Minimizing Finite Sums with the Stochastic Average Gradient

We propose the stochastic average gradient (SAG) method for optimizing the sum of a finite number of smooth convex functions. Like stochastic gradient (SG) methods, the SAG method's iteration cost is independent of the number of terms in the sum. However, by incorporating a memory of previous gradient values the SAG method achieves a faster convergence rate than black-box SG methods. The convergence rate is improved from O(1/k^{1/2}) to O(1/k) in general, and when the sum is strongly-convex the convergence rate is improved from the sub-linear O(1/k) to a linear convergence rate of the form O(p^k) for p \textless{} 1. Further, in many cases the convergence rate of the new method is also faster than black-box deterministic gradient methods, in terms of the number of gradient evaluations. Numerical experiments indicate that the new algorithm often dramatically outperforms existing SG and deterministic gradient methods, and that the performance may be further improved through the use of non-uniform sampling strategies.Comment: Revision from January 2015 submission. Major changes: updated literature follow and discussion of subsequent work, additional Lemma showing the validity of one of the formulas, somewhat simplified presentation of Lyapunov bound, included code needed for checking proofs rather than the polynomials generated by the code, added error regions to the numerical experiment

Implementation strategies for hyperspectral unmixing using Bayesian source separation

Bayesian Positive Source Separation (BPSS) is a useful unsupervised approach for hyperspectral data unmixing, where numerical non-negativity of spectra and abundances has to be ensured, such in remote sensing. Moreover, it is sensible to impose a sum-to-one (full additivity) constraint to the estimated source abundances in each pixel. Even though non-negativity and full additivity are two necessary properties to get physically interpretable results, the use of BPSS algorithms has been so far limited by high computation time and large memory requirements due to the Markov chain Monte Carlo calculations. An implementation strategy which allows one to apply these algorithms on a full hyperspectral image, as typical in Earth and Planetary Science, is introduced. Effects of pixel selection, the impact of such sampling on the relevance of the estimated component spectra and abundance maps, as well as on the computation times, are discussed. For that purpose, two different dataset have been used: a synthetic one and a real hyperspectral image from Mars.Comment: 10 pages, 6 figures, submitted to IEEE Transactions on Geoscience and Remote Sensing in the special issue on Hyperspectral Image and Signal Processing (WHISPERS

VoodooFlash: authoring across physical and digital form

Design tools that integrate hardware and software components facilitate product design work across aspects of physical form and user interaction, but at the cost of requiring designers to work with other than their accustomed programming tools. In this paper we introduce VoodooFlash, a tool designed to build on the widespread use of Flash while facilitating design work across physical and digital components. VoodooFlash extends the existing practice of authoring interactive applications in terms of arranging components on a virtual stage, and provides a physical stage on which controls can be arranged, linked to software components, and appropriated with other physical design materials

Direct photon production and flow at low transverse momenta in pp, p-Pb and Pb-Pb collisions

Low transverse momentum direct photon measurements have been carried out by the ALICE experiment at the CERN LHC in small collision systems (pp, $\sqrt{s}=2.76$ and 8 TeV and p--Pb, $\sqrt{s_\text{NN}}=5.02$ TeV) as well as in heavy-ion collisions (Pb--Pb, $\sqrt{s_\text{NN}}=2.76$ TeV). For the first time, also the multiplicity dependence of direct photon production was investigated in p--Pb collisions. Whereas in the small systems no significant thermal photon signal was observed, a $\sim15\%$ excess has been measured in central Pb--Pb collisions in the region of $p_{\rm T}<3$ GeV/$c$. A signal of prompt photon production at high transverse momentum consistent with binary scaling has been observed in all collision systems following NLO pQCD predictions. Direct photon flow has been measured in central and semi-central Pb--Pb collisions and found to be of similar size as the charged hadron and decay photon flow.Comment: Proceedings of Hard Probes 2018, 30 September - 5 October, Aix-Les-Bains, Franc

Compacité pratique des diagrammes de décision valués. Normalisation, heuristiques et expérimentations

National audienceLes diagrammes de décision valués (VDD) sont particulièrement intéressants pour la compilation de problèmes de satisfaction de contraintes valuées (VCSP). L’intérêt des différents langages de la famille VDD (en particulier, les langages ADD, SLDD, AADD) est qu’ils ad- mettent des algorithmes en temps polynomial pour des traitements (comme l’optimisation) qui ne sont pas polynomiaux à partir des VCSP de départ. Comme l’efficacité pratique de tels trai- tements dépend de la taille du VDD compilé obtenu, il est important d’obtenir une forme la plus compacte possible. Nous décrivons dans cet article quelques résultats issus de nos travaux sur l’étude de la compacité pratique des VDD. Nous présentons un compilateur ascendant de VCSP en SLDD + (resp. SLDD ), un jeu d’heuristiques d’ordonnancement des variables, des procé- dures de traduction des langages SLDD + (resp. SLDD ) vers les langages ADD et AADD, et nous identifions quelques requêtes et transformations d’intérêt, réalisables en temps polynomial quand l’ensemble des affectations est représenté par un VDD. Les différents langages cibles et les heuristiques ont été testés sur deux familles de jeux d’essai, des VCSP additifs représentant des problèmes de configuration de voitures avec fonctions de coût, et des réseaux bayésiens. Il apparaît que, bien que le langage AADD soit strictement plus succinct en théorie que SLDD + (resp. SLDD ), le langage SLDD + (resp. SLDD ) convient bien en pratique quand il s’agit de compiler des problèmes de nature purement additive (resp. purement multiplicative)