This paper addresses a major challenge to historical research on the 19th century. Large quantities of sources have become digitally available for the first time, while extraction techniques are lagging behind. Therefore, we researched machine learning (ML) models to recognise and extract complex data structures in a high-value historical primary source, the Schematismus. It records every single person in the Habsburg civil service above a certain hierarchical level between 1702 and 1918 and documents the genesis of the central administration over two centuries. Its complex and intricate structure as well as its enormous size have so far made any more comprehensive analysis of the administrative and social structure of the later Habsburg Empire on the basis of this source impossible. We pursued two central objectives: Primarily, the improvement of the OCR quality, for which we considered an improved structure recognition to be essential; in the further course, it turned out that this also made the extraction of the data structure possible. We chose Faster R-CNN as base for the ML architecture for structure recognition. In order to obtain the required amount of training data quickly and economically, we synthesised Hof- und Staatsschematismus-style data, which we used to train our model. The model was then fine-tuned with a smaller set of manually annotated historical source data. We then used Tesseract-OCR, which was further optimised for the style of our documents, to complete the combined structure extraction and OCR process. Results show a significant decrease in the two standard parameters of OCR-performance, WER and CER (where lower values are better). Combined structure detection and fine-tuned OCR improved CER and WER values by remarkable 71.98 percent (CER) respectively 52.49 percent (WER).

Gaussian processes (GPs) are a Bayesian machine learning approach widely used to construct surrogate models for the uncertainty quantification of computer simulation codes in industrial applications. It provides both a mean predictor and an estimate of the posterior prediction variance, the latter being used to produce Bayesian credibility intervals. Interpreting these intervals relies on the Gaussianity of the simulation model as well as the well-specification of the priors which are not always appropriate. We propose to address this issue with the help of conformal prediction. In the present work, a method for building adaptive cross-conformal prediction intervals is proposed by weighting the non-conformity score with the posterior standard deviation of the GP. The resulting conformal prediction intervals exhibit a level of adaptivity akin to Bayesian credibility sets and display a significant correlation with the surrogate model local approximation error, while being free from the underlying model assumptions and having frequentist coverage guarantees. These estimators can thus be used for evaluating the quality of a GP surrogate model and can assist a decision-maker in the choice of the best prior for the specific application of the GP. The performance of the method is illustrated through a panel of numerical examples based on various reference databases. Moreover, the potential applicability of the method is demonstrated in the context of surrogate modeling of an expensive-to-evaluate simulator of the clogging phenomenon in steam generators of nuclear reactors.

In numerous applications, binary reactions or event counts are observed and stored within high-order tensors. Tensor decompositions (TDs) serve as a powerful tool to handle such high-dimensional and sparse data. However, many traditional TDs are explicitly or implicitly designed based on the Gaussian distribution, which is unsuitable for discrete data. Moreover, most TDs rely on predefined multi-linear structures, such as CP and Tucker formats. Therefore, they may not be effective enough to handle complex real-world datasets. To address these issues, we propose ENTED, an \underline{E}fficient \underline{N}onparametric \underline{TE}nsor \underline{D}ecomposition for binary and count tensors. Specifically, we first employ a nonparametric Gaussian process (GP) to replace traditional multi-linear structures. Next, we utilize the \pg augmentation which provides a unified framework to establish conjugate models for binary and count distributions. Finally, to address the computational issue of GPs, we enhance the model by incorporating sparse orthogonal variational inference of inducing points, which offers a more effective covariance approximation within GPs and stochastic natural gradient updates for nonparametric models. We evaluate our model on several real-world tensor completion tasks, considering binary and count datasets. The results manifest both better performance and computational advantages of the proposed model.

For obtaining optimal first-order convergence guarantee for stochastic optimization, it is necessary to use a recurrent data sampling algorithm that samples every data point with sufficient frequency. Most commonly used data sampling algorithms (e.g., i.i.d., MCMC, random reshuffling) are indeed recurrent under mild assumptions. In this work, we show that for a particular class of stochastic optimization algorithms, we do not need any other property (e.g., independence, exponential mixing, and reshuffling) than recurrence in data sampling algorithms to guarantee the optimal rate of first-order convergence. Namely, using regularized versions of Minimization by Incremental Surrogate Optimization (MISO), we show that for non-convex and possibly non-smooth objective functions, the expected optimality gap converges at an optimal rate $O(n^{-1/2})$ under general recurrent sampling schemes. Furthermore, the implied constant depends explicitly on the `speed of recurrence', measured by the expected amount of time to visit a given data point either averaged (`target time') or supremized (`hitting time') over the current location. We demonstrate theoretically and empirically that convergence can be accelerated by selecting sampling algorithms that cover the data set most effectively. We discuss applications of our general framework to decentralized optimization and distributed non-negative matrix factorization.

