<p>In machine learning, the sample error of an ERM learner is a biased estimator of the true generalization error. Here the bias is not by choice but by necessity: we simply don't know of a way to construct an unbiased estimator of the generalization error, and I'm pretty sure it's impossible from general no-free-lunch principles.</p>

CC BY-SA 3.0
2016-10-25T07:21:18.443Z
2016-10-25T07:21:18.443Z
Aryeh
<p>Biased estimators are useful in statistics because <a href="https://en.wikipedia.org/wiki/James%E2%80%93Stein_estimator">they can optimize mean-squared error more than what an unbiased estimator can manage</a>. I was wondering if in theoryCS if there are any very notable examples of the effective use of biased estimators. I realize this list could get long, and if it does I can modify this question to a big-list CW question, but for now I'm just curious. </p>

<randomized-algorithms>
Examples of the use of biased estimators
Suresh Venkat
# Examples of the use of biased estimators

(Asked by: username_0 on 2016-10-24)

Biased estimators are useful in statistics because [they can optimize mean-squared error more than what an unbiased estimator can manage](https://en.wikipedia.org/wiki/James%E2%80%93Stein_estimator). I was wondering if in theoryCS if there are any very notable examples of the effective use of biased estimators. I realize this list could get long, and if it does I can modify this question to a big-list CW question, but for now I'm just curious.

**Tags:** randomized-algorithms


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## 1 answers

### Answer by username_1 on 2016-10-25. Score: 3

In machine learning, the sample error of an ERM learner is a biased estimator of the true generalization error. Here the bias is not by choice but by necessity: we simply don't know of a way to construct an unbiased estimator of the generalization error, and I'm pretty sure it's impossible from general no-free-lunch principles.


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