Multioutput Gaussian processes (MOGPs) are an extension of Gaussian processes (GPs) for predicting multiple output variables (also called channels/tasks) simultaneously. In this article, we use the convolution theorem to design a new kernel for MOGPs by modeling cross-channel dependencies through cross convolution of time-and phase-delayed components in the spectral domain. The resulting kernel is called multioutput convolution spectral mixture (MOCSM) kernel. The results of extensive experiments on synthetic and real-life data sets demonstrate the advantages of the proposed kernel and its state-of-the-art performance. MOCSM enjoys the desirable property to reduce to the well-known spectral mixture (SM) kernel when a single channel is considered. A comparison with the recently introduced multioutput SM kernel reveals that this is not the case for the latter kernel, which contains quadratic terms that generate undesirable scale effects when the spectral densities of different channels are either very close or very far from each other in the frequency domain.

Multitask Gaussian processes (MTGPs) are a powerful approach for modeling dependencies between multiple related tasks or functions for joint regression. Current kernels for MTGPs cannot fully model nonlinear task correlations and other types of dependencies. In this article, we address this limitation. We focus on spectral mixture (SM) kernels and propose an enhancement of this type of kernels, called multitask generalized convolution SM (MT-GCSM) kernel. The MT-GCSM kernel can model nonlinear task correlations and dependence between components, including time and phase delay dependence. Each task in MT-GCSM has its GCSM kernel with its number of convolution structures, and dependencies between all components from different tasks are considered. Another constraint of current kernels for MTGPs is that components from different tasks are aligned. Here, we lift this constraint by using inner and outer full cross convolution between a base component and the reversed complex conjugate of another base component. Extensive experiments on two synthetic and three real-life data sets illustrate the difference between MT-GCSM and previous SM kernels as well as the practical effectiveness of MT-GCSM.

In our previous study, we introduced stable specification search for cross-sectional data (S3C). It is an exploratory causal method that combines the concept of stability selection and multi-objective optimization to search for stable and parsimonious causal structures across the entire range of model complexities. S3C, however, is designed to model causal relations among observed variables. In this study, we extended S3C to S3C-Latent, to model linear causal relations between latent variables that are measured through observed proxies. We evaluated S3C-Latent on simulated data and compared the results to those of PC-MIMBuild, an extension of the PC algorithm, the state-of-the-art causal discovery method. The comparison shows that S3C-Latent achieved better performance. We also applied S3C-Latent to real-world data of children with attention deficit/hyperactivity disorder and data about measuring mental abilities among pupils. The results are consistent with those of previous studies.

The R package stablespec is an implementation of our method stable specification search . The method aims at causal discovery on both cross-sectional and longitudinal data through stable specification search in constrained structural equation models .

Emerging domains such as smart electric grids require decisions to be made autonomously, based on the observed behaviors of large numbers of connected consumers. Existing approaches either lack the flexibility to capture nuanced, individualized preference profiles, or scale poorly with the size of the dataset. We propose a preference model that combines flexible Bayesian nonparametric priors—providing state-of-the-art predictive power—with well-justified structural assumptions that allow a scalable implementation. The Gaussian process scalable preference model via Kronecker factorization ( GaSPK ) model provides accurate choice predictions and principled uncertainty estimates as input to decision-making tasks. In consumer choice settings where alternatives are described by few key attributes, inference in our model is highly efficient and scalable to tens of thousands of choices.

We consider the problem of causal structure learning from data with missing values, assumed to be drawn from a Gaussian copula model. First, we extend the 'Rank PC' algorithm, designed for Gaussian copula models with purely continuous data (so-called nonparanormal models), to incomplete data by applying rank correlation to pairwise complete observations and replacing the sample size with an effective sample size in the conditional independence tests to account for the information loss from missing values. The resulting approach works when the data are missing completely at random (MCAR). Then, we propose a Gibbs sampling procedure to draw correlation matrix samples from mixed data under missingness at random (MAR). These samples are translated into an average correlation matrix, and an effective sample size, resulting in the 'Copula PC' algorithm for incomplete data. Simulation study shows that: 1) the usage of the effective sample size significantly improves the performance of 'Rank PC' and 'Copula PC'; 2) 'Copula PC' estimates a more accurate correlation matrix and causal structure than 'Rank PC' under MCAR and, even more so, under MAR. Also, we illustrate our methods on a real-world data set about gene expression.

This paper presents a framework for optimizing the preference learning process. In many real-world applications in which preference learning is involved the available training data is scarce and obtaining labeled training data is expensive. Fortunately in many of the preference learning situations data is available from multiple subjects. We use the multi-task formalism to enhance the individual training data by making use of the preference information learned from other subjects. Furthermore, since obtaining labels is expensive, we optimally choose which data to ask a subject for labelling to obtain the most of information about her/his preferences. This paradigm—called active learning—has hardly been studied in a multi-task formalism. We propose an alternative for the standard criteria in active learning which actively chooses queries by making use of the available preference data from other subjects. The advantage of this alternative is the reduced computation costs and reduced time subjects are involved. We validate empirically our approach on three real-world data sets involving the preferences of people.

A probabilistic kernel approach to pairwise preference learning based on Gaussian processes is applied to predict preference judgments for sound quality degradation mechanisms that might be present in a hearing aid. Subjective sound quality comparisons for 14 normal-hearing and 18 hearing-impaired subjects were used for evaluating the predictive performance. Stimuli were sentences subjected to three kinds of distortion (additive noise, peak clipping, and center clipping) with eight levels of degradation for each distortion type. The kernel approach gives a significant improvement in preference predictions of hearing-impaired subjects by individualizing the learning process. A significant difference is shown between normal-hearing and hearing-impaired subjects, because of nonlinearities in the perception of hearing-impaired subjects. In particular, hearing-impaired subjects have significant nonlinear preference judgments when making pairwise comparisons between peak clipped sentences with different clipping thresholds. The probabilistic kernel approach is shown to be robust when generalizing over distortions and over subjects.

The application of a medical guideline to the treatment of a patient's disease can be seen as the execution of tasks, sequentially or in parallel, in the face of patient data. It has been shown that many of such guidelines can be represented as a "network of tasks," that is, as a sequence of steps that have a specific function or goal. In this paper, a novel methodology for verifying the quality of such guidelines is introduced. To investigate the quality of such guidelines, we propose to include medical background knowledge to task networks and to formalize criteria for good medical practice that a guideline should comply with. This framework was successfully applied to a guideline dealing with the management of diabetes mellitus type 2 by using KIV.