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temporal regularized matrix

A temporal regularized matrix refers to a data or factor matrix representation in multivariate time series modeling that incorporates explicit mathematical penalties to capture and preserve time-dependent structures across sequential observations. In high-dimensional data analysis and matrix factorization frameworks, temporal regularization is applied to latent temporal factors or matrix components using constraints such as autoregressive modeling, temporal smoothness, or difference penalties. By encoding time-ordered dependencies and correlations among variables, this structure enables machine learning models to effectively impute missing values, filter noise, and generate forecasts for complex, multi-dimensional time series.

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Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networks

Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networks

Guokun Lai, Wei-Cheng Chang, Yiming Yang, Hanxiao Liu

OrganizationsCarnegie Mellon University

Why you should read this

Introduces LSTNet, a deep learning architecture that integrates convolutional and recurrent neural networks with an autoregressive model to capture both short-term local dependencies and long-term trends while addressing scale insensitivity in multivariate time series forecasting.

Multivariate time series forecasting is an important machine learning problem across many domains, including predictions of solar plant energy output, electricity consumption, and traffic jam situation. Temporal data arise in these real-world applications often involves a mixture of long-term and short-term patterns, for which traditional approaches such as Autoregressive models and Gaussian Process may fail. In this paper, we proposed a novel deep learning framework, namely Long- and Short-term Time-series network (LSTNet), to address this open challenge. LSTNet uses the Convolution Neural Network (CNN) and the Recurrent Neural Network (RNN) to extract short-term local dependency patterns among variables and to discover long-term patterns for time series trends. Furthermore, we leverage traditional autoregressive model to tackle the scale insensitive problem of the neural network model. In our evaluation on real-world data with complex mixtures of repetitive patterns, LSTNet achieved significant performance improvements over that of several state-of-the-art baseline methods. All the data and experiment codes are available online.

Added

2026-09-14