From saberi at stanford.edu Thu Sep 3 10:15:05 2020
From: saberi at stanford.edu (Amin Saberi)
Date: Thu, 3 Sep 2020 17:15:05 +0000
Subject: [theory-seminar] Welcome David Wajc!
Message-ID:
Hello everyone,
Please welcome David Wajc to the group.
David Wajc is a Motwani postdoctoral fellow at Stanford, hosted by Amin Saberi. He is broadly interested in algorithms under uncertainty (online, dynamic, streaming, and distributed algorithms), with a focus on matching theory under uncertainty. Prior to coming to Stanford, he completed his PhD at CMU, and his MSc and BSc (summa cum laude) at the Technion ? Israel Institute of Technology.
David enjoys hiking and (recently) backcountry camping and is a firm believer in beautiful math being something that should be done in beautiful places.
I am thrilled that he is joining us!
All the best,
Amin
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From saberi at stanford.edu Thu Sep 3 10:34:39 2020
From: saberi at stanford.edu (Amin Saberi)
Date: Thu, 3 Sep 2020 17:34:39 +0000
Subject: [theory-seminar] Course Announcement: Network Structure and
Epidemics
Message-ID:
MS&E 337: Network Structure and Epidemics
Tue-Th 2:30 ? 3:50
Instructor: Amin Saberi
Course description:
Networks play a central role in our social and economic lives. They affect our well-being by influencing the information we receive, economic opportunities we enjoy, and diseases we catch from others. How do these networks form? Which network structures are likely to emerge in society? And how does the structure of the network impact the dynamics of the spread of an innovation or infection?
This course tries to survey the mathematical results developed in the last few years on analyzing the structure of popular random networks, as well as the understanding of processes on them, with particular emphasis on epidemics. The course is loosely based on the text book ?Random Graph Dynamics? by Rick Durrett (https://services.math.duke.edu/~rtd/RGD/RGD.pdf), updated to what has happened since its publication, including the topics of graphons and graph limits, plus a larger emphasis on epidemics, as well as a short introduction to the topic of the spread of information and innovation. Additional literature, including original research papers, will be provided during the course.
Prerequisites: The course is open to graduate students with a good level of mathematical maturity and a strong background in probability (including some knowledge of Markov Chains, and basic notions of stochastic processes), as well as some basic background in graph theory and differential equations.
Topics: Random Graph Models and Structure of Large Networks (50-60%):
? Erdos-Renyi random graphs: cluster growth, formation of the giant connected component, diameter
? Models with community structure: Stochastic block model and topic models
? Non-parametric models: graphons, graph limits, estimation
? Scale-free graphs: preferential attachment model and Polya urns
Epidemics Models and their Behavior (about 25%):
? Basic compartmental models (SIS, SIR, etc.)
? Differential Equation Approach: R0, exponential growth, size of an epidemic
? Mathematically rigorous derivation of Differential Equations from the underlying dynamic model
? Percolation and Oriented Percolation representation
? Analysis of contact inhomogeneities
Algorithmic Aspects (20-25%)
? Managing epidemics: algorithmic questions related to parameter estimation, testing, and contact tracing
? Viral spread of innovations in a social network: models of adoption of innovation, influence maximization, formation of social norms
The second half of the class will be joint with CS 294 (offered at UC Berkeley by Christian Borgs) with Stanford and UC Berkeley students in the same (virtual) classroom.
All the best,
Amin
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From noahshutty at gmail.com Wed Sep 9 09:00:00 2020
From: noahshutty at gmail.com (Noah Shutty)
Date: Wed, 9 Sep 2020 12:00:00 -0400
Subject: [theory-seminar] Theory Lunch 09/10: Erik Waingarten
Message-ID:
Hi all,
Theory lunch will be happening tomorrow at
https://stanford.zoom.us/j/96247688402?pwd=MmxYTi9RTzFUKzFLd3Vab1VYTUcyQT09
(12pm
PT) and Erik will tell us about *Approximating High Dimensional EMD in
Linear Time. *
*Abstract: *
The Earth Mover's Distance is a geometric min-cost matching problem. We
receive two sets of s vectors in ?d which implicitly define a complete
bipartite graph with edge costs given by distances. The task is to compute
the minimum cost matching. We give a new analysis of an old algorithm,
improving the approximation from O(log(s) log(d)) to O?(log s). The plan is
to give a broad overview of the problem and a sketch of the new analysis.
