Theory
https://csd.cmu.edu/
enWed, 13 Nov 24 12:00:00 -0500Theory Lunch Seminar — Richard Peng
https://csd.cmu.edu/calendar/theory-lunch-seminar-PENG-2024-11-13
<span>Theory Lunch Seminar — Richard Peng</span>
Reddy Conference Room, Gates Hillman 4405
<span><span>Anonymous (not verified)</span></span>
<span><time datetime="2024-11-13T12:00:00-05:00" title="Wednesday, November 13, 2024 - 12:00">Wed, 11/13/2024 - 12:00</time>
</span>
In Person
Krylov Space Methods
RICHARD PENG
In this talk I will survey (block) Krylov methods for solving systems of linear equations. Such methods have close connections with conjugate gradient, Lanczos method, Wiedemann's algorithm, and can be viewed as generalizations of the power method. What I know about these mostly occur over reals, so I'll mainly focus on the continuous setting. However, I will also attempt to discuss how such algorithms work over finite fields, and connections with matrix rank, eigenvalues, and minimum polynomials.
<time datetime="2024-11-13T17:00:00Z">November 13, 2024 12:00pm</time>
<time datetime="2024-11-13T18:00:00Z">November 13, 2024 1:00pm</time>
https://www.cs.cmu.edu/~yangp/
Associate Professor, Computer Science Department, Carnegie Mellon University
https://www.cs.cmu.edu/~theorylunch/
<a href="mailto:wrhe@cs.cmu.edu">wrhe@cs.cmu.edu</a>
Seminar Series
<a href="https://csd.cmu.edu/people/faculty/richard-peng" hreflang="en">Richard Peng</a>
<a href="https://csd.cmu.edu/research/research-areas/theory" hreflang="en">Theory</a>
Reddy Conference Room, Gates Hillman 4405
<p>Speaker: RICHARD PENG, Associate Professor, Computer Science Department, Carnegie Mellon University</p>
<p>Talk Title: Krylov Space MethodsIn this talk I will survey (block) Krylov methods for solving systems of linear equations. Such methods have close connections with conjugate gradient, Lanczos method, Wiedemann's algorithm, and can be viewed as generalizations of the power method. What I know about these mostly occur over reals, so I'll mainly focus on the continuous setting. However, I will also attempt to discuss how such algorithms work over finite fields, and connections with matrix rank, eigenvalues, and minimum polynomials.</p>
Wed, 13 Nov 2024 17:00:00 +0000Anonymous222337616 at https://csd.cmu.eduTheory Lunch Seminar - Keegan Harris
https://csd.cmu.edu/calendar/theory-lunch-seminar-keegan-harris
<span>Theory Lunch Seminar - Keegan Harris</span>
Reddy Conference Room, Gates Hillman 4405
<span><span>Anonymous (not verified)</span></span>
<span><time datetime="2024-11-06T12:00:00-05:00" title="Wednesday, November 6, 2024 - 12:00">Wed, 11/06/2024 - 12:00</time>
</span>
In Person
Regret Minimization in Stackelberg Games with Side Information
KEEGAN HARRIS
<p>Algorithms for playing in Stackelberg games have been deployed in real-world domains including airport security, anti-poaching efforts, and cyber-crime prevention. However, these algorithms often fail to take into consideration the additional information available to each player (e.g. traffic patterns, weather conditions, network congestion), which may significantly affect both players’ optimal strategies. We formalize such settings as <em>Stackelberg games with side information</em>, in which both players observe an external context before playing. The leader commits to a (context-dependent) strategy, and the follower best-responds to both the leader’s strategy and the context. We focus on the online setting in which a sequence of followers arrive over time, and the context may change from round-to-round. </p><p>In sharp contrast to the non-contextual version, we show that it is impossible for the leader to achieve no-regret in the full adversarial setting. Motivated by this result, we show that no-regret learning is possible in two natural relaxations: the setting in which the sequence of followers is chosen stochastically and the sequence of contexts is adversarial, and the setting in which contexts are stochastic and follower types are adversarial. </p><p>This talk is based on the <a href="https://arxiv.org/pdf/2402.08576" target="_blank">paper of the same name</a>, to appear at <em>NeurIPS 2024</em>.</p>
<time datetime="2024-11-06T17:00:00Z">November 6, 2024 12:00pm</time>
<time datetime="2024-11-06T18:00:00Z">November 6, 2024 1:00pm</time>
https://keeganharris.github.io/
Ph.D. Student, Machine Learning Department, Carnegie Mellon University
https://www.cs.cmu.edu/~theorylunch/
<a href="mailto:wrhe@cs.cmu.edu">wrhe@cs.cmu.edu</a>
Seminar Series
<a href="https://csd.cmu.edu/research/research-areas/theory" hreflang="en">Theory</a>
