Our proposed method directly learns the missing values ina bidirectional recurrent dynamical system, without anyspecific assumption. The imputed values are treated as variables of RNN graph and can be effectively updated during backpropagation. BRITS hasthree advantages: (a)itcanhandle multiple correlated missing values intime series; (b) itgeneralizes totime series with nonlinear dynamics underlying; (c) it provides a data-driven imputation procedure and applies to general settings with missing data. We evaluate our model on three real-world datasets, including an air quality dataset, a healthcare dataset, and a localization dataset for human activity. Experiments show that our model outperforms the state-of-the-art methods in both imputation and classification/regression.

With the rapid development of web services, large amounts of time series data are generated and accumulated across various domains such as finance, healthcare, and online platforms. As such data often co-evolves with multiple variables interacting with each other, estimating the time-varying dependencies between variables (i.e., the dynamic network structure) has become crucial for accurate modeling. However, real-world data is often represented as tensor time series with multiple modes, resulting in large, entangled networks that are hard to interpret and computationally intensive to estimate. In this paper, we propose Kronecker Time-Varying Graphical Lasso (KTVGL), a method designed for modeling tensor time series. Our approach estimates mode-specific dynamic networks in a Kronecker product form, thereby avoiding overly complex entangled structures and producing interpretable modeling results. Moreover, the partitioned network structure prevents the exponential growth of computational time with data dimension. In addition, our method can be extended to stream algorithms, making the computational time independent of the sequence length. Experiments on synthetic data show that the proposed method achieves higher edge estimation accuracy than existing methods while requiring less computation time. To further demonstrate its practical value, we also present a case study using real-world data. Our source code and datasets are available at https://github.com/Higashiguchi-Shingo/KTVGL.

Multivariate Time-Series (MTS) clustering discovers intrinsic grouping patterns of temporal data samples. Although time-series provide rich discriminative information, they also contain substantial redundancy, such as steady-state machine operation records and zero-output periods of solar power generation. Such redundancy diminishes the attention given to discriminative timestamps in representation learning, thus leading to performance bottlenecks in MTS clustering. Masking has been widely adopted to enhance the MTS representation, where temporal reconstruction tasks are designed to capture critical information from MTS. However, most existing masking strategies appear to be standalone preprocess-ing steps, isolated from the learning process, which hinders dynamic adaptation to the importance of clustering-critical timestamps. Accordingly, this paper proposes the Evolving-masked MTS Clustering (EMTC) method, whose model architecture comprises Importance-aware V ariate-wise Masking (IVM) and Multi-Endogenous Views (MEV) generation modules. IVM adaptively guides the model in learning more discriminative representations for clustering, while the reconstruction and cluster-guided contrastive learning pathways enhance and connect the representation learning to clustering tasks. Extensive experiments on 15 benchmark datasets demonstrate the superiority of EMTC over eight SOT A methods, where the EMTC achieves an average improvement of 4.85% in F1-Score over the strongest baselines.

Reliable forecasting of multivariate time series under anomalous conditions is crucial in applications such as ATM cash logistics, where sudden demand shifts can disrupt operations. Modern deep forecasters achieve high accuracy on normal data but often fail when distribution shifts occur. We propose Weighted Contrastive Adaptation (WECA), a Weighted contrastive objective that aligns normal and anomaly-augmented representations, preserving anomaly-relevant information while maintaining consistency under benign variations. Evaluations on a nationwide ATM transaction dataset with domain-informed anomaly injection show that WECA improves SMAPE on anomaly-affected data by 6.1 percentage points compared to a normally trained baseline, with negligible degradation on normal data. These results demonstrate that WECA enhances forecasting reliability under anomalies without sacrificing performance during regular operations.

