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Uncertainty Quantification (UQ) is vital for decision makers as it offers insights into the potential reliability of data and model, enabling more informed and risk-aware decision-making. Graphical models, capable of representing data with complex dependencies, are widely used across domains. Existing sampling-based UQ methods are unbiased but cannot guarantee convergence and are time-consuming on large-scale graphs. There are fast UQ methods for graphical models with closed-form solutions and convergence guarantee but with uncertainty underestimation. We propose LinUProp, a UQ method that utilizes a novel linear propagation of uncertainty to model uncertainty among related nodes additively instead of multiplicatively, to offer linear scalability, guaranteed convergence, and closed-form solutions without underestimating uncertainty. Theoretically, we decompose the expected prediction error of the graphical model and prove that the uncertainty computed by LinUProp is the generalized variance component of the decomposition. Experimentally, we demonstrate that LinUProp is consistent with the sampling-based method but with linear scalability and fast convergence. Moreover, LinUProp outperforms competitors in uncertainty-based active learning on four real-world graph datasets, achieving higher accuracy with a lower labeling budget. 

Vascular networks play a crucial role in understanding brain functionalities. Brain integrity and function, neuronal activity and plasticity, which are crucial for learning, are actively modulated by their local environments, specifically vascular networks. With recent developments in high-resolution 3D light-sheet microscopy imaging together with tissue processing techniques, it becomes feasible to obtain and examine large-scale brain vasculature in mice. To establish a structural foundation for functional study, however, we need advanced image analysis and structural modeling methods. Existing works use geometric features such as thickness, tortuosity, etc. However, geometric features cannot fully capture structural characteristics such as the richness of branches, connectivity, etc. In this paper, we study the morphology of brain vasculature through a topological lens. We extract topological features based on the theory of topological data analysis. Comparing of these robust and multi-scale topological structural features across different brain anatomical structures and between normal and obese populations sheds light on their promising future in studying neurological diseases. 

Introducing interpretability and reasoning into Multiple Instance Learning (MIL) methods for Whole Slide Image (WSI) analysis is challenging given the complexity of gigapixel slides. Traditionally MIL interpretability is limited to identifying salient regions deemed pertinent for downstream tasks offering little insight to the end-user (pathologist) regarding the rationale behind these selections. To address this we propose Self-Interpretable MIL (SI-MIL) a method intrinsically designed for interpretability from the very outset. SI-MIL employs a deep MIL framework to guide an interpretable branch grounded on handcrafted pathological features facilitating linear predictions. Beyond identifying salient regions SI-MIL uniquely provides feature-level interpretations rooted in pathological insights for WSIs. Notably SI-MIL with its linear prediction constraints challenges the prevalent myth of an inevitable trade-off between model interpretability and performance demonstrating competitive results compared to state-of-the-art methods on WSI-level prediction tasks across three cancer types. In addition we thoroughly benchmark the local- and global-interpretability of SI-MIL in terms of statistical analysis a domain expert study and desiderata of interpretability namely user-friendliness and faithfulness. 

Segmentation of curvilinear structures such as vasculature and road networks is challenging due to relatively weak signals and complex geometry/topology. To facilitate and accelerate large scale annotation, one has to adopt semi-automatic approaches such as proofreading by experts. In this work, we focus on uncertainty estimation for such tasks, so that highly uncertain, and thus error-prone structures can be identified for human annotators to verify. Unlike most existing works, which provide pixel-wise uncertainty maps, we stipulate it is crucial to estimate uncertainty in the units of topological structures, eg, small pieces of connections and branches. To achieve this, we leverage tools from topological data analysis, specifically discrete Morse theory (DMT), to first capture the structures, and then reason about their uncertainties. To model the uncertainty, we (1) propose a joint prediction model that estimates the uncertainty of a structure while taking the neighboring structures into consideration (inter-structural uncertainty); (2) propose a novel Probabilistic DMT to model the inherent uncertainty within each structure (intra-structural uncertainty) by sampling its representations via a perturb-and-walk scheme. On various 2D and 3D datasets, our method produces better structure-wise uncertainty maps compared to existing works. 

The adversarial risk of a machine learning model has been widely studied. Most previous studies assume that the data lie in the whole ambient space. We propose to take a new angle and take the manifold assumption into consideration. Assuming data lie in a manifold, we investigate two new types of adversarial risk, the normal adversarial risk due to perturbation along normal direction and the in-manifold adversarial risk due to perturbation within the manifold. We prove that the classic adversarial risk can be bounded from both sides using the normal and in-manifold adversarial risks. We also show a surprisingly pessimistic case that the standard adversarial risk can be non-zero even when both normal and in-manifold adversarial risks are zero. We finalize the study with empirical studies supporting our theoretical results. Our results suggest the possibility of improving the robustness of a classifier without sacrificing model accuracy, by only focusing on the normal adversarial risk. 

Semi-supervised crowd counting is an important yet challenging task. A popular approach is to iteratively generate pseudo-labels for unlabeled data and add them to the training set. The key is to use uncertainty to select reliable pseudo-labels. In this paper, we propose a novel method to calibrate model uncertainty for crowd counting. Our method takes a supervised uncertainty estimation strategy to train the model through a surrogate function. This ensures the uncertainty is well controlled throughout the training. We propose a matching-based patch-wise surrogate function to better approximate uncertainty for crowd counting tasks. The proposed method pays a sufficient amount of attention to details, while maintaining a proper granularity. Altogether our method is able to generate reliable uncertainty estimation, high quality pseudolabels, and achieve state-of-the-art performance in semisupervised crowd counting. 

In medical vision, different imaging modalities provide complementary information. However, in practice, not all modalities may be available during inference or even training. Previous approaches, e.g., knowledge distillation or image synthesis, often assume the availability of full modalities for all patients during training; this is unrealistic and impractical due to the variability in data collection across sites. We propose a novel approach to learn enhanced modality-agnostic representations by employing a meta-learning strategy in training, even when only limited full modality samples are available. Meta-learning enhances partial modality representations to full modality representations by meta-training on partial modality data and meta-testing on limited full modality samples. Additionally, we co-supervise this feature enrichment by introducing an auxiliary adversarial learning branch. More specifically, a missing modality detector is used as a discriminator to mimic the full modality setting. Our segmentation framework significantly outperforms state-of-the-art brain tumor segmentation techniques in missing modality scenarios.