Fast Generating A Large Number of Gumbel-Max Variables

2 Feb 2020Yiyan QiPinghui WangYuanming ZhangJunzhou ZhaoGuangjian TianXiaohong Guan

The well-known Gumbel-Max Trick for sampling elements from a categorical distribution (or more generally a nonnegative vector) and its variants have been widely used in areas such as machine learning and information retrieval. To sample a random element $i$ (or a Gumbel-Max variable $i$) in proportion to its positive weight $v_i$, the Gumbel-Max Trick first computes a Gumbel random variable $g_i$ for each positive weight element $i$, and then samples the element $i$ with the largest value of $g_i+\ln v_i$... (read more)

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