Learning the kernel matrix with semidefinite programming

Kernel-based learning algorithms work by embedding the data into a Euclidean space, and then searching for linear relations among the embedded data points. The embedding is performed implicitly, by specifying the inner products between each pair of points in the embedding space. This information is contained in the so-called kernel matrix, a symmetric and positive semidefinite matrix that encodes the relative positions of all points. Specifying this matrix amounts to specifying the geometry of the embedding space and inducing a notion of similarity in the input space - classical model selection problems in machine learning. In this paper we show how the kernel matrix can be learned from data via semidefinite programming (SDP) techniques. When applied to a kernel matrix associated with both training and test data this gives a powerful transductive algorithm -using the labeled part of the data one can learn an embedding also for the unlabeled part. The similarity between test points is inferred from training points and their labels. Importantly, these learning problems are convex, so we obtain a method for learning both the model class and the function without local minima. Furthermore, this approach leads directly to a convex method for learning the 2-norm soft margin parameter in support vector machines, solving an important open problem.

Matrix regularization techniques for online multitask learning

In this paper we examine the problem of prediction with expert advice in a setup where the learner is presented with a sequence of examples coming from different tasks. In order for the learner to be able to benefit from performing multiple tasks simultaneously, we make assumptions of task relatedness by constraining the comparator to use a lesser number of best experts than the number of tasks. We show how this corresponds naturally to learning under spectral or structural matrix constraints, and propose regularization techniques to enforce the constraints. The regularization techniques proposed here are interesting in their own right and multitask learning is just one application for the ideas. A theoretical analysis of one such regularizer is performed, and a regret bound that shows benefits of this setup is reported.

Learning the Kernel Matrix with Semi-Definite Programming

Kernel-based learning algorithms work by embedding the data into a Euclidean space, and then searching for linear relations among the embedded data points. The embedding is performed implicitly, by specifying the inner products between each pair of points in the embedding space. This information is contained in the so-called kernel matrix, a symmetric and positive definite matrix that encodes the relative positions of all points. Specifying this matrix amounts to specifying the geometry of the embedding space and inducing a notion of similarity in the input space -- classical model selection problems in machine learning. In this paper we show how the kernel matrix can be learned from data via semi-definite programming (SDP) techniques. When applied to a kernel matrix associated with both training and test data this gives a powerful transductive algorithm -- using the labelled part of the data one can learn an embedding also for the unlabelled part. The similarity between test points is inferred from training points and their labels. Importantly, these learning problems are convex, so we obtain a method for learning both the model class and the function without local minima. Furthermore, this approach leads directly to a convex method to learn the 2-norm soft margin parameter in support vector machines, solving another important open problem. Finally, the novel approach presented in the paper is supported by positive empirical results.

Inhibition of p38 pathway leads to OA-like changes in a rat animal model

Objectives The p38 mitogen-activated protein kinase (MAPK) signal transduction pathway is involved in a variety of inflammatory responses, including cytokine generation, cell differentiation proliferation and apoptosis. Here, we examined the effects of systemic p38 MAPK inhibition on cartilage cells and osteoarthritis (OA) disease progression by both in vitro and in vivo approaches. Methods p38 kinase activity was evaluated in normal and OA cartilage cells by measuring the amount of phosphorylated protein. To examine the function of p38 signaling pathway in vitro, normal chondrocytes were isolated and differentiated in the presence or absence of p38 inhibitor; SB203580 and analysed for chondrogenic phenotype. Effect of systemic p38 MAPK inhibition in normal and OA (induced by menisectomy) rats were analysed by treating animals with vehicle alone (DMS0) or p38 inhibitor (SB203580). Damage to the femur and tibial plateau was evaluated by modified Mankin score, histology and immunohistochemistry. Results Our in vitro studies have revealed that a down-regulation of chondrogenic and increase of hypertrophic gene expression occurs in the normal chondrocytes, when p38 is neutralized by a pharmacological inhibitor. We further observed that the basal levels of p38 phosphorylation were decreased in OA chondrocytes compared with normal chondrocytes. These findings together indicate the importance of this pathway in the regulation of cartilage physiology and its relevance to OA pathogenesis. At in vivo level, systematic administration of a specific p38 MAPK inhibitor, SB203580, continuously for over a month led to a significant loss of proteoglycan; aggrecan and cartilage thickness. On the other hand, SB203580 treated normal rats showed a significant increase in TUNEL positive cells, cartilage hypertrophy markers such as Type 10 collagen, Runt-related transcription factor and Matrix metalloproteinase-13 and substantially induced OA like phenotypic changes in the normal rats. In addition, menisectomy induced OA rat models that were treated with p38 inhibitor showed aggravation of cartilage damage. Conclusions In summary, this study has provided evidence that the component of the p38 MAPK pathway is important to maintain the cartilage health and its inhibition can lead to severe cartilage degenerative changes. The observations in this study highlight the possibility of using activators of the p38 pathway as an alternative approach in the treatment of OA.