<a href="https://csd.cmu.edu/research/research-areas/machine-learning" hreflang="en">Machine Learning</a>
Reddy Conference Room, Gates Hillman 4405
<p>Speaker: KEEGAN HARRIS, Ph.D. Student, Machine Learning Department, Carnegie Mellon University</p>
<p>Talk Title: Regret Minimization in Stackelberg Games with Side Information</p>
<p>Algorithms for playing in Stackelberg games have been deployed in real-world domains including airport security, anti-poaching efforts, and cyber-crime prevention. However, these algorithms often fail to take into consideration the additional information available to each player (e.g. traffic patterns, weather conditions, network congestion), which may significantly affect both players’ optimal strategies. We formalize such settings as Stackelberg games with side information, in which both players observe an external context before playing. The leader commits to a (context-dependent) strategy, and the follower best-responds to both the leader’s strategy and the context. We focus on the online setting in which a sequence of followers arrive over time, and the context may change from round-to-round. </p>
<p>In sharp contrast to the non-contextual version, we show that it is impossible for the leader to achieve no-regret in the full adversarial setting. Motivated by this result, we show that no-regret learning is possible in two natural relaxations: the setting in which the sequence of followers is chosen stochastically and the sequence of contexts is adversarial, and the setting in which contexts are stochastic and follower types are adversarial. </p>
<p>This talk is based on the paper of the same name, to appear at NeurIPS 2024.</p>
Wed, 06 Nov 2024 17:00:00 +0000Anonymous222337327 at https://csd.cmu.eduACO Seminar - Yuval Widgerson
https://csd.cmu.edu/calendar/aco-seminar-yuval-widgerson
<span>ACO Seminar - Yuval Widgerson</span>
Wean Hall 8220
<span><span>Anonymous (not verified)</span></span>
<span><time datetime="2024-10-31T15:00:00-04:00" title="Thursday, October 31, 2024 - 15:00">Thu, 10/31/2024 - 15:00</time>
</span>
In Person
Graph decompositions, Ramsey theory, and random graphs
YUVAL WIDGERSON
<p>A basic result of probabilistic combinatorics, originally due to Erdös and Rényi, is the determination of the threshold at which the random graph <em>G<sub>n,p</sub></em> contains a triangle with high probability. But one can also ask more refined versions of this question, where we ask not just for one triangle but for many triangles which interact in complicated ways. For example, what is the threshold at which we can no longer partition <em>G<sub>n,p</sub></em> into two triangle-free subgraphs? </p><p>In this talk, I will discuss the proof of the Kohayakawa–Kreuter conjecture, which gives a general answer to all such questions. Rather surprisingly, a key step of the proof is a purely deterministic graph decomposition statement, closely related to classical results such as Nash-Williams' tree decomposition theorem, whose proof uses techniques from combinatorial optimization and structural graph theory. </p><p><em>Based on joint works with Micha Christoph, Eden Kuperwasser, Anders Martinsson, Wojciech Samotij, and Raphael Steiner.</em></p>
<time datetime="2024-10-31T19:00:00Z">October 31, 2024 3:00pm</time>
<time datetime="2024-10-31T20:00:00Z">October 31, 2024 4:00pm</time>
https://n.ethz.ch/~ywigderson/
Junior Fellow, Department of Mathematics, ETH Zürich
https://aco.math.cmu.edu/abs-24-25/oct31.html
<a href="mailto:bbukh@math.cmu.edu">bbukh@math.cmu.edu</a>
Seminar Series
<a href="https://csd.cmu.edu/research/research-areas/algorithms-and-complexity" hreflang="en">Algorithms and Complexity</a>
<a href="https://csd.cmu.edu/research/research-areas/theory" hreflang="en">Theory</a>
Wean Hall 8220
<p>Speaker: YUVAL WIDGERSON, Junior Fellow, Department of Mathematics, ETH Zürich</p>
<p>Talk Title: Graph decompositions, Ramsey theory, and random graphs</p>
<p>A basic result of probabilistic combinatorics, originally due to Erdös and Rényi, is the determination of the threshold at which the random graph Gn,p contains a triangle with high probability. But one can also ask more refined versions of this question, where we ask not just for one triangle but for many triangles which interact in complicated ways. For example, what is the threshold at which we can no longer partition Gn,p into two triangle-free subgraphs? </p>
