1,623 research outputs found
From N-parameter fractional Brownian motions to N-parameter multifractional Brownian motions
Multifractional Brownian motion is an extension of the well-known fractional
Brownian motion where the Holder regularity is allowed to vary along the paths.
In this paper, two kind of multi-parameter extensions of mBm are studied: one
is isotropic while the other is not. For each of these processes, a moving
average representation, a harmonizable representation, and the covariance
structure are given. The Holder regularity is then studied. In particular, the
case of an irregular exponent function H is investigated. In this situation,
the almost sure pointwise and local Holder exponents of the multi-parameter mBm
are proved to be equal to the correspondent exponents of H. Eventually, a local
asymptotic self-similarity property is proved. The limit process can be another
process than fBm.Comment: 36 page
A set-indexed Ornstein-Uhlenbeck process
The purpose of this article is a set-indexed extension of the well-known
Ornstein-Uhlenbeck process. The first part is devoted to a stationary
definition of the random field and ends up with the proof of a complete
characterization by its -continuity, stationarity and set-indexed Markov
properties. This specific Markov transition system allows to define a general
\emph{set-indexed Ornstein-Uhlenbeck (SIOU) process} with any initial
probability measure. Finally, in the multiparameter case, the SIOU process is
proved to admit a natural integral representation.Comment: 13 page
Relational Data Mining Through Extraction of Representative Exemplars
With the growing interest on Network Analysis, Relational Data Mining is
becoming an emphasized domain of Data Mining. This paper addresses the problem
of extracting representative elements from a relational dataset. After defining
the notion of degree of representativeness, computed using the Borda
aggregation procedure, we present the extraction of exemplars which are the
representative elements of the dataset. We use these concepts to build a
network on the dataset. We expose the main properties of these notions and we
propose two typical applications of our framework. The first application
consists in resuming and structuring a set of binary images and the second in
mining co-authoring relation in a research team
The Multiparameter Fractional Brownian Motion
We define and study the multiparameter fractional Brownian motion. This
process is a generalization of both the classical fractional Brownian motion
and the multiparameter Brownian motion, when the condition of independence is
relaxed. Relations with the L\'evy fractional Brownian motion and with the
fractional Brownian sheet are discussed. Different notions of stationarity of
the increments for a multiparameter process are studied and applied to the
fractional property. Using self-similarity we present a characterization for
such processes. Finally, behavior of the multiparameter fractional Brownian
motion along increasing paths is analysed.Comment: 9 page
Local H\"older regularity for set-indexed processes
In this paper, we study the H\"older regularity of set-indexed stochastic
processes defined in the framework of Ivanoff-Merzbach. The first key result is
a Kolmogorov-like H\"older-continuity Theorem, whose novelty is illustrated on
an example which could not have been treated with anterior tools. Increments
for set-indexed processes are usually not simply written as , hence we
considered different notions of H\"older-continuity. Then, the localization of
these properties leads to various definitions of H\"older exponents, which we
compare to one another.
In the case of Gaussian processes, almost sure values are proved for these
exponents, uniformly along the sample paths. As an application, the local
regularity of the set-indexed fractional Brownian motion is proved to be equal
to the Hurst parameter uniformly, with probability one.Comment: 32 page
A Characterization of the Set-indexed Fractional Brownian Motion by Increasing Paths
We prove that a set-indexed process is a set-indexed fractional Brownian
motion if and only if its projections on all the increasing paths are
one-parameter time changed fractional Brownian motions. As an application, we
present an integral representation for such processes.Comment: 6 page
Stochastic 2-microlocal analysis
A lot is known about the H\"older regularity of stochastic processes, in
particular in the case of Gaussian processes. Recently, a finer analysis of the
local regularity of functions, termed 2-microlocal analysis, has been
introduced in a deterministic frame: through the computation of the so-called
2-microlocal frontier, it allows in particular to predict the evolution of
regularity under the action of (pseudo-) differential operators. In this work,
we develop a 2-microlocal analysis for the study of certain stochastic
processes. We show that moments of the increments allow, under fairly general
conditions, to obtain almost sure lower bounds for the 2-microlocal frontier.
In the case of Gaussian processes, more precise results may be obtained: the
incremental covariance yields the almost sure value of the 2-microlocal
frontier. As an application, we obtain new and refined regularity properties of
fractional Brownian motion, multifractional Brownian motion, stochastic
generalized Weierstrass functions, Wiener and stable integrals.Comment: 35 page
Improving Semantic Embedding Consistency by Metric Learning for Zero-Shot Classification
This paper addresses the task of zero-shot image classification. The key
contribution of the proposed approach is to control the semantic embedding of
images -- one of the main ingredients of zero-shot learning -- by formulating
it as a metric learning problem. The optimized empirical criterion associates
two types of sub-task constraints: metric discriminating capacity and accurate
attribute prediction. This results in a novel expression of zero-shot learning
not requiring the notion of class in the training phase: only pairs of
image/attributes, augmented with a consistency indicator, are given as ground
truth. At test time, the learned model can predict the consistency of a test
image with a given set of attributes , allowing flexible ways to produce
recognition inferences. Despite its simplicity, the proposed approach gives
state-of-the-art results on four challenging datasets used for zero-shot
recognition evaluation.Comment: in ECCV 2016, Oct 2016, amsterdam, Netherlands. 201
Generating Visual Representations for Zero-Shot Classification
This paper addresses the task of learning an image clas-sifier when some
categories are defined by semantic descriptions only (e.g. visual attributes)
while the others are defined by exemplar images as well. This task is often
referred to as the Zero-Shot classification task (ZSC). Most of the previous
methods rely on learning a common embedding space allowing to compare visual
features of unknown categories with semantic descriptions. This paper argues
that these approaches are limited as i) efficient discrimi-native classifiers
can't be used ii) classification tasks with seen and unseen categories
(Generalized Zero-Shot Classification or GZSC) can't be addressed efficiently.
In contrast , this paper suggests to address ZSC and GZSC by i) learning a
conditional generator using seen classes ii) generate artificial training
examples for the categories without exemplars. ZSC is then turned into a
standard supervised learning problem. Experiments with 4 generative models and
5 datasets experimentally validate the approach, giving state-of-the-art
results on both ZSC and GZSC
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