Beyond LoRA: Exploring Efficient Fine-Tuning Techniques for Time Series Foundational Models

Time Series Foundation Models (TSFMs) have recently garnered attention for their ability to model complex, large-scale time series data across domains such as retail, finance, and transportation. However, their application to sensitive, domain-specific fields like healthcare remains challenging, primarily due to the difficulty of fine-tuning these models for specialized, out-of-domain tasks with scarce publicly available datasets. In this work, we explore the use of Parameter-Efficient Fine-Tuning (PEFT) techniques to address these limitations, focusing on healthcare applications, particularly ICU vitals forecasting for sepsis patients. We introduce and evaluate two selective (BitFit and LayerNorm Tuning) and two additive (VeRA and FourierFT) PEFT techniques on multiple configurations of the Chronos TSFM for forecasting vital signs of sepsis patients. Our comparative analysis demonstrates that some of these PEFT methods outperform LoRA in terms of parameter efficiency and domain adaptation, establishing state-of-the-art (SOTA) results in ICU vital forecasting tasks. Interestingly, FourierFT applied to the Chronos (Tiny) variant surpasses the SOTA model while fine-tuning only 2,400 parameters compared to the 700K parameters of the benchmark.

Spatiotemporal Covariance Neural Networks

Modeling spatiotemporal interactions in multivariate time series is key to their effective processing, but challenging because of their irregular and often unknown structure. Statistical properties of the data provide useful biases to model interdependencies and are leveraged by correlation and covariance-based networks as well as by processing pipelines relying on principal component analysis (PCA). However, PCA and its temporal extensions suffer instabilities in the covariance eigenvectors when the corresponding eigenvalues are close to each other, making their application to dynamic and streaming data settings challenging. To address these issues, we exploit the analogy between PCA and graph convolutional filters to introduce the SpatioTemporal coVariance Neural Network (STVNN), a relational learning model that operates on the sample covariance matrix of the time series and leverages joint spatiotemporal convolutions to model the data. To account for the streaming and non-stationary setting, we consider an online update of the parameters and sample covariance matrix. We prove the STVNN is stable to the uncertainties introduced by these online estimations, thus improving over temporal PCA-based methods. Experimental results corroborate our theoretical findings and show that STVNN is competitive for multivariate time series processing, it adapts to changes in the data distribution, and it is orders of magnitude more stable than online temporal PCA.

Weather Prediction Using CNN-LSTM for Time Series Analysis: A Case Study on Delhi Temperature Data

As global climate change intensifies, accurate weather forecasting is increasingly crucial for sectors such as agriculture, energy management, and environmental protection. Traditional methods, which rely on physical and statistical models, often struggle with complex, nonlinear, and time-varying data, underscoring the need for more advanced techniques. This study explores a hybrid CNN-LSTM model to enhance temperature forecasting accuracy for the Delhi region, using historical meteorological data from 1996 to 2017. We employed both direct and indirect methods, including comprehensive data preprocessing and exploratory analysis, to construct and train our model. The CNN component effectively extracts spatial features, while the LSTM captures temporal dependencies, leading to improved prediction accuracy. Experimental results indicate that the CNN-LSTM model significantly outperforms traditional forecasting methods in terms of both accuracy and stability, with a mean square error (MSE) of 3.26217 and a root mean square error (RMSE) of 1.80615. The hybrid model demonstrates its potential as a robust tool for temperature prediction, offering valuable insights for meteorological forecasting and related fields. Future research should focus on optimizing model architecture, exploring additional feature extraction techniques, and addressing challenges such as overfitting and computational complexity. This approach not only advances temperature forecasting but also provides a foundation for applying deep learning to other time series forecasting tasks.

Second-order difference subspace

Subspace representation is a fundamental technique in various fields of machine learning. Analyzing a geometrical relationship among multiple subspaces is essential for understanding subspace series' temporal and/or spatial dynamics. This paper proposes the second-order difference subspace, a higher-order extension of the first-order difference subspace between two subspaces that can analyze the geometrical difference between them. As a preliminary for that, we extend the definition of the first-order difference subspace to the more general setting that two subspaces with different dimensions have an intersection. We then define the second-order difference subspace by combining the concept of first-order difference subspace and principal component subspace (Karcher mean) between two subspaces, motivated by the second-order central difference method. We can understand that the first/second-order difference subspaces correspond to the velocity and acceleration of subspace dynamics from the viewpoint of a geodesic on a Grassmann manifold. We demonstrate the validity and naturalness of our second-order difference subspace by showing numerical results on two applications: temporal shape analysis of a 3D object and time series analysis of a biometric signal.

Matrix Profile for Anomaly Detection on Multidimensional Time Series

The Matrix Profile (MP), a versatile tool for time series data mining, has been shown effective in time series anomaly detection (TSAD). This paper delves into the problem of anomaly detection in multidimensional time series, a common occurrence in real-world applications. For instance, in a manufacturing factory, multiple sensors installed across the site collect time-varying data for analysis. The Matrix Profile, named for its role in profiling the matrix storing pairwise distance between subsequences of univariate time series, becomes complex in multidimensional scenarios. If the input univariate time series has n subsequences, the pairwise distance matrix is a n x n matrix. In a multidimensional time series with d dimensions, the pairwise distance information must be stored in a n x n x d tensor. In this paper, we first analyze different strategies for condensing this tensor into a profile vector. We then investigate the potential of extending the MP to efficiently find k-nearest neighbors for anomaly detection. Finally, we benchmark the multidimensional MP against 19 baseline methods on 119 multidimensional TSAD datasets. The experiments covers three learning setups: unsupervised, supervised, and semi-supervised. MP is the only method that consistently delivers high performance across all setups.

