AI 中文总结
研究双组分对数凹混合模型，探讨给定样本时各组分分布参数的精确恢复程度，识别出混合分布的两种情况，提出用二次分类器分离组分分布的方法。
AI 中文摘要
对于双组分对数凹混合模型，我们研究在给定混合分布的足够样本时，各组分分布的权重、均值和协方差能被精确恢复的程度。一个基本障碍是混合分布自身有时可能是对数凹的，此时精确恢复不可能。本文识别出两种情况，一种是混合分布自身可能是对数凹的，另一种是混合分布从不对数凹，且能用二次分类器分离两个组分分布。
英文摘要
For a two-component log-concave mixture model, we investigate the extent to which the weight, mean, and covariance of each component distribution can be accurately recovered when given sufficient samples of the mixture distributions. One fundamental obstruction is that the mixture distribution itself could sometimes be log-concave, and in this case, accurate recovery is impossible. In this paper, we identify two regimes, one where the mixture distribution itself could be log-concave and another one where the mixture distribution is never log-concave, and one can always separate the two component distributions using a quadratic classifier.
