Diffusion models, known for their generative ability, have recently been adapted to time series analysis. Most pioneering works rely on the standard isotropic diffusion, treating each time step and the entire frequency spectrum identically. However, it may not be suitable for time series, which often have more informative low-frequency components. We empirically found that direct application of standard diffusion to time series may cause gradient contradiction during training, due to the rapid decrease of low-frequency information in the diffusion process. To this end, we proposed a novel time series diffusion model, MA-TSD, which utilizes the moving average, a natural low-frequency filter, as the forward transition. Its backward process is accelerable like DDIM and can be further considered a time series super-resolution. Our experiments on various datasets demonstrated MA-TSD’s superior performance in time series forecasting and super-resolution tasks.

The inherent non-stationarity of time series in practical applications poses significant challenges for accurate forecasting. This paper tackles the concept drift problem where the underlying distribution or environment of time series changes. To better describe the characteristics and effectively model concept drifts, we first classify them into macro-drift (stable, long-term changes) and micro-drift (sudden, short-term fluctuations). Next, we propose a unified meta-learning framework called LEAF (Learning to Extrapolate and Adjust for Forecasting), where an extrapolation module is first introduced to track and extrapolate the prediction model in latent space considering macro-drift, and then an adjustment module incorporates meta-learnable surrogate loss to capture sample-specific micro-drift patterns. LEAF’s dual-stage approach effectively addresses diverse concept drifts and is model-agnostic which can be compatible with any deep prediction model. We further provide theoretical analysis to justify why the proposed framework can handle macro-drift and micro-drift. To facilitate further research in this field, we release three electric load time series datasets collected from real-world scenarios, exhibiting diverse and typical concept drifts. Extensive experiments on multiple datasets demonstrate the effectiveness of LEAF.

Out-of-Distribution (OOD) extrapolation, where test data feature values extend beyond the training range, poses significant challenges in machine learning. While existing solutions often sacrifice interpretability, resulting in limited applicability in high-stakes applications where interpretability is a a critical requirement. In this paper, we propose Delta-GAM, an interpretable Generalized Additive Model (GAM) that achieves robust extrapolation in OOD scenarios. Our method jointly learns (1) feature-target relationships and (2) functional adaptations for extrapolating beyond the training distribution by reformulating GAM fitting as a second-order interaction problem between features and their distributional offsets. We theoretically show that smooth GAM shape functions induce an approximately low-rank structure in these interactions, enabling efficient decomposition via a specialized neural network. Experiments on synthetic and real-world data demonstrate Delta-GAM's superior performance in OOD extrapolation tasks while preserving model interpretability, bridging a key gap in trustworthy machine learning.

Variance estimation has been one of the key challenges in time series analysis for a long time. Although many ARCHtype algorithms are widely applied in variance estimation, they suffer from sensitivity to outliers and fail to handle complex data such as abrupt trend change and variance periodicity. The time warping of the periodicity makes it further complicated. To deal with these challenges, we propose a robust algorithm called RobustTSVar, based on quantile regression for robust variance estimation. To deal with variance periodicity with time warping, we propose non-local periodic filtering to further refine the variance estimate. An efficient implementation based on ADMM is also proposed to handle large-scale data. We compare our proposed RobustTSVar method with other state-of-the-art methods on both synthetic and real-world datasets, and the numerical results demonstrate the superior performance of our algorithm.

How to explain temporal models is a significant challenge due to the inherent characteristics of time series data, notably the strong temporal dependencies and interactions between observations. Unlike ordinary tabular data, data at different time steps in time series usually interact dynamically, forming influential patterns that shape the model’s predictions, rather than only acting in isolation. Existing explanatory approaches for time series often overlook these crucial temporal interactions by treating time steps as separate entities, leading to a superficial understanding of model behavior. To address this challenge, we introduce FDTempExplainer, an innovative model-agnostic explanation method based on functional decomposition, tailored to unravel the complex interplay within black-box time series models. Our approach disentangles the individual contributions from each time step, as well as the aggregated influence of their interactions, in a rigorous framework. FDTempExplainer accurately measures the strength of interactions, yielding insights that surpass those from baseline models. We demonstrate the effectiveness of our approach in a wide range of time series applications, including anomaly detection, classification, and forecasting, showing its superior performance to the state-of-the-art algorithms.

