Related papers: Joint Linear Trend Recovery Using L1 Regularizatio…
Popular regularizers with non-differentiable penalties, such as Lasso, Elastic Net, Generalized Lasso, or SLOPE, reduce the dimension of the parameter space by inducing sparsity or clustering in the estimators' coordinates. In this paper,…
Suppose we wish to recover an n-dimensional real-valued vector x_0 (e.g. a digital signal or image) from incomplete and contaminated observations y = A x_0 + e; A is a n by m matrix with far fewer rows than columns (n << m) and e is an…
Conventional compressed sensing theory assumes signals have sparse representations in a known, finite dictionary. Nevertheless, in many practical applications such as direction-of-arrival (DOA) estimation and line spectral estimation, the…
Inverse problems arise in a wide spectrum of applications in fields ranging from engineering to scientific computation. Connected with the rise of interest in inverse problems is the development and analysis of regularization methods, such…
We study trend filtering, a relatively recent method for univariate nonparametric regression. For a given positive integer $r$, the $r$-th order trend filtering estimator is defined as the minimizer of the sum of squared errors when we…
LSTD is a popular algorithm for value function approximation. Whenever the number of features is larger than the number of samples, it must be paired with some form of regularization. In particular, L1-regularization methods tend to perform…
We introduce a new constrained minimization problem that performs template and pattern detection on a multispectral image in a compressive sensing context. We use an original minimization problem from Guo and Osher that uses $L_1$…
This work considers recovery of signals that are sparse over two bases. For instance, a signal might be sparse in both time and frequency, or a matrix can be low rank and sparse simultaneously. To facilitate recovery, we consider minimizing…
Consider the problem on sequential change-point detection on multiple data streams. We provide the asymptotic lower bounds of the detection delays at all levels of change-point sparsity and we derive a smaller asymptotic lower bound of the…
We present the group fused Lasso for detection of multiple change-points shared by a set of co-occurring one-dimensional signals. Change-points are detected by approximating the original signals with a constraint on the multidimensional…
While many approaches have been proposed for discovering abrupt changes in piecewise constant signals, few methods are available to capture these changes in piecewise polynomial signals. In this paper, we propose a change point detection…
We consider the situation where a temporal process is composed of contiguous segments with differing slopes and replicated noise-corrupted time series measurements are observed. The unknown mean of the data generating process is modelled as…
Source conditions are a key tool in regularisation theory that are needed to derive error estimates and convergence rates for ill-posed inverse problems. In this paper, we provide a recipe to practically compute source condition elements as…
Estimating high-dimensional precision matrices is a fundamental problem in modern statistics, with the graphical lasso and its $\ell_1$-penalty being a standard approach for recovering sparsity patterns. However, many statistical models,…
A change point problem occurs in many statistical applications. If there exist change points in a model, it is harmful to make a statistical analysis without any consideration of the existence of the change points and the results derived…
In the past decades, exactly recovering the intrinsic data structure from corrupted observations, which is known as robust principal component analysis (RPCA), has attracted tremendous interests and found many applications in computer…
Generalized linear model with $L_1$ and $L_2$ regularization is a widely used technique for solving classification, class probability estimation and regression problems. With the numbers of both features and examples growing rapidly in the…
In recent years, change point detection for high dimensional data has become increasingly important in many scientific fields. Most literature develop a variety of separate methods designed for specified models (e.g. mean shift model,…
We study tools for inference conditioned on model selection events that are defined by the generalized lasso regularization path. The generalized lasso estimate is given by the solution of a penalized least squares regression problem, where…
The $\ell_1$-synthesis model and the $\ell_1$-analysis model recover structured signals from their undersampled measurements. The solution of former is a sparse sum of dictionary atoms, and that of the latter makes sparse correlations with…