One of best papers during NeurIPS 2019 - Distribution-Independent PAC Learning of Halfspaces with Massart Noise mentions Massart Noise in the title. What is this type of noise? How is it different from other known types of noise? I am looking for a relatively simple explanation as it is difficult to dive in the definition of the paper.
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$\begingroup$ Isn't your question answered by Definition 1.1 of the paper? $\endgroup$– g gCommented Feb 7, 2020 at 15:36
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$\begingroup$ It may well be but this definition is difficult to grasp for a person new to the field. Besides, the definitions in papers are written to impress not to explain. $\endgroup$– sophrosCommented Feb 7, 2020 at 15:43
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$\begingroup$ Well then how about the next sentence after Definition 1.1? Quote: "An equivalent formulation of the Massart model is the following: With probability 1−η , we have that y = f(x) , and with probability η the label y is controlled by an adversary". Sounds impressive yet reasonable doesn't it? $\endgroup$– g gCommented Feb 7, 2020 at 15:46
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It's actually explained in the text. Basically, it's any type of noise satisfying the condition that, when applied, there is still at least a margin of the size $\beta$ separating the class probabilities.
For example, $\beta=0.5$ in a binary setting means the least confident classification in the Massart-noisy data is [75% A, 25% B] or [25% A, 75% B], and some label probabilities may go as high as, say, [90% A, 10% B] or even [100% A, 0% B] or vice versa.
Another way of looking at it is in terms of the noise probabilistically flipping the labels to incorrect values; then a Massart noise is such a function that does it with no more than $\frac{1-\beta}{2}$ probability.
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$\begingroup$ Particularly the 2nd explanation is very easy to grasp. Thank you! $\endgroup$– sophrosCommented Feb 7, 2020 at 16:00