This is joint work with Xi Chen, Rajesh Jayaram, and Amit Levi.
See you there!
Noah
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From noaj at stanford.edu Wed Sep 9 09:28:44 2020
From: noaj at stanford.edu (Noah Shutty)
Date: Wed, 9 Sep 2020 12:28:44 -0400
Subject: [theory-seminar] Theory Lunch 09/10: Erik Waingarten
Message-ID:
Hi all,
Theory lunch will be happening tomorrow at
https://stanford.zoom.us/j/96247688402?pwd=MmxYTi9RTzFUKzFLd3Vab1VYTUcyQT09
(12pm
PT) and Erik will tell us about *Approximating High Dimensional EMD in
Linear Time. *
*Abstract: *
The Earth Mover's Distance is a geometric min-cost matching problem. We
receive two sets of s vectors in ?d which implicitly define a complete
bipartite graph with edge costs given by distances. The task is to compute
the minimum cost matching. We give a new analysis of an old algorithm,
improving the approximation from O(log(s) log(d)) to O?(log s). The plan is
to give a broad overview of the problem and a sketch of the new analysis.
This is joint work with Xi Chen, Rajesh Jayaram, and Amit Levi.
See you there!
Noah
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From yuvalwig at stanford.edu Mon Sep 14 12:03:44 2020
From: yuvalwig at stanford.edu (Yuval Wigderson)
Date: Mon, 14 Sep 2020 12:03:44 -0700
Subject: [theory-seminar] Fwd: Fall 2020 Call for DRP mentors
In-Reply-To: <068a101a43d64c8ea2f1b867ffb26e0f@BYAPR02MB3957.namprd02.prod.outlook.com>
References: <068a101a43d64c8ea2f1b867ffb26e0f@BYAPR02MB3957.namprd02.prod.outlook.com>
Message-ID:
Dear theory grad students,
The math department runs a "directed reading program", where undergrads
meet one-on-one with grad student mentors for an informal reading course.
We usually get several undergrad applicants who are interested in CS-y
topics, and we often can't match them with a mentor because not enough math
grad students know the relevant topics well enough. So if you're interested
in being a mentor, we'd love to have you! Details are below.
Best,
Yuval
---------- Forwarded message ---------
From: Vivian Zieve Kuperberg
Date: Mon, Sep 14, 2020 at 11:52 AM
Subject: Fall 2020 Call for DRP mentors
To: mathstudents at lists.stanford.edu
Hi folks,
tl;dr: if you want to DRP this quarter, fill out this form
by next Wednesday, September 23rd, at 11pm.
Some graduate students in our department organize a "Directed Reading
Program," aimed at connecting undergraduate students with graduate student
"mentors" to informally learn some mathematics over the course of a quarter.
We are gearing up for the next quarter of the program and would like to
know who's interested in mentoring. Naturally, the program will operate
online this quarter. The time commitment is about one hour per week meeting
with an undergraduate student, plus attending an end-of-quarter symposium,
during the first week of winter quarter. (The mentoring commitment is just
one quarter at a time.)
The application form is available at
https://docs.google.com/forms/d/e/1FAIpQLSdyBBSH-UFmI-y7XoRg0xqy5JPn0IRYQ3z-hVExjUmZOQs_LQ/viewform?usp=sf_link
The deadline for applying is Wednesday, September 23rd, at 11pm.
If you have no idea what I'm talking about and want to know what is going
on, please see our fancy website. The
current organizers are Cole Graham, myself, Jared Marx-Kuo, Libby Taylor,
and Yuval Wigderson ; you can email any of us with questions.
