Learning Sums of Independent Random Variables with Sparse Collective Support
Learning Sums of Independent Random Variables with Sparse Collective Support
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DOI：
10.1109/focs.2018.00036
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发表时间：
2018-07
期刊：
影响因子：
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通讯作者：
Anindya De;Philip M. Long;R. Servedio
中科院分区：
文献类型：
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作者：
Anindya De;Philip M. Long;R. Servedio
我们研究了独立整数随机变量的总和，鉴于其对非阴性整数的子集A的结合大小。 sum“本文）是一个分布s = x_1 +… + x_n，其中x_i是相互独立的（但不一定是相同分布的）整数随机变量，所有支持都包含在A中。我们给出了两个学习此类分布的主要算法结果：1）对于情况| a | = 3，我们给出了一种学习a-sums的算法，用于使用poly（1/εilon）样品并在时间上运行poly（1/am am） ，独立于n和A的元素。2）对于任意常数k> = 4，如果a = {a_1，…，a_k} at 00。
We study the learnability of sums of independent integer random variables given a bound on the size of the union of their supports. For a subset A of non-negative integers, a sum of independent random variables with collective support A (called an "A-sum" in this paper) is a distribution S = X_1 + … + X_N where the X_i's are mutually independent (but not necessarily identically distributed) integer random variables all of whose supports are contained in A. We give two main algorithmic results for learning such distributions: 1) For the case |A|=3, we give an algorithm for learning A-sums to accuracy εilon that uses poly(1/εilon) samples and runs in time poly(1/εilon), independent of N and of the elements of A. 2)For an arbitrary constant k>=4, if A = {a_1,…,a_k} with 00.