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This paper investigates the use of retrospective approximation solution paradigm in solving risk-averse optimization problems effectively via importance sampling (IS). While IS serves as a prominent means for tackling the large sample…
The classical vector autoregressive model is a fundamental tool for multivariate time series analysis. However, it involves too many parameters when the number of time series and lag order are even moderately large. This paper proposes to…
SGD (Stochastic Gradient Descent) is a popular algorithm for large scale optimization problems due to its low iterative cost. However, SGD can not achieve linear convergence rate as FGD (Full Gradient Descent) because of the inherent…
A major family of sufficient dimension reduction (SDR) methods, called inverse regression, commonly require the distribution of the predictor $X$ to have a linear $E(X|\beta^\mathsf{T}X)$ and a degenerate $\mathrm{var}(X|\beta^\mathsf{T}X)$…
We provide new theoretical results in the field of inverse regression methods for dimension reduction. Our approach is based on the study of some empirical processes that lie close to a certain dimension reduction subspace, called the…
Time series methods are of fundamental importance in virtually any field of science that deals with temporally structured data. Recently, there has been a surge of deterministic transformer models with time series-specific architectural…
Instrumental variable (IV) analysis is widely used in fields such as economics and epidemiology to address unobserved confounding and measurement error when estimating the causal effects of intermediate covariates on outcomes. However,…
A reliable and efficient representation of multivariate time series is crucial in various downstream machine learning tasks. In multivariate time series forecasting, each variable depends on its historical values and there are…
Recently, high dimensional vector auto-regressive models (VAR), have attracted a lot of interest, due to novel applications in the health, engineering and social sciences. The presence of temporal dependence poses additional challenges to…
Locally adapted parameterizations of a model (such as locally weighted regression) are expressive but often suffer from high variance. We describe an approach for reducing the variance, based on the idea of estimating simultaneously a…
Due to their unsupervised training and uncertainty estimation, deep Variational Autoencoders (VAEs) have become powerful tools for reconstruction-based Time Series Anomaly Detection (TSAD). Existing VAE-based TSAD methods, either…
As the growing demand for long sequence time-series forecasting in real-world applications, such as electricity consumption planning, the significance of time series forecasting becomes increasingly crucial across various domains. This is…
Anomaly detection of multivariate time series is meaningful for system behavior monitoring. This paper proposes an anomaly detection method based on unsupervised Short- and Long-term Mask Representation learning (SLMR). The main idea is to…
A new method of measuring long spin-lattice relaxation times ($T_1$) is proposed. Being a single scan technique, the method is at least one order of magnitude faster than the conventional technique. This method (Single-Scan or Slice…
The purpose of this paper is to propose a time-varying vector autoregressive model (TV-VAR) for forecasting multivariate time series. The model is casted into a state-space form that allows flexible description and analysis. The volatility…
In this paper, we propose new sampling approaches for the Shrinkage Inverse-Wishart (SIW) distribution, a generalized family of the Inverse-Wishart distribution originally proposed by Berger et al. (2020, Annals of Statistics). It offers a…
This is a tutorial and survey paper on various methods for Sufficient Dimension Reduction (SDR). We cover these methods with both statistical high-dimensional regression perspective and machine learning approach for dimensionality…
This article develops the asymptotic distribution of the least squares estimator of the model parameters in periodicvector autoregressive time series models (hereafter PVAR) with uncorrelated but dependent innovations. When theinnovations…
Time-series forecasting often faces challenges from non-stationarity, particularly distributional drift, where the data distribution evolves over time. This dynamic behavior can undermine the effectiveness of adaptive optimizers, such as…
By treating intervals as inseparable sets, this paper proposes sparse machine learning regressions for high-dimensional interval-valued time series. With LASSO or adaptive LASSO techniques, we develop a penalized minimum distance…