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In this paper we introduce and study fused lasso nearly-isotonic signalapproximation, which is a combination of fused lasso and generalizednearly-isotonic regression. We show how these three estimators relate to eachother, derive solution to the general problem, show that it is computationallyfeasible and provides a trade-off between piecewise monotonicity, sparsity andgoodness-of-fit. Also, we derive an unbiased estimator of the degrees offreedom of the approximator.

Fused Lasso Nearly Isotonic Signal Approximation in General Dimensions