In voxel-based neuroimaging disease prediction, it was recently found that in addition to lesion features, there exists another type of feature called "Procedural Bias", which is introduced during preprocessing and can further improve the prediction power. However, traditional sparse learning methods fail to simultaneously capture both types of features due to their heterogeneity in sparsity types. Specifically, the lesion features are spatially coherent and suffer from volumetric degeneration, while the procedural bias refers to enlarged voxels that are dispersedly distributed. In this paper, we propose a new method based on differential inclusion, which generates a sparse regularized solution path on multiple parameters that are enforced with heterogeneous sparsity to capture lesion features and the procedural bias separately. Specifically, we employ Total Variation with a non-negative constraint for the parameter associated with degenerated and spatially coherent lesions; on the other hand, we impose $\ell_1$ sparsity with a non-positive constraint on the parameter related to enlarged and scatterly distributed procedural bias. We theoretically show that our method enjoys model selection consistency and $\ell_2$ consistency in estimation. The utility of our method is demonstrated by improved prediction power and interpretability in the early prediction of Alzheimer’s Disease.

Automated anatomical labeling plays a crucial part for computer-assisted diagnostic systems targeting coronary artery diseases. Established from medical practice, the labeling conventions intrinsically carry profound prior knowledge about the results, indicating what outcome is favorable and what is illegal. However, the prior has been largely neglected by existing works. Drawing inspiration from syntax parsing in the NLP domain, we propose a neural stochastic grammar parser for anatomical labeling. Our method captures the essential parental and sibling dependencies between vessel segments, incorporates structural prior in a principled and interpretable manner, while retaining the learning capabilities of deep models. Experiments show encouraging results both for the robustness and accuracy of our method.

Inferring causal structures from time series data is the central interest of many scientific inquiries. A major barrier to such inference is the problem of subsampling, *i.e.*, the frequency of measurement is much lower than that of causal influence. To overcome this problem, numerous methods have been proposed, yet either was limited to the linear case or failed to achieve identifiability. In this paper, we propose a constraint-based algorithm that can identify the entire causal structure from subsampled time series, without any parametric constraint. Our observation is that the challenge of subsampling arises mainly from hidden variables at the unobserved time steps. Meanwhile, every hidden variable has an observed proxy, which is essentially itself at some observable time in the future, benefiting from the temporal structure. Based on these, we can leverage the proxies to remove the bias induced by the hidden variables and hence achieve identifiability. Following this intuition, we propose a proxy-based causal discovery algorithm. Our algorithm is nonparametric and can achieve full causal identification. Theoretical advantages are reflected in synthetic and real-world experiments.

In image-based disease prediction, it can be hard to give certain cases a deterministic “disease/normal” label due to lack of enough information, e.g., at its early stage. We call such cases “unsure” data. Labeling such data as unsure suggests follow-up examinations so as to avoid irreversible medical accident/loss in contrast to incautious prediction. This is a common practice in clinical diagnosis, however, mostly neglected by existing methods. Learning with unsure data also inter-weaves with two other practical issues: (i) data imbalance issue that may incur model-bias towards the majority class, and (ii) conservative/aggressive strategy consideration, i.e., the negative (normal) samples and positive (disease) samples should NOT be treated equally - the former should be detected with a high precision (conservativeness) and the latter should be detected with a high recall (aggression) to avoid missing opportunity for treatment. Mixed with these issues, learning with unsure data becomes particularly challenging. In this paper, we raise “learning with unsure data” problem and formulate it as an ordinal regression and propose a unified end-to-end learning framework, which also considers the aforementioned two issues: (i) incorporate cost-sensitive parameters to alleviate the data imbalance problem, and (ii) execute the conservative and aggressive strategies by introducing two parameters in the training procedure. The benefits of learning with unsure data and validity of our models are demonstrated on the prediction of Alzheimer's Disease and lung nodules.

Generalized fused lasso (GFL) penalizes variables with l 1 norms based both on the variables and their pairwise differences. GFL is useful when applied to data where prior information is expressed using a graph over the variables. However, the existing GFL algorithms incur high computational costs and do not scale to high-dimensional problems. In this study, we propose a fast and scalable algorithm for GFL. Based on the fact that fusion penalty is the Lovász extension of a cut function, we show that the key building block of the optimization is equivalent to recursively solving graph-cut problems. Thus, we use a parametric flow algorithm to solve GFL in an efficient manner. Runtime comparisons demonstrate a significant speedup compared to existing GFL algorithms. Moreover, the proposed optimization framework is very general; by designing different cut functions, we also discuss the extension of GFL to directed graphs. Exploiting the scalability of the proposed algorithm, we demonstrate the applications of our algorithm to the diagnosis of Alzheimer’s disease (AD) and video background subtraction (BS). In the AD problem, we formulated the diagnosis of AD as a GFL regularized classification. Our experimental evaluations demonstrated that the diagnosis performance was promising. We observed that the selected critical voxels were well structured, i.e., connected, consistent according to cross validation, and in agreement with prior pathological knowledge. In the BS problem, GFL naturally models arbitrary foregrounds without predefined grouping of the pixels. Even by applying simple background models, e.g., a sparse linear combination of former frames, we achieved state-of-the-art performance on several public datasets.

Neuroimage analysis usually involves learning thousands or even millions of variables using only a limited number of samples. In this regard, sparse models, e.g. the lasso, are applied to select the optimal features and achieve high diagnosis accuracy. The lasso, however, usually results in independent unstable features. Stability, a manifest of reproducibility of statistical results subject to reasonable perturbations to data and the model (Yu 2013), is an important focus in statistics, especially in the analysis of high dimensional data. In this paper, we explore a nonnegative generalized fused lasso model for stable feature selection in the diagnosis of Alzheimer's disease. In addition to sparsity, our model incorporates two important pathological priors: the spatial cohesion of lesion voxels and the positive correlation between the features and the disease labels. To optimize the model, we propose an efficient algorithm by proving a novel link between total variation and fast network flow algorithms via conic duality. Experiments show that the proposed nonnegative model performs much better in exploring the intrinsic structure of data via selecting stable features compared with other state-of-the-arts.