We present a probabilistic kernel approach to ordinal regression based on Gaussian processes. A threshold model that generalizes the probit function is used as the likelihood function for ordinal variables. Two inference techniques, based on the Laplace approximation and the expectation propagation algorithm respectively, are derived for hyperparameter learning and model selection. We compare t...

The Perceptron algorithm elegantly solves binary classification problems that have a margin between positive and negative examples. Isotonic regression (fitting an arbitrary increasing function in one dimension) is also a natural problem with a simple solution. By combining the two, we get a new but very simple algorithm with strong guarantees. Our ISOTRON algorithm provably learns Single Index...

We consider model selection in a hierarchical Bayes formulation of the sparse normal linear model in which individual variables have, independently, an unknown prior probability of being included in the model. The focus is on orthogonal designs, which are of particular importance in nonparametric regression via wavelet shrinkage. Empirical Bayes estimates of hyperparameters are easily obtained ...

Epidemiologists frequently encounter studies with ordered responses. Standard ordered response logit models, such as the continuation ratio model, constrain exposure to have a homogeneous effect across thresholds of the ordered response. We demonstrate a method for fitting regression models for unconstrained, partially or fully constrained continuation odds ratios using a 'person-threshold' dat...

In this research genetic and phenotypic parameters were estimated using linear and threshold models, for reproductive traits, data from 6 large industrial dairy herd of East Azerbaijan province collected by Agriculture Jihad Organization during 10 years (2001-2010). Best linear unbiased predictions of traits breeding values were estimated using Restricted Maximum Likelihood method by WOMBAT sof...