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<p>Here I’m writing the simplest form of the concept so that anyone can quickly get the idea. If you want a serious post, read <a href="https://arxiv.org/pdf/2107.07511">paper</a> or <a href="https://towardsdatascience.com/conformal-prediction-4775e78b47b6">other blog article</a>. This isn’t for you.</p>



<p>Conformal prediction outputs range for regression and multiple lables for classifications. Its purpose is to have output contains the correct answer for <img src="http://s0.wp.com/latex.php?latex=%281-%5Calpha%29%5C%25&amp;bg=ffffff&amp;fg=000000&amp;s=0" alt="(1-\alpha)\%" title="(1-\alpha)\%"> of time where <img src="http://s0.wp.com/latex.php?latex=%5Calpha&amp;bg=ffffff&amp;fg=000000&amp;s=0" alt="\alpha" title="\alpha"> is called significance level.</p>



<p>Let’s use regression example and a score function of <img src="http://s0.wp.com/latex.php?latex=%7C+%5Chat%7By%7D+-+y%7C&amp;bg=ffffff&amp;fg=000000&amp;s=0" alt="| \hat{y} - y|" title="| \hat{y} - y|">. For all the data points, calculate scores: <img src="http://s0.wp.com/latex.php?latex=S%28X_1%2C+%5Chat%7By_1%7D%29%2C+S%28X_2%2C+%5Chat%7By_2%7D%29%2C+%5Ccdots%2C+S%28X_n%2C+%5Chat%7By_n%7D%29&amp;bg=ffffff&amp;fg=000000&amp;s=0" alt="S(X_1, \hat{y_1}), S(X_2, \hat{y_2}), \cdots, S(X_n, \hat{y_n})" title="S(X_1, \hat{y_1}), S(X_2, \hat{y_2}), \cdots, S(X_n, \hat{y_n})">. And then calculate the <img src="http://s0.wp.com/latex.php?latex=1-%5Calpha&amp;bg=ffffff&amp;fg=000000&amp;s=0" alt="1-\alpha" title="1-\alpha"> quantile, e.g., sort the scores in ascending order and find the 90%th score if <img src="http://s0.wp.com/latex.php?latex=%5Calpha%3D10%5C%25&amp;bg=ffffff&amp;fg=000000&amp;s=0" alt="\alpha=10\%" title="\alpha=10\%">.</p>



<p>Now, we know how we can come up with a prediction range that would contain the answer for the 90% of time: <img src="http://s0.wp.com/latex.php?latex=%5C%7B%5Chat%7By%7D%7CS%28X_%7Bn%2B1%7D%2C+%5Chat%7By%7D%29+%3C%3D+90th+%5Censpace+score%5C%7D&amp;bg=ffffff&amp;fg=000000&amp;s=0" alt="\{\hat{y}|S(X_{n+1}, \hat{y}) <= 90th \enspace score\}" title="\{\hat{y}|S(X_{n+1}, \hat{y}) <= 90th \enspace score\}">.</p>
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Passion is like genius; a miracle.

Here I’m writing the simplest form of the concept so that anyone can quickly get the idea. If you want a serious post, read paper or other blog article. This isn’t for you. Conformal prediction outputs range for regression and multiple lables for classifications. Its purpose is to have output contains the correct answer for […]

Conformal prediction for dummies

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