304 research outputs found
Global parameter identification of stochastic reaction networks from single trajectories
We consider the problem of inferring the unknown parameters of a stochastic
biochemical network model from a single measured time-course of the
concentration of some of the involved species. Such measurements are available,
e.g., from live-cell fluorescence microscopy in image-based systems biology. In
addition, fluctuation time-courses from, e.g., fluorescence correlation
spectroscopy provide additional information about the system dynamics that can
be used to more robustly infer parameters than when considering only mean
concentrations. Estimating model parameters from a single experimental
trajectory enables single-cell measurements and quantification of cell--cell
variability. We propose a novel combination of an adaptive Monte Carlo sampler,
called Gaussian Adaptation, and efficient exact stochastic simulation
algorithms that allows parameter identification from single stochastic
trajectories. We benchmark the proposed method on a linear and a non-linear
reaction network at steady state and during transient phases. In addition, we
demonstrate that the present method also provides an ellipsoidal volume
estimate of the viable part of parameter space and is able to estimate the
physical volume of the compartment in which the observed reactions take place.Comment: Article in print as a book chapter in Springer's "Advances in Systems
Biology
Poisson-Dirichlet statistics for the extremes of a log-correlated Gaussian field
We study the statistics of the extremes of a discrete Gaussian field with
logarithmic correlations at the level of the Gibbs measure. The model is
defined on the periodic interval , and its correlation structure is
nonhierarchical. It is based on a model introduced by Bacry and Muzy [Comm.
Math. Phys. 236 (2003) 449-475] (see also Barral and Mandelbrot [Probab. Theory
Related Fields 124 (2002) 409-430]), and is similar to the logarithmic Random
Energy Model studied by Carpentier and Le Doussal [Phys. Rev. E (3) 63 (2001)
026110] and more recently by Fyodorov and Bouchaud [J. Phys. A 41 (2008)
372001]. At low temperature, it is shown that the normalized covariance of two
points sampled from the Gibbs measure is either or . This is used to
prove that the joint distribution of the Gibbs weights converges in a suitable
sense to that of a Poisson-Dirichlet variable. In particular, this proves a
conjecture of Carpentier and Le Doussal that the statistics of the extremes of
the log-correlated field behave as those of i.i.d. Gaussian variables and of
branching Brownian motion at the level of the Gibbs measure. The method of
proof is robust and is adaptable to other log-correlated Gaussian fields.Comment: Published in at http://dx.doi.org/10.1214/13-AAP952 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Variable Metric Random Pursuit
We consider unconstrained randomized optimization of smooth convex objective
functions in the gradient-free setting. We analyze Random Pursuit (RP)
algorithms with fixed (F-RP) and variable metric (V-RP). The algorithms only
use zeroth-order information about the objective function and compute an
approximate solution by repeated optimization over randomly chosen
one-dimensional subspaces. The distribution of search directions is dictated by
the chosen metric.
Variable Metric RP uses novel variants of a randomized zeroth-order Hessian
approximation scheme recently introduced by Leventhal and Lewis (D. Leventhal
and A. S. Lewis., Optimization 60(3), 329--245, 2011). We here present (i) a
refined analysis of the expected single step progress of RP algorithms and
their global convergence on (strictly) convex functions and (ii) novel
convergence bounds for V-RP on strongly convex functions. We also quantify how
well the employed metric needs to match the local geometry of the function in
order for the RP algorithms to converge with the best possible rate.
Our theoretical results are accompanied by numerical experiments, comparing
V-RP with the derivative-free schemes CMA-ES, Implicit Filtering, Nelder-Mead,
NEWUOA, Pattern-Search and Nesterov's gradient-free algorithms.Comment: 42 pages, 6 figures, 15 tables, submitted to journal, Version 3:
majorly revised second part, i.e. Section 5 and Appendi
On the Geometry of Maximum Entropy Problems
We show that a simple geometric result suffices to derive the form of the
optimal solution in a large class of finite and infinite-dimensional maximