2,850 research outputs found
Approximations for time-dependent distributions in Markovian fluid models
In this paper we study the distribution of the level at time of
Markovian fluid queues and Markovian continuous time random walks, the maximum
(and minimum) level over , and their joint distributions. We
approximate by a random variable with Erlang distribution and we
use an alternative way, with respect to the usual Laplace transform approach,
to compute the distributions. We present probabilistic interpretation of the
equations and provide a numerical illustration
Variational Bayes model averaging for graphon functions and motif frequencies inference in W-graph models
W-graph refers to a general class of random graph models that can be seen as
a random graph limit. It is characterized by both its graphon function and its
motif frequencies. In this paper, relying on an existing variational Bayes
algorithm for the stochastic block models along with the corresponding weights
for model averaging, we derive an estimate of the graphon function as an
average of stochastic block models with increasing number of blocks. In the
same framework, we derive the variational posterior frequency of any motif. A
simulation study and an illustration on a social network complete our work
Perturbation analysis of Markov modulated fluid models
We consider perturbations of positive recurrent Markov modulated fluid
models. In addition to the infinitesimal generator of the phases, we also
perturb the rate matrix, and analyze the effect of those perturbations on the
matrix of first return probabilities to the initial level. Our main
contribution is the construction of a substitute for the matrix of first return
probabilities, which enables us to analyze the effect of the perturbation under
consideration
Graphs in machine learning: an introduction
Graphs are commonly used to characterise interactions between objects of
interest. Because they are based on a straightforward formalism, they are used
in many scientific fields from computer science to historical sciences. In this
paper, we give an introduction to some methods relying on graphs for learning.
This includes both unsupervised and supervised methods. Unsupervised learning
algorithms usually aim at visualising graphs in latent spaces and/or clustering
the nodes. Both focus on extracting knowledge from graph topologies. While most
existing techniques are only applicable to static graphs, where edges do not
evolve through time, recent developments have shown that they could be extended
to deal with evolving networks. In a supervised context, one generally aims at
inferring labels or numerical values attached to nodes using both the graph
and, when they are available, node characteristics. Balancing the two sources
of information can be challenging, especially as they can disagree locally or
globally. In both contexts, supervised and un-supervised, data can be
relational (augmented with one or several global graphs) as described above, or
graph valued. In this latter case, each object of interest is given as a full
graph (possibly completed by other characteristics). In this context, natural
tasks include graph clustering (as in producing clusters of graphs rather than
clusters of nodes in a single graph), graph classification, etc. 1 Real
networks One of the first practical studies on graphs can be dated back to the
original work of Moreno [51] in the 30s. Since then, there has been a growing
interest in graph analysis associated with strong developments in the modelling
and the processing of these data. Graphs are now used in many scientific
fields. In Biology [54, 2, 7], for instance, metabolic networks can describe
pathways of biochemical reactions [41], while in social sciences networks are
used to represent relation ties between actors [66, 56, 36, 34]. Other examples
include powergrids [71] and the web [75]. Recently, networks have also been
considered in other areas such as geography [22] and history [59, 39]. In
machine learning, networks are seen as powerful tools to model problems in
order to extract information from data and for prediction purposes. This is the
object of this paper. For more complete surveys, we refer to [28, 62, 49, 45].
In this section, we introduce notations and highlight properties shared by most
real networks. In Section 2, we then consider methods aiming at extracting
information from a unique network. We will particularly focus on clustering
methods where the goal is to find clusters of vertices. Finally, in Section 3,
techniques that take a series of networks into account, where each network i
The morphing of fluid queues into Markov-modulated Brownian motion
Ramaswami showed recently that standard Brownian motion arises as the limit
of a family of Markov-modulated linear fluid processes. We pursue this analysis
with a fluid approximation for Markov-modulated Brownian motion. Furthermore,
we prove that the stationary distribution of a Markov-modulated Brownian motion
reflected at zero is the limit from the well-analyzed stationary distribution
of approximating linear fluid processes. Key matrices in the limiting
stationary distribution are shown to be solutions of a new quadratic equation,
and we describe how this equation can be efficiently solved. Our results open
the way to the analysis of more complex Markov-modulated processes.Comment: 20 page; the material on p7 (version 1) has been removed, and pp.8-9
replaced by Theorem 2.7 and its short proo
Poisson's equation for discrete-time quasi-birth-and-death processes
We consider Poisson's equation for quasi-birth-and-death processes (QBDs) and
we exploit the special transition structure of QBDs to obtain its solutions in
two different forms. One is based on a decomposition through first passage
times to lower levels, the other is based on a recursive expression for the
deviation matrix.
We revisit the link between a solution of Poisson's equation and perturbation
analysis and we show that it applies to QBDs. We conclude with the PH/M/1 queue
as an illustrative example, and we measure the sensitivity of the expected
queue size to the initial value
Extinction probabilities of branching processes with countably infinitely many types
We present two iterative methods for computing the global and partial
extinction probability vectors for Galton-Watson processes with countably
infinitely many types. The probabilistic interpretation of these methods
involves truncated Galton-Watson processes with finite sets of types and
modified progeny generating functions. In addition, we discuss the connection
of the convergence norm of the mean progeny matrix with extinction criteria.
Finally, we give a sufficient condition for a population to become extinct
almost surely even though its population size explodes on the average, which is
impossible in a branching process with finitely many types. We conclude with
some numerical illustrations for our algorithmic methods
Brokers vs. Retailers: Evidence from the French Imports Industry of Fresh Produce.
There is little discussion in the literature about trade intermediaries because data is rare. Using very original data, our article sheds light on the behavior of trade intermediaries when importing fresh fruit and vegetables in France. To do so, we distinguish among direct and indirect imports respectively operated through brokers or retailers. We then investigate the impact of country level data on the share of indirect/direct flows of imports by country of origin at the 8-digit level that enter the french market. We show that brokers are more likely to operate in context when fixed and variable costs to trade are high whereas retailers are sensitive to tariffs and product sensitivity.Agribusiness, International Relations/Trade, Q17,
- …