arXiv:2608. 11917v1 Announce Type: new Abstract: Multi-output Gaussian process regression scales cubically in the number of observations times outputs, and dense kernel-matrix methods need bespoke handling whenever different outputs are observed at different inputs.
arXiv:2606. 06576v1 Announce Type: new Abstract: In the sciences, regression tasks often require predicting high-dimensional outputs from few training examples.
arXiv:2607. 18209v1 Announce Type: cross Abstract: This paper considers a multi-environment factor model in which high-dimensional covariates are collected from heterogeneous environments, with auxiliary labels available in a subset of these environments.
The paper presents an exact, efficient solution for the Linear Model of Co‑regionalization (LMC) multitask Gaussian Process by decoupling latent processes under a mild noise‑model assumption. It introduces a full parametrization of the resulting projected LMC, enabling linear‑time optimization and simplifying tasks such as training updates and leave‑one‑out cross‑validation. Experiments on synthetic and real data demonstrate that projected LMC is competitive with state‑of‑the‑art multitask GP models while offering greater interpretability and computational ease.
This paper considers a multi-environment factor model in which high-dimensional covariates are collected from heterogeneous environments, with auxiliary labels available in a subset of these environments. The joint distribution of the covariates may vary across environments, whereas the latent structure is decomposed into invariant factors with shared loadings and heterogeneous factors with environment-specific loadings.
The paper proposes three information‑theoretic criteria for selecting the most relevant basis functions in sparse Gaussian process regression, tailored to different levels of prior knowledge. Experiments on six UCI regression datasets and three basis families (HSGP, VFF, VISH) show that the no‑data criterion is a robust default, often outperforming simple truncation, while the data‑aware criteria yield significant improvements for HSGP. The study demonstrates that careful basis‑function selection can lead to better performance without increasing computational cost.
arXiv:2412. 07041v4 Announce Type: replace-cross Abstract: Recovering incomplete multidimensional tensor-structured data is a fundamental task in many real-world applications.
arXiv:2512. 06143v2 Announce Type: replace Abstract: Despite a large corpus of recent work on scaling up Gaussian processes, a stubborn trade-off between computational speed, prediction and uncertainty quantification accuracy, and customizability persists.
arXiv:2603. 15802v2 Announce Type: replace Abstract: In many time series forecasting settings, the target time series is accompanied by exogenous covariates, such as promotions and prices in retail demand; temperature in energy load; calendar and holiday indicators for traffic or sales; and grid load or fuel costs in electricity pricing.
arXiv:2607. 27529v1 Announce Type: new Abstract: Discrete diffusion and flow-matching models denoise a sequence over many steps, but to keep each step cheap, they factorize the transition across positions and decide every token independently.
arXiv:2607. 24518v1 Announce Type: new Abstract: Symmetric non-negative matrix factorization (SymNMF) recovers latent group structure from a dependence matrix, but its dense, quadratic-memory objective has confined prior work to moderate sizes.
arXiv:2606. 02909v1 Announce Type: cross Abstract: Gradient observations can substantially improve Gaussian process (GP) surrogates, particularly in high-dimensional settings where function evaluations are expensive.
HALO introduces a hyperspherical VAE to constrain continuous latent representations to a fixed‑radius shell, stabilizing numerical fluctuations. It then employs a masked autoregressive model that balances parallel decoding with temporal correlation learning, reducing inference steps and improving stability. Experiments show HALO achieves state‑of‑the‑art generation performance with significantly better inference efficiency compared to existing baselines.