Feature Selection is a crucial procedure in Data Science tasks such as Classification, since it identifies the relevant variables, making thus the classification procedures more interpretable, cheaper in terms of measurement and more effective by reducing noise and data overfit. The relevance of features in a classification procedure is linked to the fact that misclassifications costs are frequently asymmetric, since false positive and false negative cases may have very different consequences. However, off-the-shelf Feature Selection procedures seldom take into account such cost-sensitivity of errors. In this paper we propose a mathematical-optimization-based Feature Selection procedure embedded in one of the most popular classification procedures, namely, Support Vector Machines, accommodating asymmetric misclassification costs. The key idea is to replace the traditional margin maximization by minimizing the number of features selected, but imposing upper bounds on the false positive and negative rates. The problem is written as an integer linear problem plus a quadratic convex problem for Support Vector Machines with both linear and radial kernels. The reported numerical experience demonstrates the usefulness of the proposed Feature Selection procedure. Indeed, our results on benchmark data sets show that a substantial decrease of the number of features is obtained, whilst the desired trade-off between false positive and false negative rates is achieved.

Existing semi-supervised learning (SSL) methods assume that labeled and unlabeled data share the same class space. However, in real-world applications, unlabeled data always contain classes not present in the labeled set, which may cause classification performance degradation of known classes. Therefore, open-world SSL approaches are researched to handle the presence of multiple unknown classes in the unlabeled data, which aims to accurately classify known classes while fine-grained distinguishing different unknown classes. To address this challenge, in this paper, we propose an open-world SSL method for Self-learning Open-world Classes (SSOC), which can explicitly self-learn multiple unknown classes. Specifically, SSOC first defines class center tokens for both known and unknown classes and autonomously learns token representations according to all samples with the cross-attention mechanism. To effectively discover novel classes, SSOC further designs a pairwise similarity loss in addition to the entropy loss, which can wisely exploit the information available in unlabeled data from instances' predictions and relationships. Extensive experiments demonstrate that SSOC outperforms the state-of-the-art baselines on multiple popular classification benchmarks. Specifically, on the ImageNet-100 dataset with a novel ratio of 90%, SSOC achieves a remarkable 22% improvement.

Spatial transcriptomics (ST) technologies have revolutionized the study of gene expression patterns in tissues by providing multimodality data in transcriptomic, spatial, and morphological, offering opportunities for understanding tissue biology beyond transcriptomics. However, we identify the modality bias phenomenon in ST data species, i.e., the inconsistent contribution of different modalities to the labels leads to a tendency for the analysis methods to retain the information of the dominant modality. How to mitigate the adverse effects of modality bias to satisfy various downstream tasks remains a fundamental challenge. This paper introduces Multiple-modality Structure Transformation, named MuST, a novel methodology to tackle the challenge. MuST integrates the multi-modality information contained in the ST data effectively into a uniform latent space to provide a foundation for all the downstream tasks. It learns intrinsic local structures by topology discovery strategy and topology fusion loss function to solve the inconsistencies among different modalities. Thus, these topology-based and deep learning techniques provide a solid foundation for a variety of analytical tasks while coordinating different modalities. The effectiveness of MuST is assessed by performance metrics and biological significance. The results show that it outperforms existing state-of-the-art methods with clear advantages in the precision of identifying and preserving structures of tissues and biomarkers. MuST offers a versatile toolkit for the intricate analysis of complex biological systems.

In this paper, we present a novel framework for data redundancy measurement based on probabilistic modeling of datasets, and a new criterion for redundancy detection that is resilient to noise. We also develop new methods for data redundancy reduction using both deterministic and stochastic optimization techniques. Our framework is flexible and can handle different types of features, and our experiments on benchmark datasets demonstrate the effectiveness of our methods. We provide a new perspective on feature selection, and propose effective and robust approaches for both supervised and unsupervised learning problems.

For many data-intensive tasks, feature selection is an important preprocessing step. However, most existing methods do not directly and intuitively explore the intrinsic discriminative information of features. We propose a novel feature selection framework based on the distance between class conditional distributions, measured by integral probability metrics (IPMs). Our framework directly explores the discriminative information of features in the sense of distributions for supervised classification. We analyze the theoretical and practical aspects of IPMs for feature selection, construct criteria based on IPMs. We propose several variant feature selection methods of our framework based on the 1-Wasserstein distance and implement them on real datasets from different domains. Experimental results show that our framework can outperform state-of-the-art methods in terms of classification accuracy and robustness to perturbations.

Feature selection is an important process in machine learning and knowledge discovery. By selecting the most informative features and eliminating irrelevant ones, the performance of learning algorithms can be improved and the extraction of meaningful patterns and insights from data can be facilitated. However, most existing feature selection methods, when applied to large datasets, encountered the bottleneck of high computation costs. To address this problem, we propose a novel filter feature selection method, ContrastFS, which selects discriminative features based on the discrepancies features shown between different classes. We introduce a dimensionless quantity as a surrogate representation to summarize the distributional individuality of certain classes, based on this quantity we evaluate features and study the correlation among them. We validate effectiveness and efficiency of our approach on several widely studied benchmark datasets, results show that the new method performs favorably with negligible computation in comparison with other state-of-the-art feature selection methods.