Since the PDE in Eq. 5 in the main manuscript is equivalent to the E-L equation of the quadratic

The question of what makes a data distribution suitable for deep learning is a fundamental open problem.

Multiple binary responses arise in many modern data-analytic problems. Although fitting separate logistic regressions for each response is computationally attractive, it ignores shared structure and can be statistically inefficient, especially in high-dimensional and class-imbalanced regimes. Low-rank models offer a natural way to encode latent dependence across tasks, but existing methods for binary data are largely likelihood-based and focus on pointwise classification rather than ranking performance. In this work, we propose a unified framework for learning with multiple binary responses that directly targets discrimination by minimizing a surrogate loss for the area under the ROC curve (AUC). The method aggregates pairwise AUC surrogate losses across responses while imposing a low-rank constraint on the coefficient matrix to exploit shared structure. We develop a scalable projected gradient descent algorithm based on truncated singular value decomposition. Exploiting the fact that the pairwise loss depends only on differences of linear predictors, we simplify computation and analysis. We establish non-asymptotic convergence guarantees, showing that under suitable regularity conditions, leading to linear convergence up to the minimax-optimal statistical precision. Extensive simulation studies demonstrate that the proposed method is robust in challenging settings such as label switching and data contamination and consistently outperforms likelihood-based approaches.

High-dimensional learning problems, where the number of features exceeds the sample size, often require sparse regularization for effective prediction and variable selection. While established for fully supervised data, these techniques remain underexplored in weak-supervision settings such as Positive-Confidence (Pconf) classification. Pconf learning utilizes only positive samples equipped with confidence scores, thereby avoiding the need for negative data. However, existing Pconf methods are ill-suited for high-dimensional regimes. This paper proposes a novel sparse-penalization framework for high-dimensional Pconf classification. We introduce estimators using convex (Lasso) and non-convex (SCAD, MCP) penalties to address shrinkage bias and improve feature recovery. Theoretically, we establish estimation and prediction error bounds for the L1-regularized Pconf estimator, proving it achieves near minimax-optimal sparse recovery rates under Restricted Strong Convexity condition. To solve the resulting composite objective, we develop an efficient proximal gradient algorithm. Extensive simulations demonstrate that our proposed methods achieve predictive performance and variable selection accuracy comparable to fully supervised approaches, effectively bridging the gap between weak supervision and high-dimensional statistics.

Developing fair automated machine learning algorithms is critical in making safe and trustworthy decisions. Many causality-based fairness notions have been proposed to address the above issues by quantifying the causal connections between sensitive attributes and decisions, and when the true causal graph is fully known, certain algorithms that achieve interventional fairness have been proposed. However, when the true causal graph is unknown, it is still challenging to effectively and efficiently exploit partially directed acyclic graphs (PDAGs) to achieve interventional fairness. To exploit the PDAGs for achieving interventional fairness, previous methods have been built on variable selection or causal effect identification, but limited to reduced prediction accuracy or strong assumptions. In this paper, we propose a general min-max optimization framework that can achieve interventional fairness with promising prediction accuracy and can be extended to maximally oriented PDAGs (MPDAGs) with added background knowledge. Specifically, we first estimate all possible treatment effects of sensitive attributes on a given prediction model from all possible adjustment sets of sensitive attributes via an efficient local approach. Next, we propose to alternatively update the prediction model and possible estimated causal effects, where the prediction model is trained via a min-max loss to control the worst-case fairness violations. Extensive experiments on synthetic and real-world datasets verify the superiority of our methods.

Trajectory prediction plays a vital role in the performance of autonomous driving systems, and prediction accuracy, such as average displacement error (ADE) or final displacement error (FDE), is widely used as a performance metric. However, a significant disparity exists between the accuracy of predictors on fixed datasets and driving performance when the predictors are used downstream for vehicle control, because of a dynamics gap. In the real world, the prediction algorithm influences the behavior of the ego vehicle, which, in turn, influences the behaviors of other vehicles nearby.

Large pretrained foundation models demonstrate exceptional performance and, in some high-stakes applications, even surpass human experts. However, most of these models are currently evaluated primarily on prediction accuracy, overlooking the validity of the rationales behind their accurate predictions. For the safe deployment of foundation models, there is a pressing need to ensure,, correct prediction backed by correct rationales. To achieve this, we propose a two-phase scheme: First, we curate a new dataset that offers structured rationales for visual recognition tasks. Second, we propose a rationale-informed optimization method to guide the model in disentangling and localizing visual evidence for each rationale, without requiring manual annotations. Extensive experiments and ablation studies demonstrate that our model outperforms state-of-the-art models by up to 10.1\% in prediction accuracy across a wide range of tasks. Furthermore, our method significantly improves the model's rationale correctness, improving localization by 7.5\% and disentanglement by 36.5\%.

The automation of the medical evidence acquisition and diagnosis process has recently attracted increasing attention in order to reduce the workload of doctors and democratize access to medical care. However, most works proposed in the machine learning literature focus solely on improving the prediction accuracy of a patient's pathology. We argue that this objective is insufficient to ensure doctors' acceptability of such systems. In their initial interaction with patients, doctors do not only focus on identifying the pathology a patient is suffering from; they instead generate a differential diagnosis (in the form of a short list of plausible diseases) because the medical evidence collected from patients is often insufficient to establish a final diagnosis. Moreover, doctors explicitly explore severe pathologies before potentially ruling them out from the differential, especially in acute care settings. Finally, for doctors to trust a system's recommendations, they need to understand how the gathered evidences led to the predicted diseases.