CDF and Quantile functions of Student T distribution
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Leandro Campos
Nov 13, 2022, 2:05:07 PM11/13/22
to tfprob...@tensorflow.org
Hello TFP community,
Could someone please review the PR #1639 [link] or suggest a reviewer? I apologize if this message is inappropriate for this channel, but perhaps none of the repository maintainers have been notified by GitHub.
This PR improves the cdf and quantile functions of the Student T distribution, especially when the degree of freedom `df` is large or when the square of the sample `t` is too small compared to `df`. It addresses both the values and the gradients of these functions. When `df` is large, both functions and their partial derivatives suffer moderate to heavy loss of accuracy. And when `t**2` is too small compared to `df`, the partial derivatives return `NaN`.
This PR is important to my next contribution: an implementation of the Two-Piece Student T distribution. I need the former to reparameterize the samples and to implement the cdf and quantile functions of the latter.
The following notebooks present results that allow us to compare current and proposed implementations:
All the best,
Could someone please review the PR #1639 [link] or suggest a reviewer? I apologize if this message is inappropriate for this channel, but perhaps none of the repository maintainers have been notified by GitHub.
This PR improves the cdf and quantile functions of the Student T distribution, especially when the degree of freedom `df` is large or when the square of the sample `t` is too small compared to `df`. It addresses both the values and the gradients of these functions. When `df` is large, both functions and their partial derivatives suffer moderate to heavy loss of accuracy. And when `t**2` is too small compared to `df`, the partial derivatives return `NaN`.
This PR is important to my next contribution: an implementation of the Two-Piece Student T distribution. I need the former to reparameterize the samples and to implement the cdf and quantile functions of the latter.
The following notebooks present results that allow us to compare current and proposed implementations:
- Test results for float64 and any value of t [link]
- Test results for float64 and tiny values of t [link]
- Test results for float32 and any value of t [link]
- Test results for float32 and tiny values of t [link]
All the best,
Leandro Campos
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