We present a new, fully generative model for constructing astronomical catalogs from optical telescope image sets. Each pixel intensity is treated as a Poisson random variable with a rate parameter that depends on the latent properties of stars and galaxies. These latent properties are themselves random, with scientific prior distributions constructed from large ancillary datasets. We compare two procedures for posterior inference: Markov chain Monte Carlo (MCMC) and variational inference (VI). MCMC excels at quantifying uncertainty while VI is 1000x faster. Both procedures outperform the current state-of-the-art method for measuring celestial bodies' colors, shapes, and morphologies. On a supercomputer, the VI procedure efficiently uses 665,000 CPU cores (1.3 million hardware threads) to construct an astronomical catalog from 50 terabytes of images.

In this paper, we describe a novel shape classification method which is embedded in the Bayesian paradigm. We discuss the modelling and the resulting shape classification algorithm for two and three dimensional data shapes. We conclude by evaluating the efficiency and efficacy of the proposed algorithm on the Kimia shape database for the two dimensional case.

In marketing we are often confronted with a continuous stream of responses to marketing messages. Such streaming data provide invaluable information regarding message effectiveness and segmentation. However, streaming data are hard to analyze using conventional methods: their high volume and the fact that they are continuously augmented means that it takes considerable time to analyze them. We propose a method for estimating a finite mixture of logistic regression models which can be used to cluster customers based on a continuous stream of responses. This method, which we coin oFMLR, allows segments to be identified in data streams or extremely large static datasets. Contrary to black box algorithms, oFMLR provides model estimates that are directly interpretable. We first introduce oFMLR, explaining in passing general topics such as online estimation and the EM algorithm, making this paper a high level overview of possible methods of dealing with large data streams in marketing practice. Next, we discuss model convergence, identifiability, and relations to alternative, Bayesian, methods; we also identify more general issues that arise from dealing with continuously augmented data sets. Finally, we introduce the oFMLR [R] package and evaluate the method by numerical simulation and by analyzing a large customer clickstream dataset.

Thus, large arrays of textual data, which have been rapidly accumulating on the Internet in the last decade, require ever more complex methods for their automatic processing and modeling. For this, a wide range of mathematical tools, including topic models, is used [1], but their properties and behavior remain little studied so far, which makes it impossible to choose the optimal parameters of such models. If, however, we consider the results of topic modeling as nonequilibrium complex systems (since these, as will be shown below, have the characteristics of such systems), this would make it possible to apply to them a whole range of approaches from statistical physics. First of all, these are models for analyzing the processes of self-organization of large ensembles. The basis for such an analysis may be an approach in which the behavior of the topic model of a textual collection as a word ensemble would be determined by thermodynamic functions, such as entropy or free energy. It is known that complex systems can be characterized by exponential and power law distributions, which is especially characteristic for social [2, 3], biological [4, 5] and economic systems [6, 7].

Estimating uncertainty is important to improving the safety of AI systems. Recently baseline tasks and metrics have been defined and several practical methods for estimating uncertainty developed. However, these approaches attempt to model distributional uncertainty either implicitly through model uncertainty or as data uncertainty. This work proposes a new framework for modeling predictive uncertainty called Prior Networks (PNs) which explicitly models distributional uncertainty. PNs do this by parameterizing a prior distribution over predictive distributions. This work focuses on uncertainty for classification and evaluates PNs on the tasks of identifying out-of-distribution (OOD) samples and detecting misclassification on the MNIST dataset, where they are found to outperform previous methods. Experiments on synthetic and MNIST data show that unlike previous methods PNs are able to distinguish between data and distributional uncertainty.

Complex network data may be analyzed by constructing statistical models that accurately reproduce structural properties that may be of theoretical relevance or empirical interest. In the context of the efficient fitting of models for large network data, we propose a very efficient algorithm for the maximum likelihood estimation (MLE) of the parameters of complex statistical models. The proposed algorithm is similar to the famous Metropolis algorithm but allows a Monte Carlo simulation to be performed while constraining the desired network properties. We demonstrate the algorithm in the context of exponential random graph models (ERGMs) - a family of statistical models for network data. Thus far, the lack of efficient computational methods has limited the empirical scope of ERGMs to relatively small networks with a few thousand nodes. The proposed approach allows a dramatic increase in the size of networks that may be analyzed using ERGMs. This is illustrated in an analysis of several biological networks and one social network with 104,103 nodes.

