相关论文: Generalization Guarantees for Sparse Kernel Approx…

The search for the optimal shape parameter for Radial Basis Function (RBF) kernel approximation has been an outstanding research problem for decades. In this work, we establish a theoretical framework for this problem by leveraging a…

In the field of uncertainty quantification, sparse polynomial chaos (PC) expansions are commonly used by researchers for a variety of purposes, such as surrogate modeling. Ideas from compressed sensing may be employed to exploit this…

Difference imaging is a technique for obtaining precise relative photometry of variable sources in crowded stellar fields and, as such, constitutes a crucial part of the data reduction pipeline in surveys for microlensing events or…

The performance of kernel density estimators is usually studied via Taylor expansions and asymptotic approximation arguments, in which the bandwidth parameter tends to zero with increasing sample size. In contrast, this paper focusses…

We construct near-optimal coresets for kernel density estimates for points in $\mathbb{R}^d$ when the kernel is positive definite. Specifically we show a polynomial time construction for a coreset of size $O(\sqrt{d}/\varepsilon\cdot…

The recent developments of basis pursuit and compressed sensing seek to extract information from as few samples as possible. In such applications, since the number of samples is restricted, one should deploy the sampling points wisely. We…

Graphs are useful to interpret widely used image processing methods, e.g., bilateral filtering, or to develop new ones, e.g., kernel based techniques. However, simple graph constructions are often used, where edge weight and connectivity…

This paper studies the statistical complexity of kernel hyperparameter tuning in the setting of active regression under adversarial noise. We consider the problem of finding the best interpolant from a class of kernels with unknown…

We propose new estimates for the frontier of a set of points. They are defined as kernel estimates covering all the points and whose associated support is of smallest surface. The estimates are written as linear combinatio- ns of kernel…

Sparse clustering, which aims to find a proper partition of an extremely high-dimensional data set with redundant noise features, has been attracted more and more interests in recent years. The existing studies commonly solve the problem in…

In this paper, we develop a quadrature framework for large-scale kernel machines via a numerical integration representation. Considering that the integration domain and measure of typical kernels, e.g., Gaussian kernels, arc-cosine kernels,…

Local polynomial regression struggles with several challenges when dealing with sparse data. The difficulty in capturing local features of the underlying function can lead to a potential misrepresentation of the true relationship.…

In complex visual recognition tasks it is typical to adopt multiple descriptors, that describe different aspects of the images, for obtaining an improved recognition performance. Descriptors that have diverse forms can be fused into a…

Feature selection aims to select the smallest subset of features for a specified level of performance. The optimal achievable classification performance on a feature subset is summarized by its Receiver Operating Curve (ROC). When infinite…

We introduce the Sparsity Roofline, a visual performance model for evaluating sparsity in neural networks. The Sparsity Roofline jointly models network accuracy, sparsity, and theoretical inference speedup. Our approach does not require…

Feature selection for predictive analytics is the problem of identifying a minimal-size subset of features that is maximally predictive of an outcome of interest. To apply to molecular data, feature selection algorithms need to be scalable…

Sinkhorn algorithm has been used pervasively to approximate the solution to optimal transport (OT) and unbalanced optimal transport (UOT) problems. However, its practical application is limited due to the high computational complexity. To…

This paper develops the process of using Richardson Extrapolation to improve the Kernel Density Estimation method, resulting in a more accurate (lower Mean Squared Error) estimate of a probability density function for a distribution of data…

We introduce a fast algorithm for Gaussian process regression in low dimensions, applicable to a widely-used family of non-stationary kernels. The non-stationarity of these kernels is induced by arbitrary spatially-varying vertical and…

Non-conservative uncertainty bounds are key for both assessing an estimation algorithm's accuracy and in view of downstream tasks, such as its deployment in safety-critical contexts. In this paper, we derive a tight, non-asymptotic…