A novel monotonic fixed-point algorithm for l1-regularized least square vector and matrix problem

Least square problem with l₁ regularization has been proposed as a promising method for sparse signal reconstruction (e.g., basis pursuit de-noising and compressed sensing) and feature selection (e.g., the Lasso algorithm) in signal processing, statistics, and related fields. These problems can be cast as l₁-regularized least-square program (LSP). In this paper, we propose a novel monotonic fixed point method to solve large-scale l₁-regularized LSP. And we also prove the stability and convergence of the proposed method. Furthermore we generalize this method to least square matrix problem and apply it in nonnegative matrix factorization (NMF). The method is illustrated on sparse signal reconstruction, partner recognition and blind source separation problems, and the method tends to convergent faster and sparser than other l₁-regularized algorithms.

Reconstruction of in vivo time-evolving neuroendocrine dose - response properties unveils admixed deterministic and stochastic elements

Homeostasis in the intact organism is achieved implicitly by repeated incremental feedback (inhibitory) and feedforward (stimulatory) adjustments enforced via intermittent signal exchange. In separated systems, neurohormone signals act deterministically on target cells via quantifiable effector-response functions. On the other hand, in vivo interglandular signaling dynamics have not been estimable to date. Indeed, experimentally isolating components of an interactive network definitionally disrupts time-sensitive linkages. We implement and validate analytical reconstruction of endogenous effector-response properties via a composite model comprising (i) a deterministic basic feedback and feedforward ensemble structure; (ii) judicious statistical allowance for possible stochastic variability in individual biologically interpretable dose–response properties; and (iii) the sole data requirement of serially observed concentrations of a paired signal (input) and response (output). Application of this analytical strategy to a prototypical neuroendocrine axis in the conscious uninjected horse, sheep, and human (i) illustrates probabilistic estimation of endogenous effector dose–response properties; and (ii) unmasks statistically vivid (2- to 5-fold) random fluctuations in inferred target-gland responsivity within any given pulse train. In conclusion, balanced mathematical formalism allows one to (i) reconstruct deterministic properties of interglandular signaling in the intact mammal and (ii) quantify apparent signal-response variability over short time scales in vivo. The present proof-of-principle experiments introduce a previously undescribed means to estimate time-evolving signal-response relationships without isotope infusion or pathway disruption.