Undirected graphical models are widely used to model the conditional independence structure of vector-valued data. However, in many modern applications, for example those involving EEG and fMRI data, observations are more appropriately modeled as multivariate random functions rather than vectors. Functional graphical models have been proposed to model the conditional independence structure of such functional data. We propose a neighborhood selection approach to estimate the structure of Gaussian functional graphical models, where we first estimate the neighborhood of each node via a function-on-function regression and subsequently recover the entire graph structure by combining the estimated neighborhoods. Our approach only requires assumptions on the conditional distributions of random functions, and we estimate the conditional independence structure directly. We thus circumvent the need for a well-defined precision operator that may not exist when the functions are infinite dimensional. Additionally, the neighborhood selection approach is computationally efficient and can be easily parallelized. The statistical consistency of the proposed method in the high-dimensional setting is supported by both theory and experimental results. In addition, we study the effect of the choice of the function basis used for dimensionality reduction in an intermediate step. We give a heuristic criterion for choosing a function basis and motivate two practically useful choices, which we justify by both theory and experiments.
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Using Non-negative Matrix Factorization (NMF), the observed matrix can be approximated by the product of the basis and coefficient matrices. Moreover, if the coefficient vectors are explained by the covariates for each individual, the coefficient matrix can be written as the product of the parameter matrix and the covariate matrix, and additionally described in the framework of Non-negative Matrix tri-Factorization (tri-NMF) with covariates. Consequently, this is equal to the mean structure of the Growth Curve Model (GCM). The difference is that the basis matrix for GCM is given by the analyst, whereas that for NMF with covariates is unknown and optimized. In this study, we applied NMF with covariance to longitudinal data and compared it with GCM. We have also published an R package that implements this method, and we show how to use it through examples of data analyses including longitudinal measurement, spatiotemporal data and text data. In particular, we demonstrate the usefulness of Gaussian kernel functions as covariates.
Explaining Pre-Trained Language Models with Attribution Scores: An Analysis in Low-Resource Settings
Attribution scores indicate the importance of different input parts and can, thus, explain model behaviour. Currently, prompt-based models are gaining popularity, i.a., due to their easier adaptability in low-resource settings. However, the quality of attribution scores extracted from prompt-based models has not been investigated yet. In this work, we address this topic by analyzing attribution scores extracted from prompt-based models w.r.t. plausibility and faithfulness and comparing them with attribution scores extracted from fine-tuned models and large language models. In contrast to previous work, we introduce training size as another dimension into the analysis. We find that using the prompting paradigm (with either encoder-based or decoder-based models) yields more plausible explanations than fine-tuning the models in low-resource settings and Shapley Value Sampling consistently outperforms attention and Integrated Gradients in terms of leading to more plausible and faithful explanations.
Recent studies have focused on enhancing the performance of 3D object detection models. Among various approaches, ground-truth sampling has been proposed as an augmentation technique to address the challenges posed by limited ground-truth data. However, an inherent issue with ground-truth sampling is its tendency to increase false positives. Therefore, this study aims to overcome the limitations of ground-truth sampling and improve the performance of 3D object detection models by developing a new augmentation technique called false-positive sampling. False-positive sampling involves retraining the model using point clouds that are identified as false positives in the model's predictions. We propose an algorithm that utilizes both ground-truth and false-positive sampling and an algorithm for building the false-positive sample database. Additionally, we analyze the principles behind the performance enhancement due to false-positive sampling and propose a technique that applies the concept of curriculum learning to the sampling strategy that encompasses both false-positive and ground-truth sampling techniques. Our experiments demonstrate that models utilizing false-positive sampling show a reduction in false positives and exhibit improved object detection performance. On the KITTI and Waymo Open datasets, models with false-positive sampling surpass the baseline models by a large margin.
Deep learning models, particularly those based on transformers, often employ numerous stacked structures, which possess identical architectures and perform similar functions. While effective, this stacking paradigm leads to a substantial increase in the number of parameters, posing challenges for practical applications. In today's landscape of increasingly large models, stacking depth can even reach dozens, further exacerbating this issue. To mitigate this problem, we introduce LORS (LOw-rank Residual Structure). LORS allows stacked modules to share the majority of parameters, requiring a much smaller number of unique ones per module to match or even surpass the performance of using entirely distinct ones, thereby significantly reducing parameter usage. We validate our method by applying it to the stacked decoders of a query-based object detector, and conduct extensive experiments on the widely used MS COCO dataset. Experimental results demonstrate the effectiveness of our method, as even with a 70\% reduction in the parameters of the decoder, our method still enables the model to achieve comparable or
We reformulate the Lanczos tau method for the discretization of time-delay systems in terms of a pencil of operators, allowing for new insights into this approach. As a first main result, we show that, for the choice of a shifted Legendre basis, this method is equivalent to Pad\'e approximation in the frequency domain. We illustrate that Lanczos tau methods straightforwardly give rise to sparse, self nesting discretizations. Equivalence is also demonstrated with pseudospectral collocation, where the non-zero collocation points are chosen as the zeroes of orthogonal polynomials. The importance of such a choice manifests itself in the approximation of the $H^2$-norm, where, under mild conditions, super-geometric convergence is observed and, for a special case, super convergence is proved; both significantly faster than the algebraic convergence reported in previous work.
