Category Archives: CORE Talks

Jesús De Loera; Variations on a theme by G. Dantzig: Revisiting the principles of the Simplex Algorithm

CORE Series
Jesús De Loera, UC Davis
Friday, November 30, 2018
MEB 248, 2:30pm

TITLE: Variations on a theme by G. Dantzig: Revisiting the principles of the Simplex Algorithm

ABSTRACT:
Linear programs (LPs) are, without any doubt, at the core of both the theory and the practice of modern applied and computational optimization (e.g., in discrete optimization LPs are used in practical computations using branch-and-bound, and in approximation algorithms, e.g., in rounding schemes).  Fast algorithms are indispensable.

George Dantzig’s simplex method is one of the most famous algorithms to solve LPs and SIAM even elected it as one of the top 10 most influential algorithms of the 20th Century. But despite its key importance, many simple easy-to-state mathematical properties of the simplex method and its geometry remain unknown. The geometry of the simplex method is a topic in the convex-combinatorial geometry of polyhedra. Perhaps the most famous geometric-combinatorial challenge is to determine a worst-case upper bound for the graph diameter of polyhedra.

In this talk, I will look at how abstractions of the simplex method provide useful insight into the properties of this famous algorithm. The first type of abstraction is to remove coordinates entirely and is related to combinatorial topology, the second is related to generalizing the pivoting moves. This survey lecture includes joint work with Steve Klee, Raymond Hemmecke, and Jon Lee.

BIO:
Jesús A. De Loera received his Bachelor of Science degree in Mathematics from the National University of Mexico in 1989, and a Ph.D in Applied Mathematics from Cornell University in 1995. He arrived at UC Davis in 1999, where he is now a professor of Mathematics, as well as a member of the Graduate groups in Computer Science and Applied Mathematics. He has held visiting positions at the University of Minnesota, the Swiss Federal Technology Institute (ETH Zürich), the Mathematical Science Institute at Berkeley (MSRI), Universität Magdeburg (Germany), the Institute for Pure and Applied Mathematics at UCLA (IPAM), the Newton Institute of Cambridge Univ. (UK), and the Technische Universität München.

His research covers a wide range of topics, including Combinatorics, Algorithms, Convex Geometry, Applied Algebra, and Optimization. In 2004 he received an Alexander von Humboldt Fellowship and won the 2010 INFORMS computer society prize for his work in algebraic algorithms in Optimization.  For his contributions to Discrete Geometry and Combinatorial Optimization, as well as for service to the profession, including mentoring and diversity, he was elected a fellow of the American Mathematical Society in 2014. For his mentoring and teaching he received the 2013 Chancellor’s award for mentoring undergraduate research and, in 2017, the Mathematical Association of America Golden Section Teaching Award. He has supervised twelve Ph.D students, and over 50 undergraduates research projects. He is currently an associate editor for SIAM Journal of Discrete Mathematics, SIAM Journal of Applied Algebra and Geometry, and the Boletin de la Sociedad Matematica Mexicana.

Francis Bach; Can machine learning survive the artificial intelligence revolution? 

CORE Series
Francis Bach, Inria and Ecole Normale Supérieure
Thursday, November 8, 2018
Electrical Engineering Building (EEB) 105, 11:00am

Poster PDF

TITLE: Can machine learning survive the artificial intelligence revolution?

ABSTRACT:
Data and algorithms are ubiquitous in all scientific, industrial and personal domains. Data now come in multiple forms (text, image, video, web, sensors, etc.), are massive, and require more and more complex processing beyond their mere indexation or the computation of simple statistics, such as recognizing objects in images or translating texts. For all of these tasks, commonly referred to as artificial intelligence (AI), significant recent progress has allowed algorithms to reach performances that were deemed unreachable a few years ago and that make these algorithms useful to everyone.

Many scientific fields contribute to AI, but most of the visible progress come from machine learning and tightly connected fields such as computer vision and natural language processing. Indeed, many of the recent advances are due to the availability of massive data to learn from, large computing infrastructures and new machine learning models (in particular deep neural networks).

Beyond the well publicized visibility of some advances, machine learning has always been a field characterized by the constant exchanges between theory and practice, with a stream of algorithms that exhibit both good empirical performance on real-world problems and some form of theoretical guarantees. Is this still possible?

In this talk, I will present recent illustrating machine learning successes and propose some answers to the question above.

Francis Bach is the Distinguished Visiting Faculty of the NSF-TRIPODS Algorithmic Foundations of Data Science Institute. The seminar is part of the CORE Seminar Series, the Data Science Seminar Series, and the ML Seminar Series.

