Related papers: Noise reduction for functional time series
This paper proposes a new multi-linear projection method for denoising and estimation of high-dimensional matrix-variate factor time series. It assumes that a $p_1\times p_2$ matrix-variate time series consists of a dynamically dependent,…
Functional Principal Component Analysis is a reference method for dimension reduction of curve data. Its theoretical properties are now well understood in the simplified case where the sample curves are fully observed without noise.…
Temporal data such as time series can be viewed as discretized measurements of the underlying function. To build a generative model for such data we have to model the stochastic process that governs it. We propose a solution by defining the…
Functional time series analysis, whether based on time of frequency domain methodology, has traditionally been carried out under the assumption of complete observation of the constituent series of curves, assumed stationary. Nevertheless,…
We investigate the benefits and challenges of utilizing the frequency information in differential equation identification. Solving differential equations and Fourier analysis are closely related, yet there is limited work in exploring this…
Financial time series often exhibit low signal-to-noise ratio, posing significant challenges for accurate data interpretation and prediction and ultimately decision making. Generative models have gained attention as powerful tools for…
On the basis of a local-projective with nonlinear constraints (LPNC) approach (see K. Urbanowicz, J.A. Holyst, T. Stemler and H. Benner, Acta Phys. Pol B 35 (9), 2175, 2004) we develop a method of noise reduction in time series that makes…
On the basis of a local-projective (LP) approach we develop a method of noise reduction in time series that makes use of nonlinear constraints appearing due to the deterministic character of the underlying dynamical system. The Delaunay…
The decomposition of a stochastic time series into three component series representing a dual signal - namely, the mean and dispersion - while isolating noise is presented. The decomposition is performed by applying machine learning…
When modelling time series, it is common to decompose observed variation into a "signal" process, the process of interest, and "noise", representing nuisance factors that obfuscate the signal. To separate signal from noise, assumptions must…
Denoising diffusion probabilistic models are able to generate synthetic sensor signals. The training process of such a model is controlled by a loss function which measures the difference between the noise that was added in the forward…
We consider the problem of reconstructing a discrete-time signal (sequence) with continuous-valued components corrupted by a known memoryless channel. When performance is measured using a per-symbol loss function satisfying mild regularity…
Noise reduction techniques based on deep learning have demonstrated impressive performance in enhancing the overall quality of recorded speech. While these approaches are highly performant, their application in audio engineering can be…
In practice most functional data cannot be recorded on a continuum, but rather at discrete time points. It is also quite common that these measurements come with an additive error, which one would like eliminate for the statistical…
Functional principal component analysis (FPCA) is a key tool in the study of functional data, driving both exploratory analyses and feature construction for use in formal modeling and testing procedures. However, existing methods for FPCA…
Generalization of time series prediction remains an important open issue in machine learning, wherein earlier methods have either large generalization error or local minima. We develop an analytically solvable, unsupervised learning scheme…
I introduce Forecastable Component Analysis (ForeCA), a novel dimension reduction technique for temporally dependent signals. Based on a new forecastability measure, ForeCA finds an optimal transformation to separate a multivariate time…
We present a method for audio denoising that combines processing done in both the time domain and the time-frequency domain. Given a noisy audio clip, the method trains a deep neural network to fit this signal. Since the fitting is only…
In this communication we will re-examine the widely studied technique of phase space projection. By imposing a time domain constraint (TDC) on the residual noise, we deduce a more general version of the optimal projector, which includes…
Compressed Sensing suggests that the required number of samples for reconstructing a signal can be greatly reduced if it is sparse in a known discrete basis, yet many real-world signals are sparse in a continuous dictionary. One example is…