Mathematics Dept.
  Events
University of Aberdeen
Mon 4 Jul 2016, 3:15pm SPECIAL
Topology and related seminars
ESB 4133 (PIMS Lounge)
Signature mod eight of surface bundles over surfaces, and cohomology of finite groups
ESB 4133 (PIMS Lounge)
Mon 4 Jul 2016, 3:15pm-4:15pm

Abstract


Note for Attendees

Please note: The topology seminar will take place on Monday instead of the usual Wednesday.
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Hans De Sterck
School of Mathematical Sciences, Monash University
Tue 12 Jul 2016, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
PIMS Lounge (ESB 4133)
Accelerated Parallel Optimization Algorithms for Distributed Data Analytics in Apache Spark
PIMS Lounge (ESB 4133)
Tue 12 Jul 2016, 12:30pm-1:30pm

Abstract

Scalable parallel optimization methods are gaining importance for a wide range of machine learning applications, for example, as implemented in the machine learning library of the Apache Spark distributed data processing environment. I will discuss our work on accelerating parallel algorithms for two common applications in this area: matrix factorization for recommendation systems, and line search methods for problems such as logistic regression.

For the recommendation application, we accelerate the standard Alternating Least Squares (ALS) optimisation algorithm using a nonlinear conjugate gradient (NCG) wrapper around the ALS iterations. In parallel numerical experiments on a 16 node cluster with 256 computing cores, we demonstrate that the combined ALS-NCG method requires many fewer iterations and less time (with acceleration factors of 4 and more) than standalone ALS to reach movie rankings with high accuracy on the MovieLens 20M dataset and synthetic datasets with up to nearly 1 billion ratings (http://arxiv.org/abs/1508.03110).

The second part of the talk discusses a new type of parallel line search for large-scale unconstrained minimization of smooth loss functions such as logistic regression. We present a new line search technique that computes more accurate minima by evaluating a Taylor polynomial approximation to the loss function, which also reduces the parallel communication costs, resulting in overall efficiency gains of a factor of 2 or more in parallel compared to existing approaches (http://arxiv.org/abs/1510.08345).

This is joint work with Mike Hynes.

Note for Attendees

Lunch will be provided.
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PhD Candidate: Raimundo Jose Briceno Dominguez
Mathematics, UBC
Fri 22 Jul 2016, 12:30pm SPECIAL
Room 203, Graduate Student Centre, 6371 Crescent Rd., UBC
Doctoral Exam: Combinatorial Aspects of Spatial Mixing and New Conditions for Pressure Representation
Room 203, Graduate Student Centre, 6371 Crescent Rd., UBC
Fri 22 Jul 2016, 12:30pm-2:30pm

Details

Abstract: Over the last few decades, there has been a growing interest in a measure-theoretical property of Gibbs distributions known as strong spatial mixing (SSM). SSM has connections with decay of correlations, uniqueness of equilibrium states, approximation algorithms for counting problems, and has been particularly useful for proving special representation formulas and the existence of efficient approximation algorithms for (topological) pressure. We look into conditions for the existence of Gibbs distributions satisfying SSM, with special emphasis in hard constrained models, and apply this for pressure representation and approximation techniques in Z^d lattice models.

Given a locally finite countable graph G and a finite graph H, we consider Hom(G,H) the set of graph homomorphisms from G to H, and we study Gibbs measures supported on Hom(G,H). We develop some sufficient and other necessary conditions on Hom(G,H) for the existence of Gibbs specifications satisfying SSM (with exponential decay). In particular, we introduce a new combinatorial condition on the support of Gibbs distributions called topological strong spatial mixing (TSSM). We establish many useful properties of TSSM for studying SSM on systems with hard constraints, and we prove that TSSM combined with SSM is sufficient for having an efficient approximation algorithm for pressure. We also show that TSSM is, in fact, necessary for SSM to hold at high decay rate.

Later, we prove a new pressure representation theorem for nearest-neighbour Gibbs interactions on Z^d shift spaces, and apply this to obtain efficient approximation algorithms for pressure in the Z^2 (ferromagnetic) Potts, (multi-type) Widom-Rowlinson, and hard-core lattice gas models. For Potts, the results apply to every inverse temperature except the critical. For Widom-Rowlinson and hard-core lattice gas, they apply to certain subsets of both the subcritical and supercritical regions. The main novelty of this work is in the latter, where SSM cannot hold.

Note for Attendees

Latecomers will not be admitted.
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PdD Candidate: Maxime Octave Bergeron
Mathematics, UBC
Mon 25 Jul 2016, 12:30pm SPECIAL
Room 203, Graduate Student Centre, 6371 Crescent Road, UBC
Doctoral Exam: The Topology of Representation Varieties
Room 203, Graduate Student Centre, 6371 Crescent Road, UBC
Mon 25 Jul 2016, 12:30pm-2:30pm

Details

Abstract: The goal of this thesis is to understand the topology of representation varieties. To be more precise, let G be a complex reductive linear algebraic group and let K be a maximal compact subgroup of G. Given a nilpotent group Γ generated by r elements, we consider the representation spaces Hom(Γ,G) and Hom(Γ,K) with the natural topology induced from an embedding into Gr and Kr respectively. Our main result shows that there is a strong deformation retraction of Hom(Γ,G) onto Hom(Γ,K). We also obtain a strong deformation retraction of the geometric invariant theory quotient Hom(Γ,G)//G onto the ordinary quotient Hom(Γ,K)/K. Using these deformations, we then describe the topology of these spaces.

Note for Attendees

Latecomers will not be admitted.
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