The recent surge in solar plant installations has notably decreased the reliance on fossil fuels while also presenting significant challenges to power grid. Therefore, the accurate forecasting of centralized and distributed solar power has become critically important. Although site-specific forecasting models typically perform better for utility-scale solar power plants, the model maintenance can be troublesome as the number of solar plants grows. Furthermore, the rapid growth and difficulties in real-time data collection associated with distributed solar systems exacerbate the complexity of regional gross solar power forecasting. To address these issues, we propose SolarMAE, a unified regional solar power forecasting framework enabling end-to-end precise forecasting for both centralized and distributed solar systems. It adopts masked autoencoder (MAE) pre-training strategy for numerical weather prediction (NWP) reconstruction at first, aiming to derive spatiotemporal correlations within meteorological variables, and then fine-tunes a temporal convolutional neural network which predicts future solar power generation. Experiments show that this framework outperforms state-of-the-art centralized or distributed solar power forecasting methods in accuracy, and significantly reduces model maintenance cost. It also demonstrates strong few-shot learning capabilities, which is particularly useful for the cold start problem of newly installed solar plants. The unified solar power forecasting system has been deployed in a province in eastern China, serving solar systems with over 73 GW gross installed capacity and more than 400 centralized solar plants.

Spatio-temporal forecasting is crucial in various fields and requires a careful balance between identifying subtle patterns and filtering out noise. Vector quantization (VQ) appears well-suited for this purpose, as it quantizes input vectors into a set of codebook vectors or patterns. Although VQ has shown promise in various computer vision tasks, it surprisingly falls short in enhancing the accuracy of spatio-temporal forecasting. We attribute this to two main issues: inaccurate optimization due to non-differentiability and limited representation power caused by hard-VQ structure. To tackle these challenges, we introduce Differentiable Sparse Soft-Vector Quantization (SVQ), the first VQ method to enhance spatio-temporal forecasting. SVQ balances detail preservation with noise reduction, offering full differentiability and a solid foundation in sparse regression. The method employs a two-layer MLP and an extensive codebook to streamline the sparse regression process, significantly cutting computational costs while simplifying training and improving performance. Empirical studies on five spatio-temporal benchmark datasets show SVQ achieves state-of-the-art results, including a 7.9% improvement on the WeatherBench-S temperature dataset and an average mean absolute error reduction of 9.4% in video prediction benchmarks (Human3.6M, KTH, and KittiCaltech), along with a 17.3% enhancement in image quality (measured by LPIPS).

Accurate periodicity detection of performance metrics in cloud platform is essential for enhancing monitoring accuracy and ensure service quality of cloud computing. However, in real-world industrial settings, such as large-scale cloud computing platform MaxCompute at Alibaba Cloud, performance metrics often exhibit complex multi-periodicity and temporal nonstationarity. Additionally, these metrics are frequently contaminated by noise and anomalies, rendering traditional periodicity detection methods ineffective. To address these challenges, this paper proposes a robust and general period detection method with low deployment cost and high usability. The method employs Empirical Mode Decomposition (EMD) to decompose complex time series into Intrinsic Mode Functions (IMFs), isolating noise, periodic, and trend components. Significant periods are identified using statistical tests to eliminate irrelevant components, while an automatic clustering mechanism mitigates the mode-mixing problem inherent in EMD. Extensive experiments on synthetic and real-world datasets demonstrate that the proposed method outperforms state-of-the-art periodicity detection techniques, achieving over 10% and 17% performance improvements in public single and multiple periodicity detection tasks, respectively. Deployed in Alibaba Cloud's MaxCompute platform, it monitors millions of tasks, resulting in a 7.8% increase in fault detection coverage and enabling faults to be detected 13.15% more rapidly. The method's low deployment cost and user-friendly implementation make it highly accessible and practical for diverse cloud monitoring applications.

Weather forecasting is essential but remains computationally intensive and physically incomplete in traditional numerical weather prediction (NWP) methods.Deep learning (DL) models offer efficiency and accuracy but often ignore physical laws, limiting interpretability and generalization.We propose PhyDL-NWP, a physicsguided deep learning framework that integrates physical equations with latent force parameterization into data-driven models.It predicts weather variables from arbitrary spatiotemporal coordinates, computes physical terms via automatic differentiation, and uses a physics-informed loss to align predictions with governing dynamics.PhyDL-NWP enables resolution-free downscaling by modeling weather as a continuous function and fine-tunes pre-trained models with minimal overhead, achieving up to 170× faster inference with only 55K parameters.Experiments show that PhyDL-NWP improves both forecasting performance and physical consistency.

