Bounded Rationality (Posts about differentials)http://bjlkeng.github.io/enSat, 10 Dec 2022 02:26:13 GMTNikola (getnikola.com)http://blogs.law.harvard.edu/tech/rssThe Calculus of Variationshttp://bjlkeng.github.io/posts/the-calculus-of-variations/Brian Keng<div><p>This post is going to describe a specialized type of calculus called
variational calculus.
Analogous to the usual methods of calculus that we learn in university,
this one deals with functions <em>of functions</em> and how to
minimize or maximize them. It's used extensively in physics problems such as
finding the minimum energy path a particle takes under certain conditions. As
you can also imagine, it's also used in machine learning/statistics where you
want to find a density that optimizes an objective <a class="footnote-reference brackets" href="http://bjlkeng.github.io/posts/the-calculus-of-variations/#id4" id="id1">1</a>. The explanation I'm
going to use (at least for the first part) is heavily based upon Svetitsky's
<a class="reference external" href="http://julian.tau.ac.il/bqs/functionals/functionals.html">Notes on Functionals</a>, which so far is
the most intuitive explanation I've read. I'll try to follow Svetitsky's
notes to give some intuition on how we arrive at variational calculus from
regular calculus with a bunch of examples along the way. Eventually we'll
get to an application that relates back to probability. I think with the right
intuition and explanation, it's actually not too difficult, enjoy!</p>
<p><a href="http://bjlkeng.github.io/posts/the-calculus-of-variations/">Read moreā¦</a> (16 min remaining to read)</p></div>differentialsentropylagrange multipliersmathjaxprobabilityvariational calculushttp://bjlkeng.github.io/posts/the-calculus-of-variations/Sun, 26 Feb 2017 15:08:38 GMT