In real-world microservice systems, the newly deployed service - one kind of change service, could lead to a new type of minority fault. Existing state-of-the-art (SOTA) methods for fault localization rarely consider the imbalanced fault classification in change service. This paper proposes a novel method that utilizes decision rule sets to deal with highly imbalanced data by optimizing the F1 score subject to cardinality constraints. The proposed method greedily generates the rule with maximal marginal gain and uses an efficient minorize-maximization (MM) approach to select rules iteratively, maximizing a non-monotone submodular lower bound. Compared with existing fault localization algorithms, our algorithm can adapt to the imbalanced fault scenario of change service, and provide interpretable fault causes which are easy to understand and verify. Our method can also be deployed in the online training setting, with only about 15% training overhead compared to the current SOTA methods. Empirical studies demonstrate the superior performance of our algorithm to existing fault localization algorithms in terms of both accuracy and model interpretability.

Interpretable models are crucial in many high-stakes decision-making applications. In this paper, we focus on learning a decision rule list for binary and multi-class classification. Different from rule set learning problems, learning an optimal rule list involves not only learning a set of rules, but also their orders. In addition, many existing algorithms rely on rule pre-mining to handle large-scale high-dimensional data, which leads to suboptimal rule list model and degrades its generalization accuracy and interpretablity. In this paper, we learn a rule list from the sequence submodular perspective. We consider the rule list as a sequence and define the cover set for each rule. Then we formulate a sequence function which combines both model complexity and classification accuracy. Based on its appealing sequence submodular property, we propose a general distorted greedy insert algorithm under Minorization-Maximization (MM) framework, which gradually inserts rules with highest inserting gain to the rule list. The rule generation process is treated as a subproblem, allowing our method to learn the rule list through a unified framework which avoids rule pre-mining. We further provide a theoretical lower bound of our greedy insert algorithm in rule list learning. Experimental results show that our algorithm achieves better accuracy and interpretability than the state-of-the-art rule learning methods, and in particular it scales well on large-scale datasets, especially on high-dimensional data.

In causal inference, estimating heterogeneous treatment effects (HTE) is critical for identifying how different subgroups respond to interventions, with broad applications in fields such as precision medicine and personalized advertising. Although HTE estimation methods aim to improve accuracy, how to provide explicit subgroup descriptions remains unclear, hindering data interpretation and strategic intervention management. In this paper, we propose CURLS, a novel rule learning method leveraging HTE, which can effectively describe subgroups with significant treatment effects. Specifically, we frame causal rule learning as a discrete optimization problem, finely balancing treatment effect with variance and considering the rule interpretability. We design an iterative procedure based on the minorize-maximization algorithm and solve a submodular lower bound as an approximation for the original. Quantitative experiments and qualitative case studies verify that compared with state-of-the-art methods, CURLS can find subgroups where the estimated and true effects are 16.1% and 13.8% higher and the variance is 12.0% smaller, while maintaining similar or better estimation accuracy and rule interpretability. Code is available at https://osf.io/zwp2k/.

Time series analysis is widely used in many fields such as power energy, economics, and transportation, including different tasks such as forecasting, anomaly detection, classification, etc. Missing values are widely observed in these tasks, and often leading to unpredictable negative effects on existing methods, hindering their further application. In response to this situation, existing time series imputation methods mainly focus on restoring sequences based on their data characteristics, while ignoring the performance of the restored sequences in downstream tasks. Considering different requirements of downstream tasks (e.g., forecasting), this paper proposes an efficient downstream task-oriented time series imputation evaluation approach. By combining time series imputation with neural network models used for downstream tasks, the gain of different imputation strategies on downstream tasks is estimated without retraining, and the most favorable imputation value for downstream tasks is given by combining different imputation strategies according to the estimated gain.

