Related papers: On information plus noise kernel random matrices
The purpose of this review article is to present some of the latest developments using random techniques, and in particular, random matrix techniques in quantum information theory. Our review is a blend of a rather exhaustive review,…
Kernel two-sample testing is a useful statistical tool in determining whether data samples arise from different distributions without imposing any parametric assumptions on those distributions. However, raw data samples can expose sensitive…
Neural networks are known to use spurious correlations such as background information for classification. While prior work has looked at spurious correlations that are widespread in the training data, in this work, we investigate how…
Local differential privacy has become the gold-standard of privacy literature for gathering or releasing sensitive individual data points in a privacy-preserving manner. However, locally differential data can twist the probability density…
Learning representations of nodes in a low dimensional space is a crucial task with numerous interesting applications in network analysis, including link prediction, node classification, and visualization. Two popular approaches for this…
Quantum noise is conventionally viewed as a fundamental obstacle in near-term quantum computing, motivating extensive error correction and mitigation strategies. We present numerical evidence that challenges this consensus. Through…
Through one decade's development, the kernel-based regularization method (KRM) has become a complement to the classical maximum likelihood/prediction error method and an emerging new system identification paradigm. One recent example is its…
In Magnetic Resonance Imaging (MRI) data samples are collected in the spatial frequency domain (k-space), typically by time-consuming line-by-line scanning on a Cartesian grid. Scans can be accelerated by simultaneous acquisition of data…
The kernel polynomial method allows to sample overall spectral properties of a quantum system, while sparse diagonalization provides accurate information about a few important states. We present a method combining these two approaches…
We consider the problem of reconstructing a function from a finite set of noise-corrupted samples. Two kernel algorithms are analyzed, namely kernel ridge regression and $\varepsilon$-support vector regression. By assuming the ground-truth…
We study the problem of detecting a structured, low-rank signal matrix corrupted with additive Gaussian noise. This includes clustering in a Gaussian mixture model, sparse PCA, and submatrix localization. Each of these problems is…
The fields of signal processing and information theory have evolved with the goal of developing formulations to extract intrinsic information from limited amount of data. When one considers the modeling of unpredictably varying processes…
The use of covariance kernels is ubiquitous in the field of spatial statistics. Kernels allow data to be mapped into high-dimensional feature spaces and can thus extend simple linear additive methods to nonlinear methods with higher order…
Kernel density estimation is a widely used nonparametric approach to estimate an unknown distribution. Recent work in Bayesian predictive inference has considered stochastic processes formed by specifying the predictive distribution for the…
As helioseismology matures and turns into a precision science, modeling finite-frequency, geometric and systematical effects is becoming increasingly important. Here we introduce a general formulation for treating perturbations of arbitrary…
This paper studies problems of inferring order given noisy information. In these problems there is an unknown order (permutation) $\pi$ on $n$ elements denoted by $1,...,n$. We assume that information is generated in a way correlated with…
The performance of spectral clustering relies on the fluctuations of the entries of the eigenvectors of a similarity matrix, which has been left uncharacterized until now. In this letter, it is shown that the signal $+$ noise structure of a…
Probabilistic machine learning models are distinguished by their ability to integrate prior knowledge of noise statistics, smoothness parameters, and training data uncertainty. A common approach involves modeling data with Gaussian…
Procedural noise is a fundamental component of computer graphics pipelines, offering a flexible way to generate textures that exhibit "natural" random variation. Many different types of noise exist, each produced by a separate algorithm. In…
In kernel methods, temporal information on the data is commonly included by using time-delayed embeddings as inputs. Recently, an alternative formulation was proposed by defining a gamma-filter explicitly in a reproducing kernel Hilbert…