Related papers: Polynomial Order Selection for Savitzky-Golay Smoo…
Savitzky-Golay (SG) filters are finite impulse response (FIR) realizations of least-squares polynomial regression and they are widely used for filtering (e.g. smoothing, interpolating, predicting, differentiating) and processing (e.g.…
Local polynomial smoothing is a widespread technique in data analysis, and Savitzky-Golay (SG) filters are one of its most well-known realizations. In real settings, the effectiveness of SG filtering depends critically on proper tuning of…
The Savitzky-Golay FIR digital filter is based on a least-squares polynomial fit to a sample of equally spaced data. The polynomial fit gives the filter the ability to preserve moments of features in the data like peak width. However the…
One of the widely used denoising methods in different domains is the Savitzky-Golay (SG) filter. The SG filter has two design parameters: window length and the filter order. As the length of the window increases, the estimation variance…
The Savitzky-Golay FIR digital filter is based on a least-squares polynomial fit to a hypothetical sample of equally spaced data. This gives the filter the ability to preserve moments of features like peaks in the input. Descriptions of the…
The order of smoothness chosen in nonparametric estimation problems is critical. This choice balances the tradeoff between model parsimony and data overfitting. The most common approach used in this context is cross-validation. However,…
The idea of using polynomial methods to improve simple smoother iterations within a multigrid method for a symmetric positive definite (SPD) system is revisited. When the single-step smoother itself corresponds to an SPD operator, there is…
The solution to the Poisson equation arising from the spectral element discretization of the incompressible Navier-Stokes equation requires robust preconditioning strategies. One such strategy is multigrid. To realize the potential of…
We study the query complexity of sampling from high-dimensional Gaussian distributions using gradient information. In the standard oracle model, exact gradients expose only matrix-vector products with the precision matrix, leading to…
Label smoothing (LS) is a popular regularisation method for training neural networks as it is effective in improving test accuracy and is simple to implement. ``Hard'' one-hot labels are ``smoothed'' by uniformly distributing probability…
Deep neural networks (DNNs) experience significant performance degradation when processing noisy labels, primarily due to overfitting on mislabeled data. Current mainstream approaches attempt to mitigate this issue by passively filtering…
Any classifier can be "smoothed out" under Gaussian noise to build a new classifier that is provably robust to $\ell_2$-adversarial perturbations, viz., by averaging its predictions over the noise via randomized smoothing. Under the…
We study stochastic zeroth-order (ZO) optimization of smooth nonconvex objectives under heavy-tailed sample-gradient noise. This regime is motivated by empirical evidence that gradient noise in modern machine learning can violate the…
Our topic is the use of machine learning to improve software by making choices which do not compromise the correctness of the output, but do affect the time taken to produce such output. We are particularly concerned with computer algebra…
A comprehensive methodology is provided for smoothing noisy, irregularly sampled data with non-Gaussian noise using smoothing splines. We demonstrate how the spline order and tension parameter can be chosen a priori from physical reasoning.…
Support vector classification (SVC) is a classical and well-performed learning method for classification problems. A regularization parameter, which significantly affects the classification performance, has to be chosen and this is usually…
A body of recent work has focused on constructing a variational family of filtered distributions using Sequential Monte Carlo (SMC). Inspired by this work, we introduce Particle Smoothing Variational Objectives (SVO), a novel backward…
We present a simple algorithm for identifying and correcting real-valued noisy labels from a mixture of clean and corrupted sample points using Gaussian process regression. A heteroscedastic noise model is employed, in which additive…
We study bilevel optimization with a fixed polyhedral lower feasible set. Such problems are challenging for two reasons: active-set changes can make the upper objective nonsmooth, and existing hypergradient methods typically require…
Spectral Graph Neural Networks (GNNs) based on polynomial filters, such as ChebyNet, suffer from two critical limitations: 1) performance collapse on "heterophilic" graphs and 2) performance collapse at high polynomial degrees (K), known as…