5) Suppose we are given a list of floating-point values 1.2,...,n. The following quantity, known as...

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5) Suppose we are given a list of floating-point values 1.2,...,n. The following quantity, known as their "log-sum-exp", appears in many machine learning problems: I(.....) In ( k=1 1. The value p = e often represents a probability P E (0, 1]. In this case, what is the range of possible 's? 2. Suppose many of the r's are very negative (r< 0). Explain why evaluating the log-sum-exp formula as written above may cause numerical error in this case. 3. Show that for any a ER, 11 1(x1.....In)= To avoid the issues you explained in question 2, suggest a value a that may improve computing 1(1,....). = a + In 5) Suppose we are given a list of floating-point values 1.2,...,n. The following quantity, known as their "log-sum-exp", appears in many machine learning problems: I(.....) In ( k=1 1. The value p = e often represents a probability P E (0, 1]. In this case, what is the range of possible 's? 2. Suppose many of the r's are very negative (r< 0). Explain why evaluating the log-sum-exp formula as written above may cause numerical error in this case. 3. Show that for any a ER, 11 1(x1.....In)= To avoid the issues you explained in question 2, suggest a value a that may improve computing 1(1,....). = a + In

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1 The range of possible values for p is 0 1 This is because p is a probability and probabilities must be between 0 and 1 2 The logsumexp functionalso ... View the full answer