Robustness to outliers is a central issue in real-world machine learning applications. While replacing a model to a heavy-tailed one (e.g., from Gaussian to Student-t) is a standard approach for robustification, it can only be applied to simple models. In this paper, based on Zellner's optimization and variational formulation of Bayesian inference, we propose an outlier-robust pseudo-Bayesian variational method by replacing the Kullback-Leibler divergence used for data fitting to a robust divergence such as the beta- and gamma-divergences. An advantage of our approach is that superior but complex models such as deep networks can also be handled. We theoretically prove that, for deep networks with ReLU activation functions, the \emph{influence function} in our proposed method is bounded, while it is unbounded in the ordinary variational inference. This implies that our proposed method is robust to both of input and output outliers, while the ordinary variational method is not. We experimentally demonstrate that our robust variational method outperforms ordinary variational inference in regression and classification with deep networks.

We propose a framework for modeling and estimating the state of controlled dynamical systems, where an agent can affect the system through actions and receives partial observations. Based on this framework, we propose the Predictive State Representation with Random Fourier Features (RFFPSR). A key property in RFF-PSRs is that the state estimate is represented by a conditional distribution of future observations given future actions. RFF-PSRs combine this representation with moment-matching, kernel embedding and local optimization to achieve a method that enjoys several favorable qualities: It can represent controlled environments which can be affected by actions; it has an efficient and theoretically justified learning algorithm; it uses a non-parametric representation that has expressive power to represent continuous non-linear dynamics. We provide a detailed formulation, a theoretical analysis and an experimental evaluation that demonstrates the effectiveness of our method.

The rapid growth of storage capacity and processing power has caused machine learning applications to increasingly rely on using immense amounts of labeled data. It has become more important than ever to have fast and inexpensive ways to annotate vast amounts of data. With the emergence of crowdsourcing services, the research direction has gravitated toward putting the wisdom of crowds to better use. Unfortunately, spammers and inattentive annotators pose a threat to the quality and trustworthiness of the consensus. Thus, high quality consensus estimation from crowd annotated data requires a meticulous choice of the candidate annotator and the sample in need of a new annotation. Due to time and budget limitations, it is of utmost importance that this choice is carried out while the annotation collection is in progress. We call this process active crowd-labeling. To this end, we propose an active crowd-labeling approach for actively estimating consensus from continuous-valued crowd annotations. Our method is based on annotator models with unknown parameters, and Bayesian inference is employed to reach a consensus in the form of ordinal, binary, or continuous values. We introduce ranking functions for choosing the candidate annotator and sample pair for requesting an annotation. In addition, we propose a penalizing method for preventing annotator domination, investigate the explore-exploit trade-off for incorporating new annotators into the system, and study the effects of inducing a stopping criterion based on consensus quality. We also introduce the crowd-labeled Head Pose Annotations datasets. Experimental results on the benchmark datasets used in the literature and the Head Pose Annotations datasets suggest that our method provides high-quality consensus by using as few as one fifth of the annotations (~80% cost reduction), thereby providing a budget and time-sensitive solution to the crowd-labeling problem.

Owing to the recent advances in "Big Data" modeling and prediction tasks, variational Bayesian estimation has gained popularity due to their ability to provide exact solutions to approximate posteriors. One key technique for approximate inference is stochastic variational inference (SVI). SVI poses variational inference as a stochastic optimization problem and solves it iteratively using noisy gradient estimates. It aims to handle massive data for predictive and classification tasks by applying complex Bayesian models that have observed as well as latent variables. This paper aims to decentralize it allowing parallel computation, secure learning and robustness benefits. We use Alternating Direction Method of Multipliers in a top-down setting to develop a distributed SVI algorithm such that independent learners running inference algorithms only require sharing the estimated model parameters instead of their private datasets. Our work extends the distributed SVI-ADMM algorithm that we first propose, to an ADMM-based networked SVI algorithm in which not only are the learners working distributively but they share information according to rules of a graph by which they form a network. This kind of work lies under the umbrella of `deep learning over networks' and we verify our algorithm for a topic-modeling problem for corpus of Wikipedia articles. We illustrate the results on latent Dirichlet allocation (LDA) topic model in large document classification, compare performance with the centralized algorithm, and use numerical experiments to corroborate the analytical results.