What machine learning approach requires minimum input data to be significant enough to consider?

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I have to a choose machine learning method (binary logistic, SVM, random forest, discriminant analysis, neural networks) for finding significant predictors of a disease relapse. I have sets of 70 and 48 patients with 5 parameters as input variables and 2 classes: with and without the disease relapse. I have computed using all mentioned methods and binary logistic regression showed the best classification, however, I need to know an expert opinion: what approach is the best for my small data? Thanks.

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There is no definitive answer to your question... it depends upon the nature and statistics of your data. You should read about the bias-variance tradeoff in statistics, or machine learning, or pattern classification, to understand why. For some problems of a given size data sets, one type of classifier will give the best results, for some problems of the same size data sets, a different classifier will give the best results.

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The decease relapse is in sink with ability of the body to get rid of more dangerous condition by setting in smaller evil, so to say. If the disease ,of which person was treated successfully, was playing role of a smaller evil, (for example, think, if this disease was never happening in a first place, what possible worst outcomes could this patient have suffered? Signs should be in blood test, etc.s and other previous, before the disease, symptoms), then you can be sure that it will come back to play the same protective role. However, if there is no relapse, person is on a path to more dangerous condition.