Given our current funding sources, mentoring will continue to be on an
unpaid basis for the present. We do have funding to buy each student a
relevant book to read.
Best,
Vivian Kuperberg,on behalf of the DRP organiziing team.
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From noaj at stanford.edu Wed Sep 16 10:16:00 2020
From: noaj at stanford.edu (Noah Shutty)
Date: Wed, 16 Sep 2020 10:16:00 -0700
Subject: [theory-seminar] Theory Lunch 09/17: Neha Gupta
Message-ID:
Hi all,
Theory lunch will be happening tomorrow at
https://stanford.zoom.us/j/96247688402?pwd=MmxYTi9RTzFUKzFLd3Vab1VYTUcyQT09
(12pm
PT) and Neha will tell us about *Active Local Learning. *
*Abstract: *
In this work we consider active local learning: given a query point x, and
active access to an unlabeled training set S, output the prediction h(x) of
a near-optimal h \in H using significantly fewer labels than would be
needed to actually learn h fully. In particular, the number of label
queries should be independent of the complexity of H, and the function h
should be well-defined, independent of x. This immediately also implies an
algorithm for error estimation: estimating the value opt(H) from many fewer
labels than needed to actually learn a near-optimal h \in H, by running
local learning on a few random query points and computing the average error.
For the hypothesis class consisting of functions supported on the interval
[0,1] with Lipschitz constant bounded by L, we present an algorithm for
active local learning and error estimation that makes Otilde(1/epsilon^6)
label queries from an unlabeled pool of Otilde(L /epsilon^4) samples.
Joint work with Arturs Backurs and Avrim Blum.
See you there!
Noah
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From noaj at stanford.edu Wed Sep 16 10:16:00 2020
From: noaj at stanford.edu (Noah Shutty)
Date: Wed, 16 Sep 2020 10:16:00 -0700
Subject: [theory-seminar] Theory Lunch 09/17: Neha Gupta
Message-ID:
Hi all,
Theory lunch will be happening tomorrow at
https://stanford.zoom.us/j/96247688402?pwd=MmxYTi9RTzFUKzFLd3Vab1VYTUcyQT09
(12pm
PT) and Neha will tell us about *Active Local Learning. *
*Abstract: *
In this work we consider active local learning: given a query point x, and
active access to an unlabeled training set S, output the prediction h(x) of
a near-optimal h \in H using significantly fewer labels than would be
needed to actually learn h fully. In particular, the number of label
queries should be independent of the complexity of H, and the function h
should be well-defined, independent of x. This immediately also implies an
algorithm for error estimation: estimating the value opt(H) from many fewer
labels than needed to actually learn a near-optimal h \in H, by running
local learning on a few random query points and computing the average error.
For the hypothesis class consisting of functions supported on the interval
[0,1] with Lipschitz constant bounded by L, we present an algorithm for
active local learning and error estimation that makes Otilde(1/epsilon^6)
label queries from an unlabeled pool of Otilde(L /epsilon^4) samples.
Joint work with Arturs Backurs and Avrim Blum.
See you there!
Noah
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From jneu at stanford.edu Wed Sep 16 12:39:55 2020
From: jneu at stanford.edu (Joachim Neu)
Date: Wed, 16 Sep 2020 12:39:55 -0700
Subject: [theory-seminar]
=?utf-8?q?ISL_Colloquium=3A_=22Quantum_Renyi_rel?=
=?utf-8?q?ative_entropies_and_their_use=22_=E2=80=93_Mark_Wilde_=28Thu=2C?=
=?utf-8?q?_17-Sep_=40_4=3A30pm_PT=29?=
In-Reply-To: <2c1e7e1239da5d5ec8000a8392a95daf3cdcc67e.camel@stanford.edu>
References: <2c1e7e1239da5d5ec8000a8392a95daf3cdcc67e.camel@stanford.edu>
Message-ID: <6bdde5ccaae2dc6f2b8b8c14c224072756ca5ae9.camel@stanford.edu>
Reminder: This talk is tomorrow, Thu, 17-Sept, 4:30pm, via Zoom, see
link below.
