We consider the problem of exploration-exploitation in communicating Markov Decision Processes. We provide an analysis of UCRL2 with Empirical Bernstein inequalities (UCRL2B). For any MDP with $S$ states, $A$ actions, $\Gamma \leq S$ next states and diameter $D$, the regret of UCRL2B is bounded as $\widetilde{O}(\sqrt{D\Gamma S A T})$.

The maximum entropy principle advocates to evaluate events' probabilities using a distribution that maximizes entropy among those that satisfy certain expectations' constraints. Such principle can be generalized for arbitrary decision problems where it corresponds to minimax approaches. This paper establishes a framework for supervised classification based on the generalized maximum entropy principle that leads to minimax risk classifiers (MRCs). We develop learning techniques that determine MRCs for general entropy functions and provide performance guarantees by means of convex optimization. In addition, we describe the relationship of the presented techniques with existing classification methods, and quantify MRCs performance in comparison with the proposed bounds and conventional methods.

Continuously-indexed flows (CIFs) have recently achieved improvements over baseline normalizing flows in a variety of density estimation tasks. In this paper, we adapt CIFs to the task of variational inference (VI) through the framework of auxiliary VI, and demonstrate that the advantages of CIFs over baseline flows can also translate to the VI setting for both sampling from posteriors with complicated topology and performing maximum likelihood estimation in latent-variable models.

Diagnosing diseases such as leukemia or anemia requires reliable counts of blood cells. Hematologists usually label and count microscopy images of blood cells manually. In many cases, however, cells in different maturity states are difficult to distinguish, and in combination with image noise and subjectivity, humans are prone to make labeling mistakes. This results in labels that are often not reproducible, which can directly affect the diagnoses. We introduce TIMELY, a probabilistic model that combines pseudotime inference methods with inhomogeneous hidden Markov trees, which addresses this challenge of label inconsistency. We show first on simulation data that TIMELY is able to identify and correct wrong labels with higher precision and recall than baseline methods for labeling correction. We then apply our method to two real-world datasets of blood cell data and show that TIMELY successfully finds inconsistent labels, thereby improving the quality of human-generated labels.

Convolutional Neural Networks (CNN) possess many positive qualities when it comes to spatial raster data. Translation invariance enables CNNs to detect features regardless of their position in the scene. However, in some domains, like geospatial, not all locations are exactly equal. In this work, we propose localized convolutional neural networks that enable convolutional architectures to learn local features in addition to the global ones. We investigate their instantiations in the form of learnable inputs, local weights, and a more general form. They can be added to any convolutional layers, easily end-to-end trained, introduce minimal additional complexity, and let CNNs retain most of their benefits to the extent that they are needed. In this work we address spatio-temporal prediction: test the effectiveness of our methods on a synthetic benchmark dataset and tackle three real-world wind prediction datasets. For one of them, we propose a method to spatially order the unordered data. We compare the recent state-of-the-art spatio-temporal prediction models on the same data. Models that use convolutional layers can be and are extended with our localizations. In all these cases our extensions improve the results, and thus often the state-of-the-art. We share all the code at a public repository.

We train an agent to navigate in 3D environments using a hierarchical strategy including a high-level graph based planner and a local policy. Our main contribution is a data driven learning based approach for planning under uncertainty in topological maps, requiring an estimate of shortest paths in valued graphs with a probabilistic structure. Whereas classical symbolic algorithms achieve optimal results on noise-less topologies, or optimal results in a probabilistic sense on graphs with probabilistic structure, we aim to show that machine learning can overcome missing information in the graph by taking into account rich high-dimensional node features, for instance visual information available at each location of the map. Compared to purely learned neural white box algorithms, we structure our neural model with an inductive bias for dynamic programming based shortest path algorithms, and we show that a particular parameterization of our neural model corresponds to the Bellman-Ford algorithm. By performing an empirical analysis of our method in simulated photo-realistic 3D environments, we demonstrate that the inclusion of visual features in the learned neural planner outperforms classical symbolic solutions for graph based planning.

