We work out a classification scheme for quantum modeling in Hilbert space of any kind of composite entity violating Bell's inequalities and exhibiting entanglement. Our theoretical framework includes situations with entangled states and product measurements ('customary quantum situation'), and also situations with both entangled states and entangled measurements ('nonlocal box situation', 'nonlocal non-marginal box situation'). We show that entanglement is structurally a joint property of states and measurements. Furthermore, entangled measurements enable quantum modeling of situations that are usually believed to be 'beyond quantum'. Our results are also extended from pure states to quantum mixtures.

The change of two orders of magnitude in the 'new DCF' of NIST's SRE'10, relative to the 'old DCF' evaluation criterion, posed a difficult challenge for participants and evaluator alike. Initially, participants were at a loss as to how to calibrate their systems, while the evaluator underestimated the required number of evaluation trials. After the fact, it is now obvious that both calibration and evaluation require very large sets of trials. This poses the challenges of (i) how to decide what number of trials is enough, and (ii) how to process such large data sets with reasonable memory and CPU requirements. After SRE'10, at the BOSARIS Workshop, we built solutions to these problems into the freely available BOSARIS Toolkit. This paper explains the principles and algorithms behind this toolkit. The main contributions of the toolkit are: 1. The Normalized Bayes Error-Rate Plot, which analyses likelihood- ratio calibration over a wide range of DCF operating points. These plots also help in judging the adequacy of the sizes of calibration and evaluation databases. 2. Efficient algorithms to compute DCF and minDCF for large score files, over the range of operating points required by these plots. 3. A new score file format, which facilitates working with very large trial lists. 4. A faster logistic regression optimizer for fusion and calibration. 5. A principled way to define EER (equal error rate), which is of practical interest when the absolute error count is small.

Most learning methods with rank or sparsity constraints use convex relaxations, which lead to optimization with the nuclear norm or the $\ell_1$-norm. However, several important learning applications cannot benefit from this approach as they feature these convex norms as constraints in addition to the non-convex rank and sparsity constraints. In this setting, we derive efficient sparse projections onto the simplex and its extension, and illustrate how to use them to solve high-dimensional learning problems in quantum tomography, sparse density estimation and portfolio selection with non-convex constraints.

Roborobo! is a multi-platform, highly portable, robot simulator for large-scale collective robotics experiments. Roborobo! is coded in C++, and follows the KISS guideline ("Keep it simple"). Therefore, its external dependency is solely limited to the widely available SDL library for fast 2D Graphics. Roborobo! is based on a Khepera/ePuck model. It is targeted for fast single and multi-robots simulation, and has already been used in more than a dozen published research mainly concerned with evolutionary swarm robotics, including environment-driven self-adaptation and distributed evolutionary optimization, as well as online onboard embodied evolution and embodied morphogenesis.

This paper studies convergence behavior of latent mixing measures that arise in finite and infinite mixture models, using transportation distances (i.e., Wasserstein metrics). The relationship between Wasserstein distances on the space of mixing measures and f-divergence functionals such as Hellinger and Kullback-Leibler distances on the space of mixture distributions is investigated in detail using various identifiability conditions. Convergence in Wasserstein metrics for discrete measures implies convergence of individual atoms that provide support for the measures, thereby providing a natural interpretation of convergence of clusters in clustering applications where mixture models are typically employed. Convergence rates of posterior distributions for latent mixing measures are established, for both finite mixtures of multivariate distributions and infinite mixtures based on the Dirichlet process.

We investigate the detectability of modules in large networks when the number of modules is not known in advance. We employ the minimum description length (MDL) principle which seeks to minimize the total amount of information required to describe the network, and avoid overfitting. According to this criterion, we obtain general bounds on the detectability of any prescribed block structure, given the number of nodes and edges in the sampled network. We also obtain that the maximum number of detectable blocks scales as $\sqrt{N}$, where $N$ is the number of nodes in the network, for a fixed average degree $$. We also show that the simplicity of the MDL approach yields an efficient multilevel Monte Carlo inference algorithm with a complexity of $O(\tau N\log N)$, if the number of blocks is unknown, and $O(\tau N)$ if it is known, where $\tau$ is the mixing time of the Markov chain. We illustrate the application of the method on a large network of actors and films with over $10^6$ edges, and a dissortative, bipartite block structure.

There has been much recent interest in application of the pool-adjacent-violators (PAV) algorithm for the purpose of calibrating the probabilistic outputs of automatic pattern recognition and machine learning algorithms. Special cost functions, known as proper scoring rules form natural objective functions to judge the goodness of such calibration. We show that for binary pattern classifiers, the non-parametric optimization of calibration, subject to a monotonicity constraint, can be solved by PAV and that this solution is optimal for all regular binary proper scoring rules. This extends previous results which were limited to convex binary proper scoring rules. We further show that this result holds not only for calibration of probabilities, but also for calibration of log-likelihood-ratios, in which case optimality holds independently of the prior probabilities of the pattern classes.

Approaches for testing sets of variants, such as a set of rare or common variants within a gene or pathway, for association with complex traits are important. In particular, set tests allow for aggregation of weak signal within a set, can capture interplay among variants, and reduce the burden of multiple hypothesis testing. Until now, these approaches did not address confounding by family relatedness and population structure, a problem that is becoming more important as larger data sets are used to increase power. Results: We introduce a new approach for set tests that handles confounders. Our model is based on the linear mixed model and uses two random effects-one to capture the set association signal and one to capture confounders. We also introduce a computational speedup for two-random-effects models that makes this approach feasible even for extremely large cohorts. Using this model with both the likelihood ratio test and score test, we find that the former yields more power while controlling type I error. Application of our approach to richly structured GAW14 data demonstrates that our method successfully corrects for population structure and family relatedness, while application of our method to a 15,000 individual Crohn's disease case-control cohort demonstrates that it additionally recovers genes not recoverable by univariate analysis. Availability: A Python-based library implementing our approach is available at http://mscompbio.codeplex.com

The Dirichlet process (DP) is a fundamental mathematical tool for Bayesian nonparametric modeling, and is widely used in tasks such as density estimation, natural language processing, and time series modeling. Although MCMC inference methods for the DP often provide a gold standard in terms asymptotic accuracy, they can be computationally expensive and are not obviously parallelizable. We propose a reparameterization of the Dirichlet process that induces conditional independencies between the atoms that form the random measure. This conditional independence enables many of the Markov chain transition operators for DP inference to be simulated in parallel across multiple cores. Applied to mixture modeling, our approach enables the Dirichlet process to simultaneously learn clusters that describe the data and superclusters that define the granularity of parallelization. Unlike previous approaches, our technique does not require alteration of the model and leaves the true posterior distribution invariant. It also naturally lends itself to a distributed software implementation in terms of Map-Reduce, which we test in cluster configurations of over 50 machines and 100 cores. We present experiments exploring the parallel efficiency and convergence properties of our approach on both synthetic and real-world data, including runs on 1MM data vectors in 256 dimensions.

In machine learning, the choice of a learning algorithm that is suitable for the application domain is critical. The performance metric used to compare different algorithms must also reflect the concerns of users in the application domain under consideration. In this work, we propose a novel probability-based performance metric called Relevance Score for evaluating supervised learning algorithms. We evaluate the proposed metric through empirical analysis on a dataset gathered from an intelligent lighting pilot installation. In comparison to the commonly used Classification Accuracy metric, the Relevance Score proves to be more appropriate for a certain class of applications.