<p>In this talk, I will discuss the proof of the Kohayakawa–Kreuter conjecture, which gives a general answer to all such questions. Rather surprisingly, a key step of the proof is a purely deterministic graph decomposition statement, closely related to classical results such as Nash-Williams' tree decomposition theorem, whose proof uses techniques from combinatorial optimization and structural graph theory. </p>
<p>Based on joint works with Micha Christoph, Eden Kuperwasser, Anders Martinsson, Wojciech Samotij, and Raphael Steiner.</p>
Thu, 31 Oct 2024 19:00:00 +0000Anonymous222337299 at https://csd.cmu.eduTheory Lunch Seminar - Jason Li
https://csd.cmu.edu/calendar/theory-lunch-seminar-jason-li
<span>Theory Lunch Seminar - Jason Li</span>
Reddy Conference Room, Gates Hillman 4405
<span><span>Anonymous (not verified)</span></span>
<span><time datetime="2024-10-30T12:00:00-04:00" title="Wednesday, October 30, 2024 - 12:00">Wed, 10/30/2024 - 12:00</time>
</span>
In Person
Minimum Isolating Cuts: A new tool for solving minimum cut problems
JASON LI
<p>Minimum cut problems are among the most well-studied questions in combinatorial optimization. In this talk, I will introduce a simple but powerful new tool for solving minimum cut problems called the minimum isolating cuts. I will show how this tool can be employed to obtain faster algorithms for several fundamental min-cut problems, namely global min-cut, Steiner min-cut, and all-pairs min-cut. For these problems, the new results represent the first improvement in their runtimes in several decades. </p><p><em>These results are in collaboration with Amir Abboud, Robert Krauthgamer, Danupon Nanongkai, Thatchaphol Saranurak, and Ohad Trabelsi.</em></p>
<time datetime="2024-10-30T16:00:00Z">October 30, 2024 12:00pm</time>
<time datetime="2024-10-30T17:00:00Z">October 30, 2024 1:00pm</time>
https://q3r.github.io/
Assistant Professor, Carnegie Mellon University
<a href="mailto:wrhe@cs.cmu.edu">wrhe@cs.cmu.edu</a>
Seminar Series
<a href="https://csd.cmu.edu/people/faculty/jason-li" hreflang="en">Jason Li</a>
<a href="https://csd.cmu.edu/research/research-areas/theory" hreflang="en">Theory</a>
Reddy Conference Room, Gates Hillman 4405
<p>Speaker: JASON LI, Assistant Professor, Carnegie Mellon University</p>
<p>Talk Title: Minimum Isolating Cuts: A new tool for solving minimum cut problems</p>
<p>Minimum cut problems are among the most well-studied questions in combinatorial optimization. In this talk, I will introduce a simple but powerful new tool for solving minimum cut problems called the minimum isolating cuts. I will show how this tool can be employed to obtain faster algorithms for several fundamental min-cut problems, namely global min-cut, Steiner min-cut, and all-pairs min-cut. For these problems, the new results represent the first improvement in their runtimes in several decades. </p>
<p>These results are in collaboration with Amir Abboud, Robert Krauthgamer, Danupon Nanongkai, Thatchaphol Saranurak, and Ohad Trabelsi.</p>
Wed, 30 Oct 2024 16:00:00 +0000Anonymous222337309 at https://csd.cmu.eduOperations Research Seminar - Karthik Chandrasekaran
https://csd.cmu.edu/calendar/operations-research-seminar-karthik-chandrasekaran
<span>Operations Research Seminar - Karthik Chandrasekaran</span>
Tepper 5219
<span><span>Anonymous (not verified)</span></span>
<span><time datetime="2024-10-25T13:30:00-04:00" title="Friday, October 25, 2024 - 13:30">Fri, 10/25/2024 - 13:30</time>
</span>
In Person
Splitting-off in Hypergraphs
KARTHIK CHANDRASEKARAN
<p>The splitting-off operation in undirected graphs is a fundamental reduction operation that detaches all edges incident to a given vertex and adds new edges between the neighbors of that vertex while preserving their degrees. Lovász (1974) and Mader (1978) showed the existence of this operation while preserving global and local connectivities respectively in graphs under mild conditions. These results have been influential in structural graph theory as an induction tool and in graph algorithms as a recursion tool. </p><p>In this talk, I will introduce a splitting-off operation in hypergraphs. The main result is that there exists a local connectivity preserving complete splitting-off in hypergraphs and a strongly polynomial-time algorithm to compute it in weighted hypergraphs. I will outline two applications of our local connectivity preserving splitting-off result in hypergraphs: (1) constructive characterization of k-hyperedge-connected hypergraphs and (2) alternate proof of an approximate min-max relation for max Steiner rooted-connected orientation of graphs and hypergraphs (due to Király and Lau, 2008). Our