论文标题
用于机器学习的概率线性求解器
Probabilistic Linear Solvers for Machine Learning
论文作者
论文摘要
线性系统几乎是所有数值计算的基岩。机器学习由于其规模，特征结构，随机性和不确定性在现场的核心作用而对解决方案的解决方案构成了特定的挑战。统一早期的工作，我们提出了一类概率线性求解器，这些概率线性求解器共同推断矩阵，其逆和矩阵矢量产物观测的溶液。该类别来自一组基本的desiderata，该集合限制了可能的算法的空间，并在某些条件下恢复了共轭梯度的方法。我们演示了如何合并先前的光谱信息，以校准不确定性并实验展示此类求解器对机器学习的潜力。
Linear systems are the bedrock of virtually all numerical computation. Machine learning poses specific challenges for the solution of such systems due to their scale, characteristic structure, stochasticity and the central role of uncertainty in the field. Unifying earlier work we propose a class of probabilistic linear solvers which jointly infer the matrix, its inverse and the solution from matrix-vector product observations. This class emerges from a fundamental set of desiderata which constrains the space of possible algorithms and recovers the method of conjugate gradients under certain conditions. We demonstrate how to incorporate prior spectral information in order to calibrate uncertainty and experimentally showcase the potential of such solvers for machine learning.
