受赫布学习启发的基于查询的线性回归参数估计
Hebbian learning inspired estimation of the linear regression parameters from queries
AI总结：
本研究探索一种赫布学习规则变体用于线性回归向量恢复，证明仅能获取损失查询时该零阶方法可达近最优速率，且快于所有非自适应查询方法。
摘要：
生物神经网络（BNNs）中的局部学习规则通常被称为赫布学习（Hebbian learning）。文献[26]将一种受生物启发的赫布学习规则与一种特定的零阶优化方法关联起来。在本研究中，我们探究该赫布学习规则的一种变体，用于恢复线性回归模型中的回归向量。众所周知，对于大参数维度，零阶优化方法的收敛速率不如梯度下降等一阶方法最优，因此通常被认为整体性能更差。但我们通过建立上下界证明，当仅能获取线性回归损失的查询值时，这类方法能达到接近最优的收敛速率。此外，我们还证明，该赫布学习规则的收敛速率远快于任何独立于数据选择查询的非自适应方法。
英文摘要：
Local learning rules in biological neural networks (BNNs) are commonly referred to as Hebbian learning. [26] links a biologically motivated Hebbian learning rule to a specific zeroth-order optimization method. In this work, we study a variation of this Hebbian learning rule to recover the regression vector in the linear regression model. Zeroth-order optimization methods are known to converge with suboptimal rate for large parameter dimension compared to first-order methods like gradient descent, and are therefore thought to be in general inferior. By establishing upper and lower bounds, we show, however, that such methods achieve near-optimal rates if only queries of the linear regression loss are available. Moreover, we prove that this Hebbian learning rule can achieve considerably faster rates than any non-adaptive method that selects the queries independently of the data.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
