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Found 21 papers, 11 papers with code
Point Processes and spatial statistics in time-frequency analysis
The zeros of the spectrogram of a noisy signal are then the zeros of a random analytic function, hence forming a Point Process in $\mathbb{C}$.
Monte Carlo with kernel-based Gibbs measures: Guarantees for probabilistic herding
In spite of strong experimental support, it has revealed difficult to prove that this worst-case error decreases at a faster rate than the standard square root of the number of quadrature nodes, at least in the usual case where the RKHS is infinite-dimensional.
Benchmarking multi-component signal processing methods in the time-frequency plane
For instance, detection and denoising based on the zeros of the spectrogram have been proposed since 2015, contrasting with a long history of focusing on larger values of the spectrogram.
On sampling determinantal and Pfaffian point processes on a quantum computer
Most applications require sampling from a DPP, and given their quantum origin, it is natural to wonder whether sampling a DPP on a quantum computer is easier than on a classical one.
Sparsification of the regularized magnetic Laplacian with multi-type spanning forests
We provide statistical guarantees for a choice of natural estimators of the connection Laplacian, and investigate two practical applications of our sparsifiers: ranking with angular synchronization and graph-based semi-supervised learning.
A covariant, discrete time-frequency representation tailored for zero-based signal detection
Recent work in time-frequency analysis proposed to switch the focus from the maxima of the spectrogram toward its zeros, which, for signals corrupted by Gaussian noise, form a random point pattern with a very stable structure leveraged by modern spatial statistics tools to perform component disentanglement and signal detection.
Nonparametric estimation of continuous DPPs with kernel methods
Determinantal Point Process (DPPs) are statistical models for repulsive point patterns.
On proportional volume sampling for experimental design in general spaces
Optimal design for linear regression is a fundamental task in statistics.
Computation
Learning from DPPs via Sampling: Beyond HKPV and symmetry
Our approach is scalable and applies to very general DPPs, beyond traditional symmetric kernels.
Kernel interpolation with continuous volume sampling
A fundamental task in kernel methods is to pick nodes and weights, so as to approximate a given function from an RKHS by the weighted sum of kernel translates located at the nodes.
On two ways to use determinantal point processes for Monte Carlo integration
In the absence of DPP machinery to derive an efficient sampler and analyze their estimator, the idea of Monte Carlo integration with DPPs was stored in the cellar of numerical integration.
Kernel quadrature with DPPs
We study quadrature rules for functions from an RKHS, using nodes sampled from a determinantal point process (DPP).
A determinantal point process for column subset selection
We give bounds on the ratio of the expected approximation error for this DPP over the optimal error of PCA.
DPPy: Sampling DPPs with Python
Determinantal point processes (DPPs) are specific probability distributions over clouds of points that are used as models and computational tools across physics, probability, statistics, and more recently machine learning.
Time-frequency transforms of white noises and Gaussian analytic functions
Finally, we provide quantitative estimates concerning the finite-dimensional approximations of these white noises, which is of practical interest when it comes to implementing signal processing algorithms based on GAFs.
Probability Classical Analysis and ODEs Methodology
Zonotope hit-and-run for efficient sampling from projection DPPs
Previous theoretical results yield a fast mixing time of our chain when targeting a distribution that is close to a projection DPP, but not a DPP in general.
Monte Carlo with Determinantal Point Processes
We show that repulsive random variables can yield Monte Carlo methods with faster convergence rates than the typical $N^{-1/2}$, where $N$ is the number of integrand evaluations.
Probability Classical Analysis and ODEs Computation Methodology
Inference for determinantal point processes without spectral knowledge
DPPs possess desirable properties, such as exact sampling or analyticity of the moments, but learning the parameters of kernel $K$ through likelihood-based inference is not straightforward.
On Markov chain Monte Carlo methods for tall data
Finally, we have only been able so far to propose subsampling-based methods which display good performance in scenarios where the Bernstein-von Mises approximation of the target posterior distribution is excellent.
Algorithms for Hyper-Parameter Optimization
Random search has been shown to be sufficiently efficient for learning neural networks for several datasets, but we show it is unreliable for training DBNs.
