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With computational models becoming more expensive and complex, surrogate models have gained increasing attention in many scientific disciplines and are often necessary to conduct sensitivity studies, parameter optimization etc. In the scientific discipline of uncertainty quantification (UQ), model input quantities are often described by probability distributions. For the construction of surrogate models, space-filling designs are generated in the input space to define training points, and evaluations of the computational model at these points are then conducted. The physical parameter space is often transformed into an i.i.d. uniform input space in order to apply space-filling training procedures in a sensible way. Due to this transformation surrogate modeling techniques tend to suffer with regard to their prediction accuracy. Therefore, a new method is proposed in this paper where input parameter transformations are applied to basis functions for universal kriging. To speed up hyperparameter optimization for universal kriging, suitable expressions for efficient gradient-based optimization are developed. Several benchmark functions are investigated and the proposed method is compared with conventional methods.

We study the Landau-de Gennes Q-tensor model of liquid crystals subjected to an electric field and develop a fully discrete numerical scheme for its solution. The scheme uses a convex splitting of the bulk potential, and we introduce a truncation operator for the Q-tensors to ensure well-posedness of the problem. We prove the stability and well-posedness of the scheme. Finally, making a restriction on the admissible parameters of the scheme, we show that up to a subsequence, solutions to the fully discrete scheme converge to weak solutions of the Q-tensor model as the time step and mesh are refined. We then present numerical results computed by the numerical scheme, among which, we show that it is possible to simulate the Fr\'eedericksz transition with this scheme.

In crowdsourcing, quality control is commonly achieved by having workers examine items and vote on their correctness. To minimize the impact of unreliable worker responses, a $\delta$-margin voting process is utilized, where additional votes are solicited until a predetermined threshold $\delta$ for agreement between workers is exceeded. The process is widely adopted but only as a heuristic. Our research presents a modeling approach using absorbing Markov chains to analyze the characteristics of this voting process that matter in crowdsourced processes. We provide closed-form equations for the quality of resulting consensus vote, the expected number of votes required for consensus, the variance of vote requirements, and other distribution moments. Our findings demonstrate how the threshold $\delta$ can be adjusted to achieve quality equivalence across voting processes that employ workers with varying accuracy levels. We also provide efficiency-equalizing payment rates for voting processes with different expected response accuracy levels. Additionally, our model considers items with varying degrees of difficulty and uncertainty about the difficulty of each example. Our simulations, using real-world crowdsourced vote data, validate the effectiveness of our theoretical model in characterizing the consensus aggregation process. The results of our study can be effectively employed in practical crowdsourcing applications.

Many machine learning regression methods leverage large datasets for training predictive models. However, using large datasets may not be feasible due to computational limitations or high labelling costs. Therefore, sampling small training sets from large pools of unlabelled data points is essential to maximize model performance while maintaining computational efficiency. In this work, we study a sampling approach aimed to minimize the fill distance of the selected set. We derive an upper bound for the maximum expected prediction error that linearly depends on the training set fill distance, conditional to the knowledge of data features. For empirical validation, we perform experiments using two regression models on two datasets. We empirically show that selecting a training set by aiming to minimize the fill distance, thereby minimizing the bound, significantly reduces the maximum prediction error of various regression models, outperforming existing sampling approaches by a large margin.

Trajectory and control secrecy is an important issue in robotics security. This paper proposes a novel algorithm for the control input inference of a mobile agent without knowing its control objective. Specifically, the algorithm first estimates the target state by applying external perturbations. Then we identify the objective function based on the inverse optimal control, providing the well-posedness proof and the identifiability analysis. Next, we obtain the optimal estimate of the control horizon using binary search. Finally, the agent's control optimization problem is reconstructed and solved to predict its input. Simulation illustrates the efficiency and the performance of the algorithm.

