In fchamroukhi/SNMoE: Skew-Normal Mixture-of-Experts for Clustering Heterogeneous Non-Normal Data

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Overview

SNMoE (Skew-Normal Mixtures-of-Experts) provides a flexible modelling framework for heterogenous data with possibly skewed distributions to generalize the standard Normal mixture of expert model. SNMoE consists of a mixture of K skew-Normal 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, and the skewness parameters lambda's. SNMoE thus generalises mixtures of (normal, skew-normal) distributions and mixtures of regressions with these distributions. For example, when $q=0$, we retrieve mixtures of (skew-normal, or normal) regressions, and when both $p=0$ and $q=0$, it is a mixture of (skew-normal, or normal) distributions. It also reduces to the standard (normal, skew-normal) 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 SNMoE from GitHub with:

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

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

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

Use the following command to display vignettes:

browseVignettes("SNMoE")

Usage

library(SNMoE)

# Application 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
lambdak <- c(3, 5) # Skewness parameters of the experts
sigmak <- c(1, 1) # Standard deviations of the experts
x <- seq.int(from = -1, to = 1, length.out = n) # Inputs (predictors)

# Generate sample of size n
sample <- sampleUnivSNMoE(alphak = alphak, betak = betak, 
                          sigmak = sigmak, lambdak = lambdak, 
                          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)

snmoe <- emSNMoE(X = x, Y = y, K = K, p = p, q = q, verbose = TRUE)

snmoe$summary()

snmoe$plot()

# Application to a real data set

data("tempanomalies")
x <- tempanomalies$Year
y <- tempanomalies$AnnualAnomaly

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

snmoe <- emSNMoE(X = x, Y = y, K = K, p = p, q = q, verbose = TRUE)

snmoe$summary()

snmoe$plot()

fchamroukhi/SNMoE documentation built on Sept. 23, 2019, 11:25 a.m.