Weather forecasting has long posed a significant challenge for humanity. While recent AI-based models have surpassed traditional numerical weather prediction (NWP) methods in global forecasting tasks, overfitting remains a critical issue due to the limited availability of real-world weather data spanning only a few decades. Unlike fields like computer vision or natural language processing, where data abundance can mitigate overfitting, weather forecasting demands innovative strategies to address this challenge with existing data. In this paper, we explore pre-training methods for weather forecasting, finding that selecting an appropriately challenging pre-training task introduces locality bias, effectively mitigating overfitting and enhancing performance. We introduce Baguan, a novel data-driven model for medium-range weather forecasting, built on a Siamese Autoencoder pre-trained in a self-supervised manner and fine-tuned for different lead times. Experimental results show that Baguan outperforms traditional methods, delivering more accurate forecasts. Additionally, the pre-trained Baguan demonstrates robust overfitting control and excels in downstream tasks, such as subseasonal-to-seasonal (S2S) modeling and regional forecasting, after fine-tuning.

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.

Time series anomaly detection is of significant importance in many real-world applications, including finance, healthcare, network security, industrial equipment, complex computing systems, and space probes. Most of these applications involve multi-sensor systems, thus how to perform multivariate time series anomaly detection (MTSAD) has garnered widespread attention. This broad attention has fueled extensive research endeavors aimed to innovate and develop methods and techniques to improve the efficiency and precision of anomaly detection on multivariate time series data, including both classic machine learning methods and deep learning methods. However, evaluating the performance of these methods remains challenging due to the limited availability of public benchmark datasets for MTSAD, which are often criticized for various reasons. Additionally, there is no consensus on the best metrics for time series anomaly detection, further complicating MTSAD research. In this paper, we advance the benchmarking of time series anomaly detection by addressing datasets, evaluation metrics, and algorithm comparison. To the best of our knowledge, we have generated the largest real-world datasets for MTSAD using the Hologres AIOps system in the Alibaba Cloud platform. We review and compare popular evaluation metrics including recently proposed ones. To evaluate classic machine learning and recent deep learning methods fairly, we have conducted extensive comparisons of these methods on various datasets. We believe that our benchmarks and datasets will promote reproducible results and accelerate the progress of MTSAD research.

Accurate solar power forecasting is crucial to integrate photovoltaic plants into the electric grid, schedule and secure the power grid safety. This problem becomes more demanding for those newly installed solar plants which lack sufficient operational data. Current research predominantly relies on historical solar power data or numerical weather prediction in a single-modality format, ignoring the complementary information provided in different modalities. In this paper, we propose a multi-modality fusion framework to integrate historical power data, numerical weather prediction, and satellite images, significantly improving forecast performance. We introduce a vector quantized framework that aligns modalities with varying information densities, striking a balance between integrating sufficient information and averting model overfitting. Our framework demonstrates strong zero-shot forecasting capability, which is especially useful for those newly installed plants. Moreover, we collect and release a multi-modal solar power (MMSP) dataset from real-world plants to further promote the research of multi-modal solar forecasting algorithms. Our extensive experiments show that our model not only operates with robustness but also boosts accuracy in both zero-shot forecasting and scenarios rich with training data, surpassing leading models. We have incorporated it into our eForecaster platform and deployed it for more than 300 solar plants with a total capacity of over 15GW. Our code and dataset are accessible at https://github.com/DAMO-DI-ML/FusionSF.git.

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/.

The study of treatment effects is an essential area in causal inference that has received extensive attention in the sciences. When access to counterfactual groups and experimental settings is limited, the synthetic control method (SCM) emerges as a key approach for observational studies. However, conventional SCM techniques mainly concentrate on addressing confounding issues in the pre-treatment period, often overlooking the confounding effects of control groups in the post-treatment period. In this paper, we propose a new approach named Stable-SC, which integrates synthetic control with anomaly detection algorithms to mitigate the influence of confounding factors in both the pre- and post-treatment periods. Our algorithm incorporates an anomaly-detection process that identifies trends and distance anomalies within control groups, significantly impacting SCM estimation results. Subsequently, we employ a re-weighting schema to adjust the significance of these abnormal groups and utilize the Difference-in-Differences estimator to assess causal effects. Through extensive experimentation with multiple simulated and real-world datasets, we demonstrate that our Stable-SC approach yields more robust estimates compared to other existing methods in the literature. Furthermore, we have successfully applied our proposed framework in diverse business scenarios within a prominent retail company, where the need for stable and robust A/B testing is paramount in quantifying causal effects.

