Kernel methods are among the most popular techniques in machine learning. From a frequentist/discriminative perspective they play a central role in regularization theory as they provide a natural choice for the hypotheses space and the regularization functional through the notion of reproducing kernel Hilbert spaces. From a Bayesian/generative perspective they are the key in the context of Gaussian processes, where the kernel function is also known as the covariance function. Traditionally, kernel methods have been used in supervised learning problem with scalar outputs and indeed there has been a considerable amount of work devoted to designing and learning kernels. More recently there has been an increasing interest in methods that deal with multiple outputs, motivated partly by frameworks like multitask learning. In this paper, we review different methods to design or learn valid kernel functions for multiple outputs, paying particular attention to the connection between probabilistic and functional methods.

Mammalian cochlear inner hair cells (IHCs) are specialized to process developmental signals during immature stages and sound stimuli in adult animals. These signals are conveyed onto auditory afferent nerve fibres. Neurotransmitter release at IHC ribbon synapses is controlled by L-type CaV1.3 Ca2+ channels, the biophysics of which are still unknown in native mammalian cells. We have investigated the localization and elementary properties of Ca2+ channels in immature mouse IHCs under near-physiological recording conditions. CaV1.3 Ca2+ channels at the cell pre-synaptic site co-localize with about half of the total number of ribbons present in immature IHCs. These channels activated at about −70 mV, showed a relatively short first latency and weak inactivation, which would allow IHCs to generate and accurately encode spontaneous Ca2+ action potential activity characteristic of these immature cells. The CaV1.3 Ca2+ channels showed a very low open probability (about 0.15 at −20 mV: near the peak of an action potential). Comparison of elementary and macroscopic Ca2+ currents indicated that very few Ca2+ channels are associated with each docked vesicle at IHC ribbon synapses. Finally, we found that the open probability of Ca2+ channels, but not their opening time, was voltage dependent. This finding provides a possible correlation between presynaptic Ca2+ channel properties and the characteristic frequency/amplitude of EPSCs in auditory afferent fibres.

The Gaussian process latent variable model (GP-LVM) is a generative approach to nonlinear low dimensional embedding, that provides a smooth probabilistic mapping from latent to data space. It is also a non-linear generalization of probabilistic PCA (PPCA) (Tipping & Bishop, 1999). While most approaches to non-linear dimensionality methods focus on preserving local distances in data space, the GP-LVM focusses on exactly the opposite. Being a smooth mapping from latent to data space, it focusses on keeping things apart in latent space that are far apart in data space. In this paper we first provide an overview of dimensionality reduction techniques, placing the emphasis on the kind of distance relation preserved. We then show how the GP-LVM can be generalized, through back constraints, to additionally preserve local distances. We give illustrative experiments on common data sets.

Expression quantitative trait loci (eQTL) studies are an integral tool to investigate the genetic component of gene expression variation. A major challenge in the analysis of such studies are hidden confounding factors, such as unobserved covariates or unknown subtle environmental perturbations. These factors can induce a pronounced artifactual correlation structure in the expression profiles, which may create spurious false associations or mask real genetic association signals. Here, we report PANAMA (Probabilistic ANAlysis of genoMic dAta), a novel probabilistic model to account for confounding factors within an eQTL analysis. In contrast to previous methods, PANAMA learns hidden factors jointly with the effect of prominent genetic regulators. As a result, this new model can more accurately distinguish true genetic association signals from confounding variation. We applied our model and compared it to existing methods on different datasets and biological systems. PANAMA consistently performs better than alternative methods, and finds in particular substantially more trans regulators. Importantly, our approach not only identifies a greater number of associations, but also yields hits that are biologically more plausible and can be better reproduced between independent studies. A software implementation of PANAMA is freely available online at http://ml.sheffield.ac.uk/qtl/.

A consistent clinical feature of amyotrophic lateral sclerosis (ALS) is the sparing of eye movements and the function of external sphincters, with corresponding preservation of motor neurons in the brainstem oculomotor nuclei, and of Onuf’s nucleus in the sacral spinal cord. Studying the differences in properties of neurons that are vulnerable and resistant to the disease process in ALS may provide insights into the mechanisms of neuronal degeneration, and identify targets for therapeutic manipulation. We used microarray analysis to determine the differences in gene expression between oculomotor and spinal motor neurons, isolated by laser capture microdissection from the midbrain and spinal cord of neurologically normal human controls. We compared these to transcriptional profiles of oculomotor nuclei and spinal cord from rat and mouse, obtained from the GEO omnibus database. We show that oculomotor neurons have a distinct transcriptional profile, with significant differential expression of 1,757 named genes (q < 0.001). Differentially expressed genes are enriched for the functional categories of synaptic transmission, ubiquitin-dependent proteolysis, mitochondrial function, transcriptional regulation, immune system functions, and the extracellular matrix. Marked differences are seen, across the three species, in genes with a function in synaptic transmission, including several glutamate and GABA receptor subunits. Using patch clamp recording in acute spinal and brainstem slices, we show that resistant oculomotor neurons show a reduced AMPA-mediated inward calcium current, and a higher GABA-mediated chloride current, than vulnerable spinal motor neurons. The findings suggest that reduced susceptibility to excitotoxicity, mediated in part through enhanced GABAergic transmission, is an important determinant of the relative resistance of oculomotor neurons to degeneration in ALS.Electronic supplementary materialThe online version of this article (doi:10.1007/s00401-012-1058-5) contains supplementary material, which is available to authorized users.