The Gaussian process latent variable model (GP-LVM) provides a flexible approach for non-linear dimensionality reduction that has been widely applied. However, the current approach for training GP-LVMs is based on maximum likelihood, where the latent projection variables are maximized over rather than integrated out. In this paper we present a Bayesian method for training GP-LVMs by introducing a non-standard variational inference framework that allows to approximately integrate out the latent variables and subsequently train a GP-LVM by maximizing an analytic lower bound on the exact marginal likelihood. We apply this method for learning a GP-LVM from iid observations and for learning non-linear dynamical systems where the observations are temporally correlated. We show that a benefit of the variational Bayesian procedure is its robustness to overfitting and its ability to automatically select the dimensionality of the nonlinear latent space. The resulting framework is generic, flexible and easy to extend for other purposes, such as Gaussian process regression with uncertain inputs and semi-supervised Gaussian processes. We demonstrate our method on synthetic data and standard machine learning benchmarks, as well as challenging real world datasets, including high resolution video data.

Many diseases cause significant changes to the concentrations of small molecules (aka metabolites) that appear in a person's biofluids, which means such diseases can often be readily detected from a person's "metabolic profile". This information can be extracted from a biofluid's NMR spectrum. Today, this is often done manually by trained human experts, which means this process is relatively slow, expensive and error-prone. This paper presents a tool, Bayesil, that can quickly, accurately and autonomously produce a complex biofluid's (e.g., serum or CSF) metabolic profile from a 1D1H NMR spectrum. This requires first performing several spectral processing steps then matching the resulting spectrum against a reference compound library, which contains the "signatures" of each relevant metabolite. Many of these steps are novel algorithms and our matching step views spectral matching as an inference problem within a probabilistic graphical model that rapidly approximates the most probable metabolic profile. Our extensive studies on a diverse set of complex mixtures, show that Bayesil can autonomously find the concentration of all NMR-detectable metabolites accurately (~90% correct identification and ~10% quantification error), in <5minutes on a single CPU. These results demonstrate that Bayesil is the first fully-automatic publicly-accessible system that provides quantitative NMR spectral profiling effectively -- with an accuracy that meets or exceeds the performance of trained experts. We anticipate this tool will usher in high-throughput metabolomics and enable a wealth of new applications of NMR in clinical settings. Available at http://www.bayesil.ca.

Global convergence of an online (stochastic) limited memory version of the Broyden-Fletcher- Goldfarb-Shanno (BFGS) quasi-Newton method for solving optimization problems with stochastic objectives that arise in large scale machine learning is established. Lower and upper bounds on the Hessian eigenvalues of the sample functions are shown to suffice to guarantee that the curvature approximation matrices have bounded determinants and traces, which, in turn, permits establishing convergence to optimal arguments with probability 1. Numerical experiments on support vector machines with synthetic data showcase reductions in convergence time relative to stochastic gradient descent algorithms as well as reductions in storage and computation relative to other online quasi-Newton methods. Experimental evaluation on a search engine advertising problem corroborates that these advantages also manifest in practical applications.

Response calibration is the process of inferring how much the measured data depend on the signal one is interested in. It is essential for any quantitative signal estimation on the basis of the data. Here, we investigate self-calibration methods for linear signal measurements and linear dependence of the response on the calibration parameters. The common practice is to augment an external calibration solution using a known reference signal with an internal calibration on the unknown measurement signal itself. Contemporary self-calibration schemes try to find a self-consistent solution for signal and calibration by exploiting redundancies in the measurements. This can be understood in terms of maximizing the joint probability of signal and calibration. However, the full uncertainty structure of this joint probability around its maximum is thereby not taken into account by these schemes. Therefore better schemes -- in sense of minimal square error -- can be designed by accounting for asymmetries in the uncertainty of signal and calibration. We argue that at least a systematic correction of the common self-calibration scheme should be applied in many measurement situations in order to properly treat uncertainties of the signal on which one calibrates. Otherwise the calibration solutions suffer from a systematic bias, which consequently distorts the signal reconstruction. Furthermore, we argue that non-parametric, signal-to-noise filtered calibration should provide more accurate reconstructions than the common bin averages and provide a new, improved self-calibration scheme. We illustrate our findings with a simplistic numerical example.

In this paper, we propose a model for simulating search operators whose behaviour often changes continuously during the search. In these scenarios, the performance of the operators decreases when they are applied. This is motivated by the fact that operators for optimization problems are often roughly classified into exploitation operators and exploration operators. Our simulation model is used to compare the different performances of operator selection policies and clearly identify their ability to adapt to such specific operators behaviours. The experimental study provides interesting results on the respective behaviours of operator selection policies when faced to such non stationary search scenarios. Keywords: Island Models, Adaptive Operator Selection 1. Introduction Selecting the most suitable operators in a search algorithm when solving optimization problems is an active research area (Eiben et al., 2007; Lobo et al., 2007). Given an optimization problem, a search algorithm mainly consists in applying basic solving operators -- heuristics -- in order to explore and exploit the search space for retrieving solutions.

