Related papers: Optimal bandwidth estimation for a fast manifold l…
Motivated by the latest effort to employ banded matrices to estimate a high-dimensional covariance $\Sigma$, we propose a test for $\Sigma$ being banded with possible diverging bandwidth. The test is adaptive to the "large $p$, small $n$"…
Smooth functions on graphs have wide applications in manifold and semi-supervised learning. In this paper, we study a bandit problem where the payoffs of arms are smooth on a graph. This framework is suitable for solving online learning…
We study the estimation of the reach, an ubiquitous regularity parameter in manifold estimation and geometric data analysis. Given an i.i.d. sample over an unknown $d$-dimensional $\mathcal{C}^k$-smooth submanifold of $\mathbb{R}^D$, we…
Smooth functions on graphs have wide applications in manifold and semi-supervised learning. In this work, we study a bandit problem where the payoffs of arms are smooth on a graph. This framework is suitable for solving online learning…
The effectiveness of dimensionality reduction with quadratic manifolds hinges on the choice of a reduced basis and the associated quadratic correction terms. Existing approaches typically rely on subspaces spanned by the leading principal…
Spectral dimensionality reduction is frequently used to identify low-dimensional structure in high-dimensional data. However, learning manifolds, especially from the streaming data, is computationally and memory expensive. In this paper, we…
New algorithms are devised for finding the maxima of multidimensional point samples, one of the very first problems studied in computational geometry. The algorithms are very simple and easily coded and modified for practical needs. The…
Analyzing large volumes of high-dimensional data requires dimensionality reduction: finding meaningful low-dimensional structures hidden in their high-dimensional observations. Such practice is needed in atomistic simulations of complex…
We demonstrate optimization of optical metasurfaces over $10^5$--$10^6$ degrees of freedom in two and three dimensions, 100--1000+ wavelengths ($\lambda$) in diameter, with 100+ parameters per $\lambda^2$. In particular, we show how…
The problem of identifying geometric structure in data is a cornerstone of (unsupervised) learning. As a result, Geometric Representation Learning has been widely applied across scientific and engineering domains. In this work, we…
Improved performance in higher-order spectral density estimation is achieved using a general class of infinite-order kernels. These estimates are asymptotically less biased but with the same order of variance as compared to the classical…
This work presents novel algorithms for learning Bayesian network structures with bounded treewidth. Both exact and approximate methods are developed. The exact method combines mixed-integer linear programming formulations for structure…
We present a novel kernel-based machine learning algorithm for identifying the low-dimensional geometry of the effective dynamics of high-dimensional multiscale stochastic systems. Recently, the authors developed a mathematical framework…
Despite significant advances in the field of deep learning in applications to various fields, explaining the inner processes of deep learning models remains an important and open question. The purpose of this article is to describe and…
Non-linear manifold learning enables high-dimensional data analysis, but requires out-of-sample-extension methods to process new data points. In this paper, we propose a manifold learning algorithm based on deep learning to create an…
An accurate and fast estimation of the available bandwidth in a network with varying cross-traffic is a challenging task. The accepted probing tools, based on the fluid-flow model of a bottleneck link with first-in, first-out multiplexing,…
Seeking effective neural networks is a critical and practical field in deep learning. Besides designing the depth, type of convolution, normalization, and nonlinearities, the topological connectivity of neural networks is also important.…
A new plug-in rule procedure for bandwidth selection in kernel circular density estimation is introduced. The performance of this proposal is checked throughout a simulation study considering a variety of circular distributions exhibiting…
We are interested in derivative-free optimization of high-dimensional functions. The sample complexity of existing methods is high and depends on problem dimensionality, unlike the dimensionality-independent rates of first-order methods.…
This paper proposes a new method of bandwidth selection in kernel estimation of density and distribution functions motivated by the connection between maximisation of the entropy of probability integral transforms and maximum likelihood in…