Accurate prediction of electric load is crucial in power grid planning and management. In this paper, we solve the electric load forecasting problem under extreme events such as scorching heats. One challenge for accurate forecasting is the lack of training samples under extreme conditions. Also load usually changes dramatically in these extreme conditions, which calls for interpretable model to make better decisions. In this paper, we propose a novel forecasting framework, named Self-adaptive Decomposed Interpretable framework (SaDI), which ensembles long-term trend, short-term trend, and period modelings to capture temporal characteristics in different components. The external variable triggered loss is proposed for the imbalanced learning under extreme events. Furthermore, Generalized Additive Model (GAM) is employed in the framework for desirable interpretability. The experiments on both Central China electric load and public energy meters from buildings show that the proposed SaDI framework achieves average 22.14% improvement compared with the current state-of- the-art algorithms in forecasting under extreme events in terms of daily mean of normalized RMSE. Code, Public datasets, and Appendix are available at: https://doi.org/10.24433/CO.9696980.v1.

Periodicity detection is an important task in time series analysis, but still a challenging problem due to the diverse characteristics of time series data like abrupt trend change, outlier, noise, and especially block missing data. In this paper, we propose a robust and effective periodicity detection algorithm for time series with block missing data. We first design a robust trend filter to remove the interference of complicated trend patterns under missing data. Then, we propose a robust autocorrelation function (ACF) that can handle missing values and outliers effectively. We rigorously prove that the proposed robust ACF can still work well when the length of the missing block is less than 1/3 of the period length. Last, by combining the time-frequency information, our algorithm can generate the period length accurately. The experimental results demonstrate that our algorithm outperforms existing periodicity detection algorithms on real-world time series datasets.

Electric load forecasting is an indispensable component of electric power system planning and management. Inaccurate load forecasting may lead to the threat of outages or a waste of energy. Accurate electric load forecasting is challenging when there is limited data or even no data, such as load forecasting in holiday, or under extreme weather conditions. As high-stakes decision-making usually follows after load forecasting, model interpretability is crucial for the adoption of forecasting models. In this paper, we propose an interactive GAM which is not only interpretable but also can incorporate specific domain knowledge in electric power industry for improved performance. This boosting-based GAM leverages piecewise linear functions and can be learned through our efficient algorithm. In both public benchmark and electricity datasets, our interactive GAM outperforms current state-of-the-art methods and demonstrates good generalization ability in the cases of extreme weather events. We launched a user-friendly web-based tool based on interactive GAM and already incorporated it into our eForecaster product, a unified AI platform for electricity forecasting.

Localizing the root cause of network faults is crucial to network operation and maintenance. However, due to the complicated network architectures and wireless environments, as well as limited labeled data, accurately localizing the true root cause is challenging. In this paper, we propose a novel algorithm named NetRCA to deal with this problem. Firstly, we extract effective derived features from the original raw data by considering temporal, directional, attribution, and interaction characteristics. Secondly, we adopt multivariate time series similarity and label propagation to generate new training data from both labeled and unlabeled data to overcome the lack of labeled samples. Thirdly, we design an ensemble model which combines XGBoost, rule set learning, attribution model, and graph algorithm, to fully utilize all data information and enhance performance. Finally, experiments and analysis are conducted on the real-world dataset from ICASSP 2022 AIOps Challenge to demonstrate the superiority and effectiveness of our approach.