Also, we have moved the usual Thursdays 4pm ISL coffee hour to
Gathertown at: https://gather.town/uaAn6GTFg40xKE2u/ISL Password: isl-
colloq Please do join us!
-----Original Message-----
Quantum Renyi relative entropies and their use
Mark Wilde ? Professor, Louisiana State University
Thu, 17-Sep / 4:30pm PT / Zoom:
https://stanford.zoom.us/meeting/register/tJckfuCurzkvEtKKOBvDCrPv3McapgP6HygJ
To avoid Zoom-bombing, we ask attendees to sign in
via the above URL to receive the Zoom meeting details by email.
Abstract
The past decade of research in quantum information theory has
witnessed extraordinary progress in understanding communication over
quantum channels, due in large part to quantum generalizations of the
classical Renyi relative entropy. One generalization is known as the
sandwiched Renyi relative entropy and finds its use in characterizing
asymptotic behavior in quantum hypothesis testing. It has also found
use
in establishing strong converse theorems (fundamental communication
capacity limitations) for a variety of quantum communication tasks.
Another generalization is known as the geometric Renyi relative
entropy
and finds its use in establishing strong converse theorems for
feedback
assisted protocols, which apply to quantum key distribution and
distributed quantum computing scenarios. Finally, a generalization now
known as the Petz?Renyi relative entropy plays a critical role for
statements of achievability in quantum communication. In this talk, I
will review these quantum generalizations of the classical Renyi
relative entropy, discuss their relevant information-theoretic
properties, and the applications mentioned above.
Bio
Mark M. Wilde is an Associate Professor in the Department of Physics
and Astronomy and the Center for Computation and Technology at
Louisiana
State University. He is a recipient of the Career Development Award
from the US National Science Foundation and is Associate Editor for
Quantum Information Theory at IEEE Transactions on Information Theory
and New Journal of Physics. His current research interests are in
quantum Shannon theory, quantum optical communication, quantum
computational complexity theory, and quantum error correction.
Mailing list:
https://mailman.stanford.edu/mailman/listinfo/isl-colloq
This talk:
http://isl.stanford.edu/talks/talks/2020q4/mark-wilde/
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From jneu at stanford.edu Thu Sep 17 18:58:04 2020
From: jneu at stanford.edu (Joachim Neu)
Date: Thu, 17 Sep 2020 18:58:04 -0700
Subject: [theory-seminar]
=?utf-8?q?IT_Forum=3A_=22Learning_to_Bid_in_Repe?=
=?utf-8?q?ated_First-price_Auctions=22_=E2=80=93_Yanjun_Han_=28Fri=2C_18-?=
=?utf-8?q?Sep_=40_1=3A15pm=29?=
In-Reply-To:
References:
Message-ID:
Reminder: This talk is tomorrow, Fri, 18-Sept, at 1:15pm PT. Zoom link
below.
-----Original Message-----
Learning to Bid in Repeated First-price Auctions
Yanjun Han ? PhD Candidate, Stanford University
Fri, 18-Sep / 1:15pm / Zoom:
https://stanford.zoom.us/meeting/register/tJwkf-uvqjoqHNIWxY4HHon4K107QMo22PVR
To avoid Zoom-bombing, we ask attendees to sign in
via the above URL to receive the Zoom meeting details by email.
Abstract
First-price auctions have very recently swept the online advertising
industry, replacing second-price auctions as the predominant auction
mechanism on many platforms. This shift has brought forth important
challenges for a bidder: how should one bid in a first-price auction
where it is no longer optimal to bid one?s private value truthfully
and
hard to know the others? bidding behaviors? To answer this question,
we
study online learning in repeated first-price auctions, and consider
various scenarios involving different assumptions on the
characteristics
of the other bidders? bids, of the bidder?s private valuation, of the
feedback structure of the auction, and of the reference policies with
which our bidder competes. For all of them, we characterize the
essentially optimal performance and identify computationally efficient
algorithms achieving it. Experimentation on first-price auction
datasets
from Verizon Media demonstrates the promise of our schemes relative
to
existing bidding algorithms.
