Related papers: Forecastable Component Analysis (ForeCA)
We propose the Fourier Adaptive Lite Diffusion Architecture (FALDA), a novel probabilistic framework for time series forecasting. First, we introduce the Diffusion Model for Residual Regression (DMRR) framework, which unifies…
This paper introduces a multiscale analysis based on optimal piecewise linear approximations of time series. An optimality criterion is formulated and on its base a computationally effective algorithm is constructed for decomposition of a…
In the context of online Robust Principle Component Analysis (RPCA) for the video foreground-background separation, we propose a compressive online RPCA with optical flow that separates recursively a sequence of frames into sparse…
Independent component analysis (ICA) is a method for recovering statistically independent signals from observations of unknown linear combinations of the sources. Some of the most accurate ICA decomposition methods require searching for the…
We propose a new high dimensional semiparametric principal component analysis (PCA) method, named Copula Component Analysis (COCA). The semiparametric model assumes that, after unspecified marginally monotone transformations, the…
Time series forecasting is one of the most essential and ubiquitous tasks in many business problems, including demand forecasting and logistics optimization. Traditional time series forecasting methods, however, have resulted in small…
Principal component analysis (PCA) is a widely used method for data processing, such as for dimension reduction and visualization. Standard PCA is known to be sensitive to outliers, and thus, various robust PCA methods have been proposed.…
Time Series forecasting (univariate and multivariate) is a problem of high complexity due the different patterns that have to be detected in the input, ranging from high to low frequencies ones. In this paper we propose a new model for…
Principal component analysis (PCA) is a foundational tool in modern data analysis, and a crucial step in PCA is selecting the number of components to keep. However, classical selection methods (e.g., scree plots, parallel analysis, etc.)…
Sparse principal component analysis (SPCA) methods have proven to efficiently analyze high-dimensional data. Among them, threshold-based SPCA (TSPCA) is computationally more cost-effective than regularized SPCA, based on L1 penalties. We…
Canonical correlation analysis (CCA) is a multivariate statistical method which describes the associations between two sets of variables. The objective is to find linear combinations of the variables in each data set having maximal…
Modern time series forecasting methods, such as Transformer and its variants, have shown strong ability in sequential data modeling. To achieve high performance, they usually rely on redundant or unexplainable structures to model complex…
Process monitoring based on neural networks is getting more and more attention. Compared with classical neural networks, high-order neural networks have natural advantages in dealing with heteroscedastic data. However, high-order neural…
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…
Non-gaussian component analysis (NGCA) introduced in offered a method for high dimensional data analysis allowing for identifying a low-dimensional non-Gaussian component of the whole distribution in an iterative and structure adaptive way.…
Sparse Principal Component Analysis (PCA) is a dimensionality reduction technique wherein one seeks a low-rank representation of a data matrix with additional sparsity constraints on the obtained representation. We consider two…
A core task in multi-modal learning is to integrate information from multiple feature spaces (e.g., text and audio), offering modality-invariant essential representations of data. Recent research showed that, classical tools such as {\it…
Functional Principal Component Analysis (FPCA) has become a widely-used dimension reduction tool for functional data analysis. When additional covariates are available, existing FPCA models integrate them either in the mean function or in…
Recurrence quantification analysis is a widely used method for characterizing patterns in time series. This article presents a comprehensive survey for conducting a wide range of recurrence-based analyses to quantify the dynamical structure…
Modern empirical analysis often relies on high-dimensional panel datasets with non-negligible cross-sectional and time-series correlations. Factor models are natural for capturing such dependencies. A tensor factor model describes the…