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DTSTART;TZID=America/Los_Angeles:20200205T161500
DTEND;TZID=America/Los_Angeles:20200205T171500
DTSTAMP:20200203T185415Z
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UID:10001923-1580919300-1580922900@colleges.claremont.edu
SUMMARY:Kernel approaches in global statistical distances\, local measure detection\, and active learning
DESCRIPTION:In this talk\, we’ll discuss the problem of constructing meaningful distances between probability distributions given only finite samples from each distribution.  We approach this through the use of data-adaptive and localized kernels\, and in a variety of contexts.  First\, we construct locally adaptive kernels to define fast pairwise distances between distributions\, with applications to unsupervised clustering.  Then\, we construct localized kernels to determine a statistical framework for determining where two distributions differ\, with applications to measure detection for generative models.  Finally\, we’ll begin to address the question of measure detection without a priori known labels of which distribution a point came from.  This is addressed through active learning\, in which one can choose a small number of points at which to query a label.  This is ongoing work with Xiuyuan Cheng (Duke) and Hrushikesh Mhaskar (CGU)\, among others.
URL:https://colleges.claremont.edu/ccms/event/alex-cloninger/
LOCATION:Freeberg Forum\, LC 62\, Kravis Center\, CMC
CATEGORIES:Colloquium
ORGANIZER;CN="Blerta Shtylla":MAILTO:shtyllab@pomona.edu
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DTSTART;TZID=America/Los_Angeles:20200129T161500
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DTSTAMP:20200124T210246Z
CREATED:20190830T173951Z
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UID:10001921-1580314500-1580318100@colleges.claremont.edu
SUMMARY:A Tauberian theorem and some of its applications
DESCRIPTION:In general terms\, a Tauberian theorem deals with the relationship between the properties of one transform of a measure with those of another transform. We will introduce the notion of a Tauberian theorm\, and present our own recent theorem in this direction. Our theorem provides a uniform theory for the construction of certain localized kernels in a very general context. These in turn play a fundamental role in many different applications in numerical analysis\, signal processing\, and machine learning. We will discuss a few applications\, for example\, the construction of a theory inspired neural network for the solution of Burgers equation\, inversion of Laplace transform of point masses\, and an alternative theory for function approximation in the setting of diffusion geometry in machine learning without the need for any eigen-decomposition of a large matrix.
URL:https://colleges.claremont.edu/ccms/event/hrushikesh-mhaskar/
LOCATION:Freeberg Forum\, LC 62\, Kravis Center\, CMC
CATEGORIES:Colloquium
ORGANIZER;CN="Blerta Shtylla":MAILTO:shtyllab@pomona.edu
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DTSTART;TZID=America/Los_Angeles:20180214T160000
DTEND;TZID=America/Los_Angeles:20180214T170000
DTSTAMP:20180212T231323Z
CREATED:20180212T231323Z
LAST-MODIFIED:20180212T231323Z
UID:10001558-1518624000-1518627600@colleges.claremont.edu
SUMMARY:A tribute to Euler
DESCRIPTION:Among the greatest of mathematicians is Leonhard Euler (1707-1783)\, whose insight\, industry\, and ingenuity are unsurpassed in the long history of mathematics. In this talk we sketch Euler’s life\, describe the quantity and quality of his mathematical output\, and discuss a few of his discoveries from the realms of number theory\, geometry\, analysis\, and combinatorics. We then look at a specific theorem: his proof\, using integral calculus (!)\, of what is known as “Euler’s Identity” -i.e.\, exp(ix)=cos(x)+isin(x). We should thereby get a sense of Euler’s genius and see why he is rightly known as “the Master of Us All.” NOTE: This talk should be accessible to any student who has seen calculus.
URL:https://colleges.claremont.edu/ccms/event/a-tribute-to-euler/
LOCATION:Freeberg Forum\, LC 62\, Kravis Center\, CMC
CATEGORIES:Colloquium
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