Motivated by the unceasing interest in hidden Markov models (HMMs), this paper re-examines hidden path inference in these models, using primarily a risk-based framework. While the most common maximum a posteriori (MAP), or Viterbi, path estimator and the minimum error, or Posterior Decoder (PD), have long been around, other path estimators, or decoders, have been either only hinted at or applied more recently and in dedicated applications generally unfamiliar to the statistical learning community. Over a decade ago, however, a family of algorithmically defined decoders aiming to hybridize the two standard ones was proposed (Brushe et al., 1998). The present paper gives a careful analysis of this hybridization approach, identifies several problems and issues with it and other previously proposed approaches, and proposes practical resolutions of those. Furthermore, simple modifications of the classical criteria for hidden path recognition are shown to lead to a new class of decoders. Dynamic programming algorithms to compute these decoders in the usual forward-backward manner are presented. A particularly interesting subclass of such estimators can be also viewed as hybrids of the MAP and PD estimators. Similar to previously proposed MAP-PD hybrids, the new class is parameterized by a small number of tunable parameters. Unlike their algorithmic predecessors, the new risk-based decoders are more clearly interpretable, and, most importantly, work "out of the box" in practice, which is demonstrated on some real bioinformatics tasks and data. Some further generalizations and applications are discussed in conclusion.

We present a nonparametric Bayesian method for disease subtype discovery in multi-dimensional cancer data. Our method can simultaneously analyse a wide range of data types, allowing for both agreement and disagreement between their underlying clustering structure. It includes feature selection and infers the most likely number of disease subtypes, given the data. We apply the method to 277 glioblastoma samples from The Cancer Genome Atlas, for which there are gene expression, copy number variation, methylation and microRNA data. We identify 8 distinct consensus subtypes and study their prognostic value for death, new tumour events, progression and recurrence. The consensus subtypes are prognostic of tumour recurrence (log-rank p-value of $3.6 \times 10^{-4}$ after correction for multiple hypothesis tests). This is driven principally by the methylation data (log-rank p-value of $2.0 \times 10^{-3}$) but the effect is strengthened by the other 3 data types, demonstrating the value of integrating multiple data types. Of particular note is a subtype of 47 patients characterised by very low levels of methylation. This subtype has very low rates of tumour recurrence and no new events in 10 years of follow up. We also identify a small gene expression subtype of 6 patients that shows particularly poor survival outcomes. Additionally, we note a consensus subtype that showly a highly distinctive data signature and suggest that it is therefore a biologically distinct subtype of glioblastoma. The code is available from https://sites.google.com/site/multipledatafusion/

An intrinsic problem of classifiers based on machine learning (ML) methods is that their learning time grows as the size and complexity of the training dataset increases. For this reason, it is important to have efficient computational methods and algorithms that can be applied on large datasets, such that it is still possible to complete the machine learning tasks in reasonable time. In this context, we present in this paper a more accurate simple process to speed up ML methods. An unsupervised clustering algorithm is combined with Expectation, Maximization (EM) algorithm to develop an efficient Hidden Markov Model (HMM) training. The idea of the proposed process consists of two steps. In the first step, training instances with similar inputs are clustered and a weight factor which represents the frequency of these instances is assigned to each representative cluster. Dynamic Time Warping technique is used as a dissimilarity function to cluster similar examples. In the second step, all formulas in the classical HMM training algorithm (EM) associated with the number of training instances are modified to include the weight factor in appropriate terms. This process significantly accelerates HMM training while maintaining the same initial, transition and emission probabilities matrixes as those obtained with the classical HMM training algorithm. Accordingly, the classification accuracy is preserved. Depending on the size of the training set, speedups of up to 2200 times is possible when the size is about 100.000 instances. The proposed approach is not limited to training HMMs, but it can be employed for a large variety of MLs methods.

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.

