Newest papers

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

Russian

Мы предлагаем новый метод латентной регрессии данных под названием Direct Inference on Admissible Sets (Diona), который непосредственно использует образцы для оценки состояния и его производных в точке запроса, так что вместе с их допустимыми границами, без длительного глобального обучения. Закапывая значения и производные в запросе и соседние образцы в качестве латентных переменных в ограниченной проблеме оптимизации, бремя длинных тренировочных циклов становится одним из местных решений по запросу. Мы устанавливаем эти теоретические свойства Diona, включая покрытие конечными образцами и, в шумовом случае, сближение с истинным состоянием и производными под плотным отбором. В нелинейном регрессионном ориентире на шесть функций с тремя до восьми из

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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