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Linear Dynamical System (LDS) is an elegant mathematical framework for modeling and learning multivariate time series. However, in general, it is difficult to set the dimension of its hidden state space. A small number of hidden states may…

Transformer-based and CNN-based methods demonstrate strong performance in long-term time series forecasting. However, their high computational and storage requirements can hinder large-scale deployment. To address this limitation, we…

Machine learning (ML) tools such as encoder-decoder deep convolutional neural networks (CNN) are able to extract relationships between inputs and outputs of large complex systems directly from raw data. For time-varying systems the…

Spatial-temporal forecasting systems play a crucial role in addressing numerous real-world challenges. In this paper, we investigate the potential of addressing spatial-temporal forecasting problems using general time series forecasting…

Dimensionality reduction is an effective method for learning high-dimensional data, which can provide better understanding of decision boundaries in human-readable low-dimensional subspace. Linear methods, such as principal component…

Time series forecasting (TSF) plays a crucial role in various domains, including web data analysis, energy consumption prediction, and weather forecasting. While Multi-Layer Perceptrons (MLPs) are lightweight and effective for capturing…

In the realm of cryptocurrency, the prediction of Bitcoin prices has garnered substantial attention due to its potential impact on financial markets and investment strategies. This paper propose a comparative study on hybrid machine…

Multivariate Time Series (MTS) forecasting involves modeling temporal dependencies within historical records. Transformers have demonstrated remarkable performance in MTS forecasting due to their capability to capture long-term…

Predicting time-series is of great importance in various scientific and engineering fields. However, in the context of limited and noisy data, accurately predicting dynamics of all variables in a high-dimensional system is a challenging…

Long-term time series forecasting (LTSF) has been widely applied in finance, traffic prediction, and other domains. Recently, patch-based transformers have emerged as a promising approach, segmenting data into sub-level patches that serve…

This research addresses the problem of adaptive modeling in time-series data streams with clear input-output relationships. This problem is challenging because rapid system changes (regime shifts) caused by environmental factors or input…

Tensor decomposition (TD) is essential for analyzing high-dimensional sparse data, yet its irregular computations and memory-access patterns pose major performance challenges on modern parallel processors. Prior works rely on…

The dominance of large decoder-only language models has overshadowed encoder-decoder architectures, despite their fundamental efficiency advantages in sequence processing. For small language models (SLMs) - those with 1 billion parameters…

Time series forecasting is a significant problem in many applications, e.g., financial predictions and business optimization. Modern datasets can have multiple correlated time series, which are often generated with global (shared)…

We consider the problem of forecasting complex, nonlinear space-time processes when observations provide only partial information of on the system's state. We propose a natural data-driven framework, where the system's dynamics are modelled…

Transformer-based models have emerged as promising tools for time series forecasting. However, these model cannot make accurate prediction for long input time series. On the one hand, they failed to capture global dependencies within time…

We address the problem of prediction for extreme observations by proposing an extremal linear prediction method. We construct an inner product space of nonnegative random variables derived from transformed-linear combinations of independent…

Transformer layers, which use an alternating pattern of multi-head attention and multi-layer perceptron (MLP) layers, provide an effective tool for a variety of machine learning problems. As the transformer layers use residual connections…

Transformer-based models are at the forefront in long time-series forecasting (LTSF). While in many cases, these models are able to achieve state of the art results, they suffer from a bias toward low-frequencies in the data and high…

Weather forecasting remains a crucial yet challenging domain, where recently developed models based on deep learning (DL) have approached the performance of traditional numerical weather prediction (NWP) models. However, these DL models,…