Based on joint work with Aaron Flores, Erik Ordentlich, Tsachy
Weissman, and Zhengyuan Zhou. The full papers are available online at
https://arxiv.org/abs/2003.09795
and
https://arxiv.org/abs/2007.04568.
Bio
Yanjun Han is a 6th-year PhD candidate in Electrical Engineering at
Stanford University, advised by Tsachy Weissman. His research
interests
include high-dimensional and nonparametric statistics, information
theory, online learning, applied probability, and their applications.
Mailing list:
https://mailman.stanford.edu/mailman/listinfo/information_theory_forum
This talk:
https://web.stanford.edu/group/it-forum/talks/talks/2020q4/yanjun-han1/
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From gillespl at stanford.edu Fri Sep 18 15:38:09 2020
From: gillespl at stanford.edu (Lauren Gillespie)
Date: Fri, 18 Sep 2020 22:38:09 +0000
Subject: [theory-seminar] Stanford CS Undergraduate Research (CURIS)
Outreach Assistant
Message-ID: <797D214D-E5AD-4929-B7D8-B4B87F45D4A0@stanford.edu>
Hi all,
CURIS is looking to recruit an undergraduate research outreach assistant. To note, this is an hourly pay position which means that the position is an additional pay to any financial package you might have. Please see the below message for details:
Responsible for hands-on outreach to underrepresented undergraduates to increase their participation in computer science research. The position has four major responsibilities: continually canvassing the undergraduate population to learn how CURIS can be more accessible, writing up these findings in quarterly written reports to the CS department and CURIS, reaching out to student groups to ensure they are aware of CURIS events, and developing new outreach activities. The ability to guide, advise, and successfully build relationships with underrepresented student groups is a key job requirement.
Position is hourly and pays $17/hour depending on experience for an expected 4-8 hours/week of work. Pay rate will be decided in accordance with Stanford?s undergraduate student wage scale.
Interested students should contact Yesenia Gallegos >. Please include a resume and a short (~200 word) statement of why you would be able to do a good job and help the department attract students from underrepresented populations to research opportunities.
-Lauren Gillespie
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From jneu at stanford.edu Fri Sep 18 16:44:51 2020
From: jneu at stanford.edu (Joachim Neu)
Date: Fri, 18 Sep 2020 16:44:51 -0700
Subject: [theory-seminar] =?utf-8?q?IT_Forum=3A_=22High-accuracy_Optimalit?=
=?utf-8?q?y_and_Limitation_of_the_Profile_Maximum_Likelihood=22_=E2=80=93?=
=?utf-8?q?_Yanjun_Han_=28Fri=2C_25-Sep_=40_1=3A15pm=29?=
Message-ID:
High-accuracy Optimality and Limitation of the Profile Maximum
Likelihood
Yanjun Han ? PhD Candidate, Stanford University
Fri, 25-Sep / 1:15pm / Zoom:
https://stanford.zoom.us/meeting/register/tJwkf-uvqjoqHNIWxY4HHon4K107QMo22PVR
To avoid Zoom-bombing, we ask attendees to sign in
via the above URL to receive the Zoom meeting details by email.
Abstract
Symmetric properties of distributions arise in multiple settings,
where for each of them separate estimators have been developed.
Recently, Orlitsky et al. showed that a single estimator, called the
profile maximum likelihood (PML), achieves the optimal sample
complexity
universally for many properties and any accuracy parameter larger
than
$n^{-1?4}$, where $n$ is the sample size. They
also raised the question whether this low-accuracy range is an
artifact
of the analysis or a fundamental limitation of the PML, which remained
open after several subsequent work.
In this talk, we provide a complete answer to this question and
characterize the tight performance of PML in the high-accuracy regime.
