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We consider the sparse principal component analysis for high-dimensional stationary processes. The standard principal component analysis performs poorly when the dimension of the process is large. We establish the oracle inequalities for…
Recently, the robustification of principal component analysis has attracted lots of attention from statisticians, engineers and computer scientists. In this work we study the type of outliers that are not necessarily apparent in the…
In this paper the problem of forecasting high dimensional time series is considered. Such time series can be modeled as matrices where each column denotes a measurement. In addition, when missing values are present, low rank matrix…
We consider a dynamic method, based on synchronization and adaptive control, to estimate unknown parameters of a nonlinear dynamical system from a given scalar chaotic time series. We present an important extension of the method when time…
Functional time series whose sample elements are recorded sequentially over time are frequently encountered with increasing technology. Recent studies have shown that analyzing and forecasting of functional time series can be performed…
We provide a remedy for two concerns that have dogged the use of principal components in regression: (i) principal components are computed from the predictors alone and do not make apparent use of the response, and (ii) principal components…
We propose directed time series regression, a new approach to estimating parameters of time-series models for use in certainty equivalent model predictive control. The approach combines merits of least squares regression and empirical…
Optimization algorithms can be interpreted through the lens of dynamical systems as the interconnection of linear systems and a set of subgradient nonlinearities. This dynamical systems formulation allows for the analysis and synthesis of…
Continuous-time generative models, such as diffusion models, flow matching, and rectified flow, learn time-dependent vector fields but are typically trained with objectives that treat timesteps independently, leading to high estimator…
Principal curves are natural generalizations of principal lines arising as first principal components in the Principal Component Analysis. They can be characterized from a stochastic point of view as so-called self-consistent curves based…
Time series forecasting remains a central challenge problem in almost all scientific disciplines. We introduce a novel load forecasting method in which observed dynamics are modeled as a forced linear system using Dynamic Mode Decomposition…
We give a review of some recent developments in embeddings of time series and dynamic networks. We start out with traditional principal components and then look at extensions to dynamic factor models for time series. Unlike principal…
We define trajectory predictive control (TPC) as a family of output-feedback indirect data-driven predictive control (DDPC) methods that represent the output trajectory of a discrete-time system as a linear function of the recent…
Dynamic Linear Models (DLMs) are commonly employed for time series analysis due to their versatile structure, simple recursive updating, ability to handle missing data, and probabilistic forecasting. However, the options for count time…
Computing the connected components of a graph is a fundamental problem in algorithmic graph theory. A major question in this area is whether we can compute connected components in $o(\log n)$ parallel time. Recent works showed an…
A key motivation in the development of Distributed Model Predictive Control (DMPC) is to accelerate centralized Model Predictive Control (MPC) for large-scale systems. DMPC has the prospect of scaling well by parallelizing computations…
This paper puts forward a new generalized polynomial dimensional decomposition (PDD), referred to as GPDD, comprising hierarchically ordered measure-consistent multivariate orthogonal polynomials in dependent random variables. Unlike the…
Principal component analysis (PCA) is a popular dimension reduction technique often used to visualize high-dimensional data structures. In genomics, this can involve millions of variables, but only tens to hundreds of observations.…
The literature provides strong evidence that stock prices can be predicted from past price data. Principal component analysis (PCA) is a widely used mathematical technique for dimensionality reduction and analysis of data by identifying a…
This paper develops a distributed model predictive control (DMPC) strategy for a class of discrete-time linear systems with consideration of globally coupled constraints. The DMPC under study is based on the dual problem concerning all…