The past years have witnessed many dedicated open-source projects that built and maintain implementations of Support Vector Machines (SVM), parallelized for GPU, multi-core CPUs and distributed systems. Up to this point, no comparable effort has been made to parallelize the Elastic Net, despite its popularity in many high impact applications, including genetics, neuroscience and systems biology. The first contribution in this paper is of theoretical nature. We establish a tight link between two seemingly different algorithms and prove that Elastic Net regression can be reduced to SVM with squared hinge loss classification. Our second contribution is to derive a practical algorithm based on this reduction. The reduction enables us to utilize prior efforts in speeding up and parallelizing SVMs to obtain a highly optimized and parallel solver for the Elastic Net and Lasso. With a simple wrapper, consisting of only 11 lines of MATLAB code, we obtain an Elastic Net implementation that naturally utilizes GPU and multi-core CPUs. We demonstrate on twelve real world data sets, that our algorithm yields identical results as the popular (and highly optimized) glmnet implementation but is one or several orders of magnitude faster.

In this work, we propose the marginal structured SVM (MSSVM) for structured prediction with hidden variables. MSSVM properly accounts for the uncertainty of hidden variables, and can significantly outperform the previously proposed latent structured SVM (LSSVM; Yu & Joachims (2009)) and other state-of-art methods, especially when that uncertainty is large. Our method also results in a smoother objective function, making gradient-based optimization of MSSVMs converge significantly faster than for LSSVMs. We also show that our method consistently outperforms hidden conditional random fields (HCRFs; Quattoni et al. (2007)) on both simulated and real-world datasets. Furthermore, we propose a unified framework that includes both our and several other existing methods as special cases, and provides insights into the comparison of different models in practice.

Classification with a sparsity constraint on the solution plays a central role in many high dimensional machine learning applications. In some cases, the features can be grouped together so that entire subsets of features can be selected or not selected. In many applications, however, this can be too restrictive. In this paper, we are interested in a less restrictive form of structured sparse feature selection: we assume that while features can be grouped according to some notion of similarity, not all features in a group need be selected for the task at hand. When the groups are comprised of disjoint sets of features, this is sometimes referred to as the "sparse group" lasso, and it allows for working with a richer class of models than traditional group lasso methods. Our framework generalizes conventional sparse group lasso further by allowing for overlapping groups, an additional flexiblity needed in many applications and one that presents further challenges. The main contribution of this paper is a new procedure called Sparse Overlapping Group (SOG) lasso, a convex optimization program that automatically selects similar features for classification in high dimensions. We establish model selection error bounds for SOGlasso classification problems under a fairly general setting. In particular, the error bounds are the first such results for classification using the sparse group lasso. Furthermore, the general SOGlasso bound specializes to results for the lasso and the group lasso, some known and some new. The SOGlasso is motivated by multi-subject fMRI studies in which functional activity is classified using brain voxels as features, source localization problems in Magnetoencephalography (MEG), and analyzing gene activation patterns in microarray data analysis. Experiments with real and synthetic data demonstrate the advantages of SOGlasso compared to the lasso and group lasso.

Department of Biomedical Engineering, Biomedical Imaging Center, Rensselaer Polytechnic Institute, Troy, NY 12180, USA 2 With the existence of biologically distinctive malignant cells originated within the same tumor, intratumor functional heterogeneity is present in many cancers and is often manifested by the intermingled vascular compartments with distinct pharmacokinetics. However, intratumor vascular heterogeneity cannot be resolved directly by most in vivo dynamic imaging. We developed multi-tissue compartment modeling (MTCM), a completely unsupervised method of deconvoluting dynamic imaging series from heterogeneous tumors that can improve vascular characterization in many biological contexts. Applying MTCM to dynamic contrast-enhanced magnetic resonance imaging of breast cancers revealed characteristic intratumor vascular heterogeneity and therapeutic responses that were otherwise undetectable. MTCM is readily applicable to other dynamic imaging modalities for studying intratumor functional and phenotypic heterogeneity, together with a variety of foreseeable applications in the clinic. A formal mathematical description of the method and its detailed implementation is available in Methods.

We prove that the density function of the gradient of a sufficiently smooth function $S : \Omega \subset \mathbb{R}^d \rightarrow \mathbb{R}$, obtained via a random variable transformation of a uniformly distributed random variable, is increasingly closely approximated by the normalized power spectrum of $\phi=\exp\left(\frac{iS}{\tau}\right)$ as the free parameter $\tau \rightarrow 0$. The result is shown using the stationary phase approximation and standard integration techniques and requires proper ordering of limits. We highlight a relationship with the well-known characteristic function approach to density estimation, and detail why our result is distinct from this approach.