On the positive side, we show that the PML remains sample-optimal for
any accuracy parameter larger than $n^{-1?3}$
using a novel chaining property of the PML distributions. In
particular,
the PML distribution itself is an optimal estimator of the sorted
hidden distribution. On the negative side, we show that the PML as
well
as any adaptive approach cannot be universally sample-optimal when the
accuracy parameter is below $n^{-1?3}$, and characterize the exact
penalty for adaptation via a matching adaptation lower bound.
Based on joint work with Kirankumar Shiragur. The full papers are
available online at
https://arxiv.org/abs/2004.03166 and
https://arxiv.org/abs/2008.11964.
Bio
Yanjun Han is a 6th-year PhD candidate in Electrical Engineering at
Stanford University, advised by Tsachy Weissman. His research
interests
include high-dimensional and nonparametric statistics, information
theory, online learning, applied probability, and their applications.
Mailing list:
https://mailman.stanford.edu/mailman/listinfo/information_theory_forum
This talk:
https://web.stanford.edu/group/it-forum/talks/talks/2020q4/yanjun-han2/
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From noaj at stanford.edu Wed Sep 23 10:00:00 2020
From: noaj at stanford.edu (Noah Shutty)
Date: Wed, 23 Sep 2020 10:00:00 -0700
Subject: [theory-seminar] Theory Lunch 09/24: Jay Mardia
Message-ID:
Hi all,
Theory lunch will be happening tomorrow at
https://stanford.zoom.us/j/96247688402?pwd=MmxYTi9RTzFUKzFLd3Vab1VYTUcyQT09
(12pm
PT) and Jay will tell us about *Finding planted cliques in sublinear time*.
*Abstract: *
We discuss the planted clique problem, which has been well studied for the
statistical-computational phenomena it shows. A clique of size k is planted
in an Erdos Renyi random graph on n vertices, and our goal is to recover
this clique. Linear time algorithms can easily solve the problem for
k=Omega(sqrt(n)), and it is widely believed that smaller cliques can not be
recovered by polynomial time algorithms. This is known as the Planted
Clique Conjecture.
We uncover more interesting phenomena in the complexity of this problem.
First, we show that in the 'easy' regime, sublinear time algorithms can
actually solve the recovery problem. So either the problem is easy enough
that we don't even need to look at the entire graph. Or it is so hard that
no polynomial time algorithm can solve it.
Then we try and give fine grained computational evidence to show that our
sublinear running times are optimal. We do this by studying a natural
restricted class of algorithms and show that they can not do better than
our algorithms. It is an open problem to extend these arguments to a larger
class of algorithms. The main message will be that the non-existence of
faster sublinear time algorithms in the 'easy' regime is related to the
non-existence of polynomial time algorithms in the 'hard' regime.
This talk is based on joint work with Hilal Asi and Kabir Chandrasekher.
https://arxiv.org/abs/2004.12002
See you there!
Noah
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From noaj at stanford.edu Wed Sep 23 10:00:00 2020
From: noaj at stanford.edu (Noah Shutty)
Date: Wed, 23 Sep 2020 10:00:00 -0700
Subject: [theory-seminar] Theory Lunch 09/24: Jay Mardia
Message-ID:
Hi all,
Theory lunch will be happening tomorrow at
https://stanford.zoom.us/j/96247688402?pwd=MmxYTi9RTzFUKzFLd3Vab1VYTUcyQT09
(12pm
PT) and Jay will tell us about *Finding planted cliques in sublinear time*.
*Abstract: *
We discuss the planted clique problem, which has been well studied for the
statistical-computational phenomena it shows. A clique of size k is planted
in an Erdos Renyi random graph on n vertices, and our goal is to recover
this clique. Linear time algorithms can easily solve the problem for
k=Omega(sqrt(n)), and it is widely believed that smaller cliques can not be
recovered by polynomial time algorithms. This is known as the Planted
Clique Conjecture.
We uncover more interesting phenomena in the complexity of this problem.
First, we show that in the 'easy' regime, sublinear time algorithms can
actually solve the recovery problem. So either the problem is easy enough
that we don't even need to look at the entire graph. Or it is so hard that
no polynomial time algorithm can solve it.
