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Multiple rotation averaging plays a crucial role in computer vision and robotics domains. The conventional optimization-based methods optimize a nonlinear cost function based on certain noise assumptions, while most previous learning-based…

We propose a recurrent neural network for a "model-free" simulation of a dynamical system with unknown parameters without prior knowledge. The deep learning model aims to jointly learn the nonlinear time marching operator and the effects of…

This paper introduces a novel process for both factor and idiosyncratic volatility matrices whose eigenvalues follow the vector auto-regressive (VAR) model. We call it the factor and idiosyncratic VAR (FIVAR) model. The FIVAR model accounts…

Predictive linear and nonlinear models based on kernel machines or deep neural networks have been used to discover dependencies among time series. This paper proposes an efficient nonlinear modeling approach for multiple time series, with a…

High-dimensional multivariate time series are challenging due to the dependent and high-dimensional nature of the data, but in many applications there is additional structure that can be exploited to reduce computing time along with…

Time series analysis has proven to be a powerful method to characterize several phenomena in biology, neuroscience and economics, and to understand some of their underlying dynamical features. Despite a plethora of methods have been…

We present a technique to perform dimensionality reduction on data that is subject to uncertainty. Our method is a generalization of traditional principal component analysis (PCA) to multivariate probability distributions. In comparison to…

We propose a modeling framework for time-varying covariance matrices based on the assumption that the logarithm of a realized covariance matrix follows a matrix-variate oNrmal distribution. By operating in the space of symmetric matrices,…

Dimension reduction techniques for multivariate time series decompose the observed series into a few useful independent/orthogonal univariate components. We develop a spectral domain method for multivariate second-order stationary time…

Factor-based forecasting using Principal Component Analysis (PCA) is an effective machine learning tool for dimension reduction with many applications in statistics, economics, and finance. This paper introduces a Supervised Screening and…

Principal Component Analysis (PCA) is one of the most used tools for extracting low-dimensional representations of data, in particular for time series. Performances are known to strongly depend on the quality (amount of noise) and the…

Identifying the number of factors in a high-dimensional factor model has attracted much attention in recent years and a general solution to the problem is still lacking. A promising ratio estimator based on the singular values of the lagged…

This paper addresses the fundamental task of estimating covariance matrix functions for high-dimensional functional data/functional time series. We consider two functional factor structures encompassing either functional factors with scalar…

In this work, we develop a scalable approach for a flexible latent factor model for high-dimensional dynamical systems. Each latent factor process has its own correlation and variance parameters, and the orthogonal factor loading matrix can…

In high-dimensional classification problems, a commonly used approach is to first project the high-dimensional features into a lower dimensional space, and base the classification on the resulting lower dimensional projections. In this…

This paper studies the covariance matrix estimation for high-dimensional time series within a new framework that combines low-rank factor and latent variable-specific cluster structures. The popular methods based on assuming the sparse…

We propose a high-dimensional white noise test that captures serial correlations within and across component series without specifying an alternative model. The test statistic is a U-statistic based on sample autocovariances. Under the…

We propose a new unsupervised learning method for clustering a large number of time series based on a latent factor structure. Each cluster is characterized by its own cluster-specific factors in addition to some common factors which impact…

In this article, we introduce the mean independent component analysis for multivariate time series to reduce the parameter space. In particular, we seek for a contemporaneous linear transformation that detects univariate mean independent…

Income and risk coexist, yet investors are often so focused on chasing high returns that they overlook the potential risks that can lead to high losses. Therefore, risk forecasting and risk control is the cornerstone of investment. To…