Related papers: Post-Regularization Confidence Bands for Ordinary …

Training Neural Ordinary Differential Equations (ODEs) is often computationally expensive. Indeed, computing the forward pass of such models involves solving an ODE which can become arbitrarily complex during training. Recent works have…

We study distribution free, nonparametric prediction bands with a special focus on their finite sample behavior. First we investigate and develop different notions of finite sample coverage guarantees. Then we give a new prediction band…

Neural networks can be fragile to input noise and adversarial attacks. In this work, we consider Convolutional Neural Ordinary Differential Equations (NODEs), a family of continuous-depth neural networks represented by dynamical systems,…

We study the problem of estimating the coefficients in linear ordinary differential equations (ODE's) with a diverging number of variables when the solutions are observed with noise. The solution trajectories are first smoothed with local…

The paper studies the problem of constructing nonparametric simultaneous confidence bands with nonasymptotic and distribition-free guarantees. The target function is assumed to be band-limited and the approach is based on the theory of…

We study the problem of structured output learning from a regression perspective. We first provide a general formulation of the kernel dependency estimation (KDE) problem using operator-valued kernels. We show that some of the existing…

Neural ordinary differential equations (ODEs) have been attracting increasing attention in various research domains recently. There have been some works studying optimization issues and approximation capabilities of neural ODEs, but their…

We initiate the study of differentially private learning in the proportional dimensionality regime, in which the number of data samples $n$ and problem dimension $d$ approach infinity at rates proportional to one another, meaning that…

The simplicity and the efficiency of a quasi-analytical method for solving nonlinear ordinary differential equations (ODE), is illustrated on the study of anharmonic oscillators (AO) with a potential $V(x) =\beta x^{2}+x^{2m}$ ($m>0$). The…

For mathematical and experimental ease, models with time varying parameters are often simplified to assume constant parameters. However, this simplification can potentially lead to identifiability issues (lack of uniqueness of parameter…

Deep learning models have significantly improved prediction accuracy in various fields, gaining recognition across numerous disciplines. Yet, an aspect of deep learning that remains insufficiently addressed is the assessment of prediction…

Node-perturbation learning is a type of statistical gradient descent algorithm that can be applied to problems where the objective function is not explicitly formulated, including reinforcement learning. It estimates the gradient of an…

Longitudinal data tracking under Local Differential Privacy (LDP) is a challenging task. Baseline solutions that repeatedly invoke a protocol designed for one-time computation lead to linear decay in the privacy or utility guarantee with…

Nonlinear ordinary differential equations (ODEs) are powerful tools for modeling real-world dynamical systems. However, propagating initial state uncertainty through nonlinear dynamics, especially when the ODE is unknown and learned from…

Ensuring reliable performance in situations outside the Operational Design Domain (ODD) remains a primary challenge in devising resilient autonomous systems. We explore this challenge by introducing an approach for adapting probabilistic…

Connecting orbits are important invariant structures in the state space of nonlinear systems and various techniques are designed for their computation. However, a uniform analytic approximation of the whole orbit seems rare. Here, based on…

Ordinary differential equations (ODE's) are widespread models in physics, chemistry and biology. In particular, this mathematical formalism is used for describing the evolution of complex systems and it might consist of high-dimensional…

Learning models of dynamical systems with external inputs, which may be, for example, nonsmooth or piecewise, is crucial for studying complex phenomena and predicting future state evolution, which is essential for applications such as…

Guessing random additive noise decoding (GRAND) is a universal decoding paradigm that decodes by repeatedly testing error patterns until identifying a codeword, where the ordering of tests is generated by the received channel values. On one…

In this paper we establish asymptotic simultaneous confidence bands for copulas based on the local linear kernel estimator proposed by Chen and Huang [1]. For this, we prove under smoothness conditions on the copula function, a uniform in…