1. A feature point location estimation device comprising: an image input unit which receives input of a facial image from an external source; a parameter gradient direction computation unit, implemented by a processor, which computes, from a plurality of facial image templates constituted by positive examples and negative examples and a facial feature point location search parameter, a gradient direction of the facial feature point location search parameter; a search parameter update unit, implemented by the processor, which updates the facial feature point location search parameter by adding the computed gradient direction to the facial feature point location search parameter; a convergence determination unit, implemented by the processor, which determines whether the updated facial feature point location search parameter is convergent; and a search result output unit, implemented by the processor, which, when the updated facial feature point location search parameter is determined as being convergent, outputs a facial feature point location computed by the facial feature point location search parameter as a search result, wherein the parameter gradient direction computation unit obtains a nearest neighbor template from among positive examples and a nearest neighbor template from among negative examples, said nearest neighbor templates being the templates nearest to an image that is computed from the inputted facial image using the facial feature point location search parameter from among the facial image templates constituted by the positive examples and the negative examples, and computes a gradient direction of the facial feature point location search parameter on a basis of the facial feature point location search parameter and the nearest neighbor templates.