Transformer-based models have emerged as promising tools for time series forecasting. However, these models cannot make accurate prediction for long input time series. On the one hand, they failed to capture long-range dependency within time series data. On the other hand, the long input sequence usually leads to large model size and high time complexity. To address these limitations, we present GCformer, which combines a structured global convolutional branch for processing long input sequences with a local Transformer-based branch for capturing short, recent signals. A cohesive framework for a global convolution kernel has been introduced, utilizing three distinct parameterization methods. The selected structured convolutional kernel in the global branch has been specifically crafted with sublinear complexity, thereby allowing for the efficient and effective processing of lengthy and noisy input signals. Empirical studies on six benchmark datasets demonstrate that GCformer outperforms state-of-the-art methods, reducing MSE error in multivariate time series benchmarks by 4.38% and model parameters by 61.92%. In particular, the global convolutional branch can serve as a plug-in block to enhance the performance of other models, with an average improvement of 31.93%, including various recently published Transformer-based models. Our code is publicly available at https://github.com/Yanjun-Zhao/GCformer.

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.

Time series anomaly detection is critical for a wide range of applications. It aims to identify deviant samples from the normal sample distribution in time series. The most fundamental challenge for this task is to learn a representation map that enables effective discrimination of anomalies. Reconstruction-based methods still dominate, but the representation learning with anomalies might hurt the performance with its large abnormal loss. On the other hand, contrastive learning aims to find a representation that can clearly distinguish any instance from the others, which can bring a more natural and promising representation for time series anomaly detection. In this paper, we propose DCdetector, a multi-scale dual attention contrastive representation learning model. DCdetector utilizes a novel dual attention asymmetric design to create the permutated environment and pure contrastive loss to guide the learning process, thus learning a permutation invariant representation with superior discrimination abilities. Extensive experiments show that DCdetector achieves state-of-the-art results on multiple time series anomaly detection benchmark datasets. Code is publicly available at https://github.com/DAMO-DI-ML/KDD2023-DCdetector.

Dynamic time warping (DTW) is an effective dissimilarity measure in many time series applications. Despite its popularity, it is prone to noises and outliers, which leads to singularity problem and bias in the measurement. The time complexity of DTW is quadratic to the length of time series, making it inapplicable in real-time applications. In this paper, we propose a novel time series dissimilarity measure named RobustDTW to reduce the effects of noises and outliers. Specifically, the RobustDTW estimates the trend and optimizes the time warp in an alternating manner by utilizing our designed temporal graph trend filtering. To improve efficiency, we propose a multi-level framework that estimates the trend and the warp function at a lower resolution, and then repeatedly refines them at a higher resolution. Based on the proposed RobustDTW, we further extend it to periodicity detection and outlier time series detection. Experiments on real-world datasets demonstrate the superior performance of RobustDTW compared to DTW variants in both outlier time series detection and periodicity detection.

Time series anomaly detection is a challenging problem due to the complex temporal dependencies and the limited label data. Although some algorithms including both traditional and deep models have been proposed, most of them mainly focus on time-domain modeling, and do not fully utilize the information in the frequency domain of the time series data. In this paper, we propose a Time-Frequency analysis based time series Anomaly Detection model, or TFAD for short, to exploit both time and frequency domains for performance improvement. Besides, we incorporate time series decomposition and data augmentation mechanisms in the designed time-frequency architecture to further boost the abilities of performance and interpretability. Empirical studies on widely used benchmark datasets show that our approach obtains state-of-the-art performance in univariate and multivariate time series anomaly detection tasks.

Autoscaling is a critical component for efficient resource utilization with satisfactory quality of service (QoS) in cloud computing. This paper investigates proactive autoscaling for widely-used scaling-per-query applications where scaling is required for each query, such as container registry and function-as-a-service (FaaS). In these scenarios, the workload often exhibits high uncertainty with complex temporal patterns like periodicity, noises and outliers. Conservative strategies that scale out unnecessarily many instances lead to high resource costs whereas aggressive strategies may result in poor QoS. We present RobustScaler to achieve superior trade-off between cost and QoS. Specifically, we design a novel autoscaling framework based on non-homogeneous Poisson processes (NHPP) modeling and stochastically constrained optimization. Furthermore, we develop a specialized alternating direction method of multipliers (ADMM) to efficiently train the NHPP model, and rigorously prove the QoS guarantees delivered by our optimization-based proactive strategies. Extensive experiments show that RobustScaler out-performs common baseline autoscaling strategies in various real-world traces, with large margins for complex workload patterns.

