Related papers: High-Dimensional Regularized Additive Matrix Autor…

This paper introduces a novel method for approximating the dynamics of a large autonomous system projected onto a fixed subspace. The core contribution is a novel recursive algorithm to construct an effective time-dependent generator that…

High-dimensional data analysis using traditional models suffers from overparameterization. Two types of techniques are commonly used to reduce the number of parameters - regularization and dimension reduction. In this project, we combine…

We propose a computationally efficient estimator, formulated as a convex program, for a broad class of non-linear regression problems that involve difference of convex (DC) non-linearities. The proposed method can be viewed as a significant…

Reduced Rank Regression (RRR) is a widely used method for multi-response regression. However, RRR assumes a linear relationship between features and responses. While linear models are useful and often provide a good approximation, many…

Autoregressive (AR) models, the theoretical performance benchmark for learned lossless image compression, are often dismissed as impractical due to prohibitive computational cost. This work re-thinks this paradigm, introducing a framework…

In this paper, we explore the role of tensor algebra in balanced truncation (BT) based model reduction/identification for high-dimensional multilinear/linear time invariant systems. In particular, we employ tensor train decomposition (TTD),…

Additive models form a widely popular class of regression models which represent the relation between covariates and response variables as the sum of low-dimensional transfer functions. Besides flexibility and accuracy, a key benefit of…

This paper proposes a novel diffusion-index model for forecasting when predictors are high-dimensional matrix-valued time series. We apply an $\alpha$-PCA method to extract low-dimensional matrix factors and build a bilinear regression…

Time series analysis faces significant challenges in handling variable-length data and achieving robust generalization. While Transformer-based models have advanced time series tasks, they often struggle with feature redundancy and limited…

Reverse Unrestricted MIxed DAta Sampling (RU-MIDAS) regressions are used to model high-frequency responses by means of low-frequency variables. However, due to the periodic structure of RU-MIDAS regressions, the dimensionality grows quickly…

Random variables in metric spaces indexed by time and observed at equally spaced time points are receiving increased attention due to their broad applicability. The absence of inherent structure in metric spaces has resulted in a literature…

A regularized vector autoregressive hidden semi-Markov model is developed to analyze multivariate financial time series with switching data generating regimes. Furthermore, an augmented EM algorithm is proposed for parameter estimation by…

Set-based transformer models for amortized probabilistic inference and meta-learning, such as neural processes, prior-fitted networks, and tabular foundation models, excel at single-pass marginal prediction. However, many applications…

High-dimensional time series are a core ingredient of the statistical modeling toolkit, for which numerous estimation methods are known.But when observations are scarce or corrupted, the learning task becomes much harder.The question is:…

This paper considers a convex optimization problem with cost and constraints that evolve over time. The function to be minimized is strongly convex and possibly non-differentiable, and variables are coupled through linear constraints. In…

Simultaneous inference for high-dimensional non-Gaussian time series is always considered to be a challenging problem. Such tasks require not only robust estimation of the coefficients in the random process, but also deriving limiting…

Recent advances in large language models have shown that autoregressive modeling can generate complex and novel sequences that have many real-world applications. However, these models must generate outputs autoregressively, which becomes…

In additive models with many nonparametric components, a number of regularized estimators have been proposed and proven to attain various error bounds under different combinations of sparsity and fixed smoothness conditions. Some of these…

We propose a pseudo-structural framework for analyzing contemporaneous co-movements in reduced-rank matrix autoregressive (RRMAR) models. Unlike conventional vector-autoregressive (VAR) models that would discard the matrix structure, our…

Multiscale is a hallmark feature of complex nonlinear systems. While the simulation using the classical numerical methods is restricted by the local \textit{Taylor} series constraints, the multiscale techniques are often limited by finding…