论文标题
使用密度运算符的贝叶斯统计学习
Bayesian statistical learning using density operators
论文作者
论文摘要
这项简短的研究使用量子力学框架重新制定了统计的贝叶斯学习问题。代表样本波函数纯状态的集合的密度运算符用于概率密度。我们表明，这种表示允许在样本空间上不同坐标系统中制定统计的贝叶斯学习问题。我们进一步表明，这种表示可以使用内核技巧来学习密度运算符的预测。特别是，该研究强调了分解波功能而不是概率密度的研究，正如内核嵌入中所做的那样，可以保留概率运算符的性质。使用一个简单的示例使用离散的正交小波转换来说明结果密度运算符。
This short study reformulates the statistical Bayesian learning problem using a quantum mechanics framework. Density operators representing ensembles of pure states of sample wave functions are used in place probability densities. We show that such representation allows to formulate the statistical Bayesian learning problem in different coordinate systems on the sample space. We further show that such representation allows to learn projections of density operators using a kernel trick. In particular, the study highlights that decomposing wave functions rather than probability densities, as it is done in kernel embedding, allows to preserve the nature of probability operators. Results are illustrated with a simple example using discrete orthogonal wavelet transform of density operators.
