论文标题
对图的协作似然比估计
Collaborative likelihood-ratio estimation over graphs
论文作者
论文摘要
假设我们从两个未知的概率密度函数（PDF），$ p $和$ q $的IID观察结果中，则可能仅通过依靠可用数据来比较两个PDF。 In this paper, we introduce the first -to the best of our knowledge-graph-based extension of this problem, which reads as follows: Suppose each node $v$ of a fixed graph has access to observations coming from two unknown node-specific pdfs, $p_v$ and $q_v$, and the goal is to estimate for each node the likelihood-ratio between both pdfs by also taking into account the information provided by the graph structure.节点级估计任务应该表现出图表传达的相似性，这表明节点可以协作以更有效地解决它们。我们以一种具体的非参数方法来开发这个想法，我们称基于图的相对不受限制最小二乘的重要性拟合（Grulsif）。我们为协作方法得出收敛率，该方法突出了变量所起的作用，例如每个节点的可用观测值，图的大小以及图表结构编码任务之间的相似性的准确性。这些理论上的结果阐明了与独立解决每个问题相比，协作估计有效地导致绩效改善的情况。最后，在一系列实验中，我们说明了GrulsIF如何与图形的节点相比，与最先进的LRE方法相比，该方法在图的节点上更准确，该方法将在每个节点下独立运行，并且我们还验证了Grulsif的行为是否与我们先前的理论分析相一致。
Assuming we have iid observations from two unknown probability density functions (pdfs), $p$ and $q$, the likelihood-ratio estimation (LRE) is an elegant approach to compare the two pdfs only by relying on the available data. In this paper, we introduce the first -to the best of our knowledge-graph-based extension of this problem, which reads as follows: Suppose each node $v$ of a fixed graph has access to observations coming from two unknown node-specific pdfs, $p_v$ and $q_v$, and the goal is to estimate for each node the likelihood-ratio between both pdfs by also taking into account the information provided by the graph structure. The node-level estimation tasks are supposed to exhibit similarities conveyed by the graph, which suggests that the nodes could collaborate to solve them more efficiently. We develop this idea in a concrete non-parametric method that we call Graph-based Relative Unconstrained Least-squares Importance Fitting (GRULSIF). We derive convergence rates for our collaborative approach that highlights the role played by variables such as the number of available observations per node, the size of the graph, and how accurately the graph structure encodes the similarity between tasks. These theoretical results explicit the situations where collaborative estimation effectively leads to an improvement in performance compared to solving each problem independently. Finally, in a series of experiments, we illustrate how GRULSIF infers the likelihood-ratios at the nodes of the graph more accurately compared to state-of-the art LRE methods, which would operate independently at each node, and we also verify that the behavior of GRULSIF is aligned with our previous theoretical analysis.
