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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

Spanish

Proponemos un nuevo método de regresión latente de datos llamado Direct Inference on Admissible Sets (Diona) que utiliza muestras directamente para estimar el estado y sus derivados en un punto de consulta, así que con sus límites admisibles, sin mucho entrenamiento global. Al castar los valores y los derivados en la consulta y las muestras vecinas como variables latentes en un problema de optimización restringida, la carga de los loops de entrenamiento largos se convierte en una de las soluciones locales en demanda. Establecemos las propiedades teóricas de Diona, incluyendo la cobertura de muestras finitas y, en el caso sin ruido, la convergencia al estado verdadero y los derivados en la muestra densa. En un benchmark de regresión no lineal en seis funciones de entrenamiento de tres a ocho dimensiones

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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