  A communication network can be modeled as a directed connected graph with
edge weights that characterize performance metrics such as loss and delay.
Network tomography aims to infer these edge weights from their pathwise
versions measured on a set of intersecting paths between a subset of boundary
vertices, and even the underlying graph when this is not known. Recent work has
established conditions under which the underlying directed graph can be
recovered exactly the pairwise Path Correlation Data, namely, the set of
weights of intersection of each pair of directed paths to and from each
endpoint. Algorithmically, this enables us to consistently fused tree-based
view of the set of network paths to and from each endpoint to reconstruct the
underlying network.
  However, in practice the PCD is not consistently determined by path
measurements. Statistical fluctuations give rise to inconsistent inferred
weight of edges from measurement based on different endpoints, as do
operational constraints on synchronization, and deviations from the underlying
packet transmission model. Furthermore, ad hoc solutions to eliminate noise,
such as pruning small weight inferred links, are hard to apply in a consistent
manner that preserves known end-to-end metric values.
  This paper takes a unified approach to the problem of inconsistent weight
estimation. We formulate two type of inconsistency: \textsl{intrinsic}, when
the weight set is internally inconsistent, and \textsl{extrinsic}, when they
are inconsistent with a set of known end-to-end path metrics. In both cases we
map inconsistent weight to consistent PCD within a least-squares framework. We
evaluate the performance of this mapping in composition with tree-based
inference algorithms.
