Given a collection of probability distributions $p_{1},\ldots,p_{m}$, the minimum entropy coupling is the coupling $X_{1},\ldots,X_{m}$ ($X_{i}\sim p_{i}$) with the smallest entropy $H(X_{1},\ldots,X_{m})$. While this problem is known to be NP-hard, we present an efficient algorithm for computing a coupling with entropy within 2 bits from the optimal value. More precisely, we construct a coupling with entropy within 2 bits from the entropy of the greatest lower bound of $p_{1},\ldots,p_{m}$ with respect to majorization. This construction is also valid when the collection of distributions is infinite, and when the supports of the distributions are infinite. Potential applications of our results include random number generation, entropic causal inference, and functional representation of random variables.
翻译：根据概率分布 $p ⁇ 1},\ldots,p ⁇ m}$1},最小的酶联结是 $X ⁇ 1},\ldots,X ⁇ m}$(X ⁇ i ⁇ sim p ⁇ i}$) 与最小的酶联产(H) (X ⁇ 1},\ldots,X ⁇ m}$)。虽然这个问题已知是NP硬的,但我们提出了一个高效的算法,用于计算从最佳值中2位内与酶联产。更确切地说,我们从最大较低约束 $p ⁇ 1},\ldots,p ⁇ m}的酶联产中,2位内,与酶联产的联产。当分布的收集是无限,当分布的支撑是无限时,这种构造也是有效的。我们结果的潜在应用包括随机数字生成、诱因果和随机变量的功能表示。
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