267 research outputs found
The split-and-drift random graph, a null model for speciation
We introduce a new random graph model motivated by biological questions
relating to speciation. This random graph is defined as the stationary
distribution of a Markov chain on the space of graphs on .
The dynamics of this Markov chain is governed by two types of events: vertex
duplication, where at constant rate a pair of vertices is sampled uniformly and
one of these vertices loses its incident edges and is rewired to the other
vertex and its neighbors; and edge removal, where each edge disappears at
constant rate. Besides the number of vertices , the model has a single
parameter .
Using a coalescent approach, we obtain explicit formulas for the first
moments of several graph invariants such as the number of edges or the number
of complete subgraphs of order . These are then used to identify five
non-trivial regimes depending on the asymptotics of the parameter . We
derive an explicit expression for the degree distribution, and show that under
appropriate rescaling it converges to classical distributions when the number
of vertices goes to infinity. Finally, we give asymptotic bounds for the number
of connected components, and show that in the sparse regime the number of edges
is Poissonian.Comment: added Proposition 2.4 and formal proofs of Proposition 2.3 and 2.
Moving towards appropriability of academic knowledge: a post-actionalist perspective
Based on recent contributions in managerial research, this article aims to suggest a new perspective for appraising and developing knowledge usability by studying the processes underlying its production: appropriation. The underlying problem is the following: how can the academic community help a community of practitioners appropriate knowledge it produced, co-produced or stimulated? First, a preliminary analysis is put forward as regards management sciences and the concept of knowledge 'actionability'. Some limitations are raised (1.). Then, the authors suggest to move from an 'actionability' (rather coherent with a classic vision of management sciences linked to the "sciences of the artificial") to an 'appropriability' perspective (2.). Lastly, the specificities of both perspectives are discussed (3.). Some limitations of this new vision are also pointed out, especially from a psychological standpoint.Management sciences; actionable knowledge; appropriability of knowledge; epistemology; methodology
A New PAC-Bayesian Perspective on Domain Adaptation
We study the issue of PAC-Bayesian domain adaptation: We want to learn, from
a source domain, a majority vote model dedicated to a target one. Our
theoretical contribution brings a new perspective by deriving an upper-bound on
the target risk where the distributions' divergence---expressed as a
ratio---controls the trade-off between a source error measure and the target
voters' disagreement. Our bound suggests that one has to focus on regions where
the source data is informative.From this result, we derive a PAC-Bayesian
generalization bound, and specialize it to linear classifiers. Then, we infer a
learning algorithmand perform experiments on real data.Comment: Published at ICML 201
PAC-Bayes and Domain Adaptation
We provide two main contributions in PAC-Bayesian theory for domain
adaptation where the objective is to learn, from a source distribution, a
well-performing majority vote on a different, but related, target distribution.
Firstly, we propose an improvement of the previous approach we proposed in
Germain et al. (2013), which relies on a novel distribution pseudodistance
based on a disagreement averaging, allowing us to derive a new tighter domain
adaptation bound for the target risk. While this bound stands in the spirit of
common domain adaptation works, we derive a second bound (introduced in Germain
et al., 2016) that brings a new perspective on domain adaptation by deriving an
upper bound on the target risk where the distributions' divergence-expressed as
a ratio-controls the trade-off between a source error measure and the target
voters' disagreement. We discuss and compare both results, from which we obtain
PAC-Bayesian generalization bounds. Furthermore, from the PAC-Bayesian
specialization to linear classifiers, we infer two learning algorithms, and we
evaluate them on real data.Comment: Neurocomputing, Elsevier, 2019. arXiv admin note: substantial text
overlap with arXiv:1503.0694
PAC-Bayesian Learning and Domain Adaptation
In machine learning, Domain Adaptation (DA) arises when the distribution gen-
erating the test (target) data differs from the one generating the learning
(source) data. It is well known that DA is an hard task even under strong
assumptions, among which the covariate-shift where the source and target
distributions diverge only in their marginals, i.e. they have the same labeling
function. Another popular approach is to consider an hypothesis class that
moves closer the two distributions while implying a low-error for both tasks.
