The text refers to the density function when considering the invertibility. In fact, the density function need not be invertible, it is the transformation function that should be invertible.
Location
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Draft (2020-09-12) of “Mathematics for Machine Learning”
Chapter 6
page 216
First line of the second paragraph (excluding the example)
Proposed solution
The text considers the function $3x^2$. However, this is the density function, which though monotonic, need not be. Monotonicity is a condition that we want to impose on the transformation which here is $x^2$. I feel this might be confusing to some.
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Describe the mistake
The text refers to the density function when considering the invertibility. In fact, the density function need not be invertible, it is the transformation function that should be invertible.
Location Please provide the
Proposed solution
The text considers the function $3x^2$. However, this is the density function, which though monotonic, need not be. Monotonicity is a condition that we want to impose on the transformation which here is $x^2$. I feel this might be confusing to some.
Additional context Add any other context about the problem here.