Then we try and give fine grained computational evidence to show that our
sublinear running times are optimal. We do this by studying a natural
restricted class of algorithms and show that they can not do better than
our algorithms. It is an open problem to extend these arguments to a larger
class of algorithms. The main message will be that the non-existence of
faster sublinear time algorithms in the 'easy' regime is related to the
non-existence of polynomial time algorithms in the 'hard' regime.
This talk is based on joint work with Hilal Asi and Kabir Chandrasekher.
https://arxiv.org/abs/2004.12002
See you there!
Noah
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From jneu at stanford.edu Thu Sep 24 01:01:51 2020
From: jneu at stanford.edu (Joachim Neu)
Date: Thu, 24 Sep 2020 01:01:51 -0700
Subject: [theory-seminar]
=?utf-8?q?IT_Forum=3A_=22High-accuracy_Optimalit?=
=?utf-8?q?y_and_Limitation_of_the_Profile_Maximum_Likelihood=22_=E2=80=93?=
=?utf-8?q?_Yanjun_Han_=28Fri=2C_25-Sep_=40_1=3A15pm=29?=
In-Reply-To:
References:
Message-ID: <7f1dab66fc93206c19593b71005dab918e2f23c5.camel@stanford.edu>
Reminder: This talk is on Friday, 25-Sept, at 1:15pm PT, via Zoom.
-----Original Message-----
High-accuracy Optimality and Limitation of the Profile Maximum
Likelihood
Yanjun Han ? PhD Candidate, Stanford University
Fri, 25-Sep / 1:15pm / Zoom:
https://stanford.zoom.us/meeting/register/tJwkf-uvqjoqHNIWxY4HHon4K107QMo22PVR
To avoid Zoom-bombing, we ask attendees to sign in
via the above URL to receive the Zoom meeting details by email.
Abstract
Symmetric properties of distributions arise in multiple settings,
where for each of them separate estimators have been developed.
Recently, Orlitsky et al. showed that a single estimator, called the
profile maximum likelihood (PML), achieves the optimal sample
complexity
universally for many properties and any accuracy parameter larger
than
$n^{-1?4}$, where $n$ is the sample size. They
also raised the question whether this low-accuracy range is an
artifact
of the analysis or a fundamental limitation of the PML, which remained
open after several subsequent work.
In this talk, we provide a complete answer to this question and
characterize the tight performance of PML in the high-accuracy regime.
On the positive side, we show that the PML remains sample-optimal for
any accuracy parameter larger than $n^{-1?3}$
using a novel chaining property of the PML distributions. In
particular,
the PML distribution itself is an optimal estimator of the sorted
hidden distribution. On the negative side, we show that the PML as
well
as any adaptive approach cannot be universally sample-optimal when the
accuracy parameter is below $n^{-1?3}$, and characterize the exact
penalty for adaptation via a matching adaptation lower bound.
Based on joint work with Kirankumar Shiragur. The full papers are
available online at
https://arxiv.org/abs/2004.03166 and
https://arxiv.org/abs/2008.11964.
Bio
Yanjun Han is a 6th-year PhD candidate in Electrical Engineering at
Stanford University, advised by Tsachy Weissman. His research
interests
include high-dimensional and nonparametric statistics, information
theory, online learning, applied probability, and their applications.
Mailing list:
https://mailman.stanford.edu/mailman/listinfo/information_theory_forum
This talk:
https://web.stanford.edu/group/it-forum/talks/talks/2020q4/yanjun-han2/
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From jneu at stanford.edu Sat Sep 26 23:26:28 2020
From: jneu at stanford.edu (Joachim Neu)
Date: Sat, 26 Sep 2020 23:26:28 -0700
Subject: [theory-seminar] IBM Research Workshop on the Informational Lens
Message-ID:
The IBM Research Workshop on the Informational Lens (29 Sept to 2 Oct)
might be of interest to some on this list. Many interesting speakers.
RSVP required but free.
