As a response to the increasing linkages between the macroeconomy and the financial sector, as well as the expanding interconnectedness of the global economy, empirical macroeconomic models have increased both in complexity and size. For that reason, estimation of modern models that inform macroeconomic decisions - such as linear and nonlinear versions of dynamic stochastic general equilibrium (DSGE) and vector autoregressive (VAR) models - many times relies on Bayesian inference via powerful Markov chain Monte Carlo (MCMC) methods. 1 However, existing posterior simulation algorithms cannot scale up to very high-dimensions due to the computational inefficiency and the larger numerical error associated with repeated sampling via Monte Carlo; see Angelino et al. (2016) for a thorough review of such computational issues from a machine learning and high-dimensional data perspective. In that respect, while Bayesian inference is a natural probabilistic framework for learning about parameters by utilizing all information in the data likelihood and prior, computational restrictions might make it less suitable for supporting real-time decision-making in very high dimensions. This paper introduces to the econometric literature the framework of factor graphs (Kschischang et al., 2001) for the purpose of designing computationally efficient, and easy to maintain, Bayesian estimation algorithms. The focus is not only on "faster" posterior inference broadly interpreted, but on designing algorithms that have such low complexity that are future-proof and can be used in high-dimensional econometric problems with possibly thousands or millions of coefficients.

Most topic models are constructed under the assumption that documents follow a multinomial distribution. The Poisson distribution is an alternative distribution to describe the probability of count data. For topic modelling, the Poisson distribution describes the number of occurrences of a word in documents of fixed length. The Poisson distribution has been successfully applied in text classification, but its application to topic modelling is not well documented, specifically in the context of a generative probabilistic model. Furthermore, the few Poisson topic models in literature are admixture models, making the assumption that a document is generated from a mixture of topics. In this study, we focus on short text. Many studies have shown that the simpler assumption of a mixture model fits short text better. With mixture models, as opposed to admixture models, the generative assumption is that a document is generated from a single topic. One topic model, which makes this one-topic-per-document assumption, is the Dirichlet-multinomial mixture model. The main contributions of this work are a new Gamma-Poisson mixture model, as well as a collapsed Gibbs sampler for the model. The benefit of the collapsed Gibbs sampler derivation is that the model is able to automatically select the number of topics contained in the corpus. The results show that the Gamma-Poisson mixture model performs better than the Dirichlet-multinomial mixture model at selecting the number of topics in labelled corpora. Furthermore, the Gamma-Poisson mixture produces better topic coherence scores than the Dirichlet-multinomial mixture model, thus making it a viable option for the challenging task of topic modelling of short text.

Some challenging problems in tracking multiple objects include the time-dependent cardinality, unordered measurements and object parameter labeling. In this paper, we employ Bayesian Bayesian nonparametric methods to address these challenges. In particular, we propose modeling the multiple object parameter state prior using the dependent Dirichlet and Pitman-Yor processes. These nonparametric models have been shown to be more flexible and robust, when compared to existing methods, for estimating the time-varying number of objects, providing object labeling and identifying measurement to object associations. Monte Carlo sampling methods are then proposed to efficiently learn the trajectory of objects from noisy measurements. Using simulations, we demonstrate the estimation performance advantage of the new methods when compared to existing algorithms such as the generalized labeled multi-Bernoulli filter.

Networks of spiking neurons and Winner-Take-All spiking circuits (WTA-SNNs) can detect information encoded in spatio-temporal multi-valued events. These are described by the timing of events of interest, e.g., clicks, as well as by categorical numerical values assigned to each event, e.g., like or dislike. Other use cases include object recognition from data collected by neuromorphic cameras, which produce, for each pixel, signed bits at the times of sufficiently large brightness variations. Existing schemes for training WTA-SNNs are limited to rate-encoding solutions, and are hence able to detect only spatial patterns. Developing more general training algorithms for arbitrary WTA-SNNs inherits the challenges of training (binary) Spiking Neural Networks (SNNs). These amount, most notably, to the non-differentiability of threshold functions, to the recurrent behavior of spiking neural models, and to the difficulty of implementing backpropagation in neuromorphic hardware. In this paper, we develop a variational online local training rule for WTA-SNNs, referred to as VOWEL, that leverages only local pre- and post-synaptic information for visible circuits, and an additional common reward signal for hidden circuits. The method is based on probabilistic generalized linear neural models, control variates, and variational regularization. Experimental results on real-world neuromorphic datasets with multi-valued events demonstrate the advantages of WTA-SNNs over conventional binary SNNs trained with state-of-the-art methods, especially in the presence of limited computing resources.

We consider three modern roles for logic in artificial intelligence, which are based on the theory of tractable Boolean circuits: (1) logic as a basis for computation, (2) logic for learning from a combination of data and knowledge, and (3) logic for reasoning about the behavior of machine learning systems.

