We report on the potential for using algorithms for non-negative matrix factorization (NMF) to improve parameter estimation in topic models. While several papers have studied connections between NMF and topic models, none have suggested leveraging these connections to develop new algorithms for fitting topic models. Importantly, NMF avoids the "sum-to-one" constraints on the topic model parameters, resulting in an optimization problem with simpler structure and more efficient computations. Building on recent advances in optimization algorithms for NMF, we show that first solving the NMF problem then recovering the topic model fit can produce remarkably better fits, and in less time, than standard algorithms for topic models. While we focus primarily on maximum likelihood estimation, we show that this approach also has the potential to improve variational inference for topic models. Our methods are implemented in the R package fastTopics.

We present a Bayesian treatment for deep regression using an Errors-in-Variables model which accounts for the uncertainty associated with the input to the employed neural network. It is shown how the treatment can be combined with already existing approaches for uncertainty quantification that are based on variational inference. Our approach yields a decomposition of the predictive uncertainty into an aleatoric and epistemic part that is more complete and, in many cases, more consistent from a statistical perspective. We illustrate and discuss the approach along various toy and real world examples.

The viral load of patients infected with SARS-CoV-2 varies on logarithmic scales and possibly with age. Controversial claims have been made in the literature regarding whether the viral load distribution actually depends on the age of the patients. Such a dependence would have implications for the COVID-19 spreading mechanism, the age-dependent immune system reaction, and thus for policymaking. We hereby develop a method to analyze viral-load distribution data as a function of the patients' age within a flexible, non-parametric, hierarchical, Bayesian, and causal model. This method can be applied to other contexts as well, and for this purpose, it is made freely available. The developed reconstruction method also allows testing for bias in the data. This could be due to, e.g., bias in patient-testing and data collection or systematic errors in the measurement of the viral load. We perform these tests by calculating the Bayesian evidence for each implied possible causal direction. When applying these tests to publicly available age and SARS-CoV-2 viral load data, we find a statistically significant increase in the viral load with age, but only for one of the two analyzed datasets. If we consider this dataset, and based on the current understanding of viral load's impact on patients' infectivity, we expect a non-negligible difference in the infectivity of different age groups. This difference is nonetheless too small to justify considering any age group as noninfectious.

Ordinary differential equations (ODEs), commonly used to characterize the dynamic systems, are difficult to propose in closed-form for many complicated scientific applications, even with the help of domain expert. We propose a fast and accurate data-driven method, MAGI-X, to learn the unknown dynamic from the observation data in a non-parametric fashion, without the need of any domain knowledge. Unlike the existing methods that mainly rely on the costly numerical integration, MAGI-X utilizes the powerful functional approximator of neural network to learn the unknown nonlinear dynamic within the MAnifold-constrained Gaussian process Inference (MAGI) framework that completely circumvents the numerical integration. Comparing against the state-of-the-art methods on three realistic examples, MAGI-X achieves competitive accuracy in both fitting and forecasting while only taking a fraction of computational time. Moreover, MAGI-X provides practical solution for the inference of partial observed systems, which no previous method is able to handle.

Deep ensembles can be seen as the current state-of-the-art for uncertainty quantification in deep learning. While the approach was originally proposed as an non-Bayesian technique, arguments towards its Bayesian footing have been put forward as well. We show that deep ensembles can be viewed as an approximate Bayesian method by specifying the corresponding assumptions. Our finding leads to an improved approximation which results in an increased epistemic part of the uncertainty. Numerical examples suggest that the improved approximation can lead to more reliable uncertainties. Analytical derivations ensure easy calculation of results.

"The key distinguishing property of a Bayesian approach is marginalization instead of optimization, where we represent solutions given by all settings of parameters weighted by their posterior probabilities, rather than bet everything on a single setting of parameters." The time is ripe to dig into marginalization vs optimization, and broaden our general understanding of the Bayesian approach.

We consider the problem of modeling trajectories of drivers in a road network from the perspective of inverse reinforcement learning. As rational agents, drivers are trying to maximize some reward function unknown to an external observer as they make up their trajectories. We apply the concept of random utility from microeconomic theory to model the unknown reward function as a function of observable features plus an error term which represents features known only to the driver. We develop a parameterized generative model for the trajectories based on a random utility Markov decision process formulation of drivers decisions. We show that maximum entropy inverse reinforcement learning is a particular case of our proposed formulation when we assume a Gumbel density function for the unobserved reward error terms. We illustrate Bayesian inference on model parameters through a case study with real trajectory data from a large city obtained from sensors placed on sparsely distributed points on the street network.

Bayesian structure learning allows inferring Bayesian network structure from data while reasoning about the epistemic uncertainty -- a key element towards enabling active causal discovery and designing interventions in real world systems. In this work, we propose a general, fully differentiable framework for Bayesian structure learning (DiBS) that operates in the continuous space of a latent probabilistic graph representation. Building on recent advances in variational inference, we use DiBS to devise an efficient method for approximating posteriors over structural models. Contrary to existing work, DiBS is agnostic to the form of the local conditional distributions and allows for joint posterior inference of both the graph structure and the conditional distribution parameters. This makes our method directly applicable to posterior inference of nonstandard Bayesian network models, e.g., with nonlinear dependencies encoded by neural networks. In evaluations on simulated and real-world data, DiBS significantly outperforms related approaches to joint posterior inference.

A test is adaptive when its sequence and number of questions is dynamically tuned on the basis of the estimated skills of the taker. Graphical models, such as Bayesian networks, are used for adaptive tests as they allow to model the uncertainty about the questions and the skills in an explainable fashion, especially when coping with multiple skills. A better elicitation of the uncertainty in the question/skills relations can be achieved by interval probabilities. This turns the model into a credal network, thus making more challenging the inferential complexity of the queries required to select questions. This is especially the case for the information theoretic quantities used as scores to drive the adaptive mechanism. We present an alternative family of scores, based on the mode of the posterior probabilities, and hence easier to explain. This makes considerably simpler the evaluation in the credal case, without significantly affecting the quality of the adaptive process. Numerical tests on synthetic and real-world data are used to support this claim.

After the tremendous advances of deep learning and other AI methods, more attention is flowing into other properties of modern approaches, such as interpretability, fairness, etc. combined in frameworks like Responsible AI. Two research directions, namely Explainable AI and Uncertainty Quantification are becoming more and more important, but have been so far never combined and jointly explored. In this paper, I show how both research areas provide potential for combination, why more research should be done in this direction and how this would lead to an increase in trustability in AI systems.