From February to April 2020, many countries introduced variations on social distancing measures to slow the ravages of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Publicly available data show that Germany has been particularly successful in minimizing death rates. Dehning et al. quantified three governmental interventions introduced to control the outbreak. The authors predicted that the third governmental intervention—a strict contact ban since 22 March—switched incidence from growth to decay. They emphasize that relaxation of controls must be done carefully, not only because there is a 2-week lag between a measure being enacted and the effect on case reports but also because the three measures used in Germany only just kept virus spread below the growth threshold. Science , this issue p. [eabb9789][1] ### INTRODUCTION When faced with the outbreak of a novel epidemic such as coronavirus disease 2019 (COVID-19), rapid response measures are required by individuals, as well as by society as a whole, to mitigate the spread of the virus. During this initial, time-critical period, neither the central epidemiological parameters nor the effectiveness of interventions such as cancellation of public events, school closings, or social distancing is known. ### RATIONALE As one of the key epidemiological parameters, we inferred the spreading rate λ from confirmed SARS-CoV-2 infections using the example of Germany. We apply Bayesian inference based on Markov chain Monte Carlo sampling to a class of compartmental models [susceptible-infected-recovered (SIR)]. Our analysis characterizes the temporal change of the spreading rate and allows us to identify potential change points. Furthermore, it enables short-term forecast scenarios that assume various degrees of social distancing. A detailed description is provided in the accompanying paper, and the models, inference, and forecasts are available on GitHub ([https://github.com/Priesemann-Group/covid19\_inference\_forecast][2]). Although we apply the model to Germany, our approach can be readily adapted to other countries or regions. ### RESULTS In Germany, interventions to contain the COVID-19 outbreak were implemented in three steps over 3 weeks: (i) Around 9 March 2020, large public events such as soccer matches were canceled; (ii) around 16 March 2020, schools, childcare facilities, and many stores were closed; and (iii) on 23 March 2020, a far-reaching contact ban ( Kontaktsperre ) was imposed by government authorities; this included the prohibition of even small public gatherings as well as the closing of restaurants and all nonessential stores. From the observed case numbers of COVID-19, we can quantify the impact of these measures on the disease spread using change point analysis. Essentially, we find that at each change point the spreading rate λ decreased by ~40%. At the first change point, assumed around 9 March 2020, λ decreased from 0.43 to 0.25, with 95% credible intervals (CIs) of [0.35, 0.51] and [0.20, 0.30], respectively. At the second change point, assumed around 16 March 2020, λ decreased to 0.15 (CI [0.12, 0.20]). Both changes in λ slowed the spread of the virus but still implied exponential growth (see red and orange traces in the figure). To contain the disease spread, i.e., to turn exponential growth into a decline of new cases, the spreading rate has to be smaller than the recovery rate μ = 0.13 (CI [0.09, 0.18]). This critical transition was reached with the third change point, which resulted in λ = 0.09 (CI [0.06, 0.13]; see blue trace in the figure), assumed around 23 March 2020. From the peak position of daily new cases, one could conclude that the transition from growth to decline was already reached at the end of March. However, the observed transient decline can be explained by a short-term effect that originates from a sudden change in the spreading rate (see Fig. 2C in the main text). As long as interventions and the concurrent individual behavior frequently change the spreading rate, reliable short- and long-term forecasts are very difficult. As the figure shows, the three example scenarios (representing the effects up to the first, second, and third change point) quickly diverge from each other and, consequently, span a considerable range of future case numbers. Inference and subsequent forecasts are further complicated by the delay of ~2 weeks between an intervention and the first useful estimates of the new λ (which are derived from the reported case numbers). Because of this delay, any uncertainty in the magnitude of social distancing in the previous 2 weeks can have a major impact on the case numbers in the subsequent 2 weeks. Beyond 2 weeks, the case numbers depend on our future behavior, for which we must make explicit assumptions. In sum, future interventions (such as lifting restrictions) should be implemented cautiously to respect the delayed visibility of their effects. ### CONCLUSION We developed a Bayesian framework for the spread of COVID-19 to infer central epidemiological parameters and the timing and magnitude of intervention effects. With such an approach, the effects of interventions can be assessed in a timely manner. Future interventions and lifting of restrictions can be modeled as additional change points, enabling short-term forecasts for case numbers. In general, our approach may help to infer the efficiency of measures taken in other countries and inform policy-makers about tightening, loosening, and selecting appropriate measures for containment of COVID-19. ![Figure][3] Bayesian inference of SIR model parameters from daily new cases of COVID-19 enables us to assess the impact of interventions. In Germany, three interventions (mild social distancing, strong social distancing, and contact ban) were enacted consecutively (circles). Colored lines depict the inferred models that include the impact of one, two, or three interventions (red, orange, or green, respectively, with individual data cutoff) or all available data until 21 April 2020 (blue). Forecasts (dashed lines) show how case numbers would have developed without the effects of the subsequent change points. Note the delay between intervention and first possible inference of parameters caused by the reporting delay and the necessary accumulation of evidence (gray arrows). Shaded areas indicate 50% and 95% Bayesian credible intervals. As coronavirus disease 2019 (COVID-19) is rapidly spreading across the globe, short-term modeling forecasts provide time-critical information for decisions on containment and mitigation strategies. A major challenge for short-term forecasts is the assessment of key epidemiological parameters and how they change when first interventions show an effect. By combining an established epidemiological model with Bayesian inference, we analyzed the time dependence of the effective growth rate of new infections. Focusing on COVID-19 spread in Germany, we detected change points in the effective growth rate that correlate well with the times of publicly announced interventions. Thereby, we could quantify the effect of interventions and incorporate the corresponding change points into forecasts of future scenarios and case numbers. Our code is freely available and can be readily adapted to any country or region. [1]: /lookup/doi/10.1126/science.abb9789 [2]: https://github.com/Priesemann-Group/covid19_inference_forecast [3]: pending:yes