Over this decade, an increasing number of processes is being automated through classification algorithms, being essential that these are robust and reliable if we are to trust key operations based on their output. State-of-the-art classifiers perform extraordinarily well on standard data, but they have been shown to be vulnerable to adversarial examples, data instances specifically targeted at fooling the algorithms (Comiter, 2019). As a fundamental hypothesis, algorithms rely on the use of independent and identically distributed (iid) data for both the training and test phases. However, security aspects in classification, which form part of the field of adversarial machine learning (AML), question such hypothesis due to the presence of adversaries ready to modify the data to obtain a benefit and, thus, making both distributions differ. Stemming from the pioneering work in adversarial classification (AC) in Dalvi et al. (2004), the paradigm used to model the confrontation between adversaries and classification systems has been game theory, see recent reviews in Biggio and Roli (2018) and Zhou et al. (2018). As an example, the most popular attacks, including the fast gradient sign method (FGSM) (Goodfellow et al., 2014b), may be viewed from a game-theoretic perspective. Similarly, two of the most promising defence techniques, adversarial training (AT) (Madry et al., 2018), which trains the defender model with attacked samples, and adversarial logit pairing (ALP) (Kannan et al., 2018), which encourages the logits of the model to be the same for both standard and adversarial inputs, may be framed in game theoretic terms. This perspective typically entails common knowledge hypothesis (Hargreaves-Heap and Varoufakis, 2004) which, from a fundamental point of view, are not sustainable in settings such as security, as adversaries try to hide and conceal information. Recent work (Naveiro et al., 2019) presented ACRA, a novel approach for AC based on Adversarial Risk

In this letter, we present a novel Gaussian Process Learning-based Probabilistic Optimal Power Flow (GP-POPF) for solving POPF under renewable and load uncertainties of arbitrary distribution. The proposed method relies on a non-parametric Bayesian inference-based uncertainty propagation approach, called Gaussian Process (GP). We also suggest a new type of sensitivity called Subspace-wise Sensitivity, using observations on the interpretability of GP-POPF hyperparameters. The simulation results on 14-bus and 30-bus systems show that the proposed method provides reasonably accurate solutions when compared with Monte-Carlo Simulations (MCS) solutions at different levels of uncertain renewable penetration as well as load uncertainties, while requiring much less number of samples and elapsed time.

Equity research analysts at financial institutions play a pivotal role in capital markets; they provide an efficient conduit between investors and companies' management and facilitate the efficient flow of information from companies, promoting functional and liquid markets. However, previous research in the academic finance and behavioral economics communities has found that analysts' estimates of future company earnings and other financial quantities can be affected by a number of behavioral, incentive-based and discriminatory biases and systematic errors, which can detrimentally affect both investors and public companies. We propose a Bayesian latent variable model for analysts' systematic errors and biases which we use to generate a robust bias-adjusted consensus estimate of company earnings. Experiments using historical earnings estimates data show that our model is more accurate than the consensus average of estimates and other related approaches.

Autonomous vehicles must be comprehensively evaluated before deployed in cities and highways. Current evaluation procedures lack the abilities of weakness-aiming and evolving, thus they could hardly generate adversarial environments for autonomous vehicles, leading to insufficient challenges. To overcome the shortage of static evaluation methods, this paper proposes a novel method to generate adversarial environments with deep reinforcement learning, and to cluster them with a nonparametric Bayesian method. As a representative task of autonomous driving, lane-change is used to demonstrate the superiority of the proposed method. First, two lane-change models are separately developed by a rule-based method and a learning-based method, waiting for evaluation and comparison. Next, adversarial environments are generated by training surrounding interactive vehicles with deep reinforcement learning for local optimal ensembles. Then, a nonparametric Bayesian approach is utilized to cluster the adversarial policies of the interactive vehicles. Finally, the adversarial environment patterns are illustrated and the performances of two lane-change models are evaluated and compared. The simulation results indicate that both models perform significantly worse in adversarial environments than in naturalistic environments, with plenty of weaknesses successfully extracted in a few tests.

In the past twenty years there has been an explosion of the use of graphical models to represent the relationship between a vector of random variables and perform distributed inference which takes advantage of the underlying graphical representations. Bayesian networks (BNs) (Darwiche 2009; Fenton and Neil 2012) are nowadays the most used graphical models, with applications to a wide array of domains and implementation in various software: for instance, the R packages bnlearn by Scutari (2010) and gRain by Højsgaard (2012), among others. However, BNs can only represent symmetric conditional independences which in practical applications may not be fully justified. For this reason, a variety of models that can take into account the asymmetric nature of real-world data have been proposed; for example, context-specific BNs (Boutilier, Friedman, Goldszmidt, and Koller 1996), labeled directed acyclic graphs (Pensar, Nyman, Koski, and Corander 2015) and probabilistic decision graphs (Jaeger, Nielsen, and Silander 2006). Unlike most of its competitors, the chain event graph (CEG) (Collazo, Görgen, and Smith 2018; Smith and Anderson 2008; Riccomagno and Smith 2004, 2009) can capture all (context-specific) conditional independences in a unique graph, obtained by a coalescence over the vertices of an appropriately constructed probability tree, called staged tree.