CUDA is proprietary software from NVidia that specifically works with their hardware only. It is not possible (at the moment) to use CUDA with GPUs from other manufacturers (such as Intel).
An alternatives for other GPUs is OpenCL, but this is not nearly as mature as NVidia’s CUDA. OpenCL lags behind in both performance and functionality. As far as I know pretty much everyone who’s serious about using a GPU for machine learning purposes uses NVidia / CUDA at the moment, but developments of OpenCL are moving forward too.
In short, if you have an NVidia GPU, CUDA is the way to go. If not, there is no point in installing it.