proof of the approximate min-max relation for graphs circumvents the Nash-Williams' strong orientation theorem and uses tools developed for hypergraphs. As a special case of this application, I will present a unified proof of Menger’s theorem for graphs and hypergraphs (edge version). </p><p><em>Based on joint work with Kristof Berczi, Tamas Kiraly, and Shubhang Kulkarni. </em></p><p> — </p><p><a href="https://karthik.ise.illinois.edu/" target="_blank">Karthik Chandrasekaran</a> is an associate professor in the Department of Industrial and Enterprise Systems Engineering and an affiliate in the Department of Computer Science at University of Illinois, Urbana-Champaign. He received his bachelor’s in Computer Science from IIT Madras and Ph.D. in in Algorithms, Combinatorics, and Optimization (ACO) from Georgia Tech. His Ph.D. thesis was awarded the Dissertation Prize by the College of Computing at Georgia Tech and the Best Ph.D. Thesis Award by the Sigma Xi chapter of Georgia Tech. Prior to joining UIUC, he was a Simons postdoctoral fellow at Harvard University. His research focuses on fundamental problems in Combinatorial Optimization and Algorithms and is supported by the National Science Foundation.</p>
<time datetime="2024-10-25T17:30:00Z">October 25, 2024 1:30pm</time>
<time datetime="2024-10-25T18:30:00Z">October 25, 2024 2:30pm</time>
https://karthik.ise.illinois.edu/
Associate Professor, Department of Industrial and Enterprise Systems Engineering, University of Illinois, Urbana-Champaign
https://seminartracker.tepper.cmu.edu/SeminarDetail?SeminarId=1103
<a href="mailto:pconley@andrew.cmu.edu">pconley@andrew.cmu.edu</a>
Seminar Series
<a href="https://csd.cmu.edu/research/research-areas/algorithms-and-complexity" hreflang="en">Algorithms and Complexity</a>
<a href="https://csd.cmu.edu/research/research-areas/theory" hreflang="en">Theory</a>
Tepper 5219
<p>Speaker: KARTHIK CHANDRASEKARAN, Associate Professor, Department of Industrial and Enterprise Systems Engineering, University of Illinois, Urbana-Champaign</p>
<p>Talk Title: Splitting-off in Hypergraphs</p>
<p>The splitting-off operation in undirected graphs is a fundamental reduction operation that detaches all edges incident to a given vertex and adds new edges between the neighbors of that vertex while preserving their degrees. Lovász (1974) and Mader (1978) showed the existence of this operation while preserving global and local connectivities respectively in graphs under mild conditions. These results have been influential in structural graph theory as an induction tool and in graph algorithms as a recursion tool. </p>
<p>In this talk, I will introduce a splitting-off operation in hypergraphs. The main result is that there exists a local connectivity preserving complete splitting-off in hypergraphs and a strongly polynomial-time algorithm to compute it in weighted hypergraphs. I will outline two applications of our local connectivity preserving splitting-off result in hypergraphs: (1) constructive characterization of k-hyperedge-connected hypergraphs and (2) alternate proof of an approximate min-max relation for max Steiner rooted-connected orientation of graphs and hypergraphs (due to Király and Lau, 2008). Our proof of the approximate min-max relation for graphs circumvents the Nash-Williams' strong orientation theorem and uses tools developed for hypergraphs. As a special case of this application, I will present a unified proof of Menger’s theorem for graphs and hypergraphs (edge version). </p>
<p>Based on joint work with Kristof Berczi, Tamas Kiraly, and Shubhang Kulkarni. </p>
<p> — </p>
<p>Karthik Chandrasekaran is an associate professor in the Department of Industrial and Enterprise Systems Engineering and an affiliate in the Department of Computer Science at University of Illinois, Urbana-Champaign. He received his bachelor’s in Computer Science from IIT Madras and Ph.D. in in Algorithms, Combinatorics, and Optimization (ACO) from Georgia Tech. His Ph.D. thesis was awarded the Dissertation Prize by the College of Computing at Georgia Tech and the Best Ph.D. Thesis Award by the Sigma Xi chapter of Georgia Tech. Prior to joining UIUC, he was a Simons postdoctoral fellow at Harvard University. His research focuses on fundamental problems in Combinatorial Optimization and Algorithms and is supported by the National Science Foundation.</p>
Fri, 25 Oct 2024 17:30:00 +0000Anonymous222337276 at https://csd.cmu.eduTheory Seminar - To be rescheduled
https://csd.cmu.edu/calendar/theory-seminar-to-be-rescheduled