Randomized Spline Trees for Functional Data Classification: Theory and Application to Environmental Time Series

Functional data analysis (FDA) and ensemble learning can be powerful tools for analyzing complex environmental time series. Recent literature has highlighted the key role of diversity in enhancing accuracy and reducing variance in ensemble methods.This paper introduces Randomized Spline Trees (RST), a novel algorithm that bridges these two approaches by incorporating randomized functional representations into the Random Forest framework. RST generates diverse functional representations of input data using randomized B-spline parameters, creating an ensemble of decision trees trained on these varied representations. We provide a theoretical analysis of how this functional diversity contributes to reducing generalization error and present empirical evaluations on six environmental time series classification tasks from the UCR Time Series Archive. Results show that RST variants outperform standard Random Forests and Gradient Boosting on most datasets, improving classification accuracy by up to 14\%. The success of RST demonstrates the potential of adaptive functional representations in capturing complex temporal patterns in environmental data. This work contributes to the growing field of machine learning techniques focused on functional data and opens new avenues for research in environmental time series analysis.

Recent Trends in Modelling the Continuous Time Series using Deep Learning: A Survey

Continuous-time series is essential for different modern application areas, e.g. healthcare, automobile, energy, finance, Internet of things (IoT) and other related areas. Different application needs to process as well as analyse a massive amount of data in time series structure in order to determine the data-driven result, for example, financial trend prediction, potential probability of the occurrence of a particular event occurrence identification, patient health record processing and so many more. However, modeling real-time data using a continuous-time series is challenging since the dynamical systems behind the data could be a differential equation. Several research works have tried to solve the challenges of modelling the continuous-time series using different neural network models and approaches for data processing and learning. The existing deep learning models are not free from challenges and limitations due to diversity among different attributes, behaviour, duration of steps, energy, and data sampling rate. This paper has described the general problem domain of time series and reviewed the challenges of modelling the continuous time series. We have presented a comparative analysis of recent developments in deep learning models and their contribution to solving different difficulties of modelling the continuous time series. We have also identified the limitations of the existing neural network model and open issues. The main goal of this review is to understand the recent trend of neural network models used in a different real-world application with continuous-time data.

Latent Space Score-based Diffusion Model for Probabilistic Multivariate Time Series Imputation

Accurate imputation is essential for the reliability and success of downstream tasks. Recently, diffusion models have attracted great attention in this field. However, these models neglect the latent distribution in a lower-dimensional space derived from the observed data, which limits the generative capacity of the diffusion model. Additionally, dealing with the original missing data without labels becomes particularly problematic. To address these issues, we propose the Latent Space Score-Based Diffusion Model (LSSDM) for probabilistic multivariate time series imputation. Observed values are projected onto low-dimensional latent space and coarse values of the missing data are reconstructed without knowing their ground truth values by this unsupervised learning approach. Finally, the reconstructed values are fed into a conditional diffusion model to obtain the precise imputed values of the time series. In this way, LSSDM not only possesses the power to identify the latent distribution but also seamlessly integrates the diffusion model to obtain the high-fidelity imputed values and assess the uncertainty of the dataset. Experimental results demonstrate that LSSDM achieves superior imputation performance while also providing a better explanation and uncertainty analysis of the imputation mechanism. The website of the code is \textit{https://github.com/gorgen2020/LSSDM\_imputation}.

Explaining Datasets in Words: Statistical Models with Natural Language Parameters

To make sense of massive data, we often fit simplified models and then interpret the parameters; for example, we cluster the text embeddings and then interpret the mean parameters of each cluster. However, these parameters are often high-dimensional and hard to interpret. To make model parameters directly interpretable, we introduce a family of statistical models -- including clustering, time series, and classification models -- parameterized by natural language predicates. For example, a cluster of text about COVID could be parameterized by the predicate "discusses COVID". To learn these statistical models effectively, we develop a model-agnostic algorithm that optimizes continuous relaxations of predicate parameters with gradient descent and discretizes them by prompting language models (LMs). Finally, we apply our framework to a wide range of problems: taxonomizing user chat dialogues, characterizing how they evolve across time, finding categories where one language model is better than the other, clustering math problems based on subareas, and explaining visual features in memorable images. Our framework is highly versatile, applicable to both textual and visual domains, can be easily steered to focus on specific properties (e.g. subareas), and explains sophisticated concepts that classical methods (e.g. n-gram analysis) struggle to produce.

A Survey of Anomaly Detection in In-Vehicle Networks

Modern vehicles are equipped with Electronic Control Units (ECU) that are used for controlling important vehicle functions including safety-critical operations. ECUs exchange information via in-vehicle communication buses, of which the Controller Area Network (CAN bus) is by far the most widespread representative. Problems that may occur in the vehicle's physical parts or malicious attacks may cause anomalies in the CAN traffic, impairing the correct vehicle operation. Therefore, the detection of such anomalies is vital for vehicle safety. This paper reviews the research on anomaly detection for in-vehicle networks, more specifically for the CAN bus. Our main focus is the evaluation of methods used for CAN bus anomaly detection together with the datasets used in such analysis. To provide the reader with a more comprehensive understanding of the subject, we first give a brief review of related studies on time series-based anomaly detection. Then, we conduct an extensive survey of recent deep learning-based techniques as well as conventional techniques for CAN bus anomaly detection. Our comprehensive analysis delves into anomaly detection algorithms employed in in-vehicle networks, specifically focusing on their learning paradigms, inherent strengths, and weaknesses, as well as their efficacy when applied to CAN bus datasets. Lastly, we highlight challenges and open research problems in CAN bus anomaly detection.