1,902 research outputs found
An adaptive Metropolis-Hastings scheme: sampling and optimization
We propose an adaptive Metropolis-Hastings algorithm in which sampled data
are used to update the proposal distribution. We use the samples found by the
algorithm at a particular step to form the information-theoretically optimal
mean-field approximation to the target distribution, and update the proposal
distribution to be that approximatio. We employ our algorithm to sample the
energy distribution for several spin-glasses and we demonstrate the superiority
of our algorithm to the conventional MH algorithm in sampling and in annealing
optimization.Comment: To appear in Europhysics Letter
Collective Intelligence for Control of Distributed Dynamical Systems
We consider the El Farol bar problem, also known as the minority game (W. B.
Arthur, ``The American Economic Review'', 84(2): 406--411 (1994), D. Challet
and Y.C. Zhang, ``Physica A'', 256:514 (1998)). We view it as an instance of
the general problem of how to configure the nodal elements of a distributed
dynamical system so that they do not ``work at cross purposes'', in that their
collective dynamics avoids frustration and thereby achieves a provided global
goal. We summarize a mathematical theory for such configuration applicable when
(as in the bar problem) the global goal can be expressed as minimizing a global
energy function and the nodes can be expressed as minimizers of local free
energy functions. We show that a system designed with that theory performs
nearly optimally for the bar problem.Comment: 8 page
TreeGrad: Transferring Tree Ensembles to Neural Networks
Gradient Boosting Decision Tree (GBDT) are popular machine learning
algorithms with implementations such as LightGBM and in popular machine
learning toolkits like Scikit-Learn. Many implementations can only produce
trees in an offline manner and in a greedy manner. We explore ways to convert
existing GBDT implementations to known neural network architectures with
minimal performance loss in order to allow decision splits to be updated in an
online manner and provide extensions to allow splits points to be altered as a
neural architecture search problem. We provide learning bounds for our neural
network.Comment: Technical Report on Implementation of Deep Neural Decision Forests
Algorithm. To accompany implementation here:
https://github.com/chappers/TreeGrad. Update: Please cite as: Siu, C. (2019).
"Transferring Tree Ensembles to Neural Networks". International Conference on
Neural Information Processing. Springer, 2019. arXiv admin note: text overlap
with arXiv:1909.1179
Estimating probabilities from experimental frequencies
Estimating the probability distribution 'q' governing the behaviour of a
certain variable by sampling its value a finite number of times most typically
involves an error. Successive measurements allow the construction of a
histogram, or frequency count 'f', of each of the possible outcomes. In this
work, the probability that the true distribution be 'q', given that the
frequency count 'f' was sampled, is studied. Such a probability may be written
as a Gibbs distribution. A thermodynamic potential, which allows an easy
evaluation of the mean Kullback-Leibler divergence between the true and
measured distribution, is defined. For a large number of samples, the
expectation value of any function of 'q' is expanded in powers of the inverse
number of samples. As an example, the moments, the entropy and the mutual
information are analyzed.Comment: 10 pages, 3 figures, to be published in Physical Review
Asymptotic behavior of, small eigenvalues, short geodesics and period matrices on degenerating hyperbolic Riemann surfaces
Consider {M-t} a semi-stable family of compact, connected algebraic curves which degenerate to a stable, noded curve M-0. The uniformization theorem allows us to endow each curve M-t in the family, as well as the limit curve M-0 (after its nodes have been removed), with its natural complete hyperbolic metric (i.e. constant negative curvature equal to -1), so that we are considering a degenerating family of compact hyperbolic Riemann surfaces. Assume that M-0 has k components and n nodes, so there are n families of geodesics whose lengths approach zero under degeneration and k - 1 families of eigenvalues of the Laplacian which approach zero under degeneration. A problem which has received considerable attention is to compare the rate at which the eigenvalues and the lengths of geodesics approach zero. In this paper, we will use results from complex algebraic geometry and from heat kernel analysis to obtain a precise relation involving the small eigenvalues, the short geodesics, and the period matrix of the underlying complex curve M-t. Our method leads naturally to a general conjecture in the setting of an arbitrary degenerating family of hyperbolic Riemann surfaces of finite volume
Multi-Agent Complex Systems and Many-Body Physics
Multi-agent complex systems comprising populations of decision-making
particles, have many potential applications across the biological,
informational and social sciences. We show that the time-averaged dynamics in
such systems bear a striking resemblance to conventional many-body physics. For
the specific example of the Minority Game, this analogy enables us to obtain
analytic expressions which are in excellent agreement with numerical
simulations.Comment: Accepted for publication in Europhysics Letter
Algebraic-geometrical formulation of two-dimensional quantum gravity
We find a volume form on moduli space of double punctured Riemann surfaces
whose integral satisfies the Painlev\'e I recursion relations of the genus
expansion of the specific heat of 2D gravity. This allows us to express the
asymptotic expansion of the specific heat as an integral on an infinite
dimensional moduli space in the spirit of Friedan-Shenker approach. We outline
a conjectural derivation of such recursion relations using the
Duistermaat-Heckman theorem.Comment: 10 pages, Latex fil
Geometric Aspects of the Moduli Space of Riemann Surfaces
This is a survey of our recent results on the geometry of moduli spaces and
Teichmuller spaces of Riemann surfaces appeared in math.DG/0403068 and
math.DG/0409220. We introduce new metrics on the moduli and the Teichmuller
spaces of Riemann surfaces with very good properties, study their curvatures
and boundary behaviors in great detail. Based on the careful analysis of these
new metrics, we have a good understanding of the Kahler-Einstein metric from
which we prove that the logarithmic cotangent bundle of the moduli space is
stable. Another corolary is a proof of the equivalences of all of the known
classical complete metrics to the new metrics, in particular Yau's conjectures
in the early 80s on the equivalences of the Kahler-Einstein metric to the
Teichmuller and the Bergman metric.Comment: Survey article of our recent results on the subject. Typoes
corrrecte
Robust formation of morphogen gradients
We discuss the formation of graded morphogen profiles in a cell layer by
nonlinear transport phenomena, important for patterning developing organisms.
We focus on a process termed transcytosis, where morphogen transport results
from binding of ligands to receptors on the cell surface, incorporation into
the cell and subsequent externalization. Starting from a microscopic model, we
derive effective transport equations. We show that, in contrast to morphogen
transport by extracellular diffusion, transcytosis leads to robust ligand
profiles which are insensitive to the rate of ligand production
An Exact No Free Lunch Theorem for Community Detection
A precondition for a No Free Lunch theorem is evaluation with a loss function
which does not assume a priori superiority of some outputs over others. A
previous result for community detection by Peel et al. (2017) relies on a
mismatch between the loss function and the problem domain. The loss function
computes an expectation over only a subset of the universe of possible outputs;
thus, it is only asymptotically appropriate with respect to the problem size.
By using the correct random model for the problem domain, we provide a
stronger, exact No Free Lunch theorem for community detection. The claim
generalizes to other set-partitioning tasks including core/periphery
separation, -clustering, and graph partitioning. Finally, we review the
literature of proposed evaluation functions and identify functions which
(perhaps with slight modifications) are compatible with an exact No Free Lunch
theorem
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