In the study of natural and artificial complex systems, responses that are not completely determined by the considered decision variables are commonly modelled probabilistically, resulting in response distributions varying across decision space. We consider cases where the spatial variation of these response distributions does not only concern their mean and/or variance but also other features including for instance shape or uni-modality versus multi-modality. Our contributions build upon a non-parametric Bayesian approach to modelling the thereby induced fields of probability distributions, and in particular to a spatial extension of the logistic Gaussian model. The considered models deliver probabilistic predictions of response distributions at candidate points, allowing for instance to perform (approximate) posterior simulations of probability density functions, to jointly predict multiple moments and other functionals of target distributions, as well as to quantify the impact of collecting new samples on the state of knowledge of the distribution field of interest. In particular, we introduce adaptive sampling strategies leveraging the potential of the considered random distribution field models to guide system evaluations in a goal-oriented way, with a view towards parsimoniously addressing calibration and related problems from non-linear (stochastic) inversion and global optimisation.

Today, the use of social networking data has attracted a lot of academic and commercial attention in predicting the stock market. In most studies in this area, the sentiment analysis of the content of user posts on social networks is used to predict market fluctuations. Predicting stock marketing is challenging because of the variables involved. In the short run, the market behaves like a voting machine, but in the long run, it acts like a weighing machine. The purpose of this study is to predict EUR/USD stock behavior using Capsule Network on finance texts and Candlestick images. One of the most important features of Capsule Network is the maintenance of features in a vector, which also takes into account the space between features. The proposed model, TI-Capsule (Text and Image information based Capsule Neural Network), is trained with both the text and image information simultaneously. Extensive experiments carried on the collected dataset have demonstrated the effectiveness of TI-Capsule in solving the stock exchange prediction problem with 91% accuracy.

Particle Filtering (PF) methods are an established class of procedures for performing inference in non-linear state-space models. Resampling is a key ingredient of PF, necessary to obtain low variance likelihood and states estimates. However, traditional resampling methods result in PF-based loss functions being non-differentiable with respect to model and PF parameters. In a variational inference context, resampling also yields high variance gradient estimates of the PF-based evidence lower bound. By leveraging optimal transport ideas, we introduce a principled differentiable particle filter and provide convergence results. We demonstrate this novel method on a variety of applications.

We consider the problem of minimizing a function over the manifold of orthogonal matrices. The majority of algorithms for this problem compute a direction in the tangent space, and then use a retraction to move in that direction while staying on the manifold. Unfortunately, the numerical computation of retractions on the orthogonal manifold always involves some expensive linear algebra operation, such as matrix inversion or matrix square-root. These operations quickly become expensive as the dimension of the matrices grows. To bypass this limitation, we propose the landing algorithm which does not involve retractions. The algorithm is not constrained to stay on the manifold but its evolution is driven by a potential energy which progressively attracts it towards the manifold. One iteration of the landing algorithm only involves matrix multiplications, which makes it cheap compared to its retraction counterparts. We provide an analysis of the convergence of the algorithm, and demonstrate its promises on large-scale problems, where it is faster and less prone to numerical errors than retraction-based methods.

We analyse prior risk factors for severe, critical or fatal courses of Covid-19 based on a retrospective cohort using claims data of the AOK Bayern. As our main methodological contribution, we avoid prior grouping and pre-selection of candidate risk factors. Instead, fine-grained hierarchical information from medical classification systems for diagnoses, pharmaceuticals and procedures are used, resulting in more than 33,000 covariates. Our approach has better predictive ability than well-specified morbidity groups but does not need prior subject-matter knowledge. The methodology and estimated coefficients are made available to decision makers to prioritize protective measures towards vulnerable subpopulations and to researchers who like to adjust for a large set of confounders in studies of individual risk factors.

