An Interpolating Family of Size Distributions

Csiszár指数与插值 copulas

Csiszár indices and interpolating copulas

研究f-散度和Csiszár指数的性质，探讨其与随机向量copula表示的关系，构建最小化Csiszár指数的插值copulas以保持依赖结构。

在切比雪夫和坎特利之间

Between Chebyshev and Cantelli

给出了Chebyshev插值和Cantelli插值之间的一族精确上界.

From Pareto to Weibull -- a constructive review of distributions on $\mathbb{R}^+$

Power laws and power laws with exponential cut-off are two distinct families of distributions on the positive real half-line. In the present paper, we propose a unified treatment of both families by building a family of distributions that interpolates between them, which we call Interpolating Family (IF) of distributions. Our original construction, which relies on techniques from statistical physics, provides a connection for hitherto unrelated distributions like the Pareto and Weibull distributions, and sheds new light on them. The IF also contains several distributions that are neither of po…

Interpolating between sampling and variational inference with infinite stochastic mixtures

Sampling and Variational Inference (VI) are two large families of methods for approximate inference that have complementary strengths. Sampling methods excel at approximating arbitrary probability distributions, but can be inefficient. VI methods are efficient, but may misrepresent the true distribution. Here, we develop a general framework where approximations are stochastic mixtures of simple component distributions. Both sampling and VI can be seen as special cases: in sampling, each mixture component is a delta-function and is chosen stochastically, while in standard VI a single component …