While the other answers aren't wrong, they don't touch anything about bioinformatics. I'll go into details.
In bioinformatic, simply asking for the size of the training set makes no sense. You'll need to understand deeper about bioinformatic to answer this question. There is a good reference: An ensemble approach to accurately detect somatic mutations using SomaticSeq for you.
The goal of the project is to build a gradient-boosting machine for classifying somatic mutation given an alignment file. This is very close to what you're doing.
Now, you want to know the training size? You should ask yourself the following:
- Sequencing errors
- Sequencing depth
- F1 score
- Allele frequency
In an next-generation sequencing, your sequencing machine always give you errors. How reliable is your pipeline to detect those errors?
How good are your reads for your problem? For example, if you're detecting disease related to structural variant, you might need more samples to compsenate for the short reads.
What's your sequencing depth? In the paper I quote, they have like 30x depth. It'd be pointless to talk about the training size unless you know well about your depth.
Does your sequencing cover well your region of the genome you're interested in?
Sensitivity and F1 score. You can have good idea by drawing an F1 curve something like as in the paper:
What's your expected allele frequency range? If you have something like close to 0.5 (ie: maximum heterozygosity), you'll probably be safe with a smaller sample size. However, if you're trying to detect a rare disease, something like <0.1 as in the diagram, you'll need to have more samples and most likely more features.
Empirically, we generally use spike-in standards to measure the sensitivity. Once you draw the sensitivity against training size, you'll know at what training size to use achieve whatever sensitivity you're looking for. A typical tool would be ROC.