Increasingly large datasets are rapidly driving up the computational costs of machine learning. Prototype generation methods aim to create a small set of synthetic observations that accurately represent a training dataset but greatly reduce the computational cost of learning from it. Assigning soft labels to prototypes can allow increasingly small sets of prototypes to accurately represent the original training dataset. Although foundational work on `less than one'-shot learning has proven the theoretical plausibility of learning with fewer than one observation per class, developing practical algorithms for generating such prototypes remains an unexplored territory. We propose a novel, modular method for generating soft-label prototypical lines that still maintains representational accuracy even when there are fewer prototypes than the number of classes in the data. In addition, we propose the Hierarchical Soft-Label Prototype k-Nearest Neighbor classification algorithm based on these prototypical lines. We show that our method maintains high classification accuracy while greatly reducing the number of prototypes required to represent a dataset, even when working with severely imbalanced and difficult data. Our code is available at https://github.com/ilia10000/SLkNN.

Event coreference continues to be a challenging problem in information extraction. With the absence of any external knowledge bases for events, coreference becomes a clustering task that relies on effective representations of the context in which event mentions appear. Recent advances in contextualized language representations have proven successful in many tasks, however, their use in event linking been limited. Here we present a three part approach that (1) uses representations derived from a pretrained BERT model to (2) train a neural classifier to (3) drive a simple clustering algorithm to create coreference chains. We achieve state of the art results with this model on two standard datasets for within-document event coreference task and establish a new standard on a third newer dataset.

Modern machine learning models such as deep neural networks with high accuracy tend to be miscalibrated: The predicted top probability (confidence) does not reflect the actual accuracy of the model, and tends to be over-confident. For example, a WideResNet 32 on CIFAR100 has on average a predicted top probability of 87%, while the actual test accuracy is only 72% (Guo et al., 2017). As the confidence is often comprehended as an estimate of the true accuracy, such over-confidence could be dangerous, especially in risk-sensitive domains such as medical AI (Begoli et al., 2019), self-driving cars (Michelmore et al., 2018), and so on. To address this issue, there is a growing line of research on improving the calibration of models, by either performing recalibration of well-trained models to adjust the confidence scores (Platt et al., 1999; Zadrozny and Elkan; Naeini et al., 2015; Guo et al., 2017), or by averaging the predictions over multiple models to make the confidence scores more accurate (Lakshminarayanan et al., 2016; Gal and Ghahramani, 2016). These methods in general can reduce the over-confidence and improve the calibration of the model, while preserving (or even improving) the model's accuracy (Ovadia et al., 2019). Despite these progresses, the more fundamental question of why such over-confidence happens for vanillaly trained models remains not satisfactorily understood.

Annealed Importance Sampling (AIS) and its Sequential Monte Carlo (SMC) extensions are state-of-the-art methods for estimating normalizing constants of probability distributions. We propose here a novel Monte Carlo algorithm, Annealed Flow Transport (AFT), that builds upon AIS and SMC and combines them with normalizing flows (NF) for improved performance. This method transports a set of particles using not only importance sampling (IS), Markov chain Monte Carlo (MCMC) and resampling steps - as in SMC, but also relies on NF which are learned sequentially to push particles towards the successive annealed targets. We provide limit theorems for the resulting Monte Carlo estimates of the normalizing constant and expectations with respect to the target distribution. Additionally, we show that a continuous-time scaling limit of the population version of AFT is given by a Feynman--Kac measure which simplifies to the law of a controlled diffusion for expressive NF. We demonstrate experimentally the benefits and limitations of our methodology on a variety of applications.

Natural-gradient descent on structured parameter spaces (e.g., low-rank covariances) is computationally challenging due to complicated inverse Fisher-matrix computations. We address this issue for optimization, inference, and search problems by using \emph{local-parameter coordinates}. Our method generalizes an existing evolutionary-strategy method, recovers Newton and Riemannian-gradient methods as special cases, and also yields new tractable natural-gradient algorithms for learning flexible covariance structures of Gaussian and Wishart-based distributions. We show results on a range of applications on deep learning, variational inference, and evolution strategies. Our work opens a new direction for scalable structured geometric methods via local parameterizations.