<p>I think this is a typo. </p>

<p>In the Definition 2.1 and Definition 2.2, the estimation of $c_D$ is done by empirical summation of $\mathbf{1}(c(x_i) = y_i)$. </p>

<p>Later in the Definition 3.1 it used the following notation : 
$$
... = \Pr_{...} \left( \sum_i Z_i &lt; k \right) = ...
$$
In this notation $Z_i=1$ corresponds to correct decisions or $c(x_i) = y_i$, and $Z_i=0$ corresponds to the mistakes or $c(x_i) \neq y_i$. I suppose that in this binomial representation $Z_i = 1$ (correct decision) corresponds to <code>heads" (And similarly $Z_i = 0$ (wrong decision) corresponds to</code>tail"). </p>

<p>That said, the right sentence seems to be "... having k or less errors is at least $\delta$"</p>

CC BY-SA 3.0
2014-05-26T23:30:23.160Z
2014-05-26T23:30:23.160Z
Daniel
<p>I am reading John Langford's paper on practical prediction theory (<a href="http://machinelearning.wustl.edu/mlpapers/paper_files/Langford05.pdf" rel="nofollow">link</a>), and I have the following doubt with definition of Binomial Tail inversion.</p>

<p>The paper says that binomial tail inversion is the largest true error such that the probability of having k or more errors is at least $\delta$.</p>

<p>But the expression used in the paper reads "largest true error such that probability of having k or <strong>less</strong> errors is at least $\delta$"</p>

<p>Can anyone help?</p>

<machine-learning><lg.learning>
Doubt in John Langford's "Tutorial on Practical Prediction Theory for Classiﬁcation" paper
shyamupa
# Doubt in John Langford's "Tutorial on Practical Prediction Theory for Classiﬁcation" paper

(Asked by: username_0 on 2014-05-26)

I am reading John Langford's paper on practical prediction theory ([link](http://machinelearning.wustl.edu/mlpapers/paper_files/Langford05.pdf)), and I have the following doubt with definition of Binomial Tail inversion.

The paper says that binomial tail inversion is the largest true error such that the probability of having k or more errors is at least $\delta$.

But the expression used in the paper reads "largest true error such that probability of having k or **less** errors is at least $\delta$"

Can anyone help?

**Tags:** machine-learning, lg.learning

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## 1 answers

### Answer by username_1 on 2014-05-26. Score: 1

I think this is a typo.

In the Definition 2.1 and Definition 2.2, the estimation of $c\_D$ is done by empirical summation of $\mathbf{1}(c(x\_i) = y\_i)$.

Later in the Definition 3.1 it used the following notation :
$$
... = \Pr\_{...} \left( \sum\_i Z\_i < k \right) = ...
$$
In this notation $Z\_i=1$ corresponds to correct decisions or $c(x\_i) = y\_i$, and $Z\_i=0$ corresponds to the mistakes or $c(x\_i) \neq y\_i$. I suppose that in this binomial representation $Z\_i = 1$ (correct decision) corresponds to `heads" (And similarly $Z_i = 0$ (wrong decision) corresponds to`tail").

That said, the right sentence seems to be "... having k or less errors is at least $\delta$"


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