论文标题
降低降低以最大化预测概括能力
Dimensionality reduction to maximize prediction generalization capability
论文作者
论文摘要
时间序列预测的概括仍然是机器学习中的一个重要开放问题，其中早期方法具有较大的概括错误或局部最小值。我们开发了一种可解析的，无监督的学习方案，该方案提取了预测未来输入的最有用的组成部分，称为预测性主成分分析（PredPCA）。我们的方案可以有效地消除不可预测的噪声，并通过凸优化最大程度地减少测试预测误差。数学分析表明，提供了足够的训练样本和足够高维的观察结果，PERDPCA可以渐近地识别隐藏的状态，系统参数和规范非线性生成过程的维度，并具有全球收敛保证。我们使用包含手工数字，旋转3D对象和自然场景的顺序视觉输入来证明PREDPCA的性能。它可靠地估计了不同的隐藏状态，并仅基于嘈杂的观察结果来预测以前看不见的测试输入数据的未来结果。对于神经形态硬件，PERDPCA的简单架构和低计算成本非常需要。
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.