<span>Theory Seminar - To be rescheduled</span>
Reddy Conference Room, Gates Hillman 4405
<span><span>Anonymous (not verified)</span></span>
<span><time datetime="2024-10-25T10:30:00-04:00" title="Friday, October 25, 2024 - 10:30">Fri, 10/25/2024 - 10:30</time>
</span>
In Person
Pseudorandom unitaries, t-designs, and the incompressibility of random circuits
TONY METGER - To Be Rescheduled
<p>Uniformly random unitaries, i.e. unitaries drawn from the Haar measure, have many useful properties, but cannot be implemented efficiently. This has motivated a long line of research into random unitaries that "look" sufficiently Haar random while also being efficient to implement. Two different notions of derandomisation have emerged: t-designs are random unitaries that information-theoretically reproduce the first t moments of the Haar measure, and pseudorandom unitaries (PRUs) are random unitaries that are computationally indistinguishable from Haar random. </p><p>I will explain a simple unified construction of both t-designs and PRUs from the “PFC ensemble”, the concatenation of a random Clifford unitary, a random binary phase, and a random computational basis state permutation. Then, I will show how the PFC ensemble helps us to resolve a long-standing open question about the spectral gap of random quantum circuits, implying that a random quantum circuit is essentially incompressible. This proves the Brown-Susskind conjecture from black hole physics.</p>
<time datetime="2024-10-25T14:30:00Z">October 25, 2024 10:30am</time>
<time datetime="2024-10-25T15:30:00Z">October 25, 2024 11:30am</time>
https://tonymetger.com/
PhD. Student, Institute for Theoretical Physics , ETH Zurich
<a href="mailto:ryanod@andrew.cmu.edu">ryanod@andrew.cmu.edu</a>
Seminar Series
<a href="https://csd.cmu.edu/research/research-areas/theory" hreflang="en">Theory</a>
Reddy Conference Room, Gates Hillman 4405
<p>Speaker: TONY METGER - To Be Rescheduled, PhD. Student, Institute for Theoretical Physics , ETH Zurich</p>
<p>Talk Title: Pseudorandom unitaries, t-designs, and the incompressibility of random circuits</p>
<p>Uniformly random unitaries, i.e. unitaries drawn from the Haar measure, have many useful properties, but cannot be implemented efficiently. This has motivated a long line of research into random unitaries that "look" sufficiently Haar random while also being efficient to implement. Two different notions of derandomisation have emerged: t-designs are random unitaries that information-theoretically reproduce the first t moments of the Haar measure, and pseudorandom unitaries (PRUs) are random unitaries that are computationally indistinguishable from Haar random. </p>
<p>I will explain a simple unified construction of both t-designs and PRUs from the “PFC ensemble”, the concatenation of a random Clifford unitary, a random binary phase, and a random computational basis state permutation. Then, I will show how the PFC ensemble helps us to resolve a long-standing open question about the spectral gap of random quantum circuits, implying that a random quantum circuit is essentially incompressible. This proves the Brown-Susskind conjecture from black hole physics.</p>
Fri, 25 Oct 2024 14:30:00 +0000Anonymous222337280 at https://csd.cmu.eduACO Seminar - Ramon Van Handel
https://csd.cmu.edu/calendar/aco-seminar-ramon-van-handel
<span>ACO Seminar - Ramon Van Handel</span>
Wean Hall 8220
<span><span>Anonymous (not verified)</span></span>
<span><time datetime="2024-10-24T15:00:00-04:00" title="Thursday, October 24, 2024 - 15:00">Thu, 10/24/2024 - 15:00</time>
</span>
In Person
A new approach to strong convergence
RAMON VAN HANDEL
<p>It was conjectured by Alon in the 1980s that random d-regular graphs have the largest possible spectral gap (up to negligible error) among all d-regular graphs. This conjecture was proved by Friedman in 2004 in major tour de force. In recent years, deep generalizations of Friedman's theorem, such as strong convergence of random permutation matrices due to Bordenave and Collins, have played a central role in a series of breakthrough results on random graphs, geometry, and operator algebras. </p><p>In this talk, I will discuss a surprisingly simple new approach to such results that is almost entirely based on soft arguments. This approach makes it possible to address previously inaccessible questions: for example, it enables a sharp understanding of the large deviation probabilities in Friedman's theorem, and establishes strong convergence of very high-dimensional representations of the symmetric and classical groups. I will aim to explain some of these results and the basic ideas on which they are based. </p><p><em>Joint work with Chi-Fang Chen, Jorge Garza-Vargas, Joel Tropp. </em></p><p><em>→ 4:00 pm Tea & Cookies in the Math Lounge - sponsored by Jane Street </em></p><p><em>→ Bring your own mug if you have one</em></p>
