Despite the successes of probabilistic models based on passing noise through
neural networks, recent work has identified that such methods often fail to
capture tail behavior accurately, unless the tails of the base distribution are
appropriately calibrated. To overcome this deficiency, we propose a systematic
approach for analyzing the tails of random variables, and we illustrate how
this approach can be used during the static analysis (before drawing samples)
pass of a probabilistic programming language compiler. To characterize how the
tails change under various operations, we develop an algebra which acts on a
three-parameter family of tail asymptotics and which is based on the
generalized Gamma distribution. Our algebraic operations are closed under
addition and multiplication; they are capable of distinguishing sub-Gaussians
with differing scales; and they handle ratios sufficiently well to reproduce
the tails of most important statistical distributions directly from their
definitions. Our empirical results confirm that inference algorithms that
leverage our heavy-tailed algebra attain superior performance across a number
of density modeling and variational inference tasks.

该研究提出了一种系统性的方法来分析随机变量的尾部，建立了一个基于广义 Gamma 分布的代数，该代数能够在各种操作下区分不同尺度的亚高斯函数，可以直接从定义中重现大部分重要的统计分布，并通过利用重尾代数的推理算法，实现了在多个密度建模及变分推理任务上实现了卓越的性能。

概率编程的重尾代数

A Heavy-Tailed Algebra for Probabilistic Programming

Neutrosophic set has the ability to handle uncertain, incomplete,
inconsistent, indeterminate information in a more accurate way. In this paper,
we proposed a neutrosophic recommender system to predict the diseases based on
neutrosophic set which includes single-criterion neutrosophic recommender
system (SC-NRS) and multi-criterion neutrosophic recommender system (MC-NRS).
Further, we investigated some algebraic operations of neutrosophic recommender
system such as union, complement, intersection, probabilistic sum, bold sum,
bold intersection, bounded difference, symmetric difference, convex linear sum
of min and max operators, Cartesian product, associativity, commutativity and
distributive. Based on these operations, we studied the algebraic structures
such as lattices, Kleen algebra, de Morgan algebra, Brouwerian algebra, BCK
algebra, Stone algebra and MV algebra. In addition, we introduced several types
of similarity measures based on these algebraic operations and studied some of
their theoretic properties. Moreover, we accomplished a prediction formula
using the proposed algebraic similarity measure. We also proposed a new
algorithm for medical diagnosis based on neutrosophic recommender system.
Finally to check the validity of the proposed methodology, we made experiments
on the datasets Heart, RHC, Breast cancer, Diabetes and DMD. At the end, we
presented the MSE and computational time by comparing the proposed algorithm
with the relevant ones such as ICSM, DSM, CARE, CFMD, as well as other variants
namely Variant 67, Variant 69, and Varian 71 both in tabular and graphical form
to analyze the efficiency and accuracy. Finally we analyzed the strength of all
8 algorithms by ANOVA statistical tool.

本文介绍了一种基于中性三段数学的推荐系统，探讨了该系统的代数运算、相似度测量和医学诊断等方面，并与其他相关算法进行了比较和分析。