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The objective of this study is to address the difficulty of simplifying the geometric model in which a differential problem is formulated, also called defeaturing, while simultaneously ensuring that the accuracy of the solution is maintained under control. This enables faster and more efficient simulations, without sacrificing accuracy. More precisely, we consider an isogeometric discretisation of an elliptic model problem defined on a two-dimensional hierarchical B-spline computational domain with a complex boundary. Starting with an oversimplification of the geometry, we build a goal-oriented adaptive strategy that adaptively reintroduces continuous geometrical features in regions where the analysis suggests a large impact on the quantity of interest. This strategy is driven by an a posteriori estimator of the defeaturing error based on first-order shape sensitivity analysis, and it profits from the local refinement properties of hierarchical B-splines. The adaptive algorithm is described together with a procedure to generate (partially) simplified hierarchical B-spline geometrical domains. Numerical experiments are presented to illustrate the proposed strategy and its limitations.

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Annotating costs of large corpora are still one of the main bottlenecks in empirical social science research. On the one hand, making use of the capabilities of domain transfer allows re-using annotated data sets and trained models. On the other hand, it is not clear how well domain transfer works and how reliable the results are for transfer across different dimensions. We explore the potential of domain transfer across geographical locations, languages, time, and genre in a large-scale database of political manifestos. First, we show the strong within-domain classification performance of fine-tuned transformer models. Second, we vary the genre of the test set across the aforementioned dimensions to test for the fine-tuned models' robustness and transferability. For switching genres, we use an external corpus of transcribed speeches from New Zealand politicians while for the other three dimensions, custom splits of the Manifesto database are used. While BERT achieves the best scores in the initial experiments across modalities, DistilBERT proves to be competitive at a lower computational expense and is thus used for further experiments across time and country. The results of the additional analysis show that (Distil)BERT can be applied to future data with similar performance. Moreover, we observe (partly) notable differences between the political manifestos of different countries of origin, even if these countries share a language or a cultural background.

A non-intrusive proper generalized decomposition (PGD) strategy, coupled with an overlapping domain decomposition (DD) method, is proposed to efficiently construct surrogate models of parametric linear elliptic problems. A parametric multi-domain formulation is presented, with local subproblems featuring arbitrary Dirichlet interface conditions represented through the traces of the finite element functions used for spatial discretization at the subdomain level, with no need for additional auxiliary basis functions. The linearity of the operator is exploited to devise low-dimensional problems with only few active boundary parameters. An overlapping Schwarz method is used to glue the local surrogate models, solving a linear system for the nodal values of the parametric solution at the interfaces, without introducing Lagrange multipliers to enforce the continuity in the overlapping region. The proposed DD-PGD methodology relies on a fully algebraic formulation allowing for real-time computation based on the efficient interpolation of the local surrogate models in the parametric space, with no additional problems to be solved during the execution of the Schwarz algorithm. Numerical results for parametric diffusion and convection-diffusion problems are presented to showcase the accuracy of the DD-PGD approach, its robustness in different regimes and its superior performance with respect to standard high-fidelity DD methods.

We consider parametrized linear-quadratic optimal control problems and provide their online-efficient solutions by combining greedy reduced basis methods and machine learning algorithms. To this end, we first extend the greedy control algorithm, which builds a reduced basis for the manifold of optimal final time adjoint states, to the setting where the objective functional consists of a penalty term measuring the deviation from a desired state and a term describing the control energy. Afterwards, we apply machine learning surrogates to accelerate the online evaluation of the reduced model. The error estimates proven for the greedy procedure are further transferred to the machine learning models and thus allow for efficient a posteriori error certification. We discuss the computational costs of all considered methods in detail and show by means of two numerical examples the tremendous potential of the proposed methodology.

The paper presents the main characteristics and a preliminary implementation of a novel computational framework named CompLog. Inspired by probabilistic programming systems like ProbLog, CompLog builds upon the inferential mechanisms proposed by Simplicity Theory, relying on the computation of two Kolmogorov complexities (here implemented as min-path searches via ASP programs) rather than probabilistic inference. The proposed system enables users to compute ex-post and ex-ante measures of unexpectedness of a certain situation, mapping respectively to posterior and prior subjective probabilities. The computation is based on the specification of world and mental models by means of causal and descriptive relations between predicates weighted by complexity. The paper illustrates a few examples of application: generating relevant descriptions, and providing alternative approaches to disjunction and to negation.

Optional type annotations allow for enriching dynamic programming languages with static typing features like better Integrated Development Environment (IDE) support, more precise program analysis, and early detection and prevention of type-related runtime errors. Machine learning-based type inference promises interesting results for automating this task. However, the practical usage of such systems depends on their ability to generalize across different domains, as they are often applied outside their training domain. In this work, we investigate Type4Py as a representative of state-of-the-art deep learning-based type inference systems, by conducting extensive cross-domain experiments. Thereby, we address the following problems: class imbalances, out-of-vocabulary words, dataset shifts, and unknown classes. To perform such experiments, we use the datasets ManyTypes4Py and CrossDomainTypes4Py. The latter we introduce in this paper. Our dataset enables the evaluation of type inference systems in different domains of software projects and has over 1,000,000 type annotations mined on the platforms GitHub and Libraries. It consists of data from the two domains web development and scientific calculation. Through our experiments, we detect that the shifts in the dataset and the long-tailed distribution with many rare and unknown data types decrease the performance of the deep learning-based type inference system drastically. In this context, we test unsupervised domain adaptation methods and fine-tuning to overcome these issues. Moreover, we investigate the impact of out-of-vocabulary words.

