Related papers: Fast Hyperbolic Wavelet Regression meets ANOVA
Fitting regression models with many multivariate responses and covariates can be challenging, but such responses and covariates sometimes have tensor-variate structure. We extend the classical multivariate regression model to exploit such…
The purpose is to study qualitative and quantitative rates of image compression by using different Haar wavelet banks. The experimental results of adaptive compression are provided. The paper deals with specific examples of orthogonal Haar…
Fixed-point iterative sweeping methods were developed in the literature to efficiently solve steady state solutions of Hamilton-Jacobi equations and hyperbolic conservation laws. Similar as other fast sweeping schemes, the key components of…
Probabilistic Latent Variable Models (LVMs) excel at modeling complex, high-dimensional data through lower-dimensional representations. Recent advances show that equipping these latent representations with a Riemannian metric unlocks…
It has been observed by several authors that well-known periodization strategies like tent or Chebychev transforms lead to remarkable results for the recovery of multivariate functions from few samples. So far, theoretical guarantees are…
Learning and generalizing from limited examples, i,e, few-shot learning, is of core importance to many real-world vision applications. A principal way of achieving few-shot learning is to realize an embedding where samples from different…
We introduce in this document a direct method allowing to solve numerically inverse type problems for linear parabolic equations. We consider the reconstruction of the full solution of the parabolic equation posed in $\Omega\times (0,T)$ -…
Hypergraphs have been becoming a popular choice to model complex, non-pairwise, and higher-order interactions for recommender system. However, compared with traditional graph-based methods, the constructed hypergraphs are usually much…
Waveform inversion seeks to estimate an inaccessible heterogeneous medium from data gathered by sensors that emit probing signals and measure the generated waves. It is an inverse problem for a second order wave equation or a first order…
Hyperbolic networks have shown prominent improvements over their Euclidean counterparts in several areas involving hierarchical datasets in various domains such as computer vision, graph analysis, and natural language processing. However,…
We suggest an adaptive sampling rule for obtaining information from noisy signals using wavelet methods. The technique involves increasing the sampling rate when relatively high-frequency terms are incorporated into the wavelet estimator,…
In multivariate regression, when covariates are numerous, it is often reasonable to assume that only a small number of them has predictive information. In some medical applications for instance, it is believed that only a few genes out of…
Unoriented surface reconstruction is an important task in computer graphics and has extensive applications. Based on the compact support of wavelet and orthogonality properties, classic wavelet surface reconstruction achieves good and fast…
The hyperbolic manifold is a smooth manifold of negative constant curvature. While the hyperbolic manifold is well-studied in the literature, it has gained interest in the machine learning and natural language processing communities lately…
We prove weak convergence in a separable Hilbert space for estimators of high-dimensional regression coefficients, which yields asymptotic normality and enables direct use of standard asymptotic tools such as the continuous mapping theorem.…
We consider the inverse elastic scattering of incident plane compressional and shear waves from the knowledge of the far field patterns. Specifically, three direct sampling methods for location and shape reconstruction are proposed using…
Learning representations according to the underlying geometry is of vital importance for non-Euclidean data. Studies have revealed that the hyperbolic space can effectively embed hierarchical or tree-like data. In particular, the few past…
We propose a new approach to the problem of high-dimensional multivariate ANOVA via bootstrapping max statistics that involve the differences of sample mean vectors. The proposed method proceeds via the construction of simultaneous…
The algorithm of modified wavelet analysis is discussed. It is based on the weighted least squares approximation. Contrary to the Gaussian as a weight function, we propose to use a compact weight function. The accuracy estimates using the…
High-dimensional real-world systems can often be well characterized by a small number of simultaneous low-complexity interactions. The analysis of variance (ANOVA) decomposition and the anchored decomposition are typical techniques to find…