This is a VC-dim approach that restricts the complexity of an hypothesis class
in order to get good generalization. Instead, we propose a PAC-Bayesian
approach that seeks for suitable weights to be given to each hypothesis in
order to build a majority vote. We prove a new DA bound in the PAC-Bayesian
context. This leads us to design the first DA-PAC-Bayesian algorithm based on
the minimization of the proposed bound. Doing so, we seek for a \rho-weighted
majority vote that takes into account a trade-off between three quantities. The
first two quantities being, as usual in the PAC-Bayesian approach, (a) the
complexity of the majority vote (measured by a Kullback-Leibler divergence) and
(b) its empirical risk (measured by the \rho-average errors on the source
sample). The third quantity is (c) the capacity of the majority vote to
distinguish some structural difference between the source and target samples.Comment: https://sites.google.com/site/multitradeoffs2012
On Probability Distributions for Trees: Representations, Inference and Learning
We study probability distributions over free algebras of trees. Probability
distributions can be seen as particular (formal power) tree series [Berstel et
al 82, Esik et al 03], i.e. mappings from trees to a semiring K . A widely
studied class of tree series is the class of rational (or recognizable) tree
series which can be defined either in an algebraic way or by means of
multiplicity tree automata. We argue that the algebraic representation is very
convenient to model probability distributions over a free algebra of trees.
First, as in the string case, the algebraic representation allows to design
learning algorithms for the whole class of probability distributions defined by
rational tree series. Note that learning algorithms for rational tree series
correspond to learning algorithms for weighted tree automata where both the
structure and the weights are learned. Second, the algebraic representation can
be easily extended to deal with unranked trees (like XML trees where a symbol
may have an unbounded number of children). Both properties are particularly
relevant for applications: nondeterministic automata are required for the
inference problem to be relevant (recall that Hidden Markov Models are
equivalent to nondeterministic string automata); nowadays applications for Web
Information Extraction, Web Services and document processing consider unranked
trees
Dimension-free Concentration Bounds on Hankel Matrices for Spectral Learning
International audienceLearning probabilistic models over strings is an important issue for many applications. Spectral methods propose elegant solutions to the problem of inferring weighted automata from finite samples of variable-length strings drawn from an unknown target distribution . These methods rely on a singular value decomposition of a matrix , called the empirical Hankel matrix, that records the frequencies of (some of) the observed strings . The accuracy of the learned distribution depends both on the quantity of information embedded in and on the distance between and its mean . Existing concentration bounds seem to indicate that the concentration over gets looser with its dimensions, suggesting that it might be necessary to bound the dimensions of for learning. We prove new dimension-free concentration bounds for classical Hankel matrices and several variants, based on prefixes or factors of strings, that are useful for learning. Experiments demonstrate that these bounds are tight and that they significantly improve existing (dimension-dependent) bounds. One consequence of these results is that the spectral learning approach remains consistent even if all the observations are recorded within the empirical matrix
An electronic ratchet is required in nanostructured intermediate band solar cells
We investigate in this letter the intrinsic properties that have limited the
efficiency of nanostructured intermediate band solar cells. Those devices take
advantage of intra-band transitions, which occur on narrow energy width, and
present low radiative recombination efficiency. We derive the minimum
requirements in terms of those two characteristics to achieve efficiencies in
excess of the Shockley-Queisser limit, and show that compatible nanostructures
are challenging to obtain. Especially, we evidence that currently
experimentally considered materials cannot overcome the best single junction
cells. In order to solve those issues, we consider devices including an
electronic ratchet mechanism. Firstly, such devices are shown to be much less
sensitive on the limitations of the nanostructures characteristics, so that
requirements for high efficiencies can be met. Secondly, we show that quantum
well devices present advantages over their quantum dots counterparts, although
they have attracted much less interest so far
Learning advanced mathematical computations from examples
Using transformers over large generated datasets, we train models to learn
mathematical properties of differential systems, such as local stability,
behavior at infinity and controllability. We achieve near perfect prediction of
qualitative characteristics, and good approximations of numerical features of
the system. This demonstrates that neural networks can learn to perform complex
computations, grounded in advanced theory, from examples, without built-in
mathematical knowledge
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