January 2026

arXiv:2601.19005v1 Announce Type: cross Abstract: With the advancement of machine learning and artificial intelligence technologies, recommender systems have been increasingly used across a vast variety of platforms to efficiently and effectively match users with items. As application contexts become more diverse and complex, there is a growing need for more sophisticated recommendation techniques. One example is the composite item (for example, fashion outfit) recommendation where multiple levels of user preference information might be available and relevant. In this […]

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arXiv:2601.18952v1 Announce Type: cross Abstract: We propose an (offline) multi-dimensional distributional reinforcement learning framework (KE-DRL) that leverages Hilbert space mappings to estimate the kernel mean embedding of the multi-dimensional value distribution under a proposed target policy. In our setting, the state-action variables are multi-dimensional and continuous. By mapping probability measures into a reproducing kernel Hilbert space via kernel mean embeddings, our method replaces Wasserstein metrics with an integral probability metric. This enables efficient estimation in multi-dimensional state-action spaces […]

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arXiv:2601.18938v1 Announce Type: cross Abstract: Imputing missing node features in graphs is challenging, particularly under high missing rates. Existing methods based on latent representations or global diffusion often fail to produce reliable estimates, and may propagate errors across the graph. We propose FSD-CAP, a two-stage framework designed to improve imputation quality under extreme sparsity. In the first stage, a graph-distance-guided subgraph expansion localizes the diffusion process. A fractional diffusion operator adjusts propagation sharpness based on local structure. In […]

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arXiv:2601.18932v1 Announce Type: cross Abstract: Popularized by their strong image generation performance, diffusion and related methods for generative modeling have found widespread success in visual media applications. In particular, diffusion methods have enabled new approaches to data compression, where realistic reconstructions can be generated at extremely low bit-rates. This article provides a unifying review of recent diffusion-based methods for generative lossy compression, with a focus on image compression. These methods generally encode the source into an embedding and […]

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arXiv:2601.18900v1 Announce Type: cross Abstract: As generative models continue to evolve, detecting AI-generated images remains a critical challenge. While effective detection methods exist, they often lack formal interpretability and may rely on implicit assumptions about fake content, potentially limiting robustness to distributional shifts. In this work, we introduce a rigorous, statistically grounded framework for fake image detection that focuses on producing a probability score interpretable with respect to the real-image population. Our method leverages the strengths of multiple […]

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arXiv:2601.18837v1 Announce Type: cross Abstract: Recent Transformer- and MLP-based models have demonstrated strong performance in long-term time series forecasting, yet Transformers remain limited by their quadratic complexity and permutation-equivariant attention, while MLPs exhibit spectral bias. We propose HaKAN, a versatile model based on Kolmogorov-Arnold Networks (KANs), leveraging Hahn polynomial-based learnable activation functions and providing a lightweight and interpretable alternative for multivariate time series forecasting. Our model integrates channel independence, patching, a stack of Hahn-KAN blocks with residual connections, […]

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arXiv:2601.18815v1 Announce Type: cross Abstract: Prediction markets are often described as mechanisms that “aggregate information” into prices, yet the mapping from dispersed private information to observed market histories is typically noisy, endogenous, and shaped by heterogeneous and strategic participation. This paper formulates prediction markets as Bayesian inverse problems in which the unknown event outcome (Yin{0,1}) is inferred from an observed history of market-implied probabilities and traded volumes. We introduce a mechanism-agnostic observation model in log-odds space in which […]

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arXiv:2601.19811v1 Announce Type: new Abstract: Processing high-volume, streaming data is increasingly common in modern statistics and machine learning, where batch-mode algorithms are often impractical because they require repeated passes over the full dataset. This has motivated incremental stochastic estimation methods, including the incremental stochastic Expectation-Maximization (EM) algorithm formulated via stochastic approximation. In this work, we revisit and analyze an incremental stochastic variant of the Majorization-Minimization (MM) algorithm, which generalizes incremental stochastic EM as a special case. Our approach […]

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arXiv:2601.19755v1 Announce Type: new Abstract: We propose a framework to construct practical kernel-based two-sample tests from the family of $f$-divergences. The test statistic is computed from the witness function of a regularized variational representation of the divergence, which we estimate using kernel methods. The proposed test is adaptive over hyperparameters such as the kernel bandwidth and the regularization parameter. We provide theoretical guarantees for statistical test power across our family of $f$-divergence estimates. While our test covers a […]

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arXiv:2601.19156v1 Announce Type: new Abstract: We analyze Muon as originally proposed and used in practice — using the momentum orthogonalization with a few Newton-Schulz steps. The prior theoretical results replace this key step in Muon with an exact SVD-based polar factor. We prove that Muon with Newton-Schulz converges to a stationary point at the same rate as the SVD-polar idealization, up to a constant factor for a given number $q$ of Newton-Schulz steps. We further analyze this constant […]

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