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Direct Inference on Admissible Sets (Diona)

Sabug, Lorenzo, Jr., Kerrigan Eric · 2026 · arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.31526 · cited by 0 works (OpenAlex) · open-access PDF

Chinese

我们提出了一种名为 Direct Inference on Admissible Sets(Diona)的延迟数据回归方法,该方法直接使用样本来估计状态和其衍生品在查询点,因此它们的允许界限,没有长的全球培训。通过在查询和邻近样本作为延迟变量在受限的优化问题中铸造新的数据回归方法,直接使用样本来估计状态和其衍生品在查询点上,因此我们建立了Diona的理论特性,包括有限样本覆盖,在无噪音的情况下,以真实状态和密集样本的汇聚。在六个三个到八个维度的六个函数上的非线性回归基准,Diona比在相对密集数据集中的Gaussian过程(GP)更准确。此外,与GP一样,它

Machine translation (Meta M2M100); the English original follows.

Abstract

We propose a new regression method named Direct Inference on Admissible Sets (Diona) that directly uses samples to estimate the state and its derivatives at a query point, along with their admissible bounds, without long global training. By casting the values and derivatives at the query and neighbouring samples as latent variables in a constrained optimisation problem, the burden of long training loops becomes one of on-demand local solves. We establish Diona's theoretical properties including finite-sample coverage and, in the noiseless case, convergence to the true state and derivatives under dense sampling. In a nonlinear regression benchmark on six functions of three to eight dimensions, Diona was more accurate than a Gaussian process (GP) on noiseless data especially with denser data sets. Furthermore, as with GP, it produced uncertainty bounds that contained the true value at more than 95% of query points in four functions. Diona's time to a first prediction after a data set update was three to four orders of magnitude shorter than that of the GP, and two to three orders shorter than that of a neural network, which was more accurate but offers no uncertainty quantification. This low latency is paid for by on-demand predictions, so this latency advantage applies when relatively few predictions are needed between data updates.

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Topics: Inference, Mathematics, Algorithm, Benchmark (surveying), Regression, Gaussian process

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