We present the first optimal rates for infinite-dimensional vector-valued ridge regression on a continuous scale of norms that interpolate between $L_2$ and the hypothesis space, which we consider as a vector-valued reproducing kernel Hilbert space. These rates allow to treat the misspecified case in which the true regression function is not contained in the hypothesis space. We combine standard assumptions on the capacity of the hypothesis space with a novel tensor product construction of vector-valued interpolation spaces in order to characterize the smoothness of the regression function. Our upper bound not only attains the same rate as real-valued kernel ridge regression, but also removes the assumption that the target regression function is bounded. For the lower bound, we reduce the problem to the scalar setting using a projection argument. We show that these rates are optimal in most cases and independent of the dimension of the output space. We illustrate our results for the special case of vector-valued Sobolev spaces.
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Predictive multiplicity refers to the phenomenon in which classification tasks may admit multiple competing models that achieve almost-equally-optimal performance, yet generate conflicting outputs for individual samples. This presents significant concerns, as it can potentially result in systemic exclusion, inexplicable discrimination, and unfairness in practical applications. Measuring and mitigating predictive multiplicity, however, is computationally challenging due to the need to explore all such almost-equally-optimal models, known as the Rashomon set, in potentially huge hypothesis spaces. To address this challenge, we propose a novel framework that utilizes dropout techniques for exploring models in the Rashomon set. We provide rigorous theoretical derivations to connect the dropout parameters to properties of the Rashomon set, and empirically evaluate our framework through extensive experimentation. Numerical results show that our technique consistently outperforms baselines in terms of the effectiveness of predictive multiplicity metric estimation, with runtime speedup up to $20\times \sim 5000\times$. With efficient Rashomon set exploration and metric estimation, mitigation of predictive multiplicity is then achieved through dropout ensemble and model selection.
The stability of mine dumps is contingent upon the precise arrangement of spoil piles, taking into account their geological and geotechnical attributes. Yet, on-site characterisation of individual piles poses a formidable challenge. The utilisation of image-based techniques for spoil pile characterisation, employing remotely acquired data through unmanned aerial systems, is a promising complementary solution. Image processing, such as object-based classification and feature extraction, are dependent upon effective segmentation. This study refines and juxtaposes various segmentation approaches, specifically colour-based and morphology-based techniques. The objective is to enhance and evaluate avenues for object-based analysis for spoil characterisation within the context of mining environments. Furthermore, a comparative analysis is conducted between conventional segmentation approaches and those rooted in deep learning methodologies. Among the diverse segmentation approaches evaluated, the morphology-based deep learning segmentation approach, Segment Anything Model (SAM), exhibited superior performance in comparison to other approaches. This outcome underscores the efficacy of incorporating advanced morphological and deep learning techniques for accurate and efficient spoil pile characterisation. The findings of this study contribute valuable insights to the optimisation of segmentation strategies, thereby advancing the application of image-based techniques for the characterisation of spoil piles in mining environments.
We investigate the problem of jointly testing multiple hypotheses and estimating a random parameter of the underlying distribution in a sequential setup. The aim is to jointly infer the true hypothesis and the true parameter while using on average as few samples as possible and keeping the detection and estimation errors below predefined levels. Based on mild assumptions on the underlying model, we propose an asymptotically optimal procedure, i.e., a procedure that becomes optimal when the tolerated detection and estimation error levels tend to zero. The implementation of the resulting asymptotically optimal stopping rule is computationally cheap and, hence, applicable for high-dimensional data. We further propose a projected quasi-Newton method to optimally choose the coefficients that parameterize the instantaneous cost function such that the constraints are fulfilled with equality. The proposed theory is validated by numerical examples.
The rapidly changing landscape of technology and industries leads to dynamic skill requirements, making it crucial for employees and employers to anticipate such shifts to maintain a competitive edge in the labor market. Existing efforts in this area either rely on domain-expert knowledge or regarding skill evolution as a simplified time series forecasting problem. However, both approaches overlook the sophisticated relationships among different skills and the inner-connection between skill demand and supply variations. In this paper, we propose a Cross-view Hierarchical Graph learning Hypernetwork (CHGH) framework for joint skill demand-supply prediction. Specifically, CHGH is an encoder-decoder network consisting of i) a cross-view graph encoder to capture the interconnection between skill demand and supply, ii) a hierarchical graph encoder to model the co-evolution of skills from a cluster-wise perspective, and iii) a conditional hyper-decoder to jointly predict demand and supply variations by incorporating historical demand-supply gaps. Extensive experiments on three real-world datasets demonstrate the superiority of the proposed framework compared to seven baselines and the effectiveness of the three modules.
Interpretability and transparency are essential for incorporating causal effect models from observational data into policy decision-making. They can provide trust for the model in the absence of ground truth labels to evaluate the accuracy of such models. To date, attempts at transparent causal effect estimation consist of applying post hoc explanation methods to black-box models, which are not interpretable. Here, we present BICauseTree: an interpretable balancing method that identifies clusters where natural experiments occur locally. Our approach builds on decision trees with a customized objective function to improve balancing and reduce treatment allocation bias. Consequently, it can additionally detect subgroups presenting positivity violations, exclude them, and provide a covariate-based definition of the target population we can infer from and generalize to. We evaluate the method's performance using synthetic and realistic datasets, explore its bias-interpretability tradeoff, and show that it is comparable with existing approaches.
