From my own trial-and-error experience, it seems that DirectX pixel shaders only run for pixels/fragments that are within the bounds of some geometric primitive rendered by DirectX, and are not run for pixels of the frame that are simply the clear-color.
Pixel shaders work in concert with vertex shaders; the output of a vertex shader provides the inputs for a pixel shader.
This stands in contrast to WPF pixel shaders, which are run for every pixel of the frame, because WPF doesn't render 3D primitives and therefore doesn't know or care what it means to be a geometric primitive pixel or clear-color pixel.
So for the following image, a DirectX pixel shader would only be run for the area in white, because it corresponds to a geometric primitive output by the vertex shader, but not for the black area, because that's the clear-color. A WPF pixel shader, on the other hand, would be run for every pixel of the frame, both white and black.
Is this understanding correct?