Using an Appropriate Scale (C2W3L02)  Summary and Q&A
TL;DR
Sampling hyperparameters at random doesn't mean uniformly random over the range of valid values. Instead, it is important to pick the appropriate scale, such as a log scale, to explore hyperparameters efficiently.
Key Insights
 ๐งก Sampling hyperparameters at random within a range is efficient, but the appropriate scale must be chosen.
 ๐ฅบ Linear scale sampling may not distribute samples evenly, leading to inefficient exploration.
 ๐ป Logarithmic scale sampling allows for a more balanced exploration of hyperspace, particularly for sensitive hyperparameters.
 ๐ฏ๏ธ Picking the right scale can improve resource allocation and enhance the overall performance of machine learning models.
 โ ๏ธ Sampling on a logarithmic scale is particularly useful for hyperparameters like learning rate and beta.
 ๐ป The log scale allows for a finer exploration of values that are more sensitive to changes.
 โ๏ธ Sampling on a logarithmic scale distributes resources more efficiently, improving the optimization process.
Transcript
in the last video you saw how sampling a random over the range of hyper parameters can allow you to search over the states of hyper parameters more efficiently but it turns out that sampling at random doesn't mean something uniformly at random over the range of valid values instead it is important to pick the appropriate scale on which to explore t... Read More
Questions & Answers
Q: What is the importance of picking the appropriate scale for exploring hyperparameters?
Picking the appropriate scale allows for a more efficient exploration of the hyperparameter space. It ensures that resources are dedicated to searching various regions instead of favoring certain values.
Q: How can a log scale be used to sample hyperparameters?
On a log scale, the low and high values of the hyperparameter are transformed to their respective exponents. A random sample is then chosen uniformly between these transformed values.
Q: Why is it not recommended to sample learning rate or beta uniformly on a linear scale?
Sampling uniformly on a linear scale for hyperparameters like learning rate or beta can result in a disproportionate focus on certain values. This can lead to inefficient exploration of the hyperparameter space.
Q: How does sampling hyperparameters on a logarithmic scale address the sensitivity to small changes in beta?
By sampling more densely in the regime when beta is close to 1 (or 1 minus beta is close to 0) on a logarithmic scale, the hyperspace is explored more efficiently. This helps account for the sensitivity of results to small changes in beta.
Summary & Key Takeaways

Sampling hyperparameters at random within a specified range is an efficient approach, but it is not always suitable for all hyperparameters.

For hyperparameters like the number of hidden units or layers, sampling uniformly at random within the range is reasonable.

However, for hyperparameters like learning rate or beta, it is more efficient to sample on a logarithmic scale.