Class labels are often imperfectly observed, due to mistakes and to genuine ambiguity among classes. We propose a new semi-supervised deep generative model that explicitly models noisy labels, called the Mislabeled VAE (M-VAE). The M-VAE can perform better than existing deep generative models which do not account for label noise. Additionally, the derivation of M-VAE gives new theoretical insights into the popular M1+M2 semi-supervised model.

We review common methods of solving for multi-class from binary and generalize them to a common framework. Since conditional probabilties are useful both for quantifying the accuracy of an estimate and for calibration purposes, these are a required part of the solution. There is some indication that the best solution for multi-class classification is dependent on the particular dataset. As such, we are particularly interested in data-driven solution design, whether based on a priori considerations or empirical examination of the data. Numerical results indicate that while a one-size-fits-all solution consisting of one-versus-one is appropriate for most datasets, a minority will benefit from a more customized approach. The techniques discussed in this paper allow for a large variety of multi-class configurations and solution methods to be explored so as to optimize classification accuracy, accuracy of conditional probabilities and speed.

Specialization and hierarchical organization are important features of efficient collaboration in economical, artificial, and biological systems. Here, we investigate the hypothesis that both features can be explained by the fact that each entity of such a system is limited in a certain way. We propose an information-theoretic approach based on a Free Energy principle, in order to computationally analyze systems of bounded rational agents that deal with such limitations optimally. We find that specialization allows to focus on fewer tasks, thus leading to a more efficient execution, but in turn requires coordination in hierarchical structures of specialized experts and coordinating units. Our results suggest that hierarchical architectures of specialized units at lower levels that are coordinated by units at higher levels are optimal, given that each unit's information-processing capability is limited and conforms to constraints on complexity costs.

We consider the problem of learning a binary classifier only from positive data and unlabeled data (PU learning). This problem arises in various practical situations, such as information retrieval and outlier detection (Elkan and Noto, 2008; Ward et al., 2009; Scott and Blanchard, 2009; Blanchard et al., 2010; Li et al., 2009; Nguyen et al., 2011). One of the theoretical milestones of PU learning is Elkan and Noto (2008) and there are subsequent researches called unbiased PU learning (du Plessis and Sugiyama, 2014; du Plessis et al., 2015), where the classification risk is estimated in an unbiased manner only from PU data. We consider the case-control scenario (Ward et al., 2009; Elkan and Noto, 2008), where positive data are obtained separately from unlabeled data and unlabeled data is sampled from the whole population. Under this setting, the true class-prior π p(y 1) in unlabeled data is needed for the formulation of unbiased PU learning.

A probability density function (pdf) encodes the entire stochastic knowledge about data distribution, where data may represent stochastic observations in robotics, transition state pairs in reinforcement learning or any other empirically acquired modality. Inferring data pdf is of prime importance, allowing to analyze various model hypotheses and perform smart decision making. However, most density estimation techniques are limited in their representation expressiveness to specific kernel type or predetermined distribution family, and have other restrictions. For example, kernel density estimation (KDE) methods require meticulous parameter search and are extremely slow at querying new points. In this paper we present a novel non-parametric density estimation approach, DeepPDF, that uses a neural network to approximate a target pdf given samples from thereof. Such a representation provides high inference accuracy for a wide range of target pdfs using a relatively simple network structure, making our method highly statistically robust. This is done via a new stochastic optimization algorithm, \emph{Probabilistic Surface Optimization} (PSO), that turns to advantage the stochastic nature of sample points in order to force network output to be identical to the output of a target pdf. Once trained, query point evaluation can be efficiently done in DeepPDF by a simple network forward pass, with linear complexity in the number of query points. Moreover, the PSO algorithm is capable of inferring the frequency of data samples and may also be used in other statistical tasks such as conditional estimation and distribution transformation. We compare the derived approach with KDE methods showing its superior performance and accuracy.