<time datetime="2024-10-24T19:00:00Z">October 24, 2024 3:00pm</time>
<time datetime="2024-10-24T20:00:00Z">October 24, 2024 4:00pm</time>
https://web.math.princeton.edu/~rvan/
Associate Professor, Program in Applied & Computational Mathematics, and Operations Research & Financial Engineering, Princeton University
https://aco.math.cmu.edu/abs-24-25/oct24.html
<a href="mailto:bbukh@math.cmu.edu">bbukh@math.cmu.edu</a>
Special Seminar
<a href="https://csd.cmu.edu/research/research-areas/algorithms-and-complexity" hreflang="en">Algorithms and Complexity</a>
<a href="https://csd.cmu.edu/research/research-areas/theory" hreflang="en">Theory</a>
Wean Hall 8220
<p>Speaker: RAMON VAN HANDEL, Associate Professor, Program in Applied & Computational Mathematics, and Operations Research & Financial Engineering, Princeton University</p>
<p>Talk Title: A new approach to strong convergence</p>
<p>It was conjectured by Alon in the 1980s that random d-regular graphs have the largest possible spectral gap (up to negligible error) among all d-regular graphs. This conjecture was proved by Friedman in 2004 in major tour de force. In recent years, deep generalizations of Friedman's theorem, such as strong convergence of random permutation matrices due to Bordenave and Collins, have played a central role in a series of breakthrough results on random graphs, geometry, and operator algebras. </p>
<p>In this talk, I will discuss a surprisingly simple new approach to such results that is almost entirely based on soft arguments. This approach makes it possible to address previously inaccessible questions: for example, it enables a sharp understanding of the large deviation probabilities in Friedman's theorem, and establishes strong convergence of very high-dimensional representations of the symmetric and classical groups. I will aim to explain some of these results and the basic ideas on which they are based. </p>
<p>Joint work with Chi-Fang Chen, Jorge Garza-Vargas, Joel Tropp. </p>
<p>→ 4:00 pm Tea & Cookies in the Math Lounge - sponsored by Jane Street </p>
<p>→ Bring your own mug if you have one</p>
Thu, 24 Oct 2024 19:00:00 +0000Anonymous222337261 at https://csd.cmu.eduACO Seminar - Zongchen Chen
https://csd.cmu.edu/calendar/aco-seminar-zongchen-chen
<span>ACO Seminar - Zongchen Chen</span>
Wean 8220
<span><span>Anonymous (not verified)</span></span>
<span><time datetime="2024-10-10T15:00:00-04:00" title="Thursday, October 10, 2024 - 15:00">Thu, 10/10/2024 - 15:00</time>
</span>
In Person
Entropy Contractions in Markov Chains: Half-Step, Full-Step and Continuous-Time
ZONGCHEN CHEN
<p>Given a transition matrix (i.e., a row-stochastic matrix) one can define either a discrete-time Markov chain (with the multi-step transition matrix given by the matrix power) or a continuous-time Markov process (roughly, the update times are distributed as a Poisson point process). A common way to analyze the speed of convergence of Markov chains is to study the contraction of the relative entropy (i.e., the Kullback-Leibler divergence). Such entropy contractions are characterized by the strong data processing inequality for discrete-time Markov chains, or the modified log-Sobolev inequality for continuous-time Markov processes. </p><p>In several previous works these two notions of entropy contraction were claimed to be equivalent to each other, in the sense that the rates of contraction differ by universal constant factors. We disprove this and related conjectures, and summarize known comparisons among different notions of entropy contraction. In particular, we show that: (a) entropy contraction of a continuous-time Markov process can be arbitrarily faster than its discrete-time counterpart; (b) entropy contraction of an (m+1)-step transition matrix can be arbitrarily faster than the m-step version. </p><p><em>Joint work with Pietro Caputo, Yuzhou Gu and Yury Polyanskiy. </em></p><p><em>4:00 pm → Tea & Cookies in Wean 8220 sponsored by Jane Street (bring your own mug if possible).</em> </p>
<time datetime="2024-10-10T19:00:00Z">October 10, 2024 3:00pm</time>
<time datetime="2024-10-10T20:00:00Z">October 10, 2024 4:00pm</time>
https://sites.gatech.edu/zongchenchen/
Assistant Professor, School of Computer Science, Georgia Tech.
