Related papers: Data approximation with time-frequency invariant s…
We propose a computationally tractable method for the identification of stable canonical discrete-time rational transfer function models, using frequency domain data. The problem is formulated as a global non-convex optimization problem…
We study the spectrum reconstruction technique. As is known to all, eigenvalues play an important role in many research fields and are foundation to many practical techniques such like PCA(Principal Component Analysis). We believe that…
Time-frequency scattering is a mathematical transformation of sound waves. Its core purpose is to mimick the way the human auditory system extracts information from its environment. In the context of improving the artificial intelligence of…
Let $\mathcal{H}$ be Hilbert space and $(\Omega,\mu)$ a $\sigma$-finite measure space. Multiplicatively invariant (MI) spaces are closed subspaces of $ L^2(\Omega, \mathcal{H})$ that are invariant under point-wise multiplication by…
In this paper, we consider the problem of manifold approximation with affine subspaces. Our objective is to discover a set of low dimensional affine subspaces that represents manifold data accurately while preserving the manifold's…
Let $m$ be a positive integer and $\mathcal{C}$ be a collection of closed subspaces in $L^2(\mathbb{R})$. Given the measurements $\mathcal{F}_Y=\left\lbrace \left\lbrace y_k^1 \right\rbrace_{k\in \mathbb{Z}},\ldots, \left\lbrace y_k^m…
We consider a system of interacting particles with random initial conditions. Continuum approximations of the system, based on truncations of the BBGKY hierarchy, are described and simulated for various initial distributions and types of…
Time-frequency representations are important for the analysis of time series. We have developed an online time-series analysis system and equipped it to reliably handle re-alignment in the time-frequency plane. The system can deal with…
Probabilistic programs are typically normal-looking programs describing posterior probability distributions. They intrinsically code up randomized algorithms and have long been at the heart of modern machine learning and approximate…
We give an algorithm for prediction on a quantum computer which is based on a linear regression model with least squares optimisation. Opposed to related previous contributions suffering from the problem of reading out the optimal…
The computation of global radial basis function (RBF) approximations requires the solution of a linear system which, depending on the choice of RBF parameters, may be ill-conditioned. We study the stability and accuracy of approximation…
This paper describes a class of probabilistic approximation algorithms based on bucket elimination which offer adjustable levels of accuracy and efficiency. We analyze the approximation for several tasks: finding the most probable…
Kernel methods are powerful learning methodologies that allow to perform non-linear data analysis. Despite their popularity, they suffer from poor scalability in big data scenarios. Various approximation methods, including random feature…
We present a quantum algorithm for fitting a linear regression model to a given data set using the least squares approach. Different from previous algorithms which yield a quantum state encoding the optimal parameters, our algorithm outputs…
In this paper, we introduce an algorithm that provides approximate solutions to semi-linear ordinary differential equations with highly oscillatory solutions, which, after an appropriate change of variables, can be rewritten as…
The development of fast and accurate image reconstruction algorithms is a central aspect of computed tomography. In this paper we address this issue for photoacoustic computed tomography in circular geometry. We investigate the Galerkin…
Much of statistics relies upon four key elements: a law of large numbers, a calculus to operationalize stochastic convergence, a central limit theorem, and a framework for constructing local approximations. These elements are…
We study a class of combinatorial scheduling problems characterized by a particular type of constraint often associated with electrical power or gas energy. This constraint appears in several practical applications and is expressed as a sum…
Latent variable time-series models are among the most heavily used tools from machine learning and applied statistics. These models have the advantage of learning latent structure both from noisy observations and from the temporal ordering…
A subalgebraic approximation algorithm is proposed to estimate from a set of time series the parameters of the observer representation of a discrete-time polynomial system without inputs which can generate an approximation of the observed…