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Sparse/Robust Estimation and Kalman Smoothing with Nonsmooth Log-Concave Densities: Modeling, Computation, and Theory

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Figure

Figure 1: Scalar ℓ2 (top left), ℓ1 (top right), Huber (middle left), Vapnik (middle right), elastic net(bottom left) and smooth insensitive loss (bottom right) penalties
Table 1: For each problem, we list iterations for IP, outer ADMM, cap for inner ADMM itera-tions (if applicable), total time for both algorithms and objective difference f(xADMM) -f(xIP)
Figure 2: Simulation: measurements (·) with outliers plotted on axis limits (4 and −2), true function(continuous line), smoothed estimate using either the quadratic loss (dashed line, leftpanel) or the Vapnik’s ε-insensitive loss (dashed line, right panel)
Figure 3: Estimation of the smoothing filter parameters using the Vapnik loss. Average predictionerror on the validation data set as a function of the variance process λ2 and ε.
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