Model Evaluation and Selection(Part-3)

 Hypothesis Testing


Given a hypothesis, test if it is true with a particular confidence 
• Hypotheses: errorD (h1) > errorD (h2) 
• What % of the probability mass is associated with errorD (h1) - errorD (h2) > 0 
• Example 
• Let the error rates measured for the two hypotheses h1 and h2 on a sample of size 100 be 0.3 and 0.2 respectively 
• The standard deviation for the normal distribution defined on d’ = errorS1 (h1 )- errorS2 (h2 ) is • 1.640.061 = 0.1 
• 1.64 standard deviation corresponds to the 90% confidence interval and hence the % mass of the probability distribution > 0 is 95% 
• Result: Accept the hypothesis with 95% confidence that h2 is a more accurate hypothesis than h1 on D (the underlying population)

Comparing Two Algorithms

Given two learning algorithms, L1 and L2 , which one is better, on average, at learning a particular target function 
• Estimating the relative performance 
• Calculate the Expected Value of the difference in errors 
• For all samples of size n, consider the relative performance of L1 and L2 
• Estimate the error over all training samples S of D ESD [errorD (L1 (S))- errorD (L2 (S))] 
• where L1 (S) and L2 (S) are the hypotheses generated by the learning algorithms from the sample S 
• Can be estimated by 
• Holding back part of the training data for testing 
• Using multiple samples of the training data D 
• Cross-validation 
• Bootstrapping

Cross-validation:
Cross-validation is a resampling procedure used to evaluate machine learning models on a limited data sample. The procedure has a single parameter called k that refers to the number of groups that a given data sample is to be split into. As such, the procedure is often called k-fold cross-validation.

Bootstraping
Sample, with replacement, the training data (of size N) and use the sample (of size N) to learn the model 
• The same instance in the training data can appear multiple times in the data used for learning the model 
• An instance within the training data may not appear at all in the data used for learning 
• Use remaining data as test data 
• Repeat multiple times to obtain an error estimate and a confidence interval.

Confusion Matrix 



• Contingency table containing information regarding the actual and predicted value of the class labels 

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