Related papers: PSI: Constructing ad-hoc Simplices to Interpolate …
This paper presents a polar coding scheme to achieve secrecy in block fading binary symmetric wiretap channels without the knowledge of instantaneous channel state information (CSI) at the transmitter. For this model, a coding scheme that…
We present a new approach to approximate nearest-neighbor queries in fixed dimension under a variety of non-Euclidean distances. We are given a set $S$ of $n$ points in $\mathbb{R}^d$, an approximation parameter $\varepsilon > 0$, and a…
We propose new compressive parameter estimation algorithms that make use of polar interpolation to improve the estimator precision. Our work extends previous approaches involving polar interpolation for compressive parameter estimation in…
An analytical method is advanced for constructing interpolation formulae for complicated problems of statistical mechanics, in which just a few terms of asymptotic expansions are available. The method is based on the self-similar…
We propose a new method to construct maximin distance designs with arbitrary number of dimensions and points. The proposed designs hold interleaved-layer structures and are by far the best maximin distance designs in four or more…
This article proposes an active learning method for high dimensional data, based on intrinsic data geometries learned through diffusion processes on graphs. Diffusion distances are used to parametrize low-dimensional structures on the…
We consider the following multi-component sparse PCA problem: given a set of data points, we seek to extract a small number of sparse components with disjoint supports that jointly capture the maximum possible variance. These components can…
Problems in astrophysics, space weather research and geophysics usually need to analyze noisy big data on the sphere. This paper develops distributed filtered hyperinterpolation for noisy data on the sphere, which assigns the data fitting…
We construct embeddings of simplicial complexes into a (surface of a) simplicial ball whose triangulation has bounded degrees and low volume. This construction can be used either to efficiently "simplify a complicated space" by realizing it…
Multi-dimensional optimization is widely used in virtually all areas of modern astrophysics. However, it is often too computationally expensive to evaluate a model on-the-fly. Typically, it is solved by pre-computing a grid of models for a…
This work proposes and analyzes a compressed sensing approach to polynomial approximation of complex-valued functions in high dimensions. Of particular interest is the setting where the target function is smooth, characterized by a rapidly…
In the machine learning field, dimensionality reduction is an important task. It mitigates the undesired properties of high-dimensional spaces to facilitate classification, compression, and visualization of high-dimensional data. During the…
Hierarchical matrices provide a powerful representation for significantly reducing the computational complexity associated with dense kernel matrices. For general kernel functions, interpolation-based methods are widely used for the…
Matrix factorization exploits the idea that, in complex high-dimensional data, the actual signal typically lies in lower-dimensional structures. These lower dimensional objects provide useful insight, with interpretability favored by sparse…
We present a numerical method to model dynamical systems from data. We use the recently introduced method Scalable Probabilistic Approximation (SPA) to project points from a Euclidean space to convex polytopes and represent these projected…
We give efficient data-oblivious algorithms for several fundamental geometric problems that are relevant to geographic information systems, including planar convex hulls and all-nearest neighbors. Our methods are "data-oblivious" in that…
Simulating quantum systems with their environments often requires non-unitary operations, and mapping these to quantum devices often involves expensive dilations or prohibitive measurement costs to achieve desired precisions. Building on…
Polynomial interpolation is an important component of many computational problems. In several of these computational problems, failure to preserve positivity when using polynomials to approximate or map data values between meshes can lead…
The main constraint on relative position of geometric objects, used in spatial planning for computing the C-space maps (for example, in robotics, CAD, and packaging), is the relative non-overlapping of objects. This is the simplest…
We introduce an adaptive scattered data fitting scheme as extension of local least squares approximations to hierarchical spline spaces. To efficiently deal with non-trivial data configurations, the local solutions are described in terms of…