Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Continuous nonnegative functions, such as Poisson rate functions, are sometimes approximated as piecewise-constant functions.  consider the problem of automatically smoothing such functions while maintaining the integral of each piece and maintaining nonnegativity everywhere, without specifying a parametric function.  develop logic for SMOOTH Smoothing via Mean-constrained Optimized-Objective Time Halving, a quadratic-optimization algorithm that yields a smoother nonnegative piecewise-constant rate function having twice as many time intervals, each of half the length. I-SMOOTH Iterated SMOOTH iterates the SMOOTH formulation to create a sequence of piecewise-constant rate functions that, in the limit, yields a nonparametric continuous function.  consider two contexts: finite-horizon and cyclic.  develop a sequence of computational simplifications for SMOOTH, moving from numerically minimizing the quadratic objective function, to numerically computing a matrix inverse, to a closed-form matrix inverse obtained as finite sums, to optimal decision-variable values that are linear combinations of the given rates, and to simple approximations.
['Huifen Chen', 'Bruce W. Schmeiser']
I am writing a research paper on a idea I-SMOOTH: Iteratively Smoothing Mean-Constrained and Nonnegative Piecewise-Constant Functions
[{"from": "human", "value": "I am writing a research paper on a idea I-SMOOTH: Iteratively Smoothing Mean-Constrained and Nonnegative Piecewise-Constant Functions"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Continuous nonnegative functions, such as Poisson rate functions, are sometimes approximated as piecewise-constant functions.  consider the problem of automatically smoothing such functions while maintaining the integral of each piece and maintaining nonnegativity everywhere, without specifying a parametric function.  develop logic for SMOOTH Smoothing via Mean-constrained Optimized-Objective Time Halving, a quadratic-optimization algorithm that yields a smoother nonnegative piecewise-constant rate function having twice as many time intervals, each of half the length. I-SMOOTH Iterated SMOOTH iterates the SMOOTH formulation to create a sequence of piecewise-constant rate functions that, in the limit, yields a nonparametric continuous function.  consider two contexts: finite-horizon and cyclic.  develop a sequence of computational simplifications for SMOOTH, moving from numerically minimizing the quadratic objective function, to numerically computing a matrix inverse, to a closed-form matrix inverse obtained as finite sums, to optimal decision-variable values that are linear combinations of the given rates, and to simple approximations."}]