install.packages("devtools")
devtools::install_github("fchamroukhi/StMoE")

To build vignettes for examples of usage, type the command below instead:

# install.packages("devtools")
devtools::install_github("fchamroukhi/StMoE", 
                         build_opts = c("--no-resave-data", "--no-manual"), 
                         build_vignettes = TRUE)

Use the following command to display vignettes:

browseVignettes("StMoE")

Usage

library(StMoE)

# Applicartion to a simulated data set

n <- 500 # Size of the sample
alphak <- matrix(c(0, 8), ncol = 1) # Parameters of the gating network
betak <- matrix(c(0, -2.5, 0, 2.5), ncol = 2) # Regression coefficients of the experts
sigmak <- c(0.5, 0.5) # Standard deviations of the experts
lambdak <- c(3, 5) # Skewness parameters of the experts
nuk <- c(5, 7) # Degrees of freedom of the experts network t densities
x <- seq.int(from = -1, to = 1, length.out = n) # Inputs (predictors)

# Generate sample of size n
sample <- sampleUnivStMoE(alphak = alphak, betak = betak, 
                          sigmak = sigmak, lambdak = lambdak, 
                          nuk = nuk, x = x)
y <- sample$y

K <- 2 # Number of regressors/experts
p <- 1 # Order of the polynomial regression (regressors/experts)
q <- 1 # Order of the logistic regression (gating network)

stmoe <- emStMoE(X = x, Y = y, K = K, p = p, q = q, verbose = TRUE)

stmoe$summary()

stmoe$plot()

# Applicartion to a real data set

library(MASS)
data("mcycle")
x <- mcycle$times
y <- mcycle$accel

K <- 4 # Number of regressors/experts
p <- 2 # Order of the polynomial regression (regressors/experts)
q <- 1 # Order of the logistic regression (gating network)

stmoe <- emStMoE(X = x, Y = y, K = K, p = p, q = q, verbose = TRUE)

stmoe$summary()

stmoe$plot()

fchamroukhi/StMoE documentation built on Jan. 11, 2020, 4:23 p.m.