https://aco.math.cmu.edu/abs-24-25/oct10.html
Seminar Series
<a href="https://csd.cmu.edu/research/research-areas/algorithms-and-complexity" hreflang="en">Algorithms and Complexity</a>
<a href="https://csd.cmu.edu/research/research-areas/theory" hreflang="en">Theory</a>
Wean 8220
<p>Speaker: ZONGCHEN CHEN, Assistant Professor, School of Computer Science, Georgia Tech.</p>
<p>Talk Title: Entropy Contractions in Markov Chains: Half-Step, Full-Step and Continuous-Time</p>
<p>Given a transition matrix (i.e., a row-stochastic matrix) one can define either a discrete-time Markov chain (with the multi-step transition matrix given by the matrix power) or a continuous-time Markov process (roughly, the update times are distributed as a Poisson point process). A common way to analyze the speed of convergence of Markov chains is to study the contraction of the relative entropy (i.e., the Kullback-Leibler divergence). Such entropy contractions are characterized by the strong data processing inequality for discrete-time Markov chains, or the modified log-Sobolev inequality for continuous-time Markov processes. </p>
<p>In several previous works these two notions of entropy contraction were claimed to be equivalent to each other, in the sense that the rates of contraction differ by universal constant factors. We disprove this and related conjectures, and summarize known comparisons among different notions of entropy contraction. In particular, we show that: (a) entropy contraction of a continuous-time Markov process can be arbitrarily faster than its discrete-time counterpart; (b) entropy contraction of an (m+1)-step transition matrix can be arbitrarily faster than the m-step version. </p>
<p>Joint work with Pietro Caputo, Yuzhou Gu and Yury Polyanskiy. </p>
<p>4:00 pm → Tea & Cookies in Wean 8220 sponsored by Jane Street (bring your own mug if possible). </p>
Thu, 10 Oct 2024 19:00:00 +0000Anonymous222337185 at https://csd.cmu.eduTheory Lunch Seminar - Zongrui Zou
https://csd.cmu.edu/calendar/theory-lunch-seminar-zongrui-zou
<span>Theory Lunch Seminar - Zongrui Zou</span>
Traffic21 Classroom, Gates Hillman 6501 (new location)
<span><span>Anonymous (not verified)</span></span>
<span><time datetime="2024-10-09T12:00:00-04:00" title="Wednesday, October 9, 2024 - 12:00">Wed, 10/09/2024 - 12:00</time>
</span>
In Person
Differentially Private Multiway and k-Cut
ZONGRUI ZOU
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</script><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.2/MathJax.js?config=TeX-MML-AM_CHTML"></script><p>In this talk, we show how to address the challenge of differential privacy in the context of graph cuts, specifically focusing on the minimum $k$-cut and multiway cut problems. We introduce edge-differentially private algorithms that achieve nearly optimal performance for these problems. For the multiway cut problem, we first provide a private algorithm with a multiplicative approximation ratio that matches the state-of-the-art non-private algorithm. We then present a tight information-theoretic lower bound on the additive error, demonstrating that our algorithm on weighted graphs is near-optimal for constant $k$. For the minimum $k$-cut problem, our algorithms leverage a known bound on the number of approximate $k$-cuts, resulting in a private algorithm with optimal additive error $O(k\log n)$ for fixed privacy parameter. We also establish a information-theoretic lower bound that matches this additive error. Additionally, we give an efficient private algorithm for $k$-cut even for non-constant $k$, including a polynomial-time 2-approximation with an additive error of $\tilde{O}(k^{1.5})$.</p>
<time datetime="2024-10-09T16:00:00Z">October 9, 2024 12:00pm</time>
