Forecasting time series with extreme events is critical yet challenging due to their high variance, irregular dynamics, and sparse but high-impact nature. While existing methods excel in modeling dominant regular patterns, their performance degrades significantly during extreme events, constituting the primary source of forecasting errors in real-world applications. Although some approaches incorporate auxiliary signals to improve performance, they still fail to capture extreme events' complex temporal dynamics. To address these limitations, we propose M²FMoE, an extreme-adaptive forecasting model that learns both regular and extreme patterns through multi-resolution and multi-view frequency modeling. It comprises three modules: (1) a multi-view frequency mixture-of-experts module assigns experts to distinct spectral bands in Fourier and Wavelet domains, with cross-view shared band splitter aligning frequency partitions and enabling inter-expert collaboration to capture both dominant and rare fluctuations; (2) a multi-resolution adaptive fusion module that hierarchically aggregates frequency features from coarse to fine resolutions, enhancing sensitivity to both short-term variations and sudden changes; (3) a temporal gating integration module that dynamically balances long-term trends and short-term frequency-aware features, improving adaptability to both regular and extreme temporal patterns. Experiments on real-world hydrological datasets with extreme patterns demonstrate that M²FMoE outperforms state-of-the-art baselines without requiring extreme-event labels.

Sparse reduced-rank regression is an important tool to uncover the large-scale response-predictor association network, as exemplified by modern applications such as the diffusion networks, and recommendation systems. However, the association networks recovered by existing methods are either sensitive to outliers or not scalable under the big data setup. In this paper, we propose a new statistical learning method called robust parallel pursuit (ROP) for joint estimation and outlier detection in large-scale response-predictor association network analysis. The proposed method is scalable in that it transforms the original large-scale network learning problem into a set of sparse unit-rank estimations via factor analysis, thus facilitating an effective parallel pursuit algorithm. Furthermore, we provide comprehensive theoretical guarantees including consistency in parameter estimation, rank selection, and outlier detection, and we conduct an inference procedure to quantify the uncertainty of existence of outliers. Extensive simulation studies and two real-data analyses demonstrate the effectiveness and the scalability of the suggested approach. History: Accepted by Ram Ramesh, Area Editor/Data Science & Machine Learning. Funding: This work was supported by the National Key R&D Program of China [Grant 2022YFA1008000], Natural Science Foundation of China [Grants 72071187, 72091212, 71731010, and 71921001], China Postdoctoral Science Foundation [Grant 2023M733402], and Fundamental Research Funds for the Central Universities [Grants WK3470000017, WK2040000027, and WK2040000079]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0181 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2022.0181 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Multinomial logistic regression is a useful model for predicting the probabilities of multiclass outcomes. Because of the complexity and high dimensionality of some data, it is challenging to fit a valid model with high accuracy and interpretability. We propose a novel sparse reduced-rank multinomial logistic regression model to jointly select variables and reduce the dimension via a nonconvex row constraint. We develop a block-wise iterative algorithm with a majorizing surrogate function to efficiently solve the optimization problem. From an algorithmic aspect, we show that the output estimator enjoys consistency in estimation and sparsity recovery even in a high-dimensional setting. The finite sample performance of the proposed method is investigated via simulation studies and two real image data sets. The results show that our proposal has competitive performance in both estimation accuracy and computation time. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms–Discrete. Funding: This work was supported by the National Natural Science Foundation of China [Grants 71991474, 12171449, 11801540, and 12071494] and the Natural Science Foundation of Anhui Province [Grant BJ2040170017]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/ijoc.2022.0132 .

Sparse factorization of a large matrix is fundamental in modern statistical learning. In particular, the sparse singular value decomposition has been utilized in many multivariate regression methods. The appeal of this factorization is owing to its power in discovering a highly-interpretable latent association network. However, many existing methods are either ad hoc without a general performance guarantee, or are computationally intensive. We formulate the statistical problem as a sparse factor regression and tackle it with a two-stage “deflation + stagewise learning” approach. In the first stage, we consider both sequential and parallel approaches for simplifying the task into a set of co-sparse unit-rank estimation (CURE) problems, and establish the statistical underpinnings of these commonly-adopted and yet poorly understood deflation methods. In the second stage, we innovate a contended stagewise learning technique, consisting of a sequence of simple incremental updates, to efficiently trace out the whole solution paths of CURE. Our algorithm achieves a much lower computational complexity than alternating convex search, and it enables a flexible and principled tradeoff between statistical accuracy and computational efficiency. Our work is among the first to enable stagewise learning for non-convex problems, and the idea can be applicable in many multi-convex problems. Extensive simulation studies and an application in genetics demonstrate the effectiveness and scalability of our approach.