I want to know of an online tool or formula to give a vague idea about minimum number of enrolees for a study involving use of machine or deep learning.
Depending on your task,data set,classification method, different rate of convergence is expected for different tasks of machine learning.Besides Andrew Ng covered this topic as below:
if a learning algorithm is suffering from high variance, getting more training data is likely to help.
if a learning algorithm is suffering from high bias , getting more training data will not(by itself) help much.
More over,as far as I am concerned, number of inputs (i.e. samples) must be at least the square size of the number of features (i.e. n_samples > n_features ** 2 )
As a conclusion, the greater the sample size,the better the predictions would be.you should bear this in mind that a great sample size leads training last for hours in Deep Learning tasks.
Related to your query, I suggest you to use Bayesian parametric or non parametric statistical modelling frame works. It is also called probabilistic modelling or statistical modelling frameworks. Also MCMC modelling frameworks or mixture models based on variation or Bayesian inferences etc., are based data sampling.
A good book for such data analysis is attached bellow.