<time datetime="2024-10-09T17:00:00Z">October 9, 2024 1:00pm</time>
Nanjing University
https://www.cs.cmu.edu/~theorylunch/abstractsHTML/20241009.html
<a href="mailto:wrhe@cs.cmu.edu">wrhe@cs.cmu.edu</a>
Seminar Series
<a href="https://csd.cmu.edu/research/research-areas/theory" hreflang="en">Theory</a>
Traffic21 Classroom, Gates Hillman 6501 (new location)
<p>Speaker: ZONGRUI ZOU, Nanjing University</p>
<p>Talk Title: Differentially Private Multiway and k-Cut<br>
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<p>In this talk, we show how to address the challenge of differential privacy in the context of graph cuts, specifically focusing on the minimum $k$-cut and multiway cut problems. We introduce edge-differentially private algorithms that achieve nearly optimal performance for these problems. For the multiway cut problem, we first provide a private algorithm with a multiplicative approximation ratio that matches the state-of-the-art non-private algorithm. We then present a tight information-theoretic lower bound on the additive error, demonstrating that our algorithm on weighted graphs is near-optimal for constant $k$. For the minimum $k$-cut problem, our algorithms leverage a known bound on the number of approximate $k$-cuts, resulting in a private algorithm with optimal additive error $O(k\log n)$ for fixed privacy parameter. We also establish a information-theoretic lower bound that matches this additive error. Additionally, we give an efficient private algorithm for $k$-cut even for non-constant $k$, including a polynomial-time 2-approximation with an additive error of $\tilde{O}(k^{1.5})$.</p>
Wed, 09 Oct 2024 16:00:00 +0000Anonymous222337170 at https://csd.cmu.eduACO Seminar - Chris Eur
https://csd.cmu.edu/calendar/aco-seminar-chris-eur
<span>ACO Seminar - Chris Eur</span>
Wean Hall 8220
<span><span>Anonymous (not verified)</span></span>
<span><time datetime="2024-10-03T15:00:00-04:00" title="Thursday, October 3, 2024 - 15:00">Thu, 10/03/2024 - 15:00</time>
</span>
In Person
Using Hodge–Riemann relations
CHRIS EUR
<p>We explain how one can use ideas from algebraic geometry to establish inequalities for combinatorial invariants. We do so in two case studies: Tutte polynomials of graphs and "capacity polynomials" of colorful matchings. </p><p><em>No algebraic geometry background will be required.</em><br><br><em>4:00 pm → Tea & Cookies to follow in Wean Hall 6220, sponsored by Jane Street</em> </p><p> →<em> Bring your own mug if you have one.</em></p>
<time datetime="2024-10-03T19:00:00Z">October 3, 2024 3:00pm</time>
<time datetime="2024-10-03T20:00:00Z">October 3, 2024 4:00pm</time>
https://www.math.cmu.edu/~ceur/
Assistant Professor, Department of Mathematical Sciences, Carnegie Mellon University
https://aco.math.cmu.edu/abs-24-25/oct3.html
<a href="mailto:bbukh@math.cmu.edu">bbukh@math.cmu.edu</a>
Seminar Series
<a href="https://csd.cmu.edu/research/research-areas/algorithms-and-complexity" hreflang="en">Algorithms and Complexity</a>
<a href="https://csd.cmu.edu/research/research-areas/theory" hreflang="en">Theory</a>
Wean Hall 8220
<p>Speaker: CHRIS EUR, Assistant Professor, Department of Mathematical Sciences, Carnegie Mellon University</p>
<p>Talk Title: Using Hodge–Riemann relations</p>
<p>We explain how one can use ideas from algebraic geometry to establish inequalities for combinatorial invariants. We do so in two case studies: Tutte polynomials of graphs and "capacity polynomials" of colorful matchings. </p>
<p>No algebraic geometry background will be required.</p>
<p>4:00 pm → Tea & Cookies to follow in Wean Hall 6220, sponsored by Jane Street </p>
<p> → Bring your own mug if you have one.</p>
Thu, 03 Oct 2024 19:00:00 +0000Anonymous222337130 at https://csd.cmu.edu