We consider the university course timetabling problem, which is one of the most studied problems in educational timetabling. In particular, we focus our attention on the formulation known as the curriculum-based course timetabling problem, which has been tackled by many researchers and for which there are many available benchmarks. The contribution of this paper is twofold. First, we propose an effective and robust single-stage simulated annealing method for solving the problem. Secondly, we design and apply an extensive and statistically-principled methodology for the parameter tuning procedure. The outcome of this analysis is a methodology for modeling the relationship between search method parameters and instance features that allows us to set the parameters for unseen instances on the basis of a simple inspection of the instance itself. Using this methodology, our algorithm, despite its apparent simplicity, has been able to achieve high quality results on a set of popular benchmarks. A final contribution of the paper is a novel set of real-world instances, which could be used as a benchmark for future comparison.

We consider the correlated multiarmed bandit (MAB) problem in which the rewards associated with each arm are modeled by a multivariate Gaussian random variable, and we investigate the influence of the assumptions in the Bayesian prior on the performance of the upper credible limit (UCL) algorithm and a new correlated UCL algorithm. We rigorously characterize the influence of accuracy, confidence, and correlation scale in the prior on the decision-making performance of the algorithms. Our results show how priors and correlation structure can be leveraged to improve performance.

The Boltzmann machine provides a useful framework to learn highly complex, multimodal and multiscale data distributions that occur in the real world. The default method to learn its parameters consists of minimizing the Kullback-Leibler (KL) divergence from training samples to the Boltzmann model. We propose in this work a novel approach for Boltzmann training which assumes that a meaningful metric between observations is given. This metric can be represented by the Wasserstein distance between distributions, for which we derive a gradient with respect to the model parameters. Minimization of this new Wasserstein objective leads to generative models that are better when considering the metric and that have a cluster-like structure. We demonstrate the practical potential of these models for data completion and denoising, for which the metric between observations plays a crucial role.

Making recommendations in the presence of sparsity is known to present one of the most challenging problems faced by collaborative filtering methods. In this work we tackle this problem by exploiting the innately hierarchical structure of the item space following an approach inspired by the theory of Decomposability. We view the itemspace as a Nearly Decomposable system and we define blocks of closely related elements and corresponding indirect proximity components. We study the theoretical properties of the decomposition and we derive sufficient conditions that guarantee full item space coverage even in cold-start recommendation scenarios. A comprehensive set of experiments on the MovieLens and the Yahoo!R2Music datasets, using several widely applied performance metrics, support our model's theoretically predicted properties and verify that NCDREC outperforms several state-of-the-art algorithms, in terms of recommendation accuracy, diversity and sparseness insensitivity.

We propose an efficient ADMM method with guarantees for high-dimensional problems. We provide explicit bounds for the sparse optimization problem and the noisy matrix decomposition problem. For sparse optimization, we establish that the modified ADMM method has an optimal convergence rate of $\mathcal{O}(s\log d/T)$, where $s$ is the sparsity level, $d$ is the data dimension and $T$ is the number of steps. This matches with the minimax lower bounds for sparse estimation. For matrix decomposition into sparse and low rank components, we provide the first guarantees for any online method, and prove a convergence rate of $\tilde{\mathcal{O}}((s+r)\beta^2(p) /T) + \mathcal{O}(1/p)$ for a $p\times p$ matrix, where $s$ is the sparsity level, $r$ is the rank and $\Theta(\sqrt{p})\leq \beta(p)\leq \Theta(p)$. Our guarantees match the minimax lower bound with respect to $s,r$ and $T$. In addition, we match the minimax lower bound with respect to the matrix dimension $p$, i.e. $\beta(p)=\Theta(\sqrt{p})$, for many important statistical models including the independent noise model, the linear Bayesian network and the latent Gaussian graphical model under some conditions. Our ADMM method is based on epoch-based annealing and consists of inexpensive steps which involve projections on to simple norm balls. Experiments show that for both sparse optimization and matrix decomposition problems, our algorithm outperforms the state-of-the-art methods. In particular, we reach higher accuracy with same time complexity.

We present a unified framework for low-rank matrix estimation with nonconvex penalties. We first prove that the proposed estimator attains a faster statistical rate than the traditional low-rank matrix estimator with nuclear norm penalty. Moreover, we rigorously show that under a certain condition on the magnitude of the nonzero singular values, the proposed estimator enjoys oracle property (i.e., exactly recovers the true rank of the matrix), besides attaining a faster rate. As far as we know, this is the first work that establishes the theory of low-rank matrix estimation with nonconvex penalties, confirming the advantages of nonconvex penalties for matrix completion. Numerical experiments on both synthetic and real world datasets corroborate our theory.

