Denoising Flows on Trees

树上去噪流的最小最大速率

The Minimax Rate of Denoising Flows on Trees

本文完整解决了有根树上从高斯噪声恢复流的去噪问题，确定了最小最大风险为 $\min\{V^2H_T,\sigma^2k_0\}$，并提出了达到该速率的确定性指数加权聚合估计器，同时揭示了最小二乘法的次优性。

Moving Up the Cluster Tree with the Gradient Flow

The paper establishes a strong correspondence between two important clustering approaches that emerged in the 1970's: clustering by level sets or cluster tree as proposed by Hartigan and clustering by gradient lines or gradient flow as proposed by Fukunaga and Hostetler. We do so by showing that we can move up the cluster tree by following the gradient ascent flow.

Survey: Information flow on trees

Consider a tree network T, where each edge acts as an independent copy of a given channel M, and information is propagated from the root. For which T and M does the configuration obtained at level n of T typically contain significant information on the root variable? This model appeared independently in biology, information theory, and statistical physics. Its analysis uses techniques from the theory of finite markov chains, statistics, statistical physics, information theory, cryptography and noisy computation. In this paper, we survey developments and challenges related to this problem.