Website:
https://sites.google.com/view/informational-lens-workshop-1/
Talk titles and abstracts:
https://sites.google.com/view/informational-lens-workshop-1/talk-abstracts
Description:
The "information century" was launched by Turing's 1936 invention of a
hardware-independent notion of computing, a "universal computer" that
could be programmed to simulate any other computer; and by Shannon's
1948 discovery of a mathematical theory of communications independent
of their physical form and even their meaning.
Arguably, we are today in the midst of another information revolution,
with the advent of neurons and qubits as new representation and
processing elements for information. These advances, together with the
exponential growth in memory and speed of conventional computing, have
made it hazardous to conjecture any informational task at which humans
will not be soon bested by computers.
Viewing the world through an informational lens, and understanding
constraints and tradeoffs such as energy and parallelism versus
reliability and speed, will have profound consequences throughout
technology and science. This includes not only mathematics and the
natural sciences like physics and biology, but also social sciences
such as psychology and linguistics. We aim to bring together leading
researchers in science and technology from across the globe to discuss
ideas and future research directions through the informational lens.
From noaj at stanford.edu Wed Sep 30 23:44:20 2020
From: noaj at stanford.edu (Noah Shutty)
Date: Wed, 30 Sep 2020 23:44:20 -0700
Subject: [theory-seminar] Theory Lunch 09/30 -- Carrie Wu (Talk Starts at
noon)
Message-ID:
Hi all,
Theory lunch will be happening tomorrow (Thursday at
https://stanford.zoom.us/j/96247688402?pwd=MmxYTi9RTzFUKzFLd3Vab1VYTUcyQT09
(12pm
PT) and Carrie will tell us about *Developing Data Efficient Algorithms for
AI*.
Please note the earlier start time: this talk will begin at 12pm PT.
*Abstract: *
Our increasingly ambitious goals in artificial intelligence motivate
several key algorithmic challenges, such as: how do we design algorithms
that make the best use of the data that is available, and how do we design
algorithms that are empirically and theoretically effective on the kinds of
data that we often see in practice, for example, data with temporal
dependencies and data that follow distributions that are hard to describe.
In this talk, I will give examples of algorithmic solutions that address
some of these challenges. I will first present a theoretical analysis of
rates of convergence for SGD with experience replay, which is a technique
used in Reinforcement Learning to break temporal differences in data. I
will then present an algorithm that solves Markov Decision Processes with
nearly optimal sample and runtime guarantees. Lastly, I will present an
algorithmic solution for estimating local density for an arbitrary dataset.
Thanks,
Noah
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From noaj at stanford.edu Wed Sep 30 23:44:20 2020
From: noaj at stanford.edu (Noah Shutty)
Date: Wed, 30 Sep 2020 23:44:20 -0700
Subject: [theory-seminar] Theory Lunch 09/30 -- Carrie Wu (Talk Starts at
noon)
Message-ID:
Hi all,
Theory lunch will be happening tomorrow (Thursday at
https://stanford.zoom.us/j/96247688402?pwd=MmxYTi9RTzFUKzFLd3Vab1VYTUcyQT09
(12pm
PT) and Carrie will tell us about *Developing Data Efficient Algorithms for
AI*.
Please note the earlier start time: this talk will begin at 12pm PT.
*Abstract: *
Our increasingly ambitious goals in artificial intelligence motivate
several key algorithmic challenges, such as: how do we design algorithms
that make the best use of the data that is available, and how do we design
algorithms that are empirically and theoretically effective on the kinds of
data that we often see in practice, for example, data with temporal
dependencies and data that follow distributions that are hard to describe.
In this talk, I will give examples of algorithmic solutions that address
some of these challenges. I will first present a theoretical analysis of
rates of convergence for SGD with experience replay, which is a technique
used in Reinforcement Learning to break temporal differences in data. I
will then present an algorithm that solves Markov Decision Processes with
nearly optimal sample and runtime guarantees. Lastly, I will present an
algorithmic solution for estimating local density for an arbitrary dataset.
Thanks,
Noah
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