The author provides sample code using numpy and explicit gradient calculation. However, PyTorch provides autograd mechanism and we can considerably simplify author's code and make it more readable.
Main changes:
- Separate the SVGD class into methods, so that we can call iteration outside the svgd process, which is more reasonable
- Support all PyTorch optimizers, rather than only adagrad in author's code. Currently we are using Adam optimizer
- Follow traditional PyTorch training pipeline, make it easier to understand.
- Implement 1-D Gaussian Mixture example, which is not provided by the author.
- Since we are using PyTorch, it is easy to use gpu, just change device to cuda.
- Make use of torch.distributions, in which log_prob() is offered, make code more readable.
Questions remained:
- Currently, I'm not sure if the gradient in bayesian inference examples are calculated correctly. Specifically, for log(alpha) term, currently the gradient may be w.r.t alpha rather than log(alpha). However, the author's code here or here is really hard to understand. He does not explain what is "jacobian term", and I cannot figure out where does 1 in gradient come from. So it is hard for me to find correct gradient.
- The author uses {-1,1} for logistic regression, rathan than {1,0}, which is not a normal implementation. In the code, there even appears a term that is "shape". Maybe the author should explain why. I doubt it comes from the irregular logistic regression.
- Numpy Gamma distribution and PyTorch Gamma distribution are slightly different in that one uses (shape, scale),or (k, theta) in wiki, as parameter, and the other uses (shape, 1/scale), or (alpha, beta) in wiki, as parameter. The author uses numpy to implement, but seems to calculate gradient according to (alpha, beta) formula?
Any suggestion to the code, and any answer to the questions is welcomed!