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This paper studies the asymptotic behavior of penalized spline estimates of derivatives. In particular, we show that simply differentiating the penalized spline estimator of the mean regression function itself to estimate the corresponding…
The U-curve optimization problem is characterized by a decomposable in U-shaped curves cost function over the chains of a Boolean lattice. This problem can be applied to model the classical feature selection problem in Machine Learning.…
In this paper, we explore statistical versus computational trade-off to address a basic question in the application of a distributed algorithm: what is the minimal computational cost in obtaining statistical optimality? In smoothing spline…
We propose a new algorithm called PLUTO for building logistic regression trees to binary response data. PLUTO can capture the nonlinear and interaction patterns in messy data by recursively partitioning the sample space. It fits a simple or…
Calibration$\unicode{x2014}$the problem of ensuring that predicted probabilities align with observed class frequencies$\unicode{x2014}$is a basic desideratum for reliable prediction with machine learning systems. Calibration error is…
A method is proposed for constructing a spline curve of the Bezier type, which is continuous along with its first derivative by a piecewise polynomial function. Conditions for its existence and uniqueness are given. The constructed curve…
In speech deepfake detection, one of the critical aspects is developing detectors able to generalize on unseen data and distinguish fake signals across different datasets. Common approaches to this challenge involve incorporating diverse…
This paper proposes probabilistic conformal prediction (PCP), a predictive inference algorithm that estimates a target variable by a discontinuous predictive set. Given inputs, PCP construct the predictive set based on random samples from…
Boundary feedback stabilisation of linear port-Hamiltonian systems on an interval is considered. Generation and stability results already known for linear feedback are extended to nonlinear dissipative feedback, both to static feedback…
This paper discusses a nonparametric regression model that naturally generalizes neural network models. The model is based on a finite number of one-dimensional transformations and can be estimated with a one-dimensional rate of…
It has become critical for deep learning algorithms to quantify their output uncertainties to satisfy reliability constraints and provide accurate results. Uncertainty estimation for regression has received less attention than…
In modern industrial production, the prediction ability of the remaining useful life (RUL) of bearings directly affects the safety and stability of the system. Traditional methods require rigorous physical modeling and perform poorly for…
We address numerical differentiation under coarse, non-uniform sampling and Gaussian noise. A maximum-likelihood estimator with $L_2$-norm constraint on a higher-order derivative is obtained, yielding spline-based solution. We introduce a…
Across scientific domains, a fundamental challenge is to characterize and compute the mappings from underlying physical processes to observed signals and measurements. While nonlinear neural networks have achieved considerable success, they…
Accurate quantification of model uncertainty has long been recognized as a fundamental requirement for trusted AI. In regression tasks, uncertainty is typically quantified using prediction intervals calibrated to an ad-hoc operating point,…
Design of printed circuit board (PCB) stack-up requires the consideration of characteristic impedance, insertion loss and crosstalk. As there are many parameters in a PCB stack-up design, the optimization of these parameters needs to be…
Posterior distributions often feature intractable normalizing constants, called marginal likelihoods or evidence, that are useful for model comparison via Bayes factors. This has motivated a number of methods for estimating ratios of…
In this paper, a linear model with grouped explanatory variables is considered. The idea is to perform an automatic detection of different successive groups of the unknown coefficients under the assumption that the number of groups is of…
We consider the sequential decision-making problem where the mean outcome is a non-linear function of the chosen action. Compared with the linear model, two curious phenomena arise in non-linear models: first, in addition to the "learning…
In this paper, we propose an online learning-based predictive control (LPC) approach designed for nonlinear systems that lack explicit system dynamics. Unlike traditional model predictive control (MPC) algorithms that rely on known system…