Video-assisted transoral tracheal intubation (TI) necessitates using an endoscope that helps the physician insert a tracheal tube into the glottis instead of the esophagus. The growing trend of robotic-assisted TI would require a medical robot to distinguish anatomical features like an experienced physician which can be imitated by utilizing supervised deep-learning techniques. However, the real datasets of oropharyngeal organs are often inaccessible due to limited open-source data and patient privacy. In this work, we propose a domain adaptive Sim-to-Real framework called IoU-Ranking Blend-ArtFlow (IRB-AF) for image segmentation of oropharyngeal organs. The framework includes an image blending strategy called IoU-Ranking Blend (IRB) and style-transfer method ArtFlow. Here, IRB alleviates the problem of poor segmentation performance caused by significant datasets domain differences; while ArtFlow is introduced to reduce the discrepancies between datasets further. A virtual oropharynx image dataset generated by the SOFA framework is used as the learning subject for semantic segmentation to deal with the limited availability of actual endoscopic images. We adapted IRB-AF with the state-of-the-art domain adaptive segmentation models. The results demonstrate the superior performance of our approach in further improving the segmentation accuracy and training stability.

This paper studies the efficient estimation of a large class of treatment effect parameters that arise in the analysis of experiments. Here, efficiency is understood to be with respect to a broad class of treatment assignment schemes for which the marginal probability that any unit is assigned to treatment equals a pre-specified value, e.g., one half. Importantly, we do not require that treatment status is assigned in an i.i.d. fashion, thereby accommodating complicated treatment assignment schemes that are used in practice, such as stratified block randomization and matched pairs. The class of parameters considered are those that can be expressed as the solution to a restriction on the expectation of a known function of the observed data, including possibly the pre-specified value for the marginal probability of treatment assignment. We show that this class of parameters includes, among other things, average treatment effects, quantile treatment effects, local average treatment effects as well as the counterparts to these quantities in experiments in which the unit is itself a cluster. In this setting, we establish two results. First, we derive a lower bound on the asymptotic variance of estimators of the parameter of interest in the form of a convolution theorem. Second, we show that the n\"aive method of moments estimator achieves this bound on the asymptotic variance quite generally if treatment is assigned using a "finely stratified" design. By a "finely stratified" design, we mean experiments in which units are divided into groups of a fixed size and a proportion within each group is assigned to treatment uniformly at random so that it respects the restriction on the marginal probability of treatment assignment. In this sense, "finely stratified" experiments lead to efficient estimators of treatment effect parameters "by design" rather than through ex post covariate adjustment.

Invariant risk minimization (IRM) has recently emerged as a promising alternative for domain generalization. Nevertheless, the loss function is difficult to optimize for nonlinear classifiers and the original optimization objective could fail when pseudo-invariant features and geometric skews exist. Inspired by IRM, in this paper we propose a novel formulation for domain generalization, dubbed invariant information bottleneck (IIB). IIB aims at minimizing invariant risks for nonlinear classifiers and simultaneously mitigating the impact of pseudo-invariant features and geometric skews. Specifically, we first present a novel formulation for invariant causal prediction via mutual information. Then we adopt the variational formulation of the mutual information to develop a tractable loss function for nonlinear classifiers. To overcome the failure modes of IRM, we propose to minimize the mutual information between the inputs and the corresponding representations. IIB significantly outperforms IRM on synthetic datasets, where the pseudo-invariant features and geometric skews occur, showing the effectiveness of proposed formulation in overcoming failure modes of IRM. Furthermore, experiments on DomainBed show that IIB outperforms $13$ baselines by $0.9\%$ on average across $7$ real datasets.

This paper focuses on the expected difference in borrower's repayment when there is a change in the lender's credit decisions. Classical estimators overlook the confounding effects and hence the estimation error can be magnificent. As such, we propose another approach to construct the estimators such that the error can be greatly reduced. The proposed estimators are shown to be unbiased, consistent, and robust through a combination of theoretical analysis and numerical testing. Moreover, we compare the power of estimating the causal quantities between the classical estimators and the proposed estimators. The comparison is tested across a wide range of models, including linear regression models, tree-based models, and neural network-based models, under different simulated datasets that exhibit different levels of causality, different degrees of nonlinearity, and different distributional properties. Most importantly, we apply our approaches to a large observational dataset provided by a global technology firm that operates in both the e-commerce and the lending business. We find that the relative reduction of estimation error is strikingly substantial if the causal effects are accounted for correctly.

With the rapid increase of large-scale, real-world datasets, it becomes critical to address the problem of long-tailed data distribution (i.e., a few classes account for most of the data, while most classes are under-represented). Existing solutions typically adopt class re-balancing strategies such as re-sampling and re-weighting based on the number of observations for each class. In this work, we argue that as the number of samples increases, the additional benefit of a newly added data point will diminish. We introduce a novel theoretical framework to measure data overlap by associating with each sample a small neighboring region rather than a single point. The effective number of samples is defined as the volume of samples and can be calculated by a simple formula $(1-\beta^{n})/(1-\beta)$, where $n$ is the number of samples and $\beta \in [0,1)$ is a hyperparameter. We design a re-weighting scheme that uses the effective number of samples for each class to re-balance the loss, thereby yielding a class-balanced loss. Comprehensive experiments are conducted on artificially induced long-tailed CIFAR datasets and large-scale datasets including ImageNet and iNaturalist. Our results show that when trained with the proposed class-balanced loss, the network is able to achieve significant performance gains on long-tailed datasets.

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