Related papers: Manifold-based time series forecasting

High-dimensional time series are common in many domains. Since human cognition is not optimized to work well in high-dimensional spaces, these areas could benefit from interpretable low-dimensional representations. However, most…

The factor modeling for high-dimensional time series is powerful in discovering latent common components for dimension reduction and information extraction. Most available estimation methods can be divided into two categories: the…

We discuss a method of parameter reduction in complex models known as the Manifold Boundary Approximation Method (MBAM). This approach, based on a geometric interpretation of statistics, maps the model reduction problem to a geometric…

In this paper, we study nonparametric models allowing for locally stationary regressors and a regression function that changes smoothly over time. These models are a natural extension of time series models with time-varying coefficients. We…

Fitting autoregressive moving average (ARMA) time series models requires model identification before parameter estimation. Model identification involves determining the order of the autoregressive and moving average components which is…

Over the last decade, big data have poured into econometrics, demanding new statistical methods for analysing high-dimensional data and complex non-linear relationships. A common approach for addressing dimensionality issues relies on the…

Surrogate modeling for complex physical systems typically faces a trade-off between data-fitting accuracy and physical consistency. Physics-consistent approaches typically treat physical laws as soft constraints within the loss function, a…

Motion planning is a mature area of research in robotics with many well-established methods based on optimization or sampling the state space, suitable for solving kinematic motion planning. However, when dynamic motions under constraints…

A common problem in time series analysis is to predict dynamics with only scalar or partial observations of the underlying dynamical system. For data on a smooth compact manifold, Takens theorem proves a time delayed embedding of the…

A time series represents a set of observations collected over time. Typically, these observations are captured with a uniform sampling frequency (e.g. daily). When data points are observed in uneven time intervals the time series is…

The innovations algorithm is a classical recursive forecasting algorithm used in time series analysis. We develop the innovations algorithm for a class of nonnegative regularly varying time series models constructed via transformed-linear…

In this paper, we use convolutional neural networks to address the problem of model identification for autoregressive moving average time series models. We compare the performance of several neural network architectures, trained on…

In order to avoid the curse of dimensionality, frequently encountered in Big Data analysis, there was a vast development in the field of linear and nonlinear dimension reduction techniques in recent years. These techniques (sometimes…

It is often of interest to infer lower-dimensional structure underlying complex data. As a flexible class of non-linear structures, it is common to focus on Riemannian manifolds. Most existing manifold learning algorithms replace the…

Neural networks are powerful tools in various applications, and quantifying their uncertainty is crucial for reliable decision-making. In the deep learning field, the uncertainties are usually categorized into aleatoric (data) and epistemic…

Different disciplines pursue the aim to develop models which characterize certain phenomena as accurately as possible. Climatology is a prime example, where the temporal evolution of the climate is modeled. In order to compare and improve…

Supervised learning with irregularly sampled time series have been a challenge to Machine Learning methods due to the obstacle of dealing with irregular time intervals. Some papers introduced recently recurrent neural network models that…

Modeling multivariate time series is a well-established problem with a wide range of applications from healthcare to financial markets. Traditional State Space Models (SSMs) are classical approaches for univariate time series modeling due…

Manifold learning is a popular and quickly-growing subfield of machine learning based on the assumption that one's observed data lie on a low-dimensional manifold embedded in a higher-dimensional space. This thesis presents a mathematical…

In this paper, we are concerned with improving the forecast capabilities of the Global approach to Time Series. We assume that the normal techniques of Global mapping are applied, the noise reduction is performed, etc. Then, using the…