In the context of long-tail classification on graphs, the vast majority of existing work primarily revolves around the development of model debiasing strategies, intending to mitigate class imbalances and enhance the overall performance. Despite the notable success, there is very limited literature that provides a theoretical tool for characterizing the behaviors of long-tail classes in graphs and gaining insight into generalization performance in real-world scenarios. To bridge this gap, we propose a generalization bound for long-tail classification on graphs by formulating the problem in the fashion of multi-task learning, i.e., each task corresponds to the prediction of one particular class. Our theoretical results show that the generalization performance of long-tail classification is dominated by the overall loss range and the task complexity. Building upon the theoretical findings, we propose a novel generic framework HierTail for long-tail classification on graphs. In particular, we start with a hierarchical task grouping module that allows us to assign related tasks into hypertasks and thus control the complexity of the task space; then, we further design a balanced contrastive learning module to adaptively balance the gradients of both head and tail classes to control the loss range across all tasks in a unified fashion. Extensive experiments demonstrate the effectiveness of HierTail in characterizing long-tail classes on real graphs, which achieves up to 12.9% improvement over the leading baseline method in balanced accuracy.

Bayesian learning with Gaussian processes demonstrates encouraging regression and classification performances in solving computer vision tasks. However, Bayesian methods on 3D manifold-valued vision data, such as meshes and point clouds, are seldom studied. One of the primary challenges is how to effectively and efficiently aggregate geometric features from the irregular inputs. In this paper, we propose a hierarchical Bayesian learning model to address this challenge. We initially introduce a kernel with the properties of geometry-awareness and intra-kernel convolution. This enables geometrically reasonable inferences on manifolds without using any specific hand-crafted feature descriptors. Then, we use a Gaussian process regression to organize the inputs and finally implement a hierarchical Bayesian network for the feature aggregation. Furthermore, we incorporate the feature learning of neural networks with the feature aggregation of Bayesian models to investigate the feasibility of jointly learning on manifolds. Experimental results not only show that our method outperforms existing Bayesian methods on manifolds but also demonstrate the prospect of coupling neural networks with Bayesian networks.

The alterations of brain structures and functions have been considered closely correlated to the change of cognitive performance due to neurodegenerative diseases such as Alzheimer's disease. In this paper, we introduce a variational framework to compute the optimal transformation (OT) in 3D space and propose a univariate neuroimaging index based on OT to measure such alterations. We compute the OT from each image to a template and measure the Wasserstein distance between them. By comparing the distances from all the images to the common template, we obtain a concise and informative index for each image. Our framework makes use of the Newton's method, which reduces the computational cost and enables itself to be applicable to large-scale datasets. The proposed work is a generic approach and thus may be applicable to various volumetric brain images, including structural magnetic resonance (sMR) and fluorodeoxyglucose positron emission tomography (FDG-PET) images. In the classification between Alzheimer's disease patients and healthy controls, our method achieves an accuracy of 82:30% on the Alzheimers Disease Neuroimaging Initiative (ADNI) baseline sMRI dataset and outperforms several other indices. On FDG-PET dataset, we boost the accuracy to 88:37% by leveraging pairwise Wasserstein distances. In a longitudinal study, we obtain a 5% significance with p-value = 1:13 ×105 in a t-test on FDG-PET. The results demonstrate a great potential of the proposed index for neuroimage analysis and the precision medicine research.

Half of the polyps surgically removed during conventional colonoscopy are benign with no malignant potential. Our purpose was to develop a CADx system for distinction between neoplastic and non-neoplastic lesions in CTC to reduce "unnecessary" colonoscopic polypectomy. Although computer aided detection (CADe) systems have been developed, less attention was given to the development of CADx systems. Our CADx system consists of shape-index-based coarse segmentation of lesions, 3D volume growing and sub-voxel refinement for fine segmentation of lesions, morphologic and texture feature analysis, Wilks' lambda-based stepwise feature selection, linear discriminant analysis for providing an integrated imaging biomarker for diagnosis of neoplastic lesions. Our database contained biopsy-confirmed 54 neoplastic lesions in 29 patients and 14 non-neoplastic lesions in 10 patients. Our CADx system integrating the selected features was able to determine an accurate likelihood of being a neoplasm and distinguish 87% (47/54) neoplastic lesions from 57% (8/14) non-neoplastic lesions correctly only using computed tomography (CT) images, achieving an area under the receiver operating characteristic curve (AUC) of 0.82. This study showed the potential of the use of CTC as a diagnostic tool beyond already accepted detection, thus, CTC with CADx would be potentially useful for reducing "unnecessary" polypectomy.