Related papers: Dimension Reduction for High Dimensional Vector Au…
Volatilities, in high-dimensional panels of economic time series with a dynamic factor structure on the levels or returns, typically also admit a dynamic factor decomposition. We consider a two-stage dynamic factor model method recovering…
Understanding the dynamics of functional brain connectivity patterns using noninvasive neuroimaging techniques is an important focus in human neuroscience. Vector autoregressive (VAR) processes and Granger causality analysis (GCA) have been…
Many economic variables feature changes in their conditional mean and volatility, and Time Varying Vector Autoregressive Models are often used to handle such complexity in the data. Unfortunately, when the number of series grows, they…
Real-world dark images commonly exhibit not only low visibility and contrast but also complex noise and blur, posing significant restoration challenges. Existing methods often rely on paired data or fail to model dynamic illumination and…
The Vector AutoRegressive (VAR) model is fundamental to the study of multivariate time series. Although VAR models are intensively investigated by many researchers, practitioners often show more interest in analyzing VARX models that…
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…
Principal component analysis continues to be a powerful tool in dimension reduction of high dimensional data. We assume a variance-diverging model and use the high-dimension, low-sample-size asymptotics to show that even though the…
This paper introduces non-linear dimension reduction in factor-augmented vector autoregressions to analyze the effects of different economic shocks. I argue that controlling for non-linearities between a large-dimensional dataset and the…
This article explores the generalized analysis-of-variance or ANOVA dimensional decomposition (ADD) for multivariate functions of dependent random variables. Two notable properties, stemming from weakened annihilating conditions, reveal…
Discrete diffusion models have recently shown great promise for modeling complex discrete data, with masked diffusion models (MDMs) offering a compelling trade-off between quality and generation speed. MDMs denoise by progressively…
For dynamical systems that switch between different modes of operation, parameter variation can cause periodic solutions to lose or acquire new switching events. When this causes the eigenvalues (stability multipliers) associated with the…
Here we dispel the lingering myth that Partial Directed Coherence is a Vector Autoregressive (VAR) Modelling dependent concept. In fact, our examples show that it is spectral factorization that lies at its heart, for which VAR modelling is…
The time-dependent fields obtained by solving partial differential equations in two and more dimensions quickly overwhelm the analytical capabilities of the human brain. A meaningful insight into the temporal behaviour can be obtained by…
We introduce DiverseVAR, a framework that enhances the diversity of text-conditioned visual autoregressive models (VAR) at test time without requiring retraining, fine-tuning, or substantial computational overhead. While VAR models have…
Networks of interconnected agents are essential to study complex networked systems' state evolution, stability, resilience, and control. Nevertheless, the high dimensionality and nonlinear dynamics are vital factors preventing us from…
We consider a multivariate time series model which represents a high dimensional vector process as a sum of three terms: a linear regression of some observed regressors, a linear combination of some latent and serially correlated factors,…
The data-driven recovery of the unknown governing equations of dynamical systems has recently received an increasing interest. However, the identification of governing equations remains challenging when dealing with noisy and partial…
We consider the problem of extracting a low-dimensional, linear latent variable structure from high-dimensional random variables. Specifically, we show that under mild conditions and when this structure manifests itself as a linear space…
Principal component analysis is a versatile tool to reduce dimensionality which has wide applications in statistics and machine learning. It is particularly useful for modeling data in high-dimensional scenarios where the number of…
High-dimensional time series data exist in numerous areas such as finance, genomics, healthcare, and neuroscience. An unavoidable aspect of all such datasets is missing data, and dealing with this issue has been an important focus in…