1,259 research outputs found
On the time continuity of entropy solutions
We show that any entropy solution of a convection diffusion equation
in \OT belongs to
C([0,T),L^1_{Loc}(\o\O)). The proof does not use the uniqueness of the
solution
Classification with the nearest neighbor rule in general finite dimensional spaces: necessary and sufficient conditions
Given an -sample of random vectors whose
joint law is unknown, the long-standing problem of supervised classification
aims to \textit{optimally} predict the label of a given a new observation
. In this context, the nearest neighbor rule is a popular flexible and
intuitive method in non-parametric situations.
Even if this algorithm is commonly used in the machine learning and
statistics communities, less is known about its prediction ability in general
finite dimensional spaces, especially when the support of the density of the
observations is . This paper is devoted to the study of the
statistical properties of the nearest neighbor rule in various situations. In
particular, attention is paid to the marginal law of , as well as the
smoothness and margin properties of the \textit{regression function} . We identify two necessary and sufficient conditions to
obtain uniform consistency rates of classification and to derive sharp
estimates in the case of the nearest neighbor rule. Some numerical experiments
are proposed at the end of the paper to help illustrate the discussion.Comment: 53 Pages, 3 figure
Intensity estimation of non-homogeneous Poisson processes from shifted trajectories
This paper considers the problem of adaptive estimation of a non-homogeneous
intensity function from the observation of n independent Poisson processes
having a common intensity that is randomly shifted for each observed
trajectory. We show that estimating this intensity is a deconvolution problem
for which the density of the random shifts plays the role of the convolution
operator. In an asymptotic setting where the number n of observed trajectories
tends to infinity, we derive upper and lower bounds for the minimax quadratic
risk over Besov balls. Non-linear thresholding in a Meyer wavelet basis is used
to derive an adaptive estimator of the intensity. The proposed estimator is
shown to achieve a near-minimax rate of convergence. This rate depends both on
the smoothness of the intensity function and the density of the random shifts,
which makes a connection between the classical deconvolution problem in
nonparametric statistics and the estimation of a mean intensity from the
observations of independent Poisson processes
Intensity estimation of non-homogeneous Poisson processes from shifted trajectories
In this paper, we consider the problem of estimating nonparametrically a mean pattern intensity λ from the observation of n independent and non-homogeneous Poisson processes N1,âŠ,Nn on the interval [0,1]. This problem arises when data (counts) are collected independently from n individuals according to similar Poisson processes. We show that estimating this intensity is a deconvolution problem for which the density of the random shifts plays the role of the convolution operator. In an asymptotic setting where the number n of observed trajectories tends to infinity, we derive upper and lower bounds for the minimax quadratic risk over Besov balls. Non-linear thresholding in a Meyer wavelet basis is used to derive an adaptive estimator of the intensity. The proposed estimator is shown to achieve a near-minimax rate of convergence. This rate depends both on the smoothness of the intensity function and the density of the random shifts, which makes a connection between the classical deconvolution problem in nonparametric statistics and the estimation of a mean intensity from the observations of independent Poisson processes
Les enjeux d'une restructuration de la sous-traitance sur les conditions de travail chez un donneur d'ordre
International audienceLa communication présente un cas de restructuration des rapports entre un donneur d'ordre et ses sous-traitant
Mechanical fluctuations suppress the threshold of soft-glassy solids : the secular drift scenario
We propose a dynamical mechanism leading to the fluidization of soft-glassy
amorphous mate-rial driven below the yield-stress by external mechanical
fluctuations. The model is based on the combination of memory effect and
non-linearity, leading to an accumulation of tiny effects over a long-term. We
test this scenario on a granular packing driven mechanically below the Coulomb
threshold. We bring evidences for an effective viscous response directly
related to small stress modulations in agreement with the theoretical
prediction of a generic secular drift
Classification with the nearest neighbor rule in general finite dimensional spaces
Given an n-sample of random vectors (Xi,Yi)1=i=n whose joint law is unknown, the long-standing problem of supervised classification aims to optimally predict the label Y of a given new observation X. In this context, the k-nearest neighbor rule is a popular flexible and intuitive method in nonparametric situations. Even if this algorithm is commonly used in the machine learning and statistics communities, less is known about its prediction ability in general finite dimensional spaces, especially when the support of the density of the observations is Rd . This paper is devoted to the study of the statistical properties of the k-nearest neighbor rule in various situations. In particular, attention is paid to the marginal law of X, as well as the smoothness and margin properties of the regression function n(X) = E[Y |X]. We identify two necessary and sufficient conditions to obtain uniform consistency rates of classification and derive sharp estimates in the case of the k-nearest neighbor rule. Some numerical experiments are proposed at the end of the paper to help illustrate the discussio
More than Word Cooccurrence: Exploring Support and Opposition in International Climate Negotiations with Semantic Parsing
International audienceText analysis methods widely used in digital humanities often involve word co-occurrence, e.g. concept co-occurrence networks. These methods provide a useful corpus overview, but cannot determine the predicates that relate co-occurring concepts. Our goal was identifying propositions expressing the points supported or opposed by participants in international climate negotiations. Word co-occurrence methods were not sufficient, and an analysis based on open relation extraction had limited coverage for nominal predicates. We present a pipeline which identifies the points that different actors support and oppose, via a domain model with support/opposition predicates, and analysis rules that exploit the output of semantic role labelling, syntactic dependencies and anaphora resolution. Entity linking and keyphrase extraction are also performed on the propositions related to each actor. A user interface allows examining the main concepts in points supported or opposed by each participant, which participants agree or disagree with each other, and about which issues. The system is an example of tools that digital humanities scholars are asking for, to render rich textual information (beyond word co-occurrence) more amenable to quantitative treatment. An evaluation of the tool was satisfactory
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