Time series analysis is ubiquitous and important in various areas, such as Artificial Intelligence for IT Operations (AIOps) in cloud computing, AI-powered Business Intelligence (BI) in E-commerce, Artificial Intelligence of Things (AIoT), etc. In real-world scenarios, time series data often exhibit complex patterns with trend, seasonality, outlier, and noise. In addition, as more time series data are collected and stored, how to handle the huge amount of data efficiently is crucial in many applications. We note that these significant challenges exist in various tasks like forecasting, anomaly detection, and fault cause localization. Therefore, how to design effective and efficient time series models for different tasks, which are robust to address the aforementioned challenging patterns and noise in real-world scenarios, is of great theoretical and practical interests. In this tutorial, we provide a comprehensive and organized tutorial on the state-of-the-art algorithms of robust time series analysis, ranging from traditional statistical methods to the most recent deep learning based methods. We will not only introduce the principle of time series algorithms, but also provide insights into how to apply them effectively in practical real-world industrial applications. Specifically, we organize the tutorial in a bottom-up framework. We first present preliminaries from different disciplines including robust statistics, signal processing, optimization, and deep learning. Then, we identify and discuss those most-frequently processing blocks in robust time series analysis, including periodicity detection, trend filtering, seasonal-trend decomposition, and time series similarity. Lastly, we discuss recent advances in multiple time series tasks including forecasting, anomaly detection, fault cause localization, and autoscaling, as well as practical lessons of large-scale time series applications from an industrial perspective.

Many real-world time series exhibit multiple seasonality with different lengths. The removal of seasonal components is crucial in numerous applications of time series, including forecasting and anomaly detection. However, many seasonal-trend decomposition algorithms suffer from high computational cost and require a large amount of data when multiple seasonal components exist, especially when the periodic length is long. In this paper, we propose a general and efficient multi-scale seasonal-trend decomposition algorithm for time series with multiple seasonality. We first down-sample the original time series onto a lower resolution, and then convert it to a time series with single seasonality. Thus, existing seasonal-trend decomposition algorithms can be applied directly to obtain the rough estimates of trend and the seasonal component corresponding to the longer periodic length. By considering the relationship between different resolutions, we formulate the recovery of different components on the high resolution as an optimization problem, which is solved efficiently by our alternative direction multiplier method (ADMM) based algorithm. Our experimental results demonstrate the accurate decomposition results with significantly improved efficiency.

Rule sets are highly interpretable logical models in which the predicates for decision are expressed in disjunctive normal form (DNF, OR-of-ANDs), or, equivalently, the overall model comprises an unordered collection of if-then decision rules. In this paper, we consider a submodular optimization based approach for learning rule sets. The learning problem is framed as a subset selection task in which a subset of all possible rules needs to be selected to form an accurate and interpretable rule set. We employ an objective function that exhibits submodularity and thus is amenable to submodular optimization techniques. To overcome the difficulty arose from dealing with the exponential-sized ground set of rules, the subproblem of searching a rule is casted as another subset selection task that asks for a subset of features. We show it is possible to write the induced objective function for the subproblem as a difference of two submodular (DS) functions to make it approximately solvable by DS optimization algorithms. Overall, the proposed approach is simple, scalable, and likely to be benefited from further research on submodular optimization. Experiments on real datasets demonstrate the effectiveness of our method.

The most promising feature of the fifth generation (5G) wireless networks is to support the Internet of Things (IoT) application, such as massive machine-type communications (mMTC). In mMTC scenario, a large number of users are connected to an access point, but very few of them are active at the same time, which motivates us to exploit Low-Activity Code Division Multiple Access (LA-CDMA) as the multiple access technology for MTC. The optimal maximum a posterior probability (MAP) assumes that the user activity factor is exactly known, which is in fact unknown in the practical detection scenarios. In this paper, we first formulate the LA-CDMA uplink into a multiple measurement vector (MMV) model for several continuous time slots, then we introduce a novel iterative reweighed (IR) algorithm to reconstruct the sparse signal. The new scheme overcomes the difficulty of unknown user activity factor and the simulation results over massive MTC systems demonstrate that the proposed algorithm achieves substantial performance gain over traditional detectors considerably.