Time series forecasting is a critical and challenging problem in many real applications. Recently, Transformer-based models prevail in time series forecasting due to their advancement in long-range dependencies learning. Besides, some models introduce series decomposition to further unveil reliable yet plain temporal dependencies. Unfortunately, few models could handle complicated periodical patterns, such as multiple periods, variable periods, and phase shifts in real-world datasets. Meanwhile, the notorious quadratic complexity of dot-product attentions hampers long sequence modeling. To address these challenges, we design an innovative framework Quaternion Transformer (Quatformer), along with three major components: 1). learning-to-rotate attention (LRA) based on quaternions which introduces learnable period and phase information to depict intricate periodical patterns. 2). trend normalization to normalize the series representations in hidden layers of the model considering the slowly varying characteristic of trend. 3). decoupling LRA using global memory to achieve linear complexity without losing prediction accuracy. We evaluate our framework on multiple real-world time series datasets and observe an average 8.1% and up to 18.5% MSE improvement over the best state-of-the-art baseline.

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.

As business of Alibaba expands across the world among various industries, higher standards are imposed on the service quality and reliability of big data cloud computing platforms which constitute the infrastructure of Alibaba Cloud. However, root cause analysis in these platforms is non-trivial due to the complicated system architecture. In this paper, we propose a root cause analysis framework called CloudRCA which makes use of heterogeneous multi-source data including Key Performance Indicators (KPIs), logs, as well as topology, and extracts important features via state-of-the-art anomaly detection and log analysis techniques. The engineered features are then utilized in a Knowledge-informed Hierarchical Bayesian Network (KHBN) model to infer root causes with high accuracy and efficiency. Ablation study and comprehensive experimental comparisons demonstrate that, compared to existing frameworks, CloudRCA 1) consistently outperforms existing approaches in f1-score across different cloud systems; 2) can handle novel types of root causes thanks to the hierarchical structure of KHBN; 3) performs more robustly with respect to algorithmic configurations; and 4) scales more favorably in the data and feature sizes. Experiments also show that a cross-platform transfer learning mechanism can be adopted to further improve the accuracy by more than 10%. CloudRCA has been integrated into the diagnosis system of Alibaba Cloud and employed in three typical cloud computing platforms including MaxCompute, Realtime Compute and Hologres. It saves Site Reliability Engineers (SREs) more than 20% in the time spent on resolving failures in the past twelve months and improves service reliability significantly.

Periodicity detection is a crucial step in time series tasks, including monitoring and forecasting of metrics in many areas, such as IoT applications and self-driving database management system. In many of these applications, multiple periodic components exist and are often interlaced with each other. Such dynamic and complicated periodic patterns make the accurate periodicity detection difficult. In addition, other components in the time series, such as trend, outliers and noises, also pose additional challenges for accurate periodicity detection. In this paper, we propose a robust and general framework for multiple periodicity detection. Our algorithm applies maximal overlap discrete wavelet transform to transform the time series into multiple temporal-frequency scales such that different periodic components can be isolated. We rank them by wavelet variance, and then at each scale detect single periodicity by our proposed Huber-periodogram and Huber-ACF robustly. We rigorously prove the theoretical properties of Huber-periodogram and justify the use of Fisher's test on Huber-periodogram for periodicity detection. To further refine the detected periods, we compute unbiased autocorrelation function based on Wiener-Khinchin theorem from Huber-periodogram for improved robustness and efficiency. Experiments on synthetic and real-world datasets show that our algorithm outperforms other popular ones for both single and multiple periodicity detection.

Many real-world time series data exhibit complex patterns with trend, seasonality, outlier and noise. Robustly and accurately decomposing these components would greatly facilitate time series tasks including anomaly detection, forecasting and classification. RobustSTL is an effective seasonal-trend decomposition for time series data with complicated patterns. However, it cannot handle multiple seasonal components properly. Also it suffers from its high computational complexity, which limits its usage in practice. In this paper, we extend RobustSTL to handle multiple seasonality. To speed up the computation, we propose a special generalized ADMM algorithm to perform the decomposition efficiently. We rigorously prove that the proposed algorithm converges approximately as standard ADMM while reducing the complexity from O(N2) to O(N log N) for each iteration. We empirically study our proposed algorithm with other state-of-the-art seasonal-trend decomposition methods, including MSTL, STR, TBATS, on both synthetic and real-world datasets with single and multiple seasonality. The experimental results demonstrate the superior performance of our decomposition algorithm in terms of both effectiveness and efficiency.