The Apperception Engine is an unsupervised learning system. Given a sequence of sensory inputs, it constructs a symbolic causal theory that both explains the sensory sequence and also satisfies a set of unity conditions. The unity conditions insist that the constituents of the theory - objects, properties, and laws - must be integrated into a coherent whole. Once a theory has been constructed, it can be applied to predict future sensor readings, retrodict earlier readings, or impute missing readings. In this paper, we evaluate the Apperception Engine in a diverse variety of domains, including cellular automata, rhythms and simple nursery tunes, multi-modal binding problems, occlusion tasks, and sequence induction intelligence tests. In each domain, we test our engine's ability to predict future sensor values, retrodict earlier sensor values, and impute missing sensory data. The engine performs well in all these domains, significantly outperforming neural net baselines and state of the art inductive logic programming systems. These results are significant because neural nets typically struggle to solve the binding problem (where information from different modalities must somehow be combined together into different aspects of one unified object) and fail to solve occlusion tasks (in which objects are sometimes visible and sometimes obscured from view). We note in particular that in the sequence induction intelligence tests, our system achieved human-level performance. This is notable because our system is not a bespoke system designed specifically to solve intelligence tests, but a general-purpose system that was designed to make sense of any sensory sequence.

Smart FinTech has emerged as a new area that synthesizes and transforms AI and finance, and broadly data science, machine learning, economics, etc. Smart FinTech also transforms and drives new economic and financial businesses, services and systems, and plays an increasingly important role in economy, technology and society transformation. This article presents a highly summarized research overview of smart FinTech, including FinTech businesses and challenges, various FinTech-associated data and repositories, FinTech-driven business decision and optimization, areas in smart FinTech, and research methods and techniques for smart FinTech.

In this work, we propose KeRNS: an algorithm for episodic reinforcement learning in non-stationary Markov Decision Processes (MDPs) whose state-action set is endowed with a metric. Using a non-parametric model of the MDP built with time-dependent kernels, we prove a regret bound that scales with the covering dimension of the state-action space and the total variation of the MDP with time, which quantifies its level of non-stationarity. Our method generalizes previous approaches based on sliding windows and exponential discounting used to handle changing environments. We further propose a practical implementation of KeRNS, we analyze its regret and validate it experimentally.