Real world-datasets characterized by discrete features are ubiquitous: from categorical surveys to clinical questionnaires, from unweighted networks to DNA sequences. Nevertheless, the most common unsupervised dimensional reduction methods are designed for continuous spaces, and their use for discrete spaces can lead to errors and biases. In this letter we introduce an algorithm to infer the intrinsic dimension (ID) of datasets embedded in discrete spaces. We demonstrate its accuracy on benchmark datasets, and we apply it to analyze a metagenomic dataset for species fingerprinting, finding a surprisingly small ID, of order 2. This suggests that evolutive pressure acts on a low-dimensional manifold despite the high-dimensionality of sequences' space.

Several generic methods have recently been developed for change detection in heterogeneous remote sensing data, such as images from synthetic aperture radar (SAR) and multispectral radiometers. However, these are not well suited to detect weak signatures of certain disturbances of ecological systems. To resolve this problem we propose a new approach based on image-to-image translation and one-class classification (OCC). We aim to map forest mortality caused by an outbreak of geometrid moths in a sparsely forested forest-tundra ecotone using multisource satellite images. The images preceding and following the event are collected by Landsat-5 and RADARSAT-2, respectively. Using a recent deep learning method for change-aware image translation, we compute difference images in both satellites' respective domains. These differences are stacked with the original pre- and post-event images and passed to an OCC trained on a small sample from the targeted change class. The classifier produces a credible map of the complex pattern of forest mortality.

Estimating a Gibbs density function given a sample is an important problem in computational statistics and statistical learning. Although the well established maximum likelihood method is commonly used, it requires the computation of the partition function (i.e., the normalization of the density). This function can be easily calculated for simple low-dimensional problems but its computation is difficult or even intractable for general densities and high-dimensional problems. In this paper we propose an alternative approach based on Maximum A-Posteriori (MAP) estimators, we name Maximum Recovery MAP (MR-MAP), to derive estimators that do not require the computation of the partition function, and reformulate the problem as an optimization problem. We further propose a least-action type potential that allows us to quickly solve the optimization problem as a feed-forward hyperbolic neural network. We demonstrate the effectiveness of our methods on some standard data sets.

Current work on using visual analytics to determine causal relations among variables has mostly been based on the concept of counterfactuals. As such the derived static causal networks do not take into account the effect of time as an indicator. However, knowing the time delay of a causal relation can be crucial as it instructs how and when actions should be taken. Yet, similar to static causality, deriving causal relations from observational time-series data, as opposed to designed experiments, is not a straightforward process. It can greatly benefit from human insight to break ties and resolve errors. We hence propose a set of visual analytics methods that allow humans to participate in the discovery of causal relations associated with windows of time delay. Specifically, we leverage a well-established method, logic-based causality, to enable analysts to test the significance of potential causes and measure their influences toward a certain effect. Furthermore, since an effect can be a cause of other effects, we allow users to aggregate different temporal cause-effect relations found with our method into a visual flow diagram to enable the discovery of temporal causal networks. To demonstrate the effectiveness of our methods we constructed a prototype system named DOMINO and showcase it via a number of case studies using real-world datasets. Finally, we also used DOMINO to conduct several evaluations with human analysts from different science domains in order to gain feedback on the utility of our system in practical scenarios.

Abstract-- In this paper, we present an algorithm for learning time-correlated measurement covariances for application in batch state estimation. We parameterize the inverse measurement covariance matrix to be block-banded, which conveniently factorizes and results in a computationally efficient approach for correlating measurements across the entire trajectory. We train our covariance model through supervised learning using the groundtruth trajectory. In applications where the measurements are time-correlated, we demonstrate improved performance in both the mean posterior estimate and the covariance (i.e., improved estimator consistency). We verify that our proposed method results in a consistent In the research field of probabilistic robotics, we formulate batch estimator in a controlled simulation via a statistical test state estimation using probability theory in order to handle over several trials.