Extracting noisy or incorrectly labeled samples from a labeled dataset with hard/difficult samples is an important yet under-explored topic. Two general and often independent lines of work exist, one focuses on addressing noisy labels, and another deals with hard samples. However, when both types of data are present, most existing methods treat them equally, which results in a decline in the overall performance of the model. In this paper, we first design various synthetic datasets with custom hardness and noisiness levels for different samples. Our proposed systematic empirical study enables us to better understand the similarities and more importantly the differences between hard-to-learn samples and incorrectly-labeled samples. These controlled experiments pave the way for the development of methods that distinguish between hard and noisy samples. Through our study, we introduce a simple yet effective metric that filters out noisy-labeled samples while keeping the hard samples. We study various data partitioning methods in the presence of label noise and observe that filtering out noisy samples from hard samples with this proposed metric results in the best datasets as evidenced by the high test accuracy achieved after models are trained on the filtered datasets. We demonstrate this for both our created synthetic datasets and for datasets with real-world label noise. Furthermore, our proposed data partitioning method significantly outperforms other methods when employed within a semi-supervised learning framework.

Due to the swift growth of patent applications each year, information and multimedia retrieval approaches that facilitate patent exploration and retrieval are of utmost importance. Different types of visualizations (e.g., graphs, technical drawings) and perspectives (e.g., side view, perspective) are used to visualize details of innovations in patents. The classification of these images enables a more efficient search and allows for further analysis. So far, datasets for image type classification miss some important visualization types for patents. Furthermore, related work does not make use of recent deep learning approaches including transformers. In this paper, we adopt state-of-the-art deep learning methods for the classification of visualization types and perspectives in patent images. We extend the CLEF-IP dataset for image type classification in patents to ten classes and provide manual ground truth annotations. In addition, we derive a set of hierarchical classes from a dataset that provides weakly-labeled data for image perspectives. Experimental results have demonstrated the feasibility of the proposed approaches. Source code, models, and dataset will be made publicly available.

In recent years, self-supervised learning (SSL) has emerged as a promising approach for extracting valuable representations from unlabeled data. One successful SSL method is contrastive learning, which aims to bring positive examples closer while pushing negative examples apart. Many current contrastive learning approaches utilize a parameterized projection head. Through a combination of empirical analysis and theoretical investigation, we provide insights into the internal mechanisms of the projection head and its relationship with the phenomenon of dimensional collapse. Our findings demonstrate that the projection head enhances the quality of representations by performing contrastive loss in a projected subspace. Therefore, we propose an assumption that only a subset of features is necessary when minimizing the contrastive loss of a mini-batch of data. Theoretical analysis further suggests that a sparse projection head can enhance generalization, leading us to introduce SparseHead - a regularization term that effectively constrains the sparsity of the projection head, and can be seamlessly integrated with any self-supervised learning (SSL) approaches. Our experimental results validate the effectiveness of SparseHead, demonstrating its ability to improve the performance of existing contrastive methods.

The landscape of applications and subroutines relying on shortest path computations continues to grow steadily. This growth is driven by the undeniable success of shortest path algorithms in theory and practice. It also introduces new challenges as the models and assessing the optimality of paths become more complicated. Hence, multiple recent publications in the field adapt existing labeling methods in an ad-hoc fashion to their specific problem variant without considering the underlying general structure: they always deal with multi-criteria scenarios and those criteria define different partial orders on the paths. In this paper, we introduce the partial order shortest path problem (POSP), a generalization of the multi-objective shortest path problem (MOSP) and in turn also of the classical shortest path problem. POSP captures the particular structure of many shortest path applications as special cases. In this generality, we study optimality conditions or the lack of them, depending on the objective functions' properties. Our final contribution is a big lookup table summarizing our findings and providing the reader an easy way to choose among the most recent multicriteria shortest path algorithms depending on their problem's weight structure. Examples range from time-dependent shortest path and bottleneck path problems to the fuzzy shortest path problem and complex financial weight functions studied in the public transportation community. Our results hold for general digraphs and therefore surpass previous generalizations that were limited to acyclic graphs.

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.