| 1. |
- Olsson, Carl, 1978, et al.
(författare)
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Relaxations for Non-Separable Cardinality/Rank Penalties
- 2021
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Ingår i: Proceedings of the IEEE International Conference on Computer Vision. - 1550-5499. ; 2021-October, s. 162-171
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Konferensbidrag (refereegranskat)abstract
- Rank and cardinality penalties are hard to handle in optimization frameworks due to non-convexity and discontinuity. Strong approximations have been a subject of intense study and numerous formulations have been proposed. Most of these can be described as separable, meaning that they apply a penalty to each element (or singular value) based on size, without considering the joint distribution. In this paper we present a class of non-separable penalties and give a recipe for computing strong relaxations suitable for optimization. In our analysis of this formulation we first give conditions that ensure that the global ly optimal solution of the relaxation is the same as that of the original (unrelaxed) objective. We then show how a stationary point can be guaranteed to be unique under the restricted isometry property (RIP) assumption.1
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| 2. |
- Wennberg, Bernt, 1961
(författare)
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Random many-particle systems: applications from biology, and propagation of chaos in abstract models
- 2012
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Ingår i: Rivista di Matematica della Università di Parma. ; 3:2, s. 291-344
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Konferensbidrag (refereegranskat)abstract
- The paper discusses a family of Markov processes that represent many particle systems, and their limiting behaviour when the number of particles go to infinity. The first part concerns model of biological systems: a model for sympatric speciation, i.e. the process in which a genetically homogeneous population is split in two or more different species sharing the same habitat, and models for swarming animals. The second part of the paper deals with abstract many particle systems and methods for rigorously deriving mean field models.
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| 3. |
- Lang, Annika, 1980
(författare)
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A Note on the Importance of Weak Convergence Rates for SPDE Approximations in Multilevel Monte Carlo Schemes
- 2016
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Ingår i: Springer Proceedings in Mathematics and Statistics. - Cham : Springer International Publishing. - 2194-1017 .- 2194-1009. - 9783319335056 ; 163, s. 489-505
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Konferensbidrag (refereegranskat)abstract
- It is a well-known rule of thumb that approximations of stochastic partial differential equations have essentially twice the order of weak convergence compared to the corresponding order of strong convergence. This is already known for many approximations of stochastic (ordinary) differential equations while it is recent research for stochastic partial differential equations. In this note it is shown how the availability of weak convergence results influences the number of samples in multilevel Monte Carlo schemes and therefore reduces the computational complexity of these schemes for a given accuracy of the approximations.
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| 4. |
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| 5. |
- Faraj, Maycel Isaac, 1979-, et al.
(författare)
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Motion Features from Lip Movement for Person Authentication
- 2006
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Ingår i: The 18th International Conference on Pattern Recognition. - Washington, D.C. : IEEE Computer Society. - 0769525210 ; 3, s. 1059- 1062
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Konferensbidrag (refereegranskat)abstract
- This paper describes a new motion based feature extraction technique for speaker identification using orientation estimation in 2D manifolds. The motion is estimated by computing the components of the structure tensor from which normal flows are extracted. By projecting the 3D spatiotemporal data to 2D planes, we obtain projection coefficients which we use to evaluate the 3D orientations of brightness patterns in TV like image sequences. This corresponds to the solutions of simple matrix eigenvalue problems in 2D, affording increased computational efficiency. An implementation based on joint lip movements and speech is presented along with experiments which confirm the theory, exhibiting a recognition rate of 98% on the publicly available XM2VTS database
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| 6. |
- Gu, Irene Yu-Hua, 1953, et al.
(författare)
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Domain-Shift Manifold Online Learning and Tracking of Video Objects
- 2013
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Ingår i: Swedish Symposium on Image Analysis (SSBA 2013), March 14-15, Göteborg, Sweden. ; , s. 4-
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- This paper describes a novel Grassmann manifoldobject tracking scheme that includes the modules ofmanifold online learning and occlusion handling. Whenobjects contain significant out-of-plane pose changes, thedomain where object appearances lying is shifting withtime, hence a single vector space is no longer suitable fordynamic object representation.Motivated by this, we presenta manifold-based scheme for tracking large out-of-planeobjects (i.e. camera is close to the object) in video withonline learning and long-term partial occlusion modules.The tracker uses Bayesian formulation on the manifold, performing posterior state estimation based on nonlinear state space modeling. One particle filter is applied for manifold online learning, another is for tracking. Occlusion handling is applied during the online learning to prevent learning occluding object/clutter. Tests on videos have shown very robust tracking performance when objects contain significant out-of-plane pose changes accompanied with long-term partial occlusions. Comparisons with two existing methods provide further support to the proposed method.
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| 7. |
- Gu, Irene Yu-Hua, 1953, et al.
