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 these two Gaussian process approaches with a previous ordinal regression method based on support vector machines on some benchmark and real-world data sets, including applications of ordinal regression to collaborative filtering and gene expression analysis. Experimental results on these data sets verify the usefulness of our approach.

The linear model with sparsity-favouring prior on the coefficients has important applications in many different domains. In machine learning, most methods to date search for maximum a posteriori sparse solutions and neglect to represent posterior uncertainties. In this paper, we address problems of Bayesian optimal design (or experiment planning), for which accurate estimates of uncertainty are essential. To this end, we employ expectation propagation approximate inference for the linear model with Laplace prior, giving new insight into numerical stability properties and proposing a robust algorithm. We also show how to estimate model hyperparameters by empirical Bayesian maximisation of the marginal likelihood, and propose ideas in order to scale up the method to very large underdetermined problems. We demonstrate the versatility of our framework on the application of gene regulatory network identification from micro-array expression data, where both the Laplace prior and the active experimental design approach are shown to result in significant improvements. We also address the problem of sparse coding of natural images, and show how our framework can be used for compressive sensing tasks. Part of this work appeared in Seeger et al. (2007b). The gene network identification application appears in Steinke et al. (2007).

Logit models are often used to analyze experimental data. However, randomization does not justify the model, and estimators may be inconsistent. Here, Neyman’s non-parametric setup is used as a benchmark. Each subject has two potential responses, one if treated and the other if untreated; only one of the two responses is observed. A consistent estimator is proposed for use with the logit model. There is a brief literature review, and some recommendations for practice.

This paper develops an asymptotic theory for time series binary choice models with nonstationary explanatory variables generated as integrated processes. Both logit and probit models are covered. The maximum likelihood Ž ML. estimator is consistent but a new phenomenon arises in its limit distribution theory. The estimator consists of a mixture of two components, one of which is parallel to and the other orthogonal to the direction of the true parameter vector, with the latter being the principal component. The ML estimator is shown to converge at a rate of n3�4 along its principal component but has the slower rate of n1�4 convergence in all other directions. This is the first instance known to the authors of multiple convergence rates in models where the regressors have the same Ž full rank. stochastic order and where the parameters appear in linear forms of these regressors. It is a consequence of the fact that the estimating equations involve nonlinear integrable transformations of linear forms of integrated processes as well as polynomials in these processes, and the asymptotic behavior of these elements is quite

We detail the basic theory for models of discrete choice. This encompasses methods of estimation and analysis of models with discrete dependent variables. Entry level theory is presented for the practitioner. We then describe a few of the recent, frontier developments in theory and practice. Contents

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of ordinal data with cumulative link models —

Abstract. Current status data arise in studies where the target measurement is the time of occurrence of some event, but observations are limited to indicators of whether or not the event has occurred at the time the sample is collected- only the current status of each individual with respect to event occurrence is observed. Examples of such data arise in several fields, including demography, epidemiology, econometrics and bioassay. Although estimation of the marginal distribution of times of event occurrence is well understood, techniques for incorporating covariate information are not well developed. This paper proposes a semiparametric approach to estimation for regression models of current status data, using techniques from generalized additive modeling and isotonic regression. This procedure provides simultaneous estimates of the baseline distribution of event times and covariate effects. No parametric assumptions about the form of the baseline distribution are required. The results are illustrated using data from a demographic survey of breastfeeding practices in developing countries, and from an epidemiological study of heterosexual Human Immunodeficiency Virus (HIV) transmission.

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