Systems methods and recordable media for predicting multi-variable outcomes based on multi-variable inputs. Additionally, the models described can be used to predict the multi-variable inputs themselves, based on the multi-variable inputs, providing a smoothing function, acting as a noise filter. Both multi-variable inputs and multi-variable outputs may be simultaneously predicted, based upon the multi-variable inputs. The models find a critical subset of data points, or "tent poles" to optimally model all outcome variables simultaneously to leverage communalities among outcomes.

 
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> Optical properties restoration apparatus, the restoration method, and an optical system used in the apparatus

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