相关论文: Deviation Bounds for Wavelet Shrinkage

Detailed derivations of two bounds of the minimum mean-square error (MMSE) of complex-valued multiple-input multiple-output (MIMO) systems are proposed for performance evaluation. Particularly, the lower bound is derived based on a…

In this paper we develop a nonparametric regression method that is simultaneously adaptive over a wide range of function classes for the regression function and robust over a large collection of error distributions, including those that are…

Recent work has generalized several results concerning the well-understood spiked Wigner matrix model of a low-rank signal matrix corrupted by additive i.i.d. Gaussian noise to the inhomogeneous case, where the noise has a variance profile.…

In recent studies, several asymptotic upper bounds on generalization errors on deep neural networks (DNNs) are theoretically derived. These bounds are functions of several norms of weights of the DNNs, such as the Frobenius and spectral…

The large deviation principle in the small noise limit is derived for solutions of possibly degenerate It\^o stochastic differential equations with predictable coefficients, which may depend also on the large deviation parameter. The result…

We estimate optimal thresholds for surface code in the presence of loss via an analytical method developed in statistical physics. The optimal threshold for the surface code is closely related to a special critical point in a…

The problem of reconstruction of digital images from their degraded measurements is regarded as a problem of central importance in various fields of engineering and imaging sciences. In such cases, the degradation is typically caused by the…

During recent years the interest of optimization and machine learning communities in high-probability convergence of stochastic optimization methods has been growing. One of the main reasons for this is that high-probability complexity…

We consider a linear ill-posed equation in the Hilbert space setting. Multiple independent unbiased measurements of the right hand side are available. A natural approach is to take the average of the measurements as an approximation of the…

Bayesian nonparametric regression with dependent wavelets has dual shrinkage properties: there is shrinkage through a dependent prior put on functional differences, and shrinkage through the setting of most of the wavelet coefficients to…

This paper proposes a differentiator for sampled signals with bounded noise and bounded second derivative. It is based on a linear program derived from the available sample information and requires no further tuning beyond the noise and…

We consider a microstructure model for a financial asset, allowing for price discreteness and for a diffusive behavior at large sampling scale. This model, introduced by Delattre and Jacod, consists in the observation at the high frequency…

Wavelet-based grid adaptation methods use multiresolution analysis for error estimation, offering a mathematically rigorous approach to adaptive grid refinement when solving Partial Differential Equations (PDEs). However, applying these…

Empirically it has been observed that the performance of deep neural networks steadily improves as we increase model size, contradicting the classical view on overfitting and generalization. Recently, the double descent phenomena has been…

We develop a new class of distance-aware error bounds that tightly characterize the approximation error of spline neural networks. Our bottom-up approach analyzes the error bound of each neuron (a spline) and then extends it to the full…

Prediction via deterministic continuous-time models will always be subject to model error, for example due to unexplainable phenomena, uncertainties in any data driving the model, or discretisation/resolution issues. In this paper, we build…

This paper extends the standard chaining technique to prove excess risk upper bounds for empirical risk minimization with random design settings even if the magnitude of the noise and the estimates is unbounded. The bound applies to many…

In nonparametric statistical problems, we wish to find an estimator of an unknown function f. We can split its error into bias and variance terms; Smirnov, Bickel and Rosenblatt have shown that, for a histogram or kernel estimate, the…

Tomographic reconstruction is an ill-posed inverse problem that calls for regularization. One possibility is to require sparsity of the unknown in an orthonormal wavelet basis. This in turn can be achieved by variational regularization…

When developing risk prediction models, shrinkage methods are recommended, especially when the sample size is limited. Several earlier studies have shown that the shrinkage of model coefficients can reduce overfitting of the prediction…