In experimental tests of human behavior in unstructured bargaining games, typically many joint utility outcomes are found to occur, not just one. This suggests we predict the outcome of such a game as a probability distribution. This is in contrast to what is conventionally done (e.g, in the Nash bargaining solution), which is predict a single outcome. We show how to translate Nash's bargaining axioms to provide a distribution over outcomes rather than a single outcome. We then prove that a subset of those axioms forces the distribution over utility outcomes to be a power-law distribution. Unlike Nash's original result, our result holds even if the feasible set is finite. When the feasible set is convex and comprehensive, the mode of the power law distribution is the Harsanyi bargaining solution, and if we require symmetry it is the Nash bargaining solution. However, in general these modes of the joint utility distribution are not the experimentalist's Bayes-optimal predictions for the joint utility. Nor are the bargains corresponding to the modes of those joint utility distributions the modes of the distribution over bargains in general, since more than one bargain may result in the same joint utility. After introducing distributional bargaining solution concepts, we show how an external regulator can use them to optimally design an unstructured bargaining scenario. Throughout we demonstrate our analysis in computational experiments involving flight rerouting negotiations in the National Airspace System. We emphasize that while our results are formulated for unstructured bargaining, they can also be used to make predictions for noncooperative games where the modeler knows the utility functions of the players over possible outcomes of the game, but does not know the move spaces the players use to determine those outcomes.

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.

CLUSTERCLUSTER: PARALLEL MARKOV CHAIN MONTE CARLO FOR DIRICHLET PROCESS MIXTURES By Dan Lovell, Jonathan Malmaud, Ryan P. Adams and Vikash K. Mansinghka Massachusetts Institute of Technology and Harvard University 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.

Probability answer set programming is a declarative programming that has been shown effective for representing and reasoning about a variety of probability reasoning tasks. However, the lack of probability aggregates, e.g. {\em expected values}, in the language of disjunctive hybrid probability logic programs (DHPP) disallows the natural and concise representation of many interesting problems. In this paper, we extend DHPP to allow arbitrary probability aggregates. We introduce two types of probability aggregates; a type that computes the expected value of a classical aggregate, e.g., the expected value of the minimum, and a type that computes the probability of a classical aggregate, e.g, the probability of sum of values. In addition, we define a probability answer set semantics for DHPP with arbitrary probability aggregates including monotone, antimonotone, and nonmonotone probability aggregates. We show that the proposed probability answer set semantics of DHPP subsumes both the original probability answer set semantics of DHPP and the classical answer set semantics of classical disjunctive logic programs with classical aggregates, and consequently subsumes the classical answer set semantics of the original disjunctive logic programs. We show that the proposed probability answer sets of DHPP with probability aggregates are minimal probability models and hence incomparable, which is an important property for nonmonotonic probability reasoning.

We present a unified logical framework for representing and reasoning about both probability quantitative and qualitative preferences in probability answer set programming [Saad and Pontelli, 2006; Saad, 2006; Saad, 2007a], called probability answer set optimization programs. The proposed framework is vital to allow defining probability quantitative preferences over the possible outcomes of qualitative preferences. We show the application of probability answer set optimization programs to a variant of the well-known nurse restoring problem [Bard and Purnomo, 2005], called the nurse restoring with probability preferences problem. To the best of our knowledge, this development is the first to consider a logical framework for reasoning about probability quantitative preferences, in general, and reasoning about both probability quantitative and qualitative preferences in particular.

The Swedish Institute of Computer Science (SICS) has for several years developed methods for statistical anomaly detection based on a framework called Bayesian principal anomaly (Holst and Ekman 2011). In this article we describe a novel application Addtrack is a tool developed originally by Bombardier domain for the anomaly-detection method: condition Transportation for general analysis, monitoring, monitoring of trains (Holst, Ekman, and and visualization of train conditions and Larsen 2006). It is "intelligent" in statistical models. There are currently many the sense that analysis modules, such as the one popular anomaly-detection methods based on described in this article, can be used to preprocess nonparametric models (see, for example, Ahmed, and visualize data sets. Addtrack, including the anomalydetection model is very general since the parametric module described in this article, is forms of the distributions need not be currently deployed in Sweden, India, China, and known.