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Recent research demonstrate that prediction of time series by predictive recurrent neural networks based on the noisy input generates a smooth anticipated trajectory. We examine influence of the noise component in both the training data…
Prediction of dynamical time series with additive noise using support vector machines or kernel based regression has been proved to be consistent for certain classes of discrete dynamical systems. Consistency implies that these methods are…
Background: High-throughput proteomics techniques, such as mass spectrometry (MS)-based approaches, produce very high-dimensional data-sets. In a clinical setting one is often interested in how mass spectra differ between patients of…
Reconstructing noise-driven nonlinear networks from time series of output variables is a challenging problem, which turns to be very difficult when nonlinearity of dynamics, strong noise impacts and low measurement frequencies jointly…
Reconstruction of undersampled periodic signals of unknown period is an important signal processing operation. It is especially difficult operation when the sequences of samples are short and no information on the inter-sequence time…
Deep, overparameterized regression models are notorious for their tendency to overfit. This problem is exacerbated in heteroskedastic models, which predict both mean and residual noise for each data point. At one extreme, these models fit…
Networks are powerful instruments to study complex phenomena, but they become hard to analyze in data that contain noise. Network backbones provide a tool to extract the latent structure from noisy networks by pruning non-salient edges. We…
This is a survey paper discussing one specific (and classical) system of algebraic equations - the so called "Prony system". We provide a short overview of its unusually wide connections with many different fields of Mathematics, stressing…
Sparse system identification is the data-driven process of obtaining parsimonious differential equations that describe the evolution of a dynamical system, balancing model complexity and accuracy. There has been rapid innovation in system…
Air pollution, particularly particulate matter (PM2.5), poses significant risks to public health and the environment, necessitating accurate prediction and continuous monitoring for effective air quality management. However, air quality…
Inverse problems, which involve estimating parameters from incomplete or noisy observations, arise in various fields such as medical imaging, geophysics, and signal processing. These problems are often ill-posed, requiring regularization…
Driven by global climate change and the ongoing energy transition, the coupling between power supply capabilities and meteorological factors has become increasingly significant. Over the long term, accurately quantifying the power…
Astronomical surveys of celestial sources produce streams of noisy time series measuring flux versus time ("light curves"). Unlike in many other physical domains, however, large (and source-specific) temporal gaps in data arise naturally…
Climate projections suffer from uncertain equilibrium climate sensitivity. The reason behind this uncertainty is the resolution of global climate models, which is too coarse to resolve key processes such as clouds and convection. These…
Many real-world phenomena can be represented by a spatio-temporal signal: where, when, and how much. Social media is a tantalizing data source for those who wish to monitor such signals. Unlike most prior work, we assume that the target…
The performance of state-of-the-art object detectors degrades significantly under adverse weather, causing a safety-critical domain shift problem for autonomous vehicles. Recent efforts address this problem by relying on synthetic data to…
The multiscale and turbulent nature of Earth's atmosphere has historically rendered accurate weather modeling a hard problem. Recently, there has been an explosion of interest surrounding data-driven approaches to weather modeling, which in…
Real-world data is typically a noisy manifestation of a core pattern (schema), and the purpose of data mining algorithms is to uncover that pattern, thereby splitting (i.e. decomposing) the data into schema and noise. We introduce SCHENO, a…
A promising approach to improve climate-model simulations is to replace traditional subgrid parameterizations based on simplified physical models by machine learning algorithms that are data-driven. However, neural networks (NNs) often lead…
Large-scale recurrent networks have drawn increasing attention recently because of their capabilities in modeling a large variety of real-world phenomena and physical mechanisms. This paper studies how to identify all authentic connections…