The increased use of psychological and perceptual variables in travel choice survey have motivated a number of studies that investigated the explicit effects of latent behaviour in decision-making. Analysis of travel mode choice has focused on the effects of modal travel cost, time or reliability and many recent studies have attributed latent behaviour variables to account for unobservable effects Paulssen et al. [2014], Bhat et al. [2015]. The Integrated Choice and Latent Variable (ICLV) model is a recent development in structural equation modelling (SEM) to handle hybrid endogenous and exogenous variables in decision-making Ben-Akiva et al. [2002]. The ICLV model has been shown - in some situations - to produce consistent estimates of model parameters, leading to better explanatory solutions Vij and Walker [2016]. The history of structural modelling dates back to the 1970s and have been originally used in psychology, sociology and market research, and recently it has seen growing applications in travel behaviour involving latent preference "attitudinal" variables and measurement "indicators".

Among the many approaches for reasoning about degrees of belief in the presence of noisy sensing and acting, the logical account proposed by Bacchus, Halpern, and Levesque is perhaps the most expressive. While their formalism is quite general, it is restricted to fluents whose values are drawn from discrete finite domains, as opposed to the continuous domains seen in many robotic applications. In this work, we show how this limitation in that approach can be lifted. By dealing seamlessly with both discrete distributions and continuous densities within a rich theory of action, we provide a very general logical specification of how belief should change after acting and sensing in complex noisy domains.

Continuous-time Bayesian networks (CTBNs) constitute a general and powerful framework for modeling continuous-time stochastic processes on networks. This makes them particularly attractive for learning the directed structures among interacting entities. However, if the available data is incomplete, one needs to simulate the prohibitively complex CTBN dynamics. Existing approximation techniques, such as sampling and low-order variational methods, either scale unfavorably in system size, or are unsatisfactory in terms of accuracy. Inspired by recent advances in statistical physics, we present a new approximation scheme based on cluster-variational methods significantly improving upon existing variational approximations. We can analytically marginalize the parameters of the approximate CTBN, as these are of secondary importance for structure learning. This recovers a scalable scheme for direct structure learning from incomplete and noisy time-series data. Our approach outperforms existing methods in terms of scalability.

We address the problem of Bayesian structure learning for domains with hundreds of variables by employing non-parametric bootstrap, recursively. We propose a method that covers both model averaging and model selection in the same framework. The proposed method deals with the main weakness of constraint-based learning---sensitivity to errors in the independence tests---by a novel way of combining bootstrap with constraint-based learning. Essentially, we provide an algorithm for learning a tree, in which each node represents a scored CPDAG for a subset of variables and the level of the node corresponds to the maximal order of conditional independencies that are encoded in the graph. As higher order independencies are tested in deeper recursive calls, they benefit from more bootstrap samples, and therefore more resistant to the curse-of-dimensionality. Moreover, the re-use of stable low order independencies allows greater computational efficiency. We also provide an algorithm for sampling CPDAGs efficiently from their posterior given the learned tree. We empirically demonstrate that the proposed algorithm scales well to hundreds of variables, and learns better MAP models and more reliable causal relationships between variables, than other state-of-the-art-methods.

In fuzzy decision-making processes based on linguistic information, operations on discrete fuzzy numbers are commonly performed. Aggregation and defuzzification operations are some of these often used operations. Many aggregation and defuzzification operators produce results independent to the decision makers strategy. On the other hand, the Weighted Average Based on Levels (WABL) approach can take into account the level weights and the decision makers optimism strategy. This gives flexibility to the WABL operator and, through machine learning, can be trained in the direction of the decision makers strategy, producing more satisfactory results for the decision maker. However, in order to determine the WABL value, it is necessary to calculate some integrals. In this study, the concept of WABL for discrete trapezoidal fuzzy numbers is investigated, and analytical formulas have been proven to facilitate the calculation of WABL value for these fuzzy numbers. Trapezoidal and their special form, triangular fuzzy numbers, are the most commonly used fuzzy number types in fuzzy modeling, so in this study, such numbers have been studied. Computational examples explaining the theoretical results have been performed.