Extracellular matrix of the human cyclic corpus luteum

Extracellular matrix regulates many cellular processes likely to be important for development and regression of corpora lutea. Therefore, we identified the types and components of the extracellular matrix of the human corpus luteum at different stages of the menstrual cycle. Two different types of extracellular matrix were identified by electron microscopy; subendothelial basal laminas and an interstitial matrix located as aggregates at irregular intervals between the non-vascular cells. No basal laminas were associated with luteal cells. At all stages, collagen type IV α1 and laminins α5, β2 and γ1 were localized by immunohistochemistry to subendothelial basal laminas, and collagen type IV α1 and laminins α2, α5, β1 and β2 localized in the interstitial matrix. Laminin α4 and β1 chains occurred in the subendothelial basal lamina from mid-luteal stage to regression; at earlier stages, a punctate pattern of staining was observed. Therefore, human luteal subendothelial basal laminas potentially contain laminin 11 during early luteal development and, additionally, laminins 8, 9 and 10 at the mid-luteal phase. Laminin α1 and α3 chains were not detected in corpora lutea. Versican localized to the connective tissue extremities of the corpus luteum. Thus, during the formation of the human corpus luteum, remodelling of extracellular matrix does not result in basal laminas as present in the adrenal cortex or ovarian follicle. Instead, novel aggregates of interstitial matrix of collagen and laminin are deposited within the luteal parenchyma, and it remains to be seen whether this matrix is important for maintaining the luteal cell phenotype.

Homodimerization controls the fibroblast growth factor 9 subfamily's receptor binding and heparan sulfate-dependent diffusion in the extracellular matrix

Uncontrolled fibroblast growth factor (FGF) signaling can lead to human diseases, necessitating multiple layers of self-regulatory control mechanisms to keep its activity in check. Herein, we demonstrate that FGF9 and FGF20 ligands undergo a reversible homodimerization, occluding their key receptor binding sites. To test the role of dimerization in ligand autoinhibition, we introduced structure-based mutations into the dimer interfaces of FGF9 and FGF20. The mutations weakened the ability of the ligands to dimerize, effectively increasing the concentrations of monomeric ligands capable of binding and activating their cognate FGF receptor in vitro and in living cells. Interestingly, the monomeric ligands exhibit reduced heparin binding, resulting in their increased radii of heparan sulfate-dependent diffusion and biologic action, as evidenced by the wider dilation area of ex vivo lung cultures in response to implanted mutant FGF9-loaded beads. Hence, our data demonstrate that homodimerization autoregulates FGF9 and FGF20's receptor binding and concentration gradients in the extracellular matrix. Our study is the first to implicate ligand dimerization as an autoregulatory mechanism for growth factor bioactivity and sets the stage for engineering modified FGF9 subfamily ligands, with desired activity for use in both basic and translational research.