What is the purpose of including negative samples in a training set? I am new to machine learning and advanced statistics (anything beyond first-year college statistics), and I have been exploring the effectiveness of various classifiers on modeling different hand gestures based on some IMU data I've gathered.
I have been told by multiple colleagues that I should train my model on 'positive' and 'negative' data sets in order to generate a more accurate model for my data set, but this seems a little counter-intuitive to me.
Q: How does including random noise in a training set improve the accuracy of a model? 
It seems to me that random noise would be counter-productive by introducing bias to the estimator, but on the other hand I have a feeling that this has something do to with reducing the chance of overfitting a model on a set of data.
 A: Adding random noise to a training set doesn't make a model more accurate; it makes it less accurate (albeit by adding variance, not bias, assuming the noise is unbiased, as is usually assumed).
What people mean when they say that you need negative examples in your training data is that when you have a binary classifier (e.g., a model that guesses a student's gender given an essay they wrote), you should include examples from both classes (e.g., male and female). Without examples from both classes, the model has no way of telling how the features differ between classes (e.g., what properties of an essay make it more or less likely to be written by a male student).
A: I think you're conflating known negatives with random noise.  The advice to include negatives lets you assess the specificity of the model (assuming you're creating a binary classifier, which I infer you mean by using "positive" and "negative" terms).
Think of it like this.  A good model can find true positives when they are really present; this is sensitivity or the true positive rate.  A good model can also reject true negatives when they are really not present; this is specificity or the true negative rate.  To accurately train your model, you'd need to include both.
