3 research outputs found
On the total variation regularized estimator over a class of tree graphs
We generalize to tree graphs obtained by connecting path graphs an oracle
result obtained for the Fused Lasso over the path graph. Moreover we show that
it is possible to substitute in the oracle inequality the minimum of the
distances between jumps by their harmonic mean. In doing so we prove a lower
bound on the compatibility constant for the total variation penalty. Our
analysis leverages insights obtained for the path graph with one branch to
understand the case of more general tree graphs.
As a side result, we get insights into the irrepresentable condition for such
tree graphs.Comment: 42 page
Consistent Change Point Detection for Piecewise Constant Signals With Normalized Fused LASSO
We consider the problem of offline change point detection from noisy piecewise constant signals. We propose normalized fused LASSO (FL), an extension of the FL, obtained by normalizing the columns of the sensing matrix of the LASSO equivalent. We analyze the performance of the proposed method, and in particular, we show that it is consistent in detecting change points as the noise variance tends to zero. Numerical experiments support our theoretical findings.QC 20170614</p
Consistent Change Point Detection for Piecewise Constant Signals With Normalized Fused LASSO
We consider the problem of offline change point detection from noisy piecewise constant signals. We propose normalized fused LASSO (FL), an extension of the FL, obtained by normalizing the columns of the sensing matrix of the LASSO equivalent. We analyze the performance of the proposed method, and in particular, we show that it is consistent in detecting change points as the noise variance tends to zero. Numerical experiments support our theoretical findings.QC 20170614</p