4,220 research outputs found
Minority Challenge of Majority Actions in a Close Corporation in Italy and the United States
This paper addresses the problem of segmenting a time-series with respect to changes in the mean value or in the variance. The first case is when the time data is modeled as a sequence of independent and normal distributed random variables with unknown, possibly changing, mean value but fixed variance. The main assumption is that the mean value is piecewise constant in time, and the task is to estimate the change times and the mean values within the segments. The second case is when the mean value is constant, but the variance can change. The assumption is that the variance is piecewise constant in time, and we want to estimate change times and the variance values within the segments. To find solutions to these problems, we will study an l_1 regularized maximum likelihood method, related to the fused lasso method and l_1 trend filtering, where the parameters to be estimated are free to vary at each sample. To penalize variations in the estimated parameters, the -norm of the time difference of the parameters is used as a regularization term. This idea is closely related to total variation denoising. The main contribution is that a convex formulation of this variance estimation problem, where the parametrization is based on the inverse of the variance, can be formulated as a certain mean estimation problem. This implies that results and methods for mean estimation can be applied to the challenging problem of variance segmentation/estimationQC 20140908</p
A Class of Nonconvex Penalties Preserving Overall Convexity in Optimization-Based Mean Filtering
mean filtering is a conventional, optimization-based method to
estimate the positions of jumps in a piecewise constant signal perturbed by
additive noise. In this method, the norm penalizes sparsity of the
first-order derivative of the signal. Theoretical results, however, show that
in some situations, which can occur frequently in practice, even when the jump
amplitudes tend to , the conventional method identifies false change
points. This issue is referred to as stair-casing problem and restricts
practical importance of mean filtering. In this paper, sparsity is
penalized more tightly than the norm by exploiting a certain class of
nonconvex functions, while the strict convexity of the consequent optimization
problem is preserved. This results in a higher performance in detecting change
points. To theoretically justify the performance improvements over
mean filtering, deterministic and stochastic sufficient conditions for exact
change point recovery are derived. In particular, theoretical results show that
in the stair-casing problem, our approach might be able to exclude the false
change points, while mean filtering may fail. A number of numerical
simulations assist to show superiority of our method over mean
filtering and another state-of-the-art algorithm that promotes sparsity tighter
than the norm. Specifically, it is shown that our approach can
consistently detect change points when the jump amplitudes become sufficiently
large, while the two other competitors cannot.Comment: Submitted to IEEE Transactions on Signal Processin
Reweighted nuclear norm regularization: A SPARSEVA approach
The aim of this paper is to develop a method to estimate high order FIR and
ARX models using least squares with re-weighted nuclear norm regularization.
Typically, the choice of the tuning parameter in the reweighting scheme is
computationally expensive, hence we propose the use of the SPARSEVA (SPARSe
Estimation based on a VAlidation criterion) framework to overcome this problem.
Furthermore, we suggest the use of the prediction error criterion (PEC) to
select the tuning parameter in the SPARSEVA algorithm. Numerical examples
demonstrate the veracity of this method which has close ties with the
traditional technique of cross validation, but using much less computations.Comment: This paper is accepted and will be published in The Proceedings of
the 17th IFAC Symposium on System Identification (SYSID 2015), Beijing,
China, 201
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