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<p class=MsoNormal><font size=3 face=Arial><span style='font-size:12.0pt;
font-family:Arial'>When:
Thursday,
May 22 @ 11:00am<b><span style='font-weight:bold'><o:p></o:p></span></b></span></font></p>
<p class=MsoNormal><font size=3 face=Arial><span style='font-size:12.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=3 face=Arial><span style='font-size:12.0pt;
font-family:Arial'>Where:
TTI-C Conference Room, <st1:Street w:st="on"><st1:address w:st="on">1427 E. 60<sup>th</sup>
St.</st1:address></st1:Street>, 2<sup>nd</sup> Floor<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=3 face=Arial><span style='font-size:12.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
<p style='margin:0in;margin-bottom:.0001pt'><font size=3 face=Arial><span
style='font-size:12.0pt;font-family:Arial'>Who:
Aryeh Kontorovich, Weizmann Institute of Science<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=3 face=Arial><span style='font-size:12.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal style='text-autospace:none'><font size=3 face=Arial><span
style='font-size:12.0pt;font-family:Arial'>Topic:
A Universal
Kernel for Learning Regular Languages<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=3 face=Arial><span style='font-size:12.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal style='text-autospace:none'><font size=3 face=Arial><span
style='font-size:12.0pt;font-family:Arial'>We develop a novel approach to the
classical problem of learning regular languages from labeled samples. Rather
than attempting to construct small consistent automata (long known to be a very
difficult computational problem), we embed the strings in a Hilbert space and
compute a maximum-margin hyperplane, which becomes our classifier for new
strings. We accomplish this via a universal kernel that renders all regular
languages linearly separable. Under this kernel, the image of every regular
language is linearly separable from its complement in some finite-dimensional
space with a strictly positive margin. Thus, we are able to efficiently (in
sample size) compute a maximum-margin separating hyperplane (via SVM, for
example) and use margin bounds to control the generalization error.<o:p></o:p></span></font></p>
<p class=MsoNormal style='text-autospace:none'><font size=3 face=Arial><span
style='font-size:12.0pt;font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal style='text-autospace:none'><font size=3 face=Arial><span
style='font-size:12.0pt;font-family:Arial'>A brute-force computation of this
universal kernel has super-exponential complexity. We conjecture that this
problem is intractable (a likely candidate for #P-complete). However, we
propose a simple randomized scheme for efficiently obtaining an
$\eps$-approximation to our universal kernel. We show that the approximate
kernel preserves the distances and margins with low distortion, and therefore
may be used as a surrogate for the original one.<o:p></o:p></span></font></p>
<p class=MsoNormal style='text-autospace:none'><font size=3 face=Arial><span
style='font-size:12.0pt;font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal style='text-autospace:none'><font size=3 face=Arial><span
style='font-size:12.0pt;font-family:Arial'>To our knowledge, the framework we propose
is the only one capable of inducing unrestricted regular languages from labeled
samples (modulo standard cryptographic limitations). Along the way, we touch
upon several fundamental questions in complexity, automata, and machine
learning.<o:p></o:p></span></font></p>
<p class=MsoNormal style='text-autospace:none'><font size=3 face=Arial><span
style='font-size:12.0pt;font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal style='text-autospace:none'><font size=3 face=Arial><span
style='font-size:12.0pt;font-family:Arial'>Join work with Boaz Nadler.<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=3 face=Arial><span style='font-size:12.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=3 face=Arial><span style='font-size:12.0pt;
font-family:Arial'>Contact:
Nati Srebro,
TTI-C nati@tti-c.org
834-7493<o:p></o:p></span></font></p>
<p class=MsoNormal style='margin-bottom:12.0pt'><font size=3 color=navy
face=Arial><span style='font-size:12.0pt;font-family:Arial;color:navy'><o:p> </o:p></span></font></p>
<p class=MsoNormal style='text-autospace:none'><font size=3 face=Arial><span
style='font-size:12.0pt;font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'><o:p> </o:p></span></font></p>
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