Author name cluster

Fabrizio Lecci

Possible papers associated with this exact author name in Arrow. This page groups case-insensitive exact name matches and is not a full identity disambiguation profile.

3 papers

2 author rows

JMLR Journal 2018 Journal Article

Robust Topological Inference: Distance To a Measure and Kernel Distance

Frédéric Chazal
Brittany Fasy
Fabrizio Lecci
Bertrand Michel
Alessandro Rinaldo
Larry Wasserman

Let $P$ be a distribution with support $S$. The salient features of $S$ can be quantified with persistent homology, which summarizes topological features of the sublevel sets of the distance function (the distance of any point $x$ to $S$). Given a sample from $P$ we can infer the persistent homology using an empirical version of the distance function. However, the empirical distance function is highly non-robust to noise and outliers. Even one outlier is deadly. The distance-to-a-measure (DTM), introduced by \cite{chazal2011geometric}, and the kernel distance, introduced by \cite{phillips2014goemetric}, are smooth functions that provide useful topological information but are robust to noise and outliers. \cite{massart2014} derived concentration bounds for DTM. Building on these results, we derive limiting distributions and confidence sets, and we propose a method for choosing tuning parameters. [abs] [ pdf ][ bib ] &copy JMLR 2018. ( edit, beta )

PDF Details

ICML Conference 2015 Conference Paper

Subsampling Methods for Persistent Homology

Frédéric Chazal
Brittany Terese Fasy
Fabrizio Lecci
Bertrand Michel
Alessandro Rinaldo
Larry A. Wasserman

Persistent homology is a multiscale method for analyzing the shape of sets and functions from point cloud data arising from an unknown distribution supported on those sets. When the size of the sample is large, direct computation of the persistent homology is prohibitive due to the combinatorial nature of the existing algorithms. We propose to compute the persistent homology of several subsamples of the data and then combine the resulting estimates. We study the risk of two estimators and we prove that the subsampling approach carries stable topological information while achieving a great reduction in computational complexity.

Details

JMLR Journal 2014 Journal Article

Statistical Analysis of Metric Graph Reconstruction

Fabrizio Lecci
Alessandro Rinaldo
Larry Wasserman

A metric graph is a 1-dimensional stratified metric space consisting of vertices and edges or loops glued together. Metric graphs can be naturally used to represent and model data that take the form of noisy filamentary structures, such as street maps, neurons, networks of rivers and galaxies. We consider the statistical problem of reconstructing the topology of a metric graph embedded in $\mathbb{R}^D$ from a random sample. We derive lower and upper bounds on the minimax risk for the noiseless case and tubular noise case. The upper bound is based on the reconstruction algorithm given in Aanjaneya et al. (2012). [abs] [ pdf ][ bib ] &copy JMLR 2014. ( edit, beta )

PDF Details