In this paper, a generalized multivariate Student-t mixture model is developed for classification and clustering of Low Probability of Intercept radar waveforms. A Low Probability of Intercept radar signal is characterized by a pulse compression waveform which is either frequency-modulated or phase-modulated. The proposed model can classify and cluster different modulation types such as linear frequency modulation, non linear frequency modulation, polyphase Barker, polyphase P1, P2, P3, P4, Frank and Zadoff codes. The classification method focuses on the introduction of a new prior distribution for the model hyper-parameters that gives us the possibility to handle sensitivity of mixture models to initialization and to allow a less restrictive modeling of data. Inference is processed through a Variational Bayes method and a Bayesian treatment is adopted for model learning, supervised classification and clustering. Moreover, the novel prior distribution is not a well-known probability distribution and both deterministic and stochastic methods are employed to estimate its expectations. Some numerical experiments show that the proposed method is less sensitive to initialization and provides more accurate results than the previous state of the art mixture models.

In this article, we consider a stochastic numerical simulator to assess the impact of some factors on a phenomenon. The simulator is seen as a black box with inputs and outputs. The quality of a simulation, hereafter referred to as fidelity, is assumed to be tunable by means of an additional input of the simulator (e.g., a mesh size parameter): high-fidelity simulations provide more accurate results, but are time-consuming. Using a limited computation-time budget, we want to estimate, for any value of the physical inputs, the probability that a certain scalar output of the simulator will exceed a given critical threshold at the highest fidelity level. The problem is addressed in a Bayesian framework, using a Gaussian process model of the multi-fidelity simulator. We consider a Bayesian estimator of the probability, together with an associated measure of uncertainty, and propose a new multi-fidelity sequential design strategy, called Maximum Speed of Uncertainty Reduction (MSUR), to select the value of physical inputs and the fidelity level of new simulations. The MSUR strategy is tested on an example.

One of the major hurdles preventing the full exploitation of information from online communities is the widespread concern regarding the quality and credibility of user-contributed content. Prior works in this domain operate on a static snapshot of the community, making strong assumptions about the structure of the data (e.g., relational tables), or consider only shallow features for text classification. To address the above limitations, we propose probabilistic graphical models that can leverage the joint interplay between multiple factors in online communities --- like user interactions, community dynamics, and textual content --- to automatically assess the credibility of user-contributed online content, and the expertise of users and their evolution with user-interpretable explanation. To this end, we devise new models based on Conditional Random Fields for different settings like incorporating partial expert knowledge for semi-supervised learning, and handling discrete labels as well as numeric ratings for fine-grained analysis. This enables applications such as extracting reliable side-effects of drugs from user-contributed posts in healthforums, and identifying credible content in news communities. Online communities are dynamic, as users join and leave, adapt to evolving trends, and mature over time. To capture this dynamics, we propose generative models based on Hidden Markov Model, Latent Dirichlet Allocation, and Brownian Motion to trace the continuous evolution of user expertise and their language model over time. This allows us to identify expert users and credible content jointly over time, improving state-of-the-art recommender systems by explicitly considering the maturity of users. This also enables applications such as identifying helpful product reviews, and detecting fake and anomalous reviews with limited information.

In this study, we present a multi-class graphical Bayesian predictive classifier that incorporates the uncertainty in the model selection into the standard Bayesian formalism. For each class, the dependence structure underlying the observed features is represented by a set of decomposable Gaussian graphical models. Emphasis is then placed on the Bayesian model averaging which takes full account of the class-specific model uncertainty by averaging over the posterior graph model probabilities. Even though the decomposability assumption severely reduces the model space, the size of the class of decomposable models is still immense, rendering the explicit Bayesian averaging over all the models infeasible. To address this issue, we consider the particle Gibbs strategy of Olsson et al. (2016) for posterior sampling from decomposable graphical models which utilizes the Christmas tree algorithm of Rios et al. (2016) as proposal kernel. We also derive the a strong hyper Markov law which we call the hyper normal Wishart law that allow to perform the resultant Bayesian calculations locally. The proposed predictive graphical classifier reveals superior performance compared to the ordinary Bayesian predictive rule that does not account for the model uncertainty, as well as to a number of out-of-the-box classifiers.