(författare)
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Grassmann Manifold Online Learning and Partial Occlusion Handling for Visual Object Tracking under Bayesian Formulation
- 2012
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Ingår i: Proceedings - International Conference on Pattern Recognition. - 1051-4651. - 9784990644109 ; , s. 1463-1466
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Konferensbidrag (refereegranskat)abstract
- This paper addresses issues of online learning and occlusion handling in video object tracking. Although manifold tracking is promising, large pose changes and long term partial occlusions of video objects remain challenging.We propose a novel manifold tracking scheme that tackles such problems, with the following main novelties: (a) Online estimation of object appearances on Grassmann manifolds; (b) Optimal criterion-based occlusion handling during online learning; (c) Nonlinear dynamic model for appearance basis matrix and its velocity; (b) Bayesian formulations separately for the tracking and the online learning process. Two particle filters are employed: one is on the manifold for generating appearance particles and another on the linear space for generating affine box particles. Tracking and online updating are performed in alternative fashion to mitigate the tracking drift. Experiments on videos have shown robust tracking performance especially when objects contain significantpose changes accompanied with long-term partial occlusions. Evaluations and comparisons with two existing methods provide further support to the proposed method.
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| 8. |
- Arya, Gaurav, et al.
(författare)
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Automatic Differentiation of Programs with Discrete Randomness
- 2022
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Ingår i: Advances in Neural Information Processing Systems. - 1049-5258. ; 35
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Konferensbidrag (refereegranskat)abstract
- Automatic differentiation (AD), a technique for constructing new programs which compute the derivative of an original program, has become ubiquitous throughout scientific computing and deep learning due to the improved performance afforded by gradient-based optimization. However, AD systems have been restricted to the subset of programs that have a continuous dependence on parameters. Programs that have discrete stochastic behaviors governed by distribution parameters, such as flipping a coin with probability p of being heads, pose a challenge to these systems because the connection between the result (heads vs tails) and the parameters (p) is fundamentally discrete. In this paper we develop a new reparameterization-based methodology that allows for generating programs whose expectation is the derivative of the expectation of the original program. We showcase how this method gives an unbiased and low-variance estimator which is as automated as traditional AD mechanisms. We demonstrate unbiased forward-mode AD of discrete-time Markov chains, agent-based models such as Conway's Game of Life, and unbiased reverse-mode AD of a particle filter. Our code package is available at https://github.com/gaurav-arya/StochasticAD.jl.
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| 9. |
- Beilina, Larisa, 1970, et al.
(författare)
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Convergence of explicit p1 Finite-Element Solutions to Maxwell’s Equations
- 2020
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Ingår i: Springer Proceedings in Mathematics and Statistics. - Cham : Springer International Publishing. - 2194-1017 .- 2194-1009. ; 328, s. 91-103
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Konferensbidrag (refereegranskat)abstract
- This paper is devoted to the numerical validation of an explicit finite-difference scheme for the integration in time of Maxwell’s equations in terms of the sole electric field. The space discretization is performed by the standard P1 finite element method assorted with the treatment of the time-derivative term by a technique of the mass-lumping type. The rigorous reliability analysis of this numerical model was the subject of authors’ another paper [2]. More specifically such a study applies to the particular case where the electric permittivity has a constant value outside a sub-domain, whose closure does not intersect the boundary of the domain where the problem is defined. Our numerical experiments in two-dimension space certify that the convergence results previously derived for this approach are optimal, as long as the underlying CFL condition is satisfied.
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| 10. |
- Berman, Robert, 1976
(författare)
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Determinantal point processes and fermions on polarized complex manifolds: bulk universality
- 2018
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Ingår i: Springer Proceedings in Mathematics and Statistics. - Cham : Springer International Publishing. - 2194-1017 .- 2194-1009. ; 269, s. 341-393
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Konferensbidrag (refereegranskat)abstract
- We consider determinantal point processes on a compact complex manifold X in the limit of many particles. The correlation kernels of the processes are the Bergman kernels associated to a high power of a given Hermitian holomorphic line bundle L over X. The empirical measure on X of the process, describing the particle locations, converges in probability towards the pluripotential equilibrium measure, expressed in term of the Monge–Ampère operator. The asymptotics of the corresponding fluctuations in the bulk are shown to be asymptotically normal and described by a Gaussian free field and applies to test functions (linear statistics) which are merely Lipschitz continuous. Moreover, a scaling limit of the correlation functions in the bulk is shown to be universal and expressed in terms of (the higher dimensional analog of) the Ginibre ensemble. This geometric setting applies in particular to normal random matrix ensembles, the two dimensional Coulomb gas, free fermions in a strong magnetic field and multivariate orthogonal polynomials.
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