Neural Nonlinear Shrinkage of Covariance Matrices for Minimum Variance Portfolio Optimization

This paper introduces a neural network-based nonlinear shrinkage estimator of covariance matrices for the purpose of minimum variance portfolio optimization. It is a hybrid approach that integrates statistical estimation with machine learning. Starting from the Ledoit-Wolf (LW) shrinkage estimator, we decompose the LW covariance matrix into its eigenvalues and eigenvectors, and apply a lightweight transformer-based neural network to learn a nonlinear eigenvalue shrinkage function. Trained with portfolio risk as the loss function, the resulting precision matrix (the inverse covariance matrix) estimator directly targets portfolio risk minimization. By conditioning on the sample-to-dimension ratio, the approach remains scalable across different sample sizes and asset universes. Empirical results on stock daily returns from Standard & Poor's 500 Index (S&P500) demonstrate that the proposed method consistently achieves lower out-of-sample realized risk than benchmark approaches. This highlights the promise of integrating structural statistical models with data-driven learning.

DK-Root: A Joint Data-and-Knowledge-Driven Framework for Root Cause Analysis of QoE Degradations in Mobile Networks

Diagnosing the root causes of Quality of Experience (QoE) degradations in operational mobile networks is challenging due to complex cross-layer interactions among kernel performance indicators (KPIs) and the scarcity of reliable expert annotations. Although rule-based heuristics can generate labels at scale, they are noisy and coarse-grained, limiting the accuracy of purely data-driven approaches. To address this, we propose DK-Root, a joint data-and-knowledge-driven framework that unifies scalable weak supervision with precise expert guidance for robust root-cause analysis. DK-Root first pretrains an encoder via contrastive representation learning using abundant rule-based labels while explicitly denoising their noise through a supervised contrastive objective. To supply task-faithful data augmentation, we introduce a class-conditional diffusion model that generates KPIs sequences preserving root-cause semantics, and by controlling reverse diffusion steps, it produces weak and strong augmentations that improve intra-class compactness and inter-class separability. Finally, the encoder and the lightweight classifier are jointly fine-tuned with scarce expert-verified labels to sharpen decision boundaries. Extensive experiments on a real-world, operator-grade dataset demonstrate state-of-the-art accuracy, with DK-Root surpassing traditional ML and recent semi-supervised time-series methods. Ablations confirm the necessity of the conditional diffusion augmentation and the pretrain-finetune design, validating both representation quality and classification gains.