(Solved): 3. Suppose that you are tasked with creating an algorithm that, given an image of a handwritten si ...

3. Suppose that you are tasked with creating an algorithm that, given an image of a handwritten signature of a specific person, decides whether the signature is authentic or whether it was forged by a criminal. Assume that you know that authenticity can be completely determined by the ratio of signature's height and width, measured anywhere from \( 0.4 \) to \( 0.8 \) with an increment of \( 0.01 \) (namely, the ratio for the authentic signatures is either always higher or always lower compared to the forged ones). You have 50 signatures that were randomly taken from various documents that were supposedly signed by this person, and analysed by an expert who was able to tell originals from the forged ones. Answer the following questions: (a) What are the instances/observations and the labels in this case? What is the domain set that the instances belong to? (b) What is the training data in this specific problem, and what is the sample size? (c) What is the hypothesis class that you are going to use, and what is its size/cardinality? Be as specific as possible; your answer should be consistent with your answer to question (a). (d) Is this an example of realisable or agnostic learning? Justify your answer. (e) Assume that you want to find a classifier that makes a mistake in at most \( 5 \% \) of the cases. Estimate the probability that the Empirical Risk Minimization algorithm will produce a classifier of such quality.