BIO:
Francis Bach is a researcher at Inria, leading since 2011 the machine learning team which is part of the Computer Science Department at Ecole Normale Supérieure. He graduated from Ecole Polytechnique in 1997 and completed his Ph.D. in Computer Science at U.C. Berkeley in 2005, working with Professor Michael Jordan. He spent two years in the Mathematical Morphology group at Ecole des Mines de Paris, then he joined the computer vision project-team at Inria/Ecole Normale Supérieure from 2007 to 2010. Francis Bach is primarily interested in machine learning, and especially in graphical models, sparse methods, kernel-based learning, large-scale convex optimization, computer vision and signal processing. He obtained in 2009 a Starting Grant and in 2016 a Consolidator Grant from the European Research Council, and received the Inria young researcher prize in 2012, the ICML test-of-time award in 2014, as well as the Lagrange prize in continuous optimization in 2018. In 2015, he was program co-chair of the International Conference in Machine Learning (ICML), and general chair in 2018; he is now co-editor-in-chief of the Journal of Machine Learning Research.

Yurii Nesterov; Relative smoothness condition and its application to third-order methods

CORE Series
Monday, May 21, 2018
SMI 205, 4:00PM 
Yurii Nesterov (CORE/INMA, UCL, Belgium)

TITLE:  Relative smoothness condition and its application to third-order methods

ABSTRACT:  In this talk, we show that the recently developed relative smoothness condition can be used for constructing implementable third-order methods for Unconstrained Convex Optimization. At each iteration of these methods, we need to solve an auxiliary problem of minimizing a convex multivariate polynomial, which is a sum of the third-order Taylor approximation and a regularization term. It appears that this nontrivial nonlinear optimization problem can be solved very efficiently by a gradient-type minimization method based on the relative smoothness condition. Its linear rate of convergence depends only on absolute constant. This result opens a possibility for practical implementation of the third-order methods.

BIO:  Yurii Nesterov is a professor at the Center for Operations Research and Econometrics (CORE) in Catholic University of Louvain (UCL), Belgium. He received his Ph.D. degree (Applied Mathematics) in 1984 at the Institute of Control Sciences, Moscow. Starting from 1993 he works at the Center of Operations Research and Econometrics (Catholic University of Louvain, Belgium).

His research interests are related to complexity issues and efficient methods for solving various optimization problems. The main results are obtained in Convex Optimization (optimal methods for smooth problems, polynomial-time interior-point methods, smoothing technique for structural optimization, complexity theory for second-order methods, optimization methods for huge-scale problems). He is an author of 5 monographs and more than 100 refereed papers in leading optimization journals. He has received several international prizes, among which are the Dantzig Prize from SIAM and Mathematical Programming society (2000), the von Neumann Theory Prize from INFORMS (2009), the SIAM Outstanding Paper Award (2014), and the Euro Gold Medal from the Association of European Operations Research Societies (2016). In 2018 he also won an Advanced Grant from the European Research Council.

Aaron Sidford; Faster Algorithms for Computing the Stationary Distribution

CORE Series
Tuesday, May 8, 2018
SAV 264, 4:00PM 
Aaron SidfordStanford University (Management Science and Engineering)

TITLE: Faster Algorithms for Computing the Stationary Distribution

ABSTRACT: Computing the stationary distribution of a Markov Chain is one of the most fundamental problems in optimization. It lies at the heart of numerous computational tasks including computing personalized PageRank vectors, evaluating the utility of policies in Markov decision process, and solving asymmetric diagonally dominant linear systems. Despite the ubiquity of these problems, until recently the fastest known running times for computing the stationary distribution either depended polynomially on the mixing time or desired accuracy or appealed to generic linear system solving machinery, and therefore ran in super-quadratic time.

In this talk I will present recent results showing that the stationary distribution and related quantities can all be computed in almost linear time. I will present new iterative methods for extracting structure from directed graphs and and show how they can be tailored to achieve this new running time. Moreover, I will discuss connections between this work and recent developments in solving Laplacian systems and emerging trends in combining numerical and combinatorial techniques in the design of optimization algorithms.

This talk reflects joint work with Michael B. Cohen (MIT), Jonathan Kelner (MIT), Rasmus Kyng (Harvard), John Peebles (MIT), Richard Peng (Georgia Tech), Anup Rao (Adobe Research), and Adrian Vladu (Boston University).

BIO: Aaron completed his PhD at MIT (CSAIL) advised by Jon Kelner and since then is an Assistant Professor at Stanford (MSE). He works on fast algorithms for various optimization problems. His work received best paper awards at SODA 2014 and FOCS 2014 and a best student paper award at FOCS 2015. In particular he become broadly known in the community for the development of an Interior Point Algorithm that solves LPs in sqrt(rank) many iterations (also improving the total running time compared to previous algorithms). This had been the most prominent open problem in the field of interior point methods since the work of Nesterov and Nemirovski in 1994.

John Duchi; Composite modeling and optimization, with applications to phase retrieval and nonlinear observation modeling

CORE Series
Friday, Oct 20, 2017
SMI 211, 3:30PM 
John DuchiStanford University (Departments of Statistics and Electrical Engineering)

TITLE: Composite modeling and optimization, with applications to phase retrieval and nonlinear observation modeling

ABSTRACT: We consider minimization of stochastic functionals that are compositions of a (potentially) non-smooth convex function h and smooth function c. We develop two stochastic methods–a stochastic prox-linear algorithm and a stochastic (generalized) sub-gradient procedure–and prove that, under mild technical conditions, each converges to first-order stationary points of the stochastic objective. Additionally, we analyze this problem class in the context of phase retrieval and more generic nonlinear modeling problems, showing that we can solve these problems (even with faulty measurements) with extremely high probability under appropriate random measurement models. We provide substantial experiments investigating our methods, indicating the practical effectiveness of the procedures.

