Random partition models are widely used in Bayesian methods for various
clustering tasks, such as mixture models, topic models, and community detection
problems. While the number of clusters induced by random partition models has
been studied extensively, another important model property regarding the
balancedness of partition has been largely neglected. We formulate a framework
to define and theoretically study the balancedness of exchangeable random
partition models, by analyzing how a model assigns probabilities to partitions
with different levels of balancedness. We demonstrate that the
"rich-get-richer" characteristic of many existing popular random partition
models is an inevitable consequence of two common assumptions: product-form
exchangeability and projectivity. We propose a principled way to compare the
balancedness of random partition models, which gives a better understanding of
what model works better and what doesn't for different applications. We also
introduce the "rich-get-poorer" random partition models and illustrate their
application to entity resolution tasks.

本研究设计了一种框架来定义和理论分析可交换随机分区模型的平衡性，提出了比较随机分区模型平衡性的方法，并且将其应用于实体解析任务。

为何富者愈富？随机分区模型的平衡性探究

Why the Rich Get Richer? On the Balancedness of Random Partition Models

Distance metric learning (DML), which learns a distance metric from labeled
"similar" and "dissimilar" data pairs, is widely utilized. Recently, several
works investigate orthogonality-promoting regularization (OPR), which
encourages the projection vectors in DML to be close to being orthogonal, to
achieve three effects: (1) high balancedness -- achieving comparable
performance on both frequent and infrequent classes; (2) high compactness --
using a small number of projection vectors to achieve a "good" metric; (3) good
generalizability -- alleviating overfitting to training data. While showing
promising results, these approaches suffer three problems. First, they involve
solving non-convex optimization problems where achieving the global optimal is
NP-hard. Second, it lacks a theoretical understanding why OPR can lead to
balancedness. Third, the current generalization error analysis of OPR is not
directly on the regularizer. In this paper, we address these three issues by
(1) seeking convex relaxations of the original nonconvex problems so that the
global optimal is guaranteed to be achievable; (2) providing a formal analysis
on OPR's capability of promoting balancedness; (3) providing a theoretical
analysis that directly reveals the relationship between OPR and generalization
performance. Experiments on various datasets demonstrate that our convex
methods are more effective in promoting balancedness, compactness, and
generalization, and are computationally more efficient, compared with the
nonconvex methods.

本文通过采用凸放松方法解决原始问题中的非凸问题，提供关于促进平衡性的 OPR 能力的正式分析，以及直接揭示 OPR 与泛化性能之间关系的理论分析，解决了 DML 中的三个问题。

促进正交性的距离度量学习：凸松弛和理论分析

Orthogonality-Promoting Distance Metric Learning: Convex Relaxation and  Theoretical Analysis

This paper presents a design of a non-player character (AI) for promoting
balancedness in use of body segments when engaging in full-body motion gaming.
In our experiment, we settle a battle between the proposed AI and a player by
using FightingICE, a fighting game platform for AI development. A middleware
called UKI is used to allow the player to control the game by using body motion
instead of the keyboard and mouse. During gameplay, the proposed AI analyze
health states of the player; it determines its next action by predicting how
each candidate action, recommended by a Monte-Carlo tree search algorithm, will
induce the player to move, and how the player's health tends to be affected.
Our result demonstrates successful improvement in balancedness in use of body
segments on 4 out of 5 subjects.

本文提出了一种非玩家角色（AI）设计，用于促进全身运动游戏中身体各部分平衡性的使用。在使用 FightingICE 平台进行 AI 开发的战斗中，通过使用名为 UKI 的中间件，允许玩家使用身体动作而非键盘和鼠标来控制游戏。在游戏过程中，通过预测每个候选行动如何引起玩家移动以及玩家的生命状态如何受到影响，建议的 Monte-Carlo 树搜索算法确定下一步行动。结果表明，在 4 名受试者中成功提高了身体各段的平衡性。