Direct Inference on Admissible Sets (Diona)
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.
Related
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BibTeX
@misc{jr2026direct,
title = {{Direct Inference on Admissible Sets (Diona)}},
author = {Lorenzo Sabug Jr. and Eric Kerrigan},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.31526},
eprint = {2610.31526},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.31526},
}
RIS
TY - UNPB
TI - Direct Inference on Admissible Sets (Diona)
AU - Lorenzo Sabug Jr.
AU - Eric Kerrigan
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.31526
UR - https://arxiv.org/abs/2610.31526
AB - 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.
ER -