Related papers: Predicting high-dimensional heterogeneous time ser…

Spatiotemporal chaotic systems are difficult to characterize in a model-free manner because of their high dimensionality, strong nonlinearity, and sensitivity to initial conditions. Coupled map lattices, as a representative class of…

In this paper, we explore the application of Gaussian Processes (GPs) for predicting mean-reverting time series with an underlying structure, using relatively unexplored functional and augmented data structures. While many conventional…

A multi-output Gaussian process (GP) is introduced as a model for the joint posterior distribution of the local predictive ability of set of models and/or experts, conditional on a vector of covariates, from historical predictions in the…

Time-series forecasting models often encounter abrupt changes in a given period of time which generally occur due to unexpected or unknown events. Despite their scarce occurrences in the training set, abrupt changes incur loss that…

This paper presents a new approach for Gaussian process (GP) regression for large datasets. The approach involves partitioning the regression input domain into multiple local regions with a different local GP model fitted in each region.…

Forecasting chaotic systems is a notably complex task, which in recent years has been approached with reasonable success using reservoir computing (RC), a recurrent network with fixed random weights (the reservoir) used to extract the…

Machine learning approaches have recently been leveraged as a substitute or an aid for physical/mathematical modeling approaches to dynamical systems. To develop an efficient machine learning method dedicated to modeling and prediction of…

Time series with long-term structure arise in a variety of contexts and capturing this temporal structure is a critical challenge in time series analysis for both inference and forecasting settings. Traditionally, state space models have…

In many applications of finance, biology and sociology, complex systems involve entities interacting with each other. These processes have the peculiarity of evolving over time and of comprising latent factors, which influence the system…

Motivated by earlier results on universal randomized guessing, we consider an individual-sequence approach to the guessing problem: in this setting, the goal is to guess a secret, individual (deterministic) vector $x^n=(x_1,\ldots,x_n)$, by…

The state-space model and the Kalman filter provide us with unified and computationaly efficient procedure for computing the log-likelihood of the diverse type of time series models. This paper presents an algorithm for computing the…

We introduce a novel unsupervised learning method for time series data with latent dynamical structure: the recognition-parametrized Gaussian state space model (RP-GSSM). The RP-GSSM is a probabilistic model that learns Markovian Gaussian…

Long Short-Term Memory (LSTM) networks are often used to capture temporal dependency patterns. By stacking multi-layer LSTM networks, it can capture even more complex patterns. This paper explores the effectiveness of applying stacked LSTM…

A recently proposed convolution technique for the calculation of local density of states is described more thouroughly and new results of its application are presented. For separable systems the exposed method allows to construct the ldos…

Time Series Forecasting has made significant progress with the help of Patching technique, which partitions time series into multiple patches to effectively retain contextual semantic information into a representation space beneficial for…

Current observational and simulated large-scale structure (LSS) catalogues often lack consistency in assigning galaxies to specific structures, due to the absence of a universally accepted classification criterion. With the aim to generate…

Time series classification is crucial for numerous scientific and engineering applications. In this article, we present a numerically efficient, practically competitive, and theoretically rigorous classification method for distinguishing…

This paper introduces distribution-based prediction, a novel approach to using Large Language Models (LLMs) as predictive tools by interpreting output token probabilities as distributions representing the models' learned representation of…

Latent structure methods, specifically linear continuous latent structure methods, are a type of fundamental statistical learning strategy. They are widely used for dimension reduction, regression and prediction, in the fields of…

Probabilistic inference in high-dimensional state-space models is computationally challenging. For many spatiotemporal systems, however, prior knowledge about the dependency structure of state variables is available. We leverage this…