Spatio-temporal point process models play a central role in the analysis of spatially distributed systems in several disciplines. Yet, scalable inference remains computa- tionally challenging both due to the high resolution modelling generally required and the analytically intractable likelihood function. Here, we exploit the sparsity structure typical of (spatially) discretised log-Gaussian Cox process models by using approximate message-passing algorithms. The proposed algorithms scale well with the state dimension and the length of the temporal horizon with moderate loss in distributional accuracy. They hence provide a flexible and faster alternative to both non-linear filtering-smoothing type algorithms and to approaches that implement the Laplace method or expectation propagation on (block) sparse latent Gaussian models. We infer the parameters of the latent Gaussian model using a structured variational Bayes approach. We demonstrate the proposed framework on simulation studies with both Gaussian and point-process observations and use it to reconstruct the conflict intensity and dynamics in Afghanistan from the WikiLeaks Afghan War Diary.

Neural responses are highly variable, and some portion of this variability arises from fluctuations in modulatory factors that alter their gain, such as adaptation, attention, arousal, expected or actual reward, emotion, and local metabolic resource availability. Regardless of their origin, fluctuations in these signals can confound or bias the inferences that one derives from spiking responses. Recent work demonstrates that for sensory neurons, these effects can be captured by a modulated Poisson model, whose rate is the product of a stimulus-driven response function and an unknown modulatory signal. Here, we extend this model, by incorporating explicit modulatory elements that are known (specifically, spike-history dependence, as in previous models), and by constraining the remaining latent modulatory signals to be smooth in time. We develop inference procedures for fitting the entire model, including hyperparameters, via evidence optimization, and apply these to simulated data, and to responses of ferret auditory midbrain and cortical neurons to complex sounds. We show that integrating out the latent modulators yields better (or more readily-interpretable) receptive field estimates than a standard Poisson model. Conversely, integrating out the stimulus dependence yields estimates of the slowly-varying latent modulators.

The dictionary-aided sparse regression (SR) approach has recently emerged as a promising alternative to hyperspectral unmixing (HU) in remote sensing. By using an available spectral library as a dictionary, the SR approach identifies the underlying materials in a given hyperspectral image by selecting a small subset of spectral samples in the dictionary to represent the whole image. A drawback with the current SR developments is that an actual spectral signature in the scene is often assumed to have zero mismatch with its corresponding dictionary sample, and such an assumption is considered too ideal in practice. In this paper, we tackle the spectral signature mismatch problem by proposing a dictionary-adjusted nonconvex sparsity-encouraging regression (DANSER) framework. The main idea is to incorporate dictionary correcting variables in an SR formulation. A simple and low per-iteration complexity algorithm is tailor-designed for practical realization of DANSER. Using the same dictionary correcting idea, we also propose a robust subspace solution for dictionary pruning. Extensive simulations and real-data experiments show that the proposed method is effective in mitigating the undesirable spectral signature mismatch effects.

Continued reliance on human operators for managing data centers is a major impediment for them from ever reaching extreme dimensions. Large computer systems in general, and data centers in particular, will ultimately be managed using predictive computational and executable models obtained through data-science tools, and at that point, the intervention of humans will be limited to setting high-level goals and policies rather than performing low-level operations. Data-driven autonomics, where management and control are based on holistic predictive models that are built and updated using generated data, opens one possible path towards limiting the role of operators in data centers. In this paper, we present a data-science study of a public Google dataset collected in a 12K-node cluster with the goal of building and evaluating a predictive model for node failures. We use BigQuery, the big data SQL platform from the Google Cloud suite, to process massive amounts of data and generate a rich feature set characterizing machine state over time. We describe how an ensemble classifier can be built out of many Random Forest classifiers each trained on these features, to predict if machines will fail in a future 24-hour window. Our evaluation reveals that if we limit false positive rates to 5%, we can achieve true positive rates between 27% and 88% with precision varying between 50% and 72%. We discuss the practicality of including our predictive model as the central component of a data-driven autonomic manager and operating it on-line with live data streams (rather than off-line on data logs). All of the scripts used for BigQuery and classification analyses are publicly available from the authors' website.