Electricity is traded on various markets with different time horizons and regulations. Short-term intraday trading becomes increasingly important due to the higher penetration of renewables. In Germany, the intraday electricity price typically fluctuates around the day-ahead price of the European Power EXchange (EPEX) spot markets in a distinct hourly pattern. This work proposes a probabilistic modeling approach that models the intraday price difference to the day-ahead contracts. The model captures the emerging hourly pattern by considering the four 15 min intervals in each day-ahead price interval as a four-dimensional joint probability distribution. The resulting nontrivial, multivariate price difference distribution is learned using a normalizing flow, i.e., a deep generative model that combines conditional multivariate density estimation and probabilistic regression. Furthermore, this work discusses the influence of different external impact factors based on literature insights and impact analysis using explainable artificial intelligence (XAI). The normalizing flow is compared to an informed selection of historical data and probabilistic forecasts using a Gaussian copula and a Gaussian regression model. Among the different models, the normalizing flow identifies the trends with the highest accuracy and has the narrowest prediction intervals. Both the XAI analysis and the empirical experiments highlight that the immediate history of the price difference realization and the increments of the day-ahead price have the most substantial impact on the price difference.

Retinal microsurgery is a high-precision surgery performed on an exceedingly delicate tissue. It now requires extensively trained and highly skilled surgeons. Given the restricted range of instrument motion in the confined intraocular space, and also potentially restricting instrument contact with the sclera, snake-like robots may prove to be a promising technology to provide surgeons with greater flexibility, dexterity, space access, and positioning accuracy during retinal procedures requiring high precision and advantageous tooltip approach angles, such as retinal vein cannulation and epiretinal membrane peeling. Kinematics modeling of these robots is an essential step toward accurate position control, however, as opposed to conventional manipulators, modeling of these robots does not follow a straightforward method due to their complex mechanical structure and actuation mechanisms. Especially, in wire-driven snake-like robots, the hysteresis problem due to the wire tension condition can have a significant impact on the positioning accuracy of these robots. In this paper, we proposed an experimental kinematics model with a hysteresis compensation algorithm using the probabilistic Gaussian mixture models (GMM) Gaussian mixture regression (GMR) approach. Experimental results on the two-degree-of-freedom (DOF) integrated robotic intraocular snake (I2RIS) show that the proposed model provides 0.4 deg accuracy, which is an overall 60% and 70% of improvement for yaw and pitch degrees of freedom, respectively, compared to a previous model of this robot.

Epidemic models are powerful tools in understanding infectious disease. However, as they increase in size and complexity, they can quickly become computationally intractable. Recent progress in modelling methodology has shown that surrogate models can be used to emulate complex epidemic models with a high-dimensional parameter space. We show that deep sequence-to-sequence (seq2seq) models can serve as accurate surrogates for complex epidemic models with sequence based model parameters, effectively replicating seasonal and long-term transmission dynamics. Once trained, our surrogate can predict scenarios a several thousand times faster than the original model, making them ideal for policy exploration. We demonstrate that replacing a traditional epidemic model with a learned simulator facilitates robust Bayesian inference.

Vine copulas can efficiently model multivariate probability distributions. This paper focuses on a more thorough understanding of their structures, since in the literature, vine copula representations are often ambiguous. The graph representations include the original, cherry and chordal graph sequence structures, which we show equivalence between. Importantly we also show a new result, namely that when a perfect elimination ordering of a vine structure is given, then it can always be uniquely represented with a matrix. O. M. N\'apoles has shown a way to represent vines in a matrix, and we algorithmify this previous approach, while also showing a new method for constructing such a matrix, through cherry tree sequences. We also calculate the runtime of these algorithms. Lastly, we prove that these two matrix-building algorithms are equivalent if the same perfect elimination ordering is being used.

Causal discovery aims to uncover causal structure among a set of variables. Score-based approaches mainly focus on searching for the best Directed Acyclic Graph (DAG) based on a predefined score function. However, most of them are not applicable on a large scale due to the limited searchability. Inspired by the active learning in generative flow networks, we propose a novel approach to learning a DAG from observational data called GFlowCausal. It converts the graph search problem to a generation problem, in which direct edges are added gradually. GFlowCausal aims to learn the best policy to generate high-reward DAGs by sequential actions with probabilities proportional to predefined rewards. We propose a plug-and-play module based on transitive closure to ensure efficient sampling. Theoretical analysis shows that this module could guarantee acyclicity properties effectively and the consistency between final states and fully-connected graphs. We conduct extensive experiments on both synthetic and real datasets, and results show the proposed approach to be superior and also performs well in a large-scale setting.