You need several things. First an indexed unit sphere geometry, second a buffer to store the sphere instance properties ( position, radius and color ) and third a small buffer for the API parameters yet to come. The three combines in a single 'ID3D11DeviceContext::DrawIndexedInstancedIndirect'
The remaining question is "how to feed the instance buffer ?". cpu is easy, just apply frustum culling, sort back to front because of the transparency and apply a merge based on the screen projection, update the buffer and use 'ID3D11DeviceContext::DrawIndexedInstanced'.
gpu version will do the same thing with compute shaders but will be harder to implement. The advantage, zero cpu/gpu synchronization and should support far more instance.