How does the reparameterization trick work in statistics?
Reparameterization trick is a way to rewrite the expectation so that the distribution with respect to which we take the gradient is independent of parameter θ. To achieve this, we need to make the stochastic element in q independent of θ. Hence, we write x as x = θ + ϵ, ϵ ∼ N (0, 1)
How does the reparameterization of a normal distribution work?
Introducing a new parameter ϵ allows us to reparameterize z in a way that allows backprop to flow through the deterministic nodes. Assume we have a normal distribution q that is parameterized by θ, specifically qθ(x) = N(θ, 1).
Which is a fundamental problem of the reparameterization?
A fundamental problem is that essential contributions to Gθ may come from values of x which are very rare (i.e., x values for which qθ(x) is small). The factor of 1 qθ ( x) is scaling up your estimate to account for this, but that scaling won’t help if you don’t see such a value of x when you estimate Gθ from a finite number of samples.
Can you use the reparameterization trick in machine learning?
We can use the reparameterization trick! However, note that x does not exactly follow Cat(πϕ). There is a tradeoff between having accurate one-hot samples and badly conditioned gradient with high variance (using low temperature), and having smoother samples and smaller gradient variance (with higher temperatures) .
What’s the difference between reinforce and reparameterization trick?
REINFORCE and reparameterization trick are two of the many methods which allow us to calculate gradients of expectation of a function. However both of them make different assumptions about the underlying model and data distributions and thus differ in their usefulness.
What is the reinforce rule in score function estimator?
The REINFORCE algorithm also known as the score function estimator uses a simple differentiation rule called the log-derivative trick which is simply the differentiation rule for the logarithm.