In partial multi-label learning (PML), each training example is associated with a set of candidate labels, among which only some labels are valid. As a common strategy to tackle PML problem, disambiguation aims to recover the ground-truth labeling information from such inaccurate annotations. However, existing approaches mainly rely on heuristics or ad-hoc rules to disambiguate candidate labels, which may not be universal enough in complicated real-world scenarios. To provide a principled way for disambiguation, we make a first attempt to explore the probabilistic graphical model for PML problem, where a directed graph is tailored to infer latent ground-truth labeling information from the generative process of partial multi-label data. Under the framework of stochastic gradient variational Bayes, a unified variational lower bound is derived for this graphical model, which is further relaxed probabilistically so that the desired prediction model can be induced with simultaneously identified ground-truth labeling information. Comprehensive experiments on multiple synthetic and real-world data sets show that our approach outperforms the state-of-the-art counterparts.

This paper presents a novel value-aware approach to product recommendation that simultaneously addresses the high dimensionality and sparsity of user-item data while explicitly incorporating the contribution of each product and user to overall sales revenue. The proposed framework encodes revenue contributions in the user-item matrix and computes customer similarity directly on this basis using suitable distance measures. This enables the segmentation of users according to the revenue-based similarity of their purchase baskets and supports recommendations aligned with profitability objectives. We compare conventional similarity metrics with a novel alternative tailored to high-dimensional contexts and propose three recommendation strategies based on revenue share, product popularity, and expected profit generation. The effectiveness of the proposed method is validated through simulation experiments and a real-world application using the UCI Online Retail dataset.

Deep learning models for 12-lead electrocardiogram (ECG) analysis achieve high diagnostic performance but lack the intuitive interpretability required for clinical integration. Standard feature attribution methods are limited by the inherent difficulty in mapping abstract waveform fluctuations to physical anatomical pathologies. To resolve this, we propose a cross-modal method that projects feature attributions from high-performance 12-lead ECG models onto the CineECG 3D anatomical space. Our study reveals that while models trained directly on CineECG signals suffer from reduced accuracy and incoherent attributions, the proposed mapping mechanism effectively recovers clinically relevant feature rankings. Validated against a ground-truth dataset of 20 cases annotated by domain experts, the mapped explanations yield a Dice score of 0.56, significantly outperforming the 0.47 baseline of standard 12-lead attributions. These findings indicate that cross-modal averaging mapping effectively filters attribution instability and improves the localization of pathological features, combining the diagnostic expressiveness of standard ECG with the intuitive clarity of anatomical visualization.

In this paper, we introduce the forecast reconciliation packages FoReco and FoRecoML for R (RCore Team 2026). Forecast reconciliation adjusts forecasts for linearly constrained multiple time series (such as hierarchical or grouped series, or series observed at different temporal frequencies) so that they are coherent with respect to the underlying constraints, improving both accuracy and consistency for informed decision making. The contributions of the packages are threefold. First, FoReco and FoRecoML are the first to offer functionality for forecast reconciliation methods across cross-sectional, temporal and cross-temporal frameworks. Second, the packages provide a comprehensive set of forecast reconciliation approaches, including classical (e.g., top-down, bottom-up and middle-out) and regression based reconciliation methods - in FoReco - as well as non-linear reconciliation methods using machine learning - in FoRecoML. A third key contribution is their unified design, which enables easy-to-use forecast reconciliation functions built on the same philosophy, regardless of the reconciliation framework or method.

Neural Information Processing Systems http://nips.cc/

We study the effectiveness of neural sequence models for premise selection in automated theorem proving, one of the main bottlenecks in the formalization of mathematics. We propose a two stage approach for this task that yields good results for the premise selection task on the Mizar corpus while avoiding the handengineered features of existing state-of-the-art models. To our knowledge, this is the first time deep learning has been applied to theorem proving on a large scale.

High dimensional superposition models characterize observations using parameters which can be written as a sum of multiple component parameters, each with its own structure, e.g., sum of low rank and sparse matrices, sum of sparse and rotated sparse vectors, etc. In this paper, we consider general superposition models which allow sum of any number of component parameters, and each component structure can be characterized by any norm. We present a simple estimator for such models, give a geometric condition under which the components can be accurately estimated, characterize sample complexity of the estimator, and give high probability nonasymptotic bounds on the componentwise estimation error. We use tools from empirical processes and generic chaining for the statistical analysis, and our results, which substantially generalize prior work on superposition models, are in terms of Gaussian widths of suitable sets.