Related papers: A simple noise reduction method based on nonlinear…

Linear regression is a fundamental and popular statistical method. There are various kinds of linear regression, such as mean regression and quantile regression. In this paper, we propose a new one called distribution regression, which…

Multivariate time-series forecasting holds immense value across diverse applications, requiring methods to effectively capture complex temporal and inter-variable dynamics. A key challenge lies in uncovering the intrinsic patterns that…

We introduce a deep learning model for speech denoising, a long-standing challenge in audio analysis arising in numerous applications. Our approach is based on a key observation about human speech: there is often a short pause between each…

Delay embedding---a method for reconstructing dynamical systems by delay coordinates---is widely used to forecast nonlinear time series as a model-free approach. When multivariate time series are observed, several existing frameworks can be…

In tracking of time-varying low-rank models of time-varying matrices, we present a method robust to both uniformly-distributed measurement noise and arbitrarily-distributed ``sparse'' noise. In theory, we bound the tracking error. In…

This paper studies a tensor-structured linear regression model with a scalar response variable and tensor-structured predictors, such that the regression parameters form a tensor of order $d$ (i.e., a $d$-fold multiway array) in…

Appropriate preprocessing is a fundamental prerequisite for analyzing a noisy dataset. The purpose of this paper is to apply a nonparametric preprocessing method, called Singular Spectrum Analysis (SSA), to a variety of datasets which are…

Speech denoising (SD) is an important task of many, if not all, modern signal processing chains used in devices and for everyday-life applications. While there are many published and powerful deep neural network (DNN)-based methods for SD,…

Filtering and smoothing algorithms for linear discrete-time state-space models with skewed and heavy-tailed measurement noise are presented. The algorithms use a variational Bayes approximation of the posterior distribution of models that…

Noise-induced transitions between multistable states happen in a multitude of systems, such as species extinction in biology, protein folding, or tipping points in climate science. Large deviation theory is the rigorous language to describe…

Denoising diffusion models have recently emerged as the predominant paradigm for generative modelling on image domains. In addition, their extension to Riemannian manifolds has facilitated a range of applications across the natural…

Recovering a low-rank signal matrix from its noisy observation, commonly known as matrix denoising, is a fundamental inverse problem in statistical signal processing. Matrix denoising methods are generally based on shrinkage or thresholding…

The problem of structured noise suppression is addressed by i)modelling the subspaces hosting the components of the signal conveying the information and ii)applying a non-extensive nonlinear technique for effecting the right separation.…

We present a direct approach to nonparametrically reconstruct the linear density field from an observed nonlinear map. We solve for the unique displacement potential consistent with the nonlinear density and positive definite coordinate…

Speech data collected in real-world scenarios often encounters two issues. First, multiple sources may exist simultaneously, and the number of sources may vary with time. Second, the existence of background noise in recording is inevitable.…

Diffusion models have been used for probabilistic time series forecasting and show strong potential. However, fixed noise schedules often produce intermediate states that are hard to invert and a terminal state that deviates from the near…

Accurate noise modelling is important for training of deep learning reconstruction algorithms. While noise models are well known for traditional imaging techniques, the noise distribution of a novel sensor may be difficult to determine a…

Time series data appears in a variety of applications such as smart transportation and environmental monitoring. One of the fundamental problems for time series analysis is time series forecasting. Despite the success of recent deep time…

Coherent noise regularly plagues seismic recordings, causing artefacts and uncertainties in products derived from down-the-line processing and imaging tasks. The outstanding capabilities of deep learning in denoising of natural and medical…

The paper introduces a novel topological method for prediction and modeling for a nonlinear time--series that exhibit recurring patterns. According to the model, global manifold of the reconstructed state--space can be approximated by a few…