Tag: approximation
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Quantifying Normality: Convergence Rate to Gaussian Limit for Stochastic Approximation and Unadjusted OU Algorithm
Quantifying Normality: Convergence Rate to Gaussian Limit for Stochastic Approximation and Unadjusted OU Algorithm arXiv:2602.13906v1 Announce Type: new Abstract: Stochastic approximation (SA) is a method for finding the root of an operator perturbed by noise. There is a rich literature establishing the asymptotic normality of rescaled SA iterates under fairly mild conditions. However, these asymptotic…
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Laplace Approximation For Tensor Train Kernel Machines In System Identification
Laplace Approximation For Tensor Train Kernel Machines In System Identification arXiv:2512.02532v1 Announce Type: new Abstract: To address the scalability limitations of Gaussian process (GP) regression, several approximation techniques have been proposed. One such method is based on tensor networks, which utilizes an exponential number of basis functions without incurring exponential computational cost. However, extending this…
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Distributionally robust approximation property of neural networks
Distributionally robust approximation property of neural networks arXiv:2510.09177v1 Announce Type: new Abstract: The universal approximation property uniformly with respect to weakly compact families of measures is established for several classes of neural networks. To that end, we prove that these neural networks are dense in Orlicz spaces, thereby extending classical universal approximation theorems even beyond…
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On the Rate of Gaussian Approximation for Linear Regression Problems
On the Rate of Gaussian Approximation for Linear Regression Problems arXiv:2509.14039v1 Announce Type: new Abstract: In this paper, we consider the problem of Gaussian approximation for the online linear regression task. We derive the corresponding rates for the setting of a constant learning rate and study the explicit dependence of the convergence rate upon the…
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SIM-Shapley: A Stable and Computationally Efficient Approach to Shapley Value Approximation
SIM-Shapley: A Stable and Computationally Efficient Approach to Shapley Value Approximation arXiv:2505.08198v1 Announce Type: new Abstract: Explainable artificial intelligence (XAI) is essential for trustworthy machine learning (ML), particularly in high-stakes domains such as healthcare and finance. Shapley value (SV) methods provide a principled framework for feature attribution in complex models but incur high computational costs,…
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Networks with Finite VC Dimension: Pro and Contra
Networks with Finite VC Dimension: Pro and Contra arXiv:2502.02679v1 Announce Type: new Abstract: Approximation and learning of classifiers of large data sets by neural networks in terms of high-dimensional geometry and statistical learning theory are investigated. The influence of the VC dimension of sets of input-output functions of networks on approximation capabilities is compared with…