Generalization of time series prediction remains an important open issue in machine learning, wherein earlier methods have either large generalization error or local minima. We develop an analytically solvable, unsupervised learning scheme that extracts the most informative components for predicting future inputs, termed predictive principal component analysis (PredPCA). Our scheme can effectively remove unpredictable noise and minimize test prediction error through convex optimization. Mathematical analyses demonstrate that, provided with sufficient training samples and sufficiently high-dimensional observations, PredPCA can asymptotically identify hidden states, system parameters, and dimensionalities of canonical nonlinear generative processes, with a global convergence guarantee. We demonstrate the performance of PredPCA using sequential visual inputs comprising hand-digits, rotating 3D objects, and natural scenes. It reliably estimates distinct hidden states and predicts future outcomes of previously unseen test input data, based exclusively on noisy observations. The simple architecture and low computational cost of PredPCA are highly desirable for neuromorphic hardware.
AP-BMM: Approximating Capability-Cost Pareto Sets of LLMs via Asynchronous Prior-Guided Bayesian Model Merging
Guangdong Provincial Key Laboratory of Novel Security Intelligence Technologies（广东新型安全智能技术重点实验室）；Institute of Cyberspace Security（网络空间安全研究院）；School of Computer Science and Technology（计算机科学与技术学院）
Anti-drift in electronic nose via dimensionality reduction: a discriminative subspace projection approach
School of Computing, National University of Singapore（新加坡国立大学计算机学院）；Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences（中国科学院深圳先进技术研究院）
Chaos and Complexity from Quantum Neural Network: A study with Diffusion Metric in Machine Learning
National Institute of Science Education and Research, Bhubaneswar（布巴内斯瓦尔国家科学教育与研究学院）；Homi Bhabha National Institute（霍米·巴巴国家研究所）；Max Planck Institute for Gravitational Physics (Albert Einstein Institute)（马克斯·普朗克引力物理研究所（阿尔伯特·爱因斯坦研究所））；Jadavpur University（贾达普大学）；Mississippi State University（密西西比州立大学）
