Related papers: Predicting high-dimensional heterogeneous time ser…

Reservoir computers (RCs) are powerful machine learning architectures for time series prediction. Recently, next generation reservoir computers (NGRCs) have been introduced, offering distinct advantages over RCs, such as reduced…

This paper proposes an online learning method of Gaussian process state-space model (GP-SSM). GP-SSM is a probabilistic representation learning scheme that represents unknown state transition and/or measurement models as Gaussian processes…

Hierarchical time series forecasting plays a crucial role in decision-making in various domains while presenting significant challenges for modelling as they involve multiple levels of aggregation, constraints, and availability of…

Time series forecasting remains a challenging task, particularly in the context of complex multiscale temporal patterns. This study presents LLM-Mixer, a framework that improves forecasting accuracy through the combination of multiscale…

A new statistical technique for constructing linear latent structure (LLS) models from available data, supported by well established theoretical results and an efficient algorithm, is presented. The method reduces the problem of estimating…

We scrutinize the use of machine learning, based on reservoir computing, to build data-driven effective models of multiscale chaotic systems. We show that, for a wide scale separation, machine learning generates effective models akin to…

Understanding how the collective activity of neural populations relates to computation and ultimately behavior is a key goal in neuroscience. To this end, statistical methods which describe high-dimensional neural time series in terms of…

Adopting the geometric description of steering assemblages and local hidden states (LHS) model, we construct the optimal LHS model for some two-qubit states under continuous projective measurements, and obtain a sufficient steering…

I present a data-driven predictive modeling tool that is applicable to high-dimensional chaotic systems with unstable periodic orbits. The basic idea is using deep neural networks to learn coordinate transformations between the trajectories…

Due to the dynamic nature, chaotic time series are difficult predict. In conventional signal processing approaches signals are treated either in time or in space domain only. Spatio-temporal analysis of signal provides more advantages over…

The Lopsided Lov\'{a}sz Local Lemma (LLLL) is a powerful probabilistic principle which has been used in a variety of combinatorial constructions. While originally a general statement about probability spaces, it has recently been…

Spatio-temporal data is intrinsically high dimensional, so unsupervised modeling is only feasible if we can exploit structure in the process. When the dynamics are local in both space and time, this structure can be exploited by splitting…

Generalized Coherent States (GCS) are constructed (and discussed) in order to study quasiclassical behaviour of quantum spin models of the Heisenberg type. Several such models are taken to their semiclassical limits, whose form depends on…

The aim of this study is to develop and apply an autonomous approach for predicting the probability of hydrocarbon reservoirs spreading in the studied area. The methodology uses machine learning algorithms in the problem of binary…

Granger causality (GC) is often considered not an actual form of causality. Still, it is arguably the most widely used method to assess the predictability of a time series from another one. Granger causality has been widely used in many…

This paper addresses the Variable Gapped Longest Common Subsequence (VGLCS) problem, a generalization of the classical LCS problem involving flexible gap constraints between consecutive solutions' characters. The problem arises in molecular…

The missing data issue often complicates the task of estimating generalized linear models (GLMs). We describe why the pseudo-marginal Metropolis-Hastings algorithm, used in this setting, is an effective strategy for parameter estimation.…

Capturing the inter-dependencies among multiple types of clinically-critical events is critical not only to accurate future event prediction, but also to better treatment planning. In this work, we propose a deep latent state-space…

We propose a new approach for the modeling large datasets of nonstationary spatial processes that combines a latent low rank process and a sparse covariance model. The low rank component coefficients are endowed with a flexible graphical…

In this paper, we investigate seemingly unrelated regression (SUR) models that allow the number of equations (N) to be large, and to be comparable to the number of the observations in each equation (T). It is well known in the literature…