相关论文: Assessing Prediction Error at Interpolation and Ex…

Effective verification and validation techniques for modern scientific machine learning workflows are challenging to devise. Statistical methods are abundant and easily deployed, but often rely on speculative assumptions about the data and…

Classical approximation and learning methods are typically optimized for interpolation over a sampled domain {\Omega}, with no guarantees on their behavior in an extrapolation region {\Xi}, where small in-domain errors may amplify. We…

Within the machine learning community, the widely-used uniform convergence framework has been used to answer the question of how complex, over-parameterized models can generalize well to new data. This approach bounds the test error of the…

We review the Akaike, deviance, and Watanabe-Akaike information criteria from a Bayesian perspective, where the goal is to estimate expected out-of-sample-prediction error using a biascorrected adjustment of within-sample error. We focus on…

We present three different methods to estimate error bars on the predictions made using a neural network. All of them represent lower bounds for the extrapolation errors. For example, we did not include an analysis on robustness against…

Model based signal processing or signal analysis or signal representation has a rather different point of view from the more traditional filtering and algorithm based approaches. However, in all of these, the names of Prony, Pad\'e, and…

This paper considers errors-in-variables models in a high-dimensional setting where the number of covariates can be much larger than the sample size, and there are only a small number of non-zero covariates. The presence of measurement…

Craig interpolation is a widespread method in verification, with important applications such as Predicate Abstraction, CounterExample Guided Abstraction Refinement and Lazy Abstraction With Interpolants. Most state-of-the-art model checking…

Function approximation from input and output data is one of the most investigated problems in signal processing. This problem has been tackled with various signal processing and machine learning methods. Although tensors have a rich history…

Interpolation-based methods are well-established and effective approaches for the efficient generation of accurate reduced-order surrogate models. Common challenges for such methods are the automatic selection of good or even optimal…

Evaluating predictive models is a crucial task in predictive analytics. This process is especially challenging with time series data where the observations show temporal dependencies. Several studies have analysed how different performance…

Novel reconstruction methods for electrical impedance tomography (EIT) often require voltage measurements on current-driven electrodes. Such measurements are notoriously difficult to obtain in practice as they tend to be affected by unknown…

One way to investigate the precision of estimates likely to result from planned experiments and planned epidemiological studies is to simulate a large number of possible outcomes and analyse the sets of possible results. This appears to be…

A priori error bounds have been derived for different balancing-related model reduction methods. The most classical result is a bound for balanced truncation and singular perturbation approximation that is applicable for asymptotically…

Information theoretic criteria (ITC) have been widely adopted in engineering and statistics for selecting, among an ordered set of candidate models, the one that better fits the observed sample data. The selected model minimizes a penalized…

A bias correction to Akaike's information criterion (AIC) is derived for seemingly unrelated regressions models. The correction is of particular use when the sample size is not much larger than the number of fitted parameters. A…

Bayesian parameter estimation provides a systematic approach to compare heavy ion collision models with measurements, leading to constraints on the properties of nuclear matter with proper accounting of experimental and theoretical…

We report a deep generative model for regression tasks in materials informatics. The model is introduced as a component of a data imputer, and predicts more than 20 diverse experimental properties of organic molecules. The imputer is…

This paper deals with the polynomial linear system solving with errors (PLSwE) problem. Specifically, we focus on the evaluation-interpolation technique for solving polynomial linear systems and we assume that errors can occur in the…

Practitioners building classifiers often start with a smaller pilot dataset and plan to grow to larger data in the near future. Such projects need a toolkit for extrapolating how much classifier accuracy may improve from a 2x, 10x, or 50x…