Satellite-based positioning system such as GPS often suffers from large amount of noise that degrades the positioning accuracy dramatically especially in real-time applications. In this work, we consider a data-mining approach to enhance the GPS signal. We build a large-scale high precision GPS receiver grid system to collect real-time GPS signals for training. The Gaussian Process (GP) regression is chosen to model the vertical Total Electron Content (vTEC) distribution of the ionosphere of the Earth. Our experiments show that the noise in the real-time GPS signals often exceeds the breakdown point of the conventional robust regression methods resulting in sub-optimal system performance. We propose a three-step approach to address this challenge. In the first step we perform a set of signal validity tests to separate the signals into clean and dirty groups. In the second step, we train an initial model on the clean signals and then reweigting the dirty signals based on the residual error. A final model is retrained on both the clean signals and the reweighted dirty signals. In the theoretical analysis, we prove that the proposed three-step approach is able to tolerate much higher noise level than the vanilla robust regression methods if two reweighting rules are followed. We validate the superiority of the proposed method in our real-time high precision positioning system against several popular state-of-the-art robust regression methods. Our method achieves centimeter positioning accuracy in the benchmark region with probability $78.4%$ , outperforming the second best baseline method by a margin of $8.3%$. The benchmark takes 6 hours on 20,000 CPU cores or 14 years on a single CPU.

Dimensionality reduction plays an important role in many data mining applications involving high-dimensional data. Many existing dimensionality reduction techniques can be formulated as a generalized eigenvalue problem, which does not scale to large-size problems. Prior work transforms the generalized eigenvalue problem into an equivalent least squares formulation, which can then be solved efficiently. However, the equivalence relationship only holds under certain assumptions without regularization, which severely limits their applicability in practice. In this paper, an efficient two-stage approach is proposed to solve a class of dimensionality reduction techniques, including Canonical Correlation Analysis, Orthonormal Partial Least Squares, linear Discriminant Analysis, and Hypergraph Spectral Learning. The proposed two-stage approach scales linearly in terms of both the sample size and data dimensionality. The main contributions of this paper include (1) we rigorously establish the equivalence relationship between the proposed two-stage approach and the original formulation without any assumption; and (2) we show that the equivalence relationship still holds in the regularization setting. We have conducted extensive experiments using both synthetic and real-world data sets. Our experimental results confirm the equivalence relationship established in this paper. Results also demonstrate the scalability of the proposed two-stage approach.

Effective diagnosis of Alzheimer's disease (AD), the most common type of dementia in elderly patients, is of primary importance in biomedical research. Recent studies have demonstrated that AD is closely related to the structure change of the brain network, i.e., the connectivity among different brain regions. The connectivity patterns will provide useful imaging-based biomarkers to distinguish Normal Controls (NC), patients with Mild Cognitive Impairment (MCI), and patients with AD. In this paper, we investigate the sparse inverse covariance estimation technique for identifying the connectivity among different brain regions. In particular, a novel algorithm based on the block coordinate descent approach is proposed for the direct estimation of the inverse covariance matrix. One appealing feature of the proposed algorithm is that it allows the user feedback (e.g., prior domain knowledge) to be incorporated into the estimation process, while the connectivity patterns can be discovered automatically. We apply the proposed algorithm to a collection of FDG-PET images from 232 NC, MCI, and AD subjects. Our experimental results demonstrate that the proposed algorithm is promising in revealing the brain region connectivity differences among these groups.

A hypergraph is a generalization of the traditional graph in which the edges are arbitrary non-empty subsets of the vertex set. It has been applied successfully to capture high-order relations in various domains. In this paper, we propose a hypergraph spectral learning formulation for multi-label classification, where a hypergraph is constructed to exploit the correlation information among different labels. We show that the proposed formulation leads to an eigenvalue problem, which may be computationally expensive especially for large-scale problems. To reduce the computational cost, we propose an approximate formulation, which is shown to be equivalent to a least squares problem under a mild condition. Based on the approximate formulation, efficient algorithms for solving least squares problems can be applied to scale the formulation to very large data sets. In addition, existing regularization techniques for least squares can be incorporated into the model for improved generalization performance. We have conducted experiments using large-scale benchmark data sets, and experimental results show that the proposed hypergraph spectral learning formulation is effective in capturing the high-order relations in multi-label problems. Results also indicate that the approximate formulation is much more efficient than the original one, while keeping competitive classification performance.