Learning Path
Question & Answer1
Understand Question2
Review Options3
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Explore TopicChoose the Best Answer
A
It reduces the range of the logarithmic inputs to prevent overflow.
B
It converts logarithmic values into linear values.
C
It allows for the addition of probabilities in a logarithmic scale without loss of precision.
D
It simplifies complex multiplications into easier summations.
Understanding the Answer
Let's break down why this is correct
Answer
The log‑sum‑exp function turns a sum of exponentials into a single logarithm, so you never have to add huge numbers directly. By subtracting the largest log value before exponentiating, the intermediate exponentials stay small and avoid overflow or underflow, which is common when risk scores are very large or very small. This trick uses the logarithm identity log(a + b) = max(log a, log b) + log(1 + exp(−|log a − log b|)), which keeps the calculation in a stable range. For example, if two risk log‑scores are 1000 and 999, log‑sum‑exp gives log (e¹⁰⁰⁰ + e⁹⁹⁹) ≈ 1000 + log(1 + e⁻¹) ≈ 1000. 0004, a number that can be represented without error.
Detailed Explanation
The function lets you add probabilities that are stored as logs without losing tiny differences. Other options are incorrect because The idea that it shrinks the input range is wrong; It does not turn log values into linear numbers.
Key Concepts
numerical stability
risk assessment
properties of logarithms
Topic
Log-sum-exp Function
Difficulty
hard level question
Cognitive Level
understand
Practice Similar Questions
Test your understanding with related questions
1
Question 1What does the log-sum-exp function represent, and how do its properties relate to the laws of logarithms?
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2
Question 2In a business context, how does the derivative of the log-sum-exp function relate to the exponential function in terms of optimizing a portfolio's expected return?
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3
Question 3In the context of optimization problems, how does the log-sum-exp function enhance computational efficiency while approximating the maximum of a set of values?
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4
Question 4In the context of optimization and machine learning, the log-sum-exp function is primarily used to approximate the _______ function, which helps to provide a smooth representation of the maximum value among a set of numbers.
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5
Question 5Which of the following scenarios would best utilize the log-sum-exp function for optimization in machine learning algorithms?
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6
Question 6When applying the log-sum-exp function in optimization, what is the primary reason it is preferred over using the max function directly?
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7
Question 7In what scenario would using the log-sum-exp function be more advantageous than directly applying the max function?
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8
Question 8How does the log-sum-exp function improve optimization in multi-class classification problems?
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9
Question 9In a machine learning application, you are tasked with developing a model that predicts the likelihood of different outcomes based on a set of scores from various classifiers. You notice that the scores can be very low or negative, which makes directly using them problematic. How might the log-sum-exp function help you in this situation?
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