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Diagnostic investigation has an important role in risk stratification and clinical decision making of patients with suspected and documented Coronary Artery Disease (CAD). However, the majority of existing tools are primarily focused on the selection of gatekeeper tests, whereas only a handful of systems contain information regarding the downstream testing or treatment. We propose a multi-task deep learning model to support risk stratification and down-stream test selection for patients undergoing Coronary Computed Tomography Angiography (CCTA). The analysis included 14,021 patients who underwent CCTA between 2006 and 2017. Our novel multitask deep learning framework extends the state-of-the art Perceiver model to deal with real-world CCTA report data. Our model achieved an Area Under the receiver operating characteristic Curve (AUC) of 0.76 in CAD risk stratification, and 0.72 AUC in predicting downstream tests. Our proposed deep learning model can accurately estimate the likelihood of CAD and provide recommended downstream tests based on prior CCTA data. In clinical practice, the utilization of such an approach could bring a paradigm shift in risk stratification and downstream management. Despite significant progress using deep learning models for tabular data, they do not outperform gradient boosting decision trees, and further research is required in this area. However, neural networks appear to benefit more readily from multi-task learning than tree-based models. This could offset the shortcomings of using single task learning approach when working with tabular data.

We explore two differentiable deep declarative layers, namely least squares on sphere (LESS) and implicit eigen decomposition (IED), for learning the principal matrix features (PMaF). It can be used to represent data features with a low-dimensional vector containing dominant information from a high-dimensional matrix. We first solve the problems with iterative optimization in the forward pass and then backpropagate the solution for implicit gradients under a bi-level optimization framework. Particularly, adaptive descent steps with the backtracking line search method and descent decay in the tangent space are studied to improve the forward pass efficiency of LESS. Meanwhile, exploited data structures are used to greatly reduce the computational complexity in the backward pass of LESS and IED. Empirically, we demonstrate the superiority of our layers over the off-the-shelf baselines by comparing the solution optimality and computational requirements., Comment: 16 pages, 7 figures, 10 tables, accepted to the differentiable almost everything workshop, ICML, 2023

We explore conditions for when the gradient of a deep declarative node can be approximated by ignoring constraint terms and still result in a descent direction for the global loss function. This has important practical application when training deep learning models since the approximation is often computationally much more efficient than the true gradient calculation. We provide theoretical analysis for problems with linear equality constraints and normalization constraints, and show examples where the approximation works well in practice as well as some cautionary tales for when it fails., Comment: 10 pages, 4 figures, ICML 2023 workshop on Differentiable Almost Everything

Unsupervised anomaly detection (AD) is a challenging task in realistic applications. Recently, there is an increasing trend to detect anomalies with deep neural networks (DNN). However, most popular deep AD detectors cannot protect the network from learning contaminated information brought by anomalous data, resulting in unsatisfactory detection performance and overfitting issues. In this work, we identify one reason that hinders most existing DNN-based anomaly detection methods from performing is the wide adoption of the Empirical Risk Minimization (ERM). ERM assumes that the performance of an algorithm on an unknown distribution can be approximated by averaging losses on the known training set. This averaging scheme thus ignores the distinctions between normal and anomalous instances. To break through the limitations of ERM, we propose a novel Diminishing Empirical Risk Minimization (DERM) framework. Specifically, DERM adaptively adjusts the impact of individual losses through a well-devised aggregation strategy. Theoretically, our proposed DERM can directly modify the gradient contribution of each individual loss in the optimization process to suppress the influence of outliers, leading to a robust anomaly detector. Empirically, DERM outperformed the state-of-the-art on the unsupervised AD benchmark consisting of 18 datasets., Comment: 8 pages, 4 figures, to be published in IJCNN at IEEE WCCI 2022

Optimal transport is a machine learning problem with applications including distribution comparison, feature selection, and generative adversarial networks. In this paper, we propose feature-robust optimal transport (FROT) for high-dimensional data, which solves high-dimensional OT problems using feature selection to avoid the curse of dimensionality. Specifically, we find a transport plan with discriminative features. To this end, we formulate the FROT problem as a min--max optimization problem. We then propose a convex formulation of the FROT problem and solve it using a Frank--Wolfe-based optimization algorithm, whereby the subproblem can be efficiently solved using the Sinkhorn algorithm. Since FROT finds the transport plan from selected features, it is robust to noise features. To show the effectiveness of FROT, we propose using the FROT algorithm for the layer selection problem in deep neural networks for semantic correspondence. By conducting synthetic and benchmark experiments, we demonstrate that the proposed method can find a strong correspondence by determining important layers. We show that the FROT algorithm achieves state-of-the-art performance in real-world semantic correspondence datasets.

Estimating mutual information is an important statistics and machine learning problem. To estimate the mutual information from data, a common practice is preparing a set of paired samples $\{(\mathbf{x}_i,\mathbf{y}_i)\}_{i=1}^n \stackrel{\mathrm{i.i.d.}}{\sim} p(\mathbf{x},\mathbf{y})$. However, in many situations, it is difficult to obtain a large number of data pairs. To address this problem, we propose the semi-supervised Squared-loss Mutual Information (SMI) estimation method using a small number of paired samples and the available unpaired ones. We first represent SMI through the density ratio function, where the expectation is approximated by the samples from marginals and its assignment parameters. The objective is formulated using the optimal transport problem and quadratic programming. Then, we introduce the Least-Squares Mutual Information with Sinkhorn (LSMI-Sinkhorn) algorithm for efficient optimization. Through experiments, we first demonstrate that the proposed method can estimate the SMI without a large number of paired samples. Then, we show the effectiveness of the proposed LSMI-Sinkhorn algorithm on various types of machine learning problems such as image matching and photo album summarization. Code can be found at https://github.com/csyanbin/LSMI-Sinkhorn., Comment: ECML/PKDD 2021

A meta-model is trained on a distribution of similar tasks such that it learns an algorithm that can quickly adapt to a novel task with only a handful of labeled examples. Most of current meta-learning methods assume that the meta-training set consists of relevant tasks sampled from a single distribution. In practice, however, a new task is often out of the task distribution, yielding a performance degradation. One way to tackle this problem is to construct an ensemble of meta-learners such that each meta-learner is trained on different task distribution. In this paper we present a method for constructing a mixture of meta-learners (MxML), where mixing parameters are determined by the weight prediction network (WPN) optimized to improve the few-shot classification performance. Experiments on various datasets demonstrate that MxML significantly outperforms state-of-the-art meta-learners, or their naive ensemble in the case of out-of-distribution as well as in-distribution tasks., Comment: 12 pages

The goal of few-shot learning is to learn a classifier that generalizes well even when trained with a limited number of training instances per class. The recently introduced meta-learning approaches tackle this problem by learning a generic classifier across a large number of multiclass classification tasks and generalizing the model to a new task. Yet, even with such meta-learning, the low-data problem in the novel classification task still remains. In this paper, we propose Transductive Propagation Network (TPN), a novel meta-learning framework for transductive inference that classifies the entire test set at once to alleviate the low-data problem. Specifically, we propose to learn to propagate labels from labeled instances to unlabeled test instances, by learning a graph construction module that exploits the manifold structure in the data. TPN jointly learns both the parameters of feature embedding and the graph construction in an end-to-end manner. We validate TPN on multiple benchmark datasets, on which it largely outperforms existing few-shot learning approaches and achieves the state-of-the-art results., Comment: Accepted in ICLR 2019; code available at https://github.com/csyanbin/TPN