Approximate Bayesian Computation (ABC) is a method to obtain a posterior distribution without a likelihood function, using simulations and a set of distance metrics. For that reason, it has recently been gaining popularity as an analysis tool in cosmology and astrophysics. Its drawback, however, is a slow convergence rate. We propose a novel method, which we call qABC, to accelerate ABC with Quantile Regression. In this method, we create a model of quantiles of distance measure as a function of input parameters. This model is trained on a small number of simulations and estimates which regions of the prior space are likely to be accepted into the posterior. Other regions are then immediately rejected. This procedure is then repeated as more simulations are available. We apply it to the practical problem of estimation of redshift distribution of cosmological samples, using forward modelling developed in previous work. The qABC method converges to nearly same posterior as the basic ABC. It uses, however, only 20\% of the number of simulations compared to basic ABC, achieving a fivefold gain in execution time for our problem. For other problems the acceleration rate may vary; it depends on how close the prior is to the final posterior. We discuss possible improvements and extensions to this method.

Which machine learning algorithm should I use?

Relational probabilistic models have the challenge of aggregation, where one variable depends on a population of other variables. Consider the problem of predicting gender from movie ratings; this is challenging because the number of movies per user and users per movie can vary greatly. Surprisingly, aggregation is not well understood. In this paper, we show that existing relational models (implicitly or explicitly) either use simple numerical aggregators that lose great amounts of information, or correspond to naive Bayes, logistic regression, or noisy-OR that suffer from overconfidence. We propose new simple aggregators and simple modifications of existing models that empirically outperform the existing ones. The intuition we provide on different (existing or new) models and their shortcomings plus our empirical findings promise to form the foundation for future representations.

Supervisory signals have the potential to make low-dimensional data representations, like those learned by mixture and topic models, more interpretable and useful. We propose a framework for training latent variable models that explicitly balances two goals: recovery of faithful generative explanations of high-dimensional data, and accurate prediction of associated semantic labels. Existing approaches fail to achieve these goals due to an incomplete treatment of a fundamental asymmetry: the intended application is always predicting labels from data, not data from labels. Our prediction-constrained objective for training generative models coherently integrates loss-based supervisory signals while enabling effective semi-supervised learning from partially labeled data. We derive learning algorithms for semi-supervised mixture and topic models using stochastic gradient descent with automatic differentiation. We demonstrate improved prediction quality compared to several previous supervised topic models, achieving predictions competitive with high-dimensional logistic regression on text sentiment analysis and electronic health records tasks while simultaneously learning interpretable topics.

The AMIDST Toolbox allows you to model your problem using a flexible probabilistic language based on graphical models. Then you fit your model with data using a Bayesian approach to handle modeling uncertainty. AMIDST provides tailored parallel (powered by Java 8 Streams) and distributed (powered by Flink or Spark) implementations of Bayesian parameter learning for batch and streaming data. This processing is based on flexible and scalable message passing algorithms. Data Streams: Update your models when new data is available.

Neyman-Scott is a classic example of an estimation problem with a partially-consistent posterior, for which standard estimation methods tend to produce inconsistent results. Past attempts to create consistent estimators for Neyman-Scott have led to ad-hoc solutions, to estimators that do not satisfy representation invariance, to restrictions over the choice of prior and more. We present a simple construction for a general-purpose Bayes estimator, invariant to representation, which satisfies consistency on Neyman-Scott over any nondegenerate prior. We argue that the good attributes of the estimator are due to its intrinsic properties, and generalise beyond Neyman-Scott as well. Keywords: Neyman-Scott, consistent estimation, minEKL, Kullback-Leibler, Bayes estimation, invariance 1. Introduction In [24], Neyman and Scott introduced a problem in consistent estimation that has since been studied extensively in many fields (see [18] for a review).