527 research outputs found
A priori -estimates for degenerate complex Monge-Amp\`ere equations
We study families of complex Monge-Amp\`ere equations, focusing on the case
where the cohomology classes degenerate to a non big class.
We establish uniform a priori -estimates for the normalized
solutions, generalizing the recent work of S. Kolodziej and G. Tian. This has
interesting consequences in the study of the K\"ahler-Ricci flow.Comment: 6 page
PAC-Bayesian Contrastive Unsupervised Representation Learning
Contrastive unsupervised representation learning (CURL) is the state-of-the-art technique to learn representations (as a set of features) from unlabelled data. While CURL has collected several empirical successes recently, theoretical understanding of its performance was still missing. In a recent work, Arora et al. (2019) provide the first generalisation bounds for CURL, relying on a Rademacher complexity. We extend their framework to the flexible PAC-Bayes setting, allowing to deal with the non-iid setting. We present PAC-Bayesian generalisation bounds for CURL, which are then used to derive a new representation learning algorithm. Numerical experiments on real-life datasets illustrate that our algorithm achieves competitive accuracy, and yields generalisation bounds with non-vacuous values
Dichotomize and Generalize: PAC-Bayesian Binary Activated Deep Neural Networks
We present a comprehensive study of multilayer neural networks with binary activation, relying on the PAC-Bayesian theory. Our contributions are twofold: (i) we develop an end-to-end framework to train a binary activated deep neural network, overcoming the fact that binary activation function is non-differentiable; (ii) we provide nonvacuous PAC-Bayesian generalization bounds for binary activated deep neural networks. Noteworthy, our results are obtained by minimizing the expected loss of an architecture-dependent aggregation of binary activated deep neural networks. The performance of our approach is assessed on a thorough numerical experiment protocol on real-life datasets
Green Currents for Meromorphic Maps of Compact K\"ahler Manifolds
We consider the dynamics of meromorphic maps of compact K\"ahler manifolds.
In this work, our goal is to locate the non-nef locus of invariant classes and
provide necessary and sufficient conditions for existence of Green currents in
codimension one.Comment: Statement of Theorem 1.5 is slightly improved. Proposition 5.2 and
Theorem 5.3 are adde
Analysis of Hepatitis C Viral Dynamics Using Latin Hypercube Sampling
We consider a mathematical model comprising of four coupled ordinary
differential equations (ODEs) for studying the hepatitis C (HCV) viral
dynamics. The model embodies the efficacies of a combination therapy of
interferon and ribavirin. A condition for the stability of the uninfected and
the infected steady states is presented. A large number of sample points for
the model parameters (which were physiologically feasible) were generated using
Latin hypercube sampling. Analysis of our simulated values indicated
approximately 24% cases as having an uninfected steady state. Statistical tests
like the chi-square-test and the Spearman's test were also done on the sample
values. The results of these tests indicate a distinctly differently
distribution of certain parameter values and not in case of others, vis-a-vis,
the stability of the uninfected and the infected steady states
Learning Stochastic Majority Votes by Minimizing a PAC-Bayes Generalization Bound
We investigate a stochastic counterpart of majority votes over finite ensembles of classifiers, and study its generalization properties. While our approach holds for arbitrary distributions, we instantiate it with Dirichlet distributions: this allows for a closed-form and differentiable expression for the expected risk, which then turns the generalization bound into a tractable training objective.The resulting stochastic majority vote learning algorithm achieves state-of-the-art accuracy and benefits from (non-vacuous) tight generalization bounds, in a series of numerical experiments when compared to competing algorithms which also minimize PAC-Bayes objectives -- both with uninformed (data-independent) and informed (data-dependent) priors
Préambule
En France, depuis le dĂ©but des annĂ©es 2000, lâanalyse des pratiques musicales est devenue un champ particuliĂšrement dynamique de lâanthropologie. La musique, tout comme la danse, constituent des objets stimulants pour notre discipline, que les anthropologues investissent et qui les positionnent dans un dialogue sans cesse renouvelĂ© avec des ethnomusicologues, des historiens de la musique, des sociologues de lâart, des philosophes et des gĂ©ographes. Pour ces anthropologues, la musique revĂȘt p..
Increase of precuneus metabolism correlates with reduction of PTSD symptoms after EMDR therapy in military veterans: an 18F-FDG PET study during virtual reality exposure to war
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