Related papers: Predicting high-dimensional heterogeneous time ser…

Time series data is prevalent across numerous fields, necessitating the development of robust and accurate forecasting models. Capturing patterns both within and between temporal and multivariate components is crucial for reliable…

In the prediction of oscillating time series, the interest is in the turning points of successive oscillations rather than the samples themselves. For this purpose a scheme has been proposed; the state space reconstruction is limited to the…

Locally quasi-stationary states (LQSS) were introduced as inhomogeneous generalisations of stationary states in integrable systems. Roughly speaking, LQSSs look like stationary states, but only locally. Despite their key role in…

In this work, we propose a novel framework for large-scale Gaussian process (GP) modeling. Contrary to the global, and local approximations proposed in the literature to address the computational bottleneck with exact GP modeling, we employ…

A model-based approach to forecasting chaotic dynamical systems utilizes knowledge of the physical processes governing the dynamics to build an approximate mathematical model of the system. In contrast, machine learning techniques have…

We introduce generative models for accelerating simulations of complex systems through learning and evolving their effective dynamics. In the proposed Generative Learning of Effective Dynamics (G-LED), instances of high dimensional data are…

We propose a simple method of constructing a system of differential equations of chaotic behavior based on the regression only from a scalar observable time-series data. The estimated system enables us to reconstruct invariant sets and…

Forecasting high-dimensional time series plays a crucial role in many applications such as demand forecasting and financial predictions. Modern datasets can have millions of correlated time-series that evolve together, i.e they are…

For oscillating time series, the prediction is often focused on the turning points. In order to predict the turning point magnitudes and times it is proposed to form the state space reconstruction only from the turning points and modify the…

We consider two-state Non-Homogeneous Hidden Markov Models (NHHMMs) for forecasting univariate time series. Given a set of predictors, the time series are modeled via predictive regressions with state dependent coefficients and time-varying…

Time-series forecasting has gained significant attention in machine learning due to its crucial role in various domains. However, most existing forecasting models rely heavily on point-wise loss functions like Mean Square Error, which treat…

Multivariate geo-sensory time series prediction is challenging because of the complex spatial and temporal correlation. In urban water distribution systems (WDS), numerous spatial-correlated sensors have been deployed to continuously…

The prediction of complex nonlinear dynamical systems with the help of machine learning techniques has become increasingly popular. In particular, reservoir computing turned out to be a very promising approach especially for the…

We examine an analytic variational inference scheme for the Gaussian Process State Space Model (GPSSM) - a probabilistic model for system identification and time-series modelling. Our approach performs variational inference over both the…

We propose an L1-penalized algorithm for fitting high-dimensional generalized linear mixed models. Generalized linear mixed models (GLMMs) can be viewed as an extension of generalized linear models for clustered observations. This…

Continuous-time state-space models (SSMs) are flexible tools for analysing irregularly sampled sequential observations that are driven by an underlying state process. Corresponding applications typically involve restrictive assumptions…

Collecting time series data spatially distributed in many locations is often important for analyzing climate change and its impacts on ecosystems. However, comprehensive spatial data collection is not always feasible, requiring us to…

Time Series Forecasting (TSF) is critical in many real-world domains like financial planning and health monitoring. Recent studies have revealed that Large Language Models (LLMs), with their powerful in-contextual modeling capabilities,…

We formulate a reduced-order strategy for efficiently forecasting complex high-dimensional dynamical systems entirely based on data streams. The first step of our method involves reconstructing the dynamics in a reduced-order subspace of…

A sufficient condition for a state |\psi> to minimize the Robertson-Schr\"{o}dinger uncertainty relation for two observables A and B is obtained which for A with no discrete spectrum is also a necessary one. Such states, called generalized…