Abstract
We propose a robust task learning method based on nonlinear regression model with mixtures of t-distributions. The model can adaptively reduce the effects of complex noises and accurately learn the nonlinear structure of targets. By introducing latent variables, the model is expressed into a hierarchical structure, which helps explain the advantage of flexibility compared to the traditional Gaussian based learning model. We develop a two-stage efficient estimation procedure to obtain penalized likelihood estimator of the parameters combined an expectation-maximization algorithm with Lagrange multiplier method. The learning performances of the model are investigated through experiments on both synthetic and real data sets.
Highlights
Statistical regression is one of the important methods in task learning
We propose to use mixture of t-distributions, or MoT, in this paper since MoT can enhance the robustness while inherits most of the advantages of Gaussian distribution
The specific learning procedure of MoT BASED MULTI-TASK REGRESSION (MoT-MTR) is similar to Algorithm 1, but the corresponding updating formulas should be replaced by the ones above
Summary
Statistical regression is one of the important methods in task learning. Traditional regression models are established under the assumption of normality. C. Cao et al.: Robust Task Learning Based on Nonlinear Regression With Mixtures of Student-t Distributions which can avoid the computational complexity caused by high dimensional approximation. In the new MoT model, the distribution parameters and hyper parameters are shared among tasks which can effectively reduce the risk of overfitting. This design is effective when some tasks have insufficient information or there are outliers in sparse areas. To develop a robust and adaptive approach, we may use a heavy-tailed distribution; i.e., we assume that ε follows a heavy-tailed distribution with probability distribution function (pdf) p(ε) and the regression coefficient w has a prior π (w). We propose to use mixture of t-distributions, or MoT, in this paper since MoT can enhance the robustness while inherits most of the advantages of Gaussian distribution
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