# fchamroukhi/tMoE_m

Robust Mixtures-of-Experts modelling using the t distribution for clustering and non-linear regression for heteregenous data
MATLAB
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IRLS.m
MAP.m
designmatrix_Poly_Reg.m
initialize_univ_NMoE.m
learn_TMoE_EM.m
learn_univ_NMoE_EM.m
main_demo_TMoE_RealData.m
main_demo_TMoE_SimulatedData.m
main_demo_TMoE_SimulatedData.m~
multinomial_logit.m
sample_univ_T.m
sample_univ_TMoE.m
show_TMoE_results.m

t mixture of experts (TMoE): Robust mixtures-of-experts modeling using the t distribution <<

TMoE : A Matlab/Octave toolbox for modeling, sampling, inference, regression and clustering of heterogeneous data with the t Mixture-of-Experts (TMoE) model.

TMoE provides a flexible and robust modeling framework for heterogenous data with possibly heavy-tailed distributions and corrupted by atypical observations. TMoE consists of a mixture of K t expert regressors network (of degree p) gated by a softmax gating network (with regression degree q) and is represented by - The gating net. parameters $\alpha$'s of the softmax net. - The experts network parameters: The location parameters (regression coefficients) $\beta$'s, scale parameters $\sigma$'s, and the degree of freedom (robustness) parameters $\nu$'s. TMoE thus generalises mixtures of (normal, t, and) distributions and mixtures of regressions with these distributions. For example, when $q=0$, we retrieve mixtures of (t-, or normal) regressions, and when both $p=0$ and $q=0$, it is a mixture of (t-, or normal) distributions. It also reduces to the standard (normal, 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. Real-world data examples of tone perception for musical data analysis, and the one of temperature anomalies for the analysis of climate change data, are also provided as application of the model.

To run it on the provided examples, please run "main_demo_TMoE_SimulatedData.m" or "main_demo_TMoE_RealData.m"

Please cite the code and the following papers when using this code:

• F. Chamroukhi. Robust mixture of experts modeling using the $t$-distribution. Neural Networks, V. 79, p:20?36, 2016
• F. Chamroukhi. Non-Normal Mixtures of Experts. arXiv:1506.06707, July, 2015

(c) Introduced and written by Faicel Chamroukhi (may 2015)

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