论文标题
正交多项式近似算法（OPAA）：一种估计概率密度的功能分析方法
Orthogonal Polynomials Approximation Algorithm (OPAA):a functional analytic approach to estimating probability densities
论文作者
论文摘要
我们介绍了新的正交多项式近似算法（OPAA），这是一种可行的可行算法，使用功能分析方法估算概率分布：首先，它发现概率分布的平滑功能估计，无论是否归一化；其次，该算法提供了标准化重量的估计值；第三，该算法提出了一种新的计算方案来计算此类估计。 OPAA的核心组成部分是关节分布的平方根的特殊变换，使其成为我们结构的特殊功能空间。通过这种转换，证据等同于转换功能的$ l^2 $规范。因此，可以通过转换系数的平方之和来估计证据。计算可以并行化并在一通途中完成。 OPAA可以广泛应用于概率密度函数的估计。在贝叶斯问题中，它可以应用于估计后部的正常重量，这也称为证据，可作为现有基于优化方法的替代方法。
We present the new Orthogonal Polynomials Approximation Algorithm (OPAA), a parallelizable algorithm that estimates probability distributions using functional analytic approach: first, it finds a smooth functional estimate of the probability distribution, whether it is normalized or not; second, the algorithm provides an estimate of the normalizing weight; and third, the algorithm proposes a new computation scheme to compute such estimates. A core component of OPAA is a special transform of the square root of the joint distribution into a special functional space of our construct. Through this transform, the evidence is equated with the $L^2$ norm of the transformed function, squared. Hence, the evidence can be estimated by the sum of squares of the transform coefficients. Computations can be parallelized and completed in one pass. OPAA can be applied broadly to the estimation of probability density functions. In Bayesian problems, it can be applied to estimating the normalizing weight of the posterior, which is also known as the evidence, serving as an alternative to existing optimization-based methods.
