Restricted Learner's Rule of Thumb (Lecture 11)

[jlaurentum]

Hello All:

In minute 23:45 of Lecture 11, the restricted learner's reasoning is based on a rule of thumb, whereby you should have 10 data points for every parameter you want to estimate in your model. Where (in the book or in the other lectures) can I find more information on the justification for this rule of thumb?

[yaser]

Originally Posted by jlaurentum

Hello All:

In minute 23:45 of Lecture 11, the restricted learner's reasoning is based on a rule of thumb, whereby you should have 10 data points for every parameter you want to estimate in your model. Where (in the book or in the other lectures) can I find more information on the justification for this rule of thumb?

Let me first point to that part of the lecture using the lecture tag:



The rule of thumb is a practical observation, so its real justification is simply that it has worked most of the time in practice. Once can justify the form that the number of examples is a multiple of the VC dimension by arguing that having multiple data points to fit per degree of freedom will force that degree of freedom to a 'compromise' that is likely to capture what is common between these data points, i.e., likely to generalize. Whether that multiple is 5 or 10 or 100, however, is an empirical observation that is difficult to reason about in a genuine way.

[jlaurentum]

Thank you for the answer, Professor. So I understand that it is not possible (even based on your experience) to give a single value for this multiple because a single value cannot cover all possible modeling situations (target complexity, stochastic/deterministic noise, etc.)?

[yaser]

Originally Posted by jlaurentum

Thank you for the answer, Professor. So I understand that it is not possible (even based on your experience) to give a single value for this multiple because a single value cannot cover all possible modeling situations (target complexity, stochastic/deterministic noise, etc.)?

Correct. It does depend on the situation.

[Elroch]

On a specific point of jlaurentum, I have come to the intuitive conclusion that noise effectively reduces the size of the set of data, with the more noise, the more more data points needed to achieve the same results.

This is related to the much simpler idea that if you want to estimate a mean average with noisy (i.e. non-zero variance) data, then the accuracy is inversely proportional to the square root of the number of data points. Likewise, I would conjecture that a noisy machine learning problem might be reduced to a near noiseless one by having a very large number of data points (although the quantitative details of this are less clear).

In machine learning there is the complication that this intuition only applies to genuine (stochastic) noise. As "deterministic noise" is unvarying, it is not reduced (but the variance is). On reflection, I feel the term "deterministic noise" can be a little misleading, as it is a form of error which merely mimics noise to an observer, but lacks one of its properties (randomness). As an analogy with a physical measurement, it is more similar to a calibration error than to an uncertainty in measurement.