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X-WR-CALNAME:Discrete Mathematics Group
X-ORIGINAL-URL:https://dimag.ibs.re.kr
X-WR-CALDESC:Events for Discrete Mathematics Group
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TZID:Asia/Seoul
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TZOFFSETFROM:+0900
TZOFFSETTO:+0900
TZNAME:KST
DTSTART:20190101T000000
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20200114T163000
DTEND;TZID=Asia/Seoul:20200114T173000
DTSTAMP:20260420T130924
CREATED:20191225T230320Z
LAST-MODIFIED:20240705T202054Z
UID:1961-1579019400-1579023000@dimag.ibs.re.kr
SUMMARY:Sanjeeb Dash\, Boolean decision rules via column generation
DESCRIPTION:In many applications of machine learning\, interpretable or explainable models for binary classification\, such as decision trees or decision lists\, are preferred over potentially more accurate but less interpretable models such as random forests or support vector machines. In this talk\, we consider boolean decision rule sets (equivalent to boolean functions in disjunctive normal form) as interpretable models for binary classification. We define the complexity of a rule set to be the number of rules (clauses) plus the number of conditions (literals) across all clauses\, and assume that simpler or less complex models are more interpretable. We discuss an integer programming formulation for such models that trades off classification accuracy against rule simplicity\, and obtain high-quality classifiers of this type using column generation techniques. Compared to some recent alternatives\, our algorithm dominates the accuracy-simplicity trade-off in 8 out of 16 datasets\, and also produced the winning entry in the 2018 FICO explainable machine learning challenge. When compared to rule learning methods designed for accuracy\, our algorithm sometimes finds significantly simpler solutions that are no less accurate.
URL:https://dimag.ibs.re.kr/event/2020-01-14/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20200115T163000
DTEND;TZID=Asia/Seoul:20200115T173000
DTSTAMP:20260420T130924
CREATED:20200107T040041Z
LAST-MODIFIED:20240707T084237Z
UID:1990-1579105800-1579109400@dimag.ibs.re.kr
SUMMARY:Ben Lund\, Furstenberg sets over finite fields
DESCRIPTION:An important family of incidence problems are discrete analogs of deep questions in geometric measure theory. Perhaps the most famous example of this is the finite field Kakeya conjecture\, proved by Dvir in 2008. Dvir’s proof introduced the polynomial method to incidence geometry\, which led to the solution to many long-standing problems in the area.\nI will talk about a generalization of the Kakeya conjecture posed by Ellenberg\, Oberlin\, and Tao. A $(k\,m)$-Furstenberg set S in $\mathbb F_q^n$ has the property that\, parallel to every affine $k$-plane V\, there is a k-plane W such that $|W \cap S| > m$. Using sophisticated ideas from algebraic geometry\, Ellenberg and Erman showed that if S is a $(k\,m)$-Furstenberg set\, then $|S| > c m^{n/k}$\, for a constant c depending on n and k. In recent joint work with Manik Dhar and Zeev Dvir\, we give simpler proofs of stronger bounds. For example\, if $m>2^{n+7}q$\, then $|S|=(1-o(1))mq^{n-k}$\, which is tight up to the $o(1)$ term.
URL:https://dimag.ibs.re.kr/event/2020-01-15/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20200120T163000
DTEND;TZID=Asia/Seoul:20200120T173000
DTSTAMP:20260420T130924
CREATED:20200108T022511Z
LAST-MODIFIED:20240705T202052Z
UID:1997-1579537800-1579541400@dimag.ibs.re.kr
SUMMARY:Adam Zsolt Wagner\, The largest projective cube-free subsets of $Z_{2^n}$
DESCRIPTION:What is the largest subset of $Z_{2^n}$ that doesn’t contain a projective d-cube? In the Boolean lattice\, Sperner’s\, Erdos’s\, Kleitman’s and Samotij’s theorems state that families that do not contain many chains must have a very specific layered structure. We show that if instead of $Z_2^n$ we work in $Z_{2^n}$\, analogous statements hold if one replaces the word k-chain by projective cube of dimension $2^{k-1}$. The largest d-cube-free subset of $Z_{2^n}$\, if d is not a power of two\, exhibits a much more interesting behaviour. \nThis is joint work with Jason Long.
URL:https://dimag.ibs.re.kr/event/2020-01-20/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20200128T163000
DTEND;TZID=Asia/Seoul:20200128T173000
DTSTAMP:20260420T130924
CREATED:20191216T045747Z
LAST-MODIFIED:20240705T203007Z
UID:1940-1580229000-1580232600@dimag.ibs.re.kr
SUMMARY:Dillon Mayhew\, Courcelle's Theorem for hypergraphs
DESCRIPTION:Courcelle’s Theorem is an influential meta-theorem published in 1990. It tells us that a property of graph can be tested in polynomial time\, as long as the property can expressed in the monadic second-order logic of graphs\, and as long as the input is restricted to a class of graphs with bounded tree-width. There are several properties that are NP-complete in general\, but which can be expressed in monadic logic (3-colourability\, Hamiltonicity…)\, so Courcelle’s Theorem implies that these difficult properties can be tested in polynomial time when the structural complexity of the input is limited. \nMatroids can be considered as a special class of hypergraphs. Any finite set of vectors over a field leads to a matroid\, and such a matroid is said to be representable over that field. Hlineny produced a matroid analogue of Courcelle’s Theorem for input classes with bounded branch-width that are representable over a finite field. \nWe have now identified the structural properties of hypergraph classes that allow a proof of Hliněný’s Theorem to go through. This means that we are able to extend his theorem to several other natural classes of matroids. \nThis talk will contain an introduction to matroids\, monadic logic\, and tree-automata. \nThis is joint work with Daryl Funk\, Mike Newman\, and Geoff Whittle.
URL:https://dimag.ibs.re.kr/event/2020-01-28/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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