In high-dimensional data analysis, such as financial index tracking or biomedical applications, it is crucial to select the few relevant variables while maintaining control over the false discovery rate (FDR). In these applications, strong dependencies often exist among the variables (e.g., stock returns), which can undermine the FDR control property of existing methods like the model-X knockoff method or the T-Rex selector. To address this issue, we have expanded the T-Rex framework to accommodate overlapping groups of highly correlated variables. This is achieved by integrating a nearest neighbors penalization mechanism into the framework, which provably controls the FDR at the user-defined target level. A real-world example of sparse index tracking demonstrates the proposed method's ability to accurately track the S&P 500 index over the past 20 years based on a small number of stocks. An open-source implementation is provided within the R package TRexSelector on CRAN.
A comprehensive understanding of the organizational principles in the human brain requires, among other factors, well-quantifiable descriptors of nerve fiber architecture. Three-dimensional polarized light imaging (3D-PLI) is a microscopic imaging technique that enables insights into the fine-grained organization of myelinated nerve fibers with high resolution. Descriptors characterizing the fiber architecture observed in 3D-PLI would enable downstream analysis tasks such as multimodal correlation studies, clustering, and mapping. However, best practices for observer-independent characterization of fiber architecture in 3D-PLI are not yet available. To this end, we propose the application of a fully data-driven approach to characterize nerve fiber architecture in 3D-PLI images using self-supervised representation learning. We introduce a 3D-Context Contrastive Learning (CL-3D) objective that utilizes the spatial neighborhood of texture examples across histological brain sections of a 3D reconstructed volume to sample positive pairs for contrastive learning. We combine this sampling strategy with specifically designed image augmentations to gain robustness to typical variations in 3D-PLI parameter maps. The approach is demonstrated for the 3D reconstructed occipital lobe of a vervet monkey brain. We show that extracted features are highly sensitive to different configurations of nerve fibers, yet robust to variations between consecutive brain sections arising from histological processing. We demonstrate their practical applicability for retrieving clusters of homogeneous fiber architecture and performing data mining for interactively selected templates of specific components of fiber architecture such as U-fibers.
Model generalizability to unseen datasets, concerned with in-the-wild robustness, is less studied for indoor single-image depth prediction. We leverage gradient-based meta-learning for higher generalizability on zero-shot cross-dataset inference. Unlike the most-studied image classification in meta-learning, depth is pixel-level continuous range values, and mappings from each image to depth vary widely across environments. Thus no explicit task boundaries exist. We instead propose fine-grained task that treats each RGB-D pair as a task in our meta-optimization. We first show meta-learning on limited data induces much better prior (max +29.4\%). Using meta-learned weights as initialization for following supervised learning, without involving extra data or information, it consistently outperforms baselines without the method. Compared to most indoor-depth methods that only train/ test on a single dataset, we propose zero-shot cross-dataset protocols, closely evaluate robustness, and show consistently higher generalizability and accuracy by our meta-initialization. The work at the intersection of depth and meta-learning potentially drives both research streams to step closer to practical use.
Multi-relation Question Answering is a challenging task, due to the requirement of elaborated analysis on questions and reasoning over multiple fact triples in knowledge base. In this paper, we present a novel model called Interpretable Reasoning Network that employs an interpretable, hop-by-hop reasoning process for question answering. The model dynamically decides which part of an input question should be analyzed at each hop; predicts a relation that corresponds to the current parsed results; utilizes the predicted relation to update the question representation and the state of the reasoning process; and then drives the next-hop reasoning. Experiments show that our model yields state-of-the-art results on two datasets. More interestingly, the model can offer traceable and observable intermediate predictions for reasoning analysis and failure diagnosis, thereby allowing manual manipulation in predicting the final answer.
Object detection typically assumes that training and test data are drawn from an identical distribution, which, however, does not always hold in practice. Such a distribution mismatch will lead to a significant performance drop. In this work, we aim to improve the cross-domain robustness of object detection. We tackle the domain shift on two levels: 1) the image-level shift, such as image style, illumination, etc, and 2) the instance-level shift, such as object appearance, size, etc. We build our approach based on the recent state-of-the-art Faster R-CNN model, and design two domain adaptation components, on image level and instance level, to reduce the domain discrepancy. The two domain adaptation components are based on H-divergence theory, and are implemented by learning a domain classifier in adversarial training manner. The domain classifiers on different levels are further reinforced with a consistency regularization to learn a domain-invariant region proposal network (RPN) in the Faster R-CNN model. We evaluate our newly proposed approach using multiple datasets including Cityscapes, KITTI, SIM10K, etc. The results demonstrate the effectiveness of our proposed approach for robust object detection in various domain shift scenarios.
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