We present ChronoGraph, a graph-structured multivariate time series forecasting dataset built from real-world production microservices. Each node is a service that emits a multivariate stream of system-level performance metrics, capturing CPU, memory, and network usage patterns, while directed edges encode dependencies between services. The primary task is forecasting future values of these signals at the service level. In addition, ChronoGraph provides expert-annotated incident windows as anomaly labels, enabling evaluation of anomaly detection methods and assessment of forecast robustness during operational disruptions. Compared to existing benchmarks from industrial control systems or traffic and air-quality domains, ChronoGraph uniquely combines (i) multivariate time series, (ii) an explicit, machine-readable dependency graph, and (iii) anomaly labels aligned with real incidents. We report baseline results spanning forecasting models, pretrained time-series foundation models, and standard anomaly detectors. ChronoGraph offers a realistic benchmark for studying structure-aware forecasting and incident-aware evaluation in microservice systems.

Abstract--Recent work has demonstrated the utility of Random Forest (RF) proximities for various supervised machine learning tasks, including outlier detection, missing data imputation, and visualization. However, the utility of the RF proximities depends upon the success of the RF model, which itself is not the ideal model in all contexts. RF proximities have recently been extended to time series by means of the distance-based Proximity Forest (PF) model, among others, affording time series analysis with the benefits of RF proximities. In this work, we introduce the generalized PF model, thereby extending RF proximities to all contexts in which supervised distance-based machine learning can occur . Additionally, we introduce a variant of the PF model for regression tasks. We also introduce the notion of using the generalized PF model as a meta-learning framework, extending supervised imputation capability to any pre-trained classifier . We experimentally demonstrate the unique advantages of the generalized PF model compared with both the RF model and the k-nearest neighbors model.

We present a general framework for training spiking neural networks (SNNs) to perform binary classification on multivariate time series, with a focus on step-wise prediction and high precision at low false alarm rates. The approach uses the Evolutionary Optimization of Neuromorphic Systems (EONS) algorithm to evolve sparse, stateful SNNs by jointly optimizing their architectures and parameters. Inputs are encoded into spike trains, and predictions are made by thresholding a single output neuron's spike counts. We also incorporate simple voting ensemble methods to improve performance and robustness. To evaluate the framework, we apply it with application-specific optimizations to the task of detecting low signal-to-noise ratio radioactive sources in gamma-ray spectral data. The resulting SNNs, with as few as 49 neurons and 66 synapses, achieve a 51.8% true positive rate (TPR) at a false alarm rate of 1/hr, outperforming PCA (42.7%) and deep learning (49.8%) baselines. A three-model any-vote ensemble increases TPR to 67.1% at the same false alarm rate. Hardware deployment on the microCaspian neuromorphic platform demonstrates 2mW power consumption and 20.2ms inference latency. We also demonstrate generalizability by applying the same framework, without domain-specific modification, to seizure detection in EEG recordings. An ensemble achieves 95% TPR with a 16% false positive rate, comparable to recent deep learning approaches with significant reduction in parameter count.

Time series are ubiquitous in many classification/regression applications.

Abstract-- Detecting anomalies in multivariate time series is essential for monitoring complex industrial systems, where high dimensionality, limited labeled data, and subtle dependencies between sensors cause significant challenges. This paper presents a deep reinforcement learning framework that combines a V ari-ational Autoencoder (V AE), an LSTM-based Deep Q-Network (DQN), dynamic reward shaping, and an active learning module to address these issues in a unified learning framework. The main contribution is the implementation of Dynamic Reward Scaling for Multivariate Time Series Anomaly Detection (DRSMT), which demonstrates how each component enhances the detection process. The V AE captures compact latent representations and reduces noise. The DQN enables adaptive, sequential anomaly classification, and the dynamic reward shaping balances exploration and exploitation during training by adjusting the importance of reconstruction and classification signals. In addition, active learning identifies the most uncertain samples for labeling, reducing the need for extensive manual supervision. Experiments on two multivariate benchmarks, namely Server Machine Dataset (SMD) and Water Distribution T estbed (W ADI), show that the proposed method outperforms existing baselines in F1-score and AU-PR. In many of today's applications, identifying and removing anomalies (i.e., outliers) has become essential to ensure system reliability. In multivariate time series data, specifically, different factors can result in anomalies.