There has been a growing interest in wideband spectrum sensing due to its applications in cognitive radios and electronic surveillance. To overcome the sampling rate bottleneck for wideband spectrum sensing, in this paper, we study the problem of compressed power spectrum estimation whose objective is to reconstruct the power spectrum of a wide-sense stationary signal based on sub-Nyquist samples. By exploring the sampling structure inherent in the multicoset sampling scheme, we develop a computationally efficient method for power spectrum reconstruction. An important advantage of our proposed method over existing compressed power spectrum estimation methods is that our proposed method, whose primary computational task consists of fast Fourier transform (FFT), has a very low computational complexity. Such a merit makes it possible to efficiently implement the proposed algorithm in a practical field-programmable gate array (FPGA)-based system for real-time wideband spectrum sensing. Our proposed method also provides a new perspective on the power spectrum recovery condition, which leads to a result similar to what was reported in prior works. Simulation results are presented to show the computational efficiency and the effectiveness of the proposed method.

We propose DGG: Deep clustering via a Gaussian-mixture variational autoencoder (VAE) with Graph embedding. To facilitate clustering, we apply Gaussian mixture model (GMM) as the prior in VAE. To handle data with complex spread, we apply graph embedding. Our idea is that graph information which captures local data structures is an excellent complement to deep GMM. Combining them facilitates the network to learn powerful representations that follow global model and local structural constraints. Therefore, our method unifies model-based and similarity-based approaches for clustering. To combine graph embedding with probabilistic deep GMM, we propose a novel stochastic extension of graph embedding: we treat samples as nodes on a graph and minimize the weighted distance between their posterior distributions. We apply Jenson-Shannon divergence as the distance. We combine the divergence minimization with the log-likelihood maximization of the deep GMM. We derive formulations to obtain an unified objective that enables simultaneous deep representation learning and clustering. Our experimental results show that our proposed DGG outperforms recent deep Gaussian mixture methods (model-based) and deep spectral clustering (similarity-based). Our results highlight advantages of combining model-based and similarity-based clustering as proposed in this work. Our code is published here: https:// github.com/dodoyang0929/DGG.git.

Self-supervised (SS) learning is a powerful approach for representation learning using unlabeled data. Recently, it has been applied to Generative Adversarial Networks (GAN) training. Specifically, SS tasks were proposed to address the catastrophic forgetting issue in the GAN discriminator. In this work, we perform an in-depth analysis to understand how SS tasks interact with learning of generator. From the analysis, we identify issues of SS tasks which allow a severely mode-collapsed generator to excel the SS tasks. To address the issues, we propose new SS tasks based on a multi-class minimax game. The competition between our proposed SS tasks in the game encourages the generator to learn the data distribution and generate diverse samples. We provide both theoretical and empirical analysis to support that our proposed SS tasks have better convergence property. We conduct experiments to incorporate our proposed SS tasks into two different GAN baseline models. Our approach establishes state-of-the-art FID scores on CIFAR-10, CIFAR-100, STL-10, CelebA, Imagenet $32\times32$ and Stacked-MNIST datasets, outperforming existing works by considerable margins in some cases. Our unconditional GAN model approaches performance of conditional GAN without using labeled data. Our code: \url{https://github.com/tntrung/msgan}

We consider the problem of downlink channel estimation for millimeter wave (mmWave) MIMO-OFDM systems, where both the base station (BS) and the mobile station (MS) employ large antenna arrays for directional precoding/beamforming. Hybrid analog and digital beamforming structures are employed in order to offer a compromise between hardware complexity and system performance. Different from most existing studies that are concerned with narrowband channels, we consider estimation of wideband mmWave channels with frequency selectivity, which is more appropriate for mmWave MIMO-OFDM systems. By exploiting the sparse scattering nature of mmWave channels, we propose a CANDECOMP/PARAFAC (CP) decomposition-based method for channel parameter estimation (including angles of arrival/departure, time delays, and fading coefficients). In our proposed method, the received signal at the MS is expressed as a third-order tensor. We show that the tensor has the form of a low-rank CP, and the channel parameters can be estimated from the associated factor matrices. Our analysis reveals that the uniqueness of the CP decomposition can be guaranteed even when the size of the tensor is small. Hence the proposed method has the potential to achieve substantial training overhead reduction. We also develop Cramér-Rao bound (CRB) results for channel parameters and compare our proposed method with a compressed sensing-based method. Simulation results show that the proposed method attains mean square errors that are very close to their associated CRBs and present a clear advantage over the compressed sensing-based method.

