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.

A generative probabilistic model for relational data consists of a family of probability distributions for relational structures over domains of different sizes. In most existing statistical relational learning (SRL) frameworks, these models are not projective in the sense that the marginal of the distribution for size-$n$ structures on induced sub-structures of size $k

Reinforcement learning (RL) can be used to create a tactical decision-making agent for autonomous driving. However, previous approaches only output decisions and do not provide information about the agent's confidence in the recommended actions. This paper investigates how a Bayesian RL technique, based on an ensemble of neural networks with additional randomized prior functions (RPF), can be used to estimate the uncertainty of decisions in autonomous driving. A method for classifying whether or not an action should be considered safe is also introduced. The performance of the ensemble RPF method is evaluated by training an agent on a highway driving scenario. It is shown that the trained agent can estimate the uncertainty of its decisions and indicate an unacceptable level when the agent faces a situation that is far from the training distribution. Furthermore, within the training distribution, the ensemble RPF agent outperforms a standard Deep Q-Network agent. In this study, the estimated uncertainty is used to choose safe actions in unknown situations. However, the uncertainty information could also be used to identify situations that should be added to the training process.

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.

This thesis contributes to the mathematical foundation of domain adaptation as emerging field in machine learning. In contrast to classical statistical learning, the framework of domain adaptation takes into account deviations between probability distributions in the training and application setting. Domain adaptation applies for a wider range of applications as future samples often follow a distribution that differs from the ones of the training samples. A decisive point is the generality of the assumptions about the similarity of the distributions. Therefore, in this thesis we study domain adaptation problems under as weak similarity assumptions as can be modelled by finitely many moments.

Recent work in adversarial attacks has developed provably robust methods for training deep neural network classifiers. However, although they are often mentioned in the context of robustness, deep generative models themselves have received relatively little attention in terms of formally analyzing their robustness properties. In this paper, we propose a method for training provably robust generative models, specifically a provably robust version of the variational auto-encoder (VAE). To do so, we first formally define a (certifiably) robust lower bound on the variational lower bound of the likelihood, and then show how this bound can be optimized during training to produce a robust VAE. We evaluate the method on simple examples, and show that it is able to produce generative models that are substantially more robust to adversarial attacks (i.e., an adversary trying to perturb inputs so as to drastically lower their likelihood under the model).

Discovery of causal relationships from observational data is an important problem in many areas. Several recent results have established the identifiability of causal DAGs with non-Gaussian and/or nonlinear structural equation models (SEMs). In this paper, we focus on nonlinear SEMs defined by non-invertible functions, which exist in many data domains, and propose a novel test for non-invertible bivariate causal models. We further develop a method to incorporate this test in structure learning of DAGs that contain both linear and nonlinear causal relations. By extensive numerical comparisons, we show that our algorithms outperform existing DAG learning methods in identifying causal graphical structures. We illustrate the practical application of our method in learning causal networks for combinatorial binding of transcription factors from ChIP-Seq data.

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 develop a method for computing policies in Markov decision processes with risk-sensitive measures subject to temporal logic constraints. Specifically, we use a particular risk-sensitive measure from cumulative prospect theory, which has been previously adopted in psychology and economics. The nonlinear transformation of the probabilities and utility functions yields a nonlinear programming problem, which makes computation of optimal policies typically challenging. We show that this nonlinear weighting function can be accurately approximated by the difference of two convex functions. This observation enables efficient policy computation using convex-concave programming. We demonstrate the effectiveness of the approach on several scenarios.