The efficacy of machine learning has traditionally relied on the availability of increasingly larger datasets. However, large datasets pose storage challenges and contain non-influential samples, which could be ignored during training without impacting the final accuracy of the model. In response to these limitations, the concept of distilling the information on a dataset into a condensed set of (synthetic) samples, namely a distilled dataset, emerged. One crucial aspect is the selected architecture (usually ConvNet) for linking the original and synthetic datasets. However, the final accuracy is lower if the employed model architecture differs from the model used during distillation. Another challenge is the generation of high-resolution images, e.g., 128x128 and higher. In this paper, we propose Latent Dataset Distillation with Diffusion Models (LD3M) that combine diffusion in latent space with dataset distillation to tackle both challenges. LD3M incorporates a novel diffusion process tailored for dataset distillation, which improves the gradient norms for learning synthetic images. By adjusting the number of diffusion steps, LD3M also offers a straightforward way of controlling the trade-off between speed and accuracy. We evaluate our approach in several ImageNet subsets and for high-resolution images (128x128 and 256x256). As a result, LD3M consistently outperforms state-of-the-art distillation techniques by up to 4.8 p.p. and 4.2 p.p. for 1 and 10 images per class, respectively.
Conventional deep learning models deal with images one-by-one, requiring costly and time-consuming expert labeling in the field of medical imaging, and domain-specific restriction limits model generalizability. Visual in-context learning (ICL) is a new and exciting area of research in computer vision. Unlike conventional deep learning, ICL emphasizes the model's ability to adapt to new tasks based on given examples quickly. Inspired by MAE-VQGAN, we proposed a new simple visual ICL method called SimICL, combining visual ICL pairing images with masked image modeling (MIM) designed for self-supervised learning. We validated our method on bony structures segmentation in a wrist ultrasound (US) dataset with limited annotations, where the clinical objective was to segment bony structures to help with further fracture detection. We used a test set containing 3822 images from 18 patients for bony region segmentation. SimICL achieved an remarkably high Dice coeffient (DC) of 0.96 and Jaccard Index (IoU) of 0.92, surpassing state-of-the-art segmentation and visual ICL models (a maximum DC 0.86 and IoU 0.76), with SimICL DC and IoU increasing up to 0.10 and 0.16. This remarkably high agreement with limited manual annotations indicates SimICL could be used for training AI models even on small US datasets. This could dramatically decrease the human expert time required for image labeling compared to conventional approaches, and enhance the real-world use of AI assistance in US image analysis.
Analyzing spatial varying effect is pivotal in geographic analysis. Yet, accurately capturing and interpreting this variability is challenging due to the complexity and non-linearity of geospatial data. Herein, we introduce an integrated framework that merges local spatial weighting scheme, Explainable Artificial Intelligence (XAI), and cutting-edge machine learning technologies to bridge the gap between traditional geographic analysis models and general machine learning approaches. Through tests on synthetic datasets, this framework is verified to enhance the interpretability and accuracy of predictions in both geographic regression and classification by elucidating spatial variability. It significantly boosts prediction precision, offering a novel approach to understanding spatial phenomena.
Causal inference is a fundamental research topic for discovering the cause-effect relationships in many disciplines. However, not all algorithms are equally well-suited for a given dataset. For instance, some approaches may only be able to identify linear relationships, while others are applicable for non-linearities. Algorithms further vary in their sensitivity to noise and their ability to infer causal information from coupled vs. non-coupled time series. Therefore, different algorithms often generate different causal relationships for the same input. To achieve a more robust causal inference result, this publication proposes a novel data-driven two-phase multi-split causal ensemble model to combine the strengths of different causality base algorithms. In comparison to existing approaches, the proposed ensemble method reduces the influence of noise through a data partitioning scheme in the first phase. To achieve this, the data are initially divided into several partitions and the base algorithms are applied to each partition. Subsequently, Gaussian mixture models are used to identify the causal relationships derived from the different partitions that are likely to be valid. In the second phase, the identified relationships from each base algorithm are then merged based on three combination rules. The proposed ensemble approach is evaluated using multiple metrics, among them a newly developed evaluation index for causal ensemble approaches. We perform experiments using three synthetic datasets with different volumes and complexity, which are specifically designed to test causality detection methods under different circumstances while knowing the ground truth causal relationships. In these experiments, our causality ensemble outperforms each of its base algorithms. In practical applications, the use of the proposed method could hence lead to more robust and reliable causality results.
Image segmentation is considered to be one of the critical tasks in hyperspectral remote sensing image processing. Recently, convolutional neural network (CNN) has established itself as a powerful model in segmentation and classification by demonstrating excellent performances. The use of a graphical model such as a conditional random field (CRF) contributes further in capturing contextual information and thus improving the segmentation performance. In this paper, we propose a method to segment hyperspectral images by considering both spectral and spatial information via a combined framework consisting of CNN and CRF. We use multiple spectral cubes to learn deep features using CNN, and then formulate deep CRF with CNN-based unary and pairwise potential functions to effectively extract the semantic correlations between patches consisting of three-dimensional data cubes. Effective piecewise training is applied in order to avoid the computationally expensive iterative CRF inference. Furthermore, we introduce a deep deconvolution network that improves the segmentation masks. We also introduce a new dataset and experimented our proposed method on it along with several widely adopted benchmark datasets to evaluate the effectiveness of our method. By comparing our results with those from several state-of-the-art models, we show the promising potential of our method.
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