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We consider the computation by simulation and neural net regression of conditional expectations, or more general elicitable statistics, of functionals of processes $(X, Y )$. Here an exogenous component $Y$ (Markov by itself) is…

Resistive Random Access Memories (RRAMs) are being studied by the industry and academia because it is widely accepted that they are promising candidates for the next generation of high density nonvolatile memories. Taking into account the…

This paper studies a regression model where both predictor and response variables are random functions. We consider a functional linear model where the conditional mean of the response variable at each time point is given by a linear…

Functional time series (FTS) data have become increasingly available in real-world applications. Research on such data typically focuses on two objectives: curve reconstruction and forecasting, both of which require efficient dimension…

This work proposes a causal and recursive algorithm for solving the "robust" principal components' analysis (PCA) problem. We primarily focus on robustness to correlated outliers. In recent work, we proposed a new way to look at this…

We explore the physical implications of applying principal component analysis (PCA) to translationally invariant classical systems defined on a $d$-dimensional hypercubic lattice. Using Rayleigh-Schr\"odinger perturbation theory, we…

Principal Component Analysis (PCA) is a cornerstone of dimensionality reduction, yet its classical formulation relies critically on second-order moments and is therefore fragile in the presence of heavy-tailed data and impulsive noise.…

Modelling a large collection of functional time series arises in a broad spectral of real applications. Under such a scenario, not only the number of functional variables can be diverging with, or even larger than the number of temporally…

Principal component analysis (PCA) defines a reduced space described by PC axes for a given multidimensional-data sequence to capture the variations of the data. In practice, we need multiple data sequences that accurately obey individual…

In the era of big data, reducing data dimensionality is critical in many areas of science. Widely used Principal Component Analysis (PCA) addresses this problem by computing a low dimensional data embedding that maximally explain variance…

Principal component analysis (PCA) is a well-known linear dimension-reduction method that has been widely used in data analysis and modeling. It is an unsupervised learning technique that identifies a suitable linear subspace for the input…

Factor models are a class of powerful statistical models that have been widely used to deal with dependent measurements that arise frequently from various applications from genomics and neuroscience to economics and finance. As data are…

Classical and more recent tests for detecting distributional changes in multivariate time series often lack power against alternatives that involve changes in the cross-sectional dependence structure. To be able to detect such changes…

Recently popularized randomized methods for principal component analysis (PCA) efficiently and reliably produce nearly optimal accuracy --- even on parallel processors --- unlike the classical (deterministic) alternatives. We adapt one of…

We propose to model multivariate volatility processes based on the newly defined conditionally uncorrelated components (CUCs). This model represents a parsimonious representation for matrix-valued processes. It is flexible in the sense that…

Principal component analysis (PCA) is a widely used dimension reduction tool in the analysis of many kind of high-dimensional data. It is used in signal processing, mechanical engineering, psychometrics, and other fields under different…

When modeling multivariate data, one might have an extra parameter of contextual information that could be used to treat some observations as more similar to others. For example, images of faces can vary by age, and one would expect the…

Principal Component Analysis (PCA) is widely used for dimensionality reduction and data analysis. However, PCA results are adversely affected by outliers often observed in real-world data. Existing robust PCA methods are often…

Highly accurate and predictive models of resistive switching devices are needed to enable future memory and logic design. Widely used is the memristive modeling approach considering resistive switches as dynamical systems. Here we introduce…

Classical machine learning algorithms often face scalability bottlenecks when they are applied to large-scale data. Such algorithms were designed to work with small data that is assumed to fit in the memory of one machine. In this report,…