Sparse Beyesian learning is a popular approach for sparse signal recovery, and has demonstrated superior performance in a series of experiments. Nevertheless, the sparse Bayesian learning algorithm involves a matrix inverse at each iteration. Its associated computational complexity grows significantly with the problem size, which hinders its application to many practical problems even with moderately large datasets. To address this issue, in this letter, we develop a fast inverse-free sparse Bayesian learning method. Specifically, by invoking a fundamental property for smooth functions, we obtain a relaxed evidence lower bound (relaxed-ELBO) that is computationally more amiable than the conventional ELBO used by sparse Bayesian learning. A variational expectation-maximization (EM) scheme is then employed to maximize the relaxed-ELBO, which leads to a computationally efficient inverse-free sparse Bayesian learning algorithm. Simulation results show that the proposed algorithm has a fast convergence rate and achieves lower reconstruction errors than other state-of-the-art fast sparse recovery methods in the presence of noise.

We consider a dictionary learning problem aimed at designing a dictionary such that the signals admits a sparse or an approximate sparse representation over the learned dictionary. The problem finds a variety of applications including image denoising, feature extraction, etc. In this paper, we propose a new hierarchical Bayesian model for dictionary learning, in which a Gaussian-inverse Gamma hierarchical prior is used to promote the sparsity of the representation. Suitable non-informative priors are also placed on the dictionary and the noise variance such that they can be reliably estimated from the data. Based on the hierarchical model, a Gibbs sampling method is developed for Bayesian inference. The proposed method have the advantage that it does not require the knowledge of the noise variance a priori. Numerical results show that the proposed method is able to learn the dictionary with an accuracy better than existing methods.

We consider the problem of recovering block-sparse signals with intrablock correlated entries. The block partition of the sparse signal is assumed unknown a priori. To exploit the block-sparse structure as well as the local smoothness of the sparse signal, consecutive coefficients of the sparse signal are organized into a number of 2×2 matrices, and the log-determinant function is used to promote the low rankness of these 2×2 matrices. We show that such a log-determinant function has the ability to promote the block-sparsity and local smoothness simultaneously. An iterative reweighted method is developed by iteratively minimizing a surrogate function of the original objective function. Simulation results show that our proposed method offers competitive performance for recovering block-sparse signals with intrablock correlated entries.

We consider the problem of uplink channel estimation for millimeter wave (mmWave) systems, where the base station (BS) and mobile stations (MSs) are equipped with large antenna arrays to provide sufficient beamforming gain for outdoor wireless communications. Hybrid analog and digital beamforming structures are employed by both the BS and the MS due to hardware constraints. We propose a layered pilot transmission scheme and a CANDECOMP/PARAFAC (CP) decomposition-based method for joint estimation of the channels from multiple users (i.e., MSs) to the BS. The proposed method exploits the intrinsic low-rank structure of the multiway data collected from multiple modes, where the low-rank structure is a result of the sparse scattering nature of the mmWave channel. The uniqueness of the CP decomposition is studied, and the sufficient conditions for essential uniqueness are obtained. The conditions shed light on the design of the beamforming matrix, the combining matrix, and the pilot sequences, and meanwhile provide general guidelines for choosing system parameters. Our analysis reveals that our proposed method can achieve a substantial training overhead reduction by leveraging the low-rank structure of the received signal. Simulation results show that the proposed method presents a clear advantage over a compressed sensing-based method in terms of both estimation accuracy and computational complexity.