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"),Object(m.b)("b",null," Hypothesis:"),"Fitting different machine learning algorithms or models on the data to map inputs to outputs can be thought of as testing several hypotheses about the relationships in data. For example, based on the width and length of petals, we can predict the categories of iris flowers. More on Hypothesis in Machine Learning.",Object(m.b)("p",null,"Bayes Theorem provides a probabilistic framework to describe the relationship between data and a hypothesis.  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The equation illustrates the following process: the product of a penalty (or sometimes reward) value and the joint probability of ",Object(m.b)("span",Object(s.a)({parentName:"p"},{className:"math 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The two summations to the left of the integration, therefore, are just the summing up of the products of penalty/reward value and probability of true-classified-states combinations, across all true-classified state combinations."),Object(m.b)("p",null,Object(m.b)("img",Object(s.a)({parentName:"p"},{src:"https://i.imgur.com/zaEgJ2A.jpg",alt:null}))),Object(m.b)("p",null,"The matrix above shows the penalties for (mis-)detecting cancer. The expected loss in this case will be ",Object(m.b)("b",null,"0","*","p(detect cancer & true cancer) + 1000","*","p(detecting normal & true cancer) + 1","*","p(detecting cancer & true normal) + 0","*","p(detecting normal and true normal)"),". 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