 

BIO: John Duchi is an assistant professor of Statistics and Electrical Engineering and (by courtesy) Computer Science at Stanford University, with graduate degrees from UC Berkeleyand undergraduate degrees from Stanford. His work focuses on large scale optimization problems arising out of statistical and machine learning problems, robustness and uncertain data problems, and information theoretic aspects of statistical learning. He has won a number of awards and fellowships, including a best paper award at the International Conference onMachine Learning, an NSF CAREER award, and a Sloan Fellowship in Mathematics.

Zaid Harchaoui; Catalyst, Generic Acceleration Scheme for Gradient-based Optimization

CORE Series
Tuesday, April 18, 2017
EEB 125, 4:00-5:00PM 
Zaid HarchaouiUniversity of Washington

TITLE: Catalyst, Generic Acceleration Scheme for Gradient-based Optimization

ABSTRACT: We introduce a generic scheme called Catalyst for accelerating first-order optimization methods in the sense of Nesterov, which builds upon a new analysis of the accelerated proximal point algorithm. The proposed approach consists of minimizing a convex objective by approximately solving a sequence of well-chosen auxiliary problems, leading to faster convergence. This strategy applies to a large class of algorithms, including gradient descent, block coordinate descent, SAG, SAGA, SDCA, SVRG, Finito/MISO, and their proximal variants. For all of these methods, we provide acceleration and explicit support for non-strongly convex objectives. Furthermore, the approach can be extended to venture into possibly nonconvex optimization problems without sacrificing the rate of convergence to stationary points. We present experimental results showing that the Catalyst acceleration scheme is effective in practice, especially for ill-conditioned problems where we measure significant improvements.

BIO: Zaid Harchaoui is currently a Provost’s Initiative in Data-driven Discovery Assistant Professor in the Department of Statistics and a Data Science Fellow in the eScience Institute at University of Washington. He completed his Ph.D. at ParisTech (now in Univ. Paris-Saclay), working with Eric Moulines, Stephane Canu and Francis Bach. Before joining the University of Washington, he was a visiting assistant professor at the Courant Institute for Mathematical Sciences at New York University (2015 – 2016). Prior to this, he was a permanent researcher on the LEAR team of Inria (2010 – 2015). He was a postdoctoral fellow in the Robotics Institute of Carnegie Mellon University in 2009.

He received the Inria award for scientific excellence and the NIPS reviewer award. He gave a tutorial on “Frank-Wolfe, greedy algorithms, and friends” at ICML’14, on “Large-scale visual recognition” at CVPR’13, and on “Machine learning for computer vision” at MLSS Kyoto 2015. He recently co-organized the “Future of AI” symposium at New York University, the workshop on “Optimization for MachineLearning” at NIPS’14, and the “Optimization and statistical learning” workshop in 2015 and 2013 in Ecole de Physique des Houches (France). He served/will serve as Area Chair for ICML 2015, ICML 2016, NIPS 2016, ICLR 2016. He is currently an associate editor of IEEE Signal Processing Letters.

Liza Levina; Interpretable Prediction Models for Network-Linked Data

CORE Series
Tuesday, April 11, 2017
EEB 125, 4:00-5:00PM 
Liza LevinaUniversity of Michigan

TITLE: Interpretable Prediction Models for Network-Linked Data

ABSTRACT: Prediction problems typically assume the training data are independent samples, but in many modern applications samples come from individuals connected by a network. For example, in adolescent health studies of risk-taking behaviors, information on the subjects’ social networks is often available and plays an important role through network cohesion, the empirically observed phenomenon of friends behaving similarly. Taking cohesion into account should allow us to improve prediction. Here we propose a regression-based framework with a network penalty on individual node effects to encourage similarity between predictions for linked nodes, and show that it outperforms traditional models both theoretically and empirically when network cohesion is present. The framework is easily extended to other models, such as the generalized linear model and Cox’s proportional hazard model. Applications to predicting teenagers’ behavior based on both demographic covariates and their friendship networks from the AddHealth data are discussed in detail.

BIO: Liza Levina received her PhD in Statistics from UC Berkeley in 2002 and joined the University of Michigan the same year.  Her research interestsinclude networks, high-dimensional data, and sparsity.  She has worked on estimating large covariance matrices,
graphical models, and other topics in inference for high-
dimensional data.   She also works on statistical inference for network data, including problems of community detectiona
nd link prediction.   Her research covers methodology, theory, and applications, especially to spectroscopy, remote sensing and, in the past, computer vision. She received the junior Noether Award from the ASA in 2010 and was elected a member of ISI in 2011.