- Guess value
A guess value is more commonly called a starting value or initial value. These are necessary for most nonlinear regression search
algorithms , because those algorithms are mainly deterministic anditerative , and they need to start somewhere. The quality of the initial values can have a considerable impact on the success or lack of such of the search algorithm. This is because thefitness function (in this case theSSE ) has a (conjectured ) unique shape about theglobal minimum , similar to the shape that objective functions inOperations Research problems often have. To one "side" the SSE simply increases exponentially. To the other "side" the SSE increases parabolically and thenasymptotes to the plateau of thesum of squares of the observations. Starting values that fall in the exponential region can lead to algorithm failure because ofoverflow . Starting values that fall in the asymptotic plateau region can lead to algorithm failure because of "dithering ". Deterministic NLR algorithms use a slope function to go to a minimum. If the slope is very small, then underflow errors can cause the algorithm to wander, seemingly aimlessly; this is dithering.Guess values can be determined a number of ways. Guessing is one of them. If one is familiar with the type of problem, then this is an educated guess or
guesstimate . Other techniques includelinearization , solvingsimultaneous equations , reducingdimensions , treating the problem as atime series , converting the problem to a (hopefully)linear differential equation , and usingmean values.Other methods for determining starting values and optimal values in their own right come from
stochastic methods, the most commonly known of these beingevolutionary algorithms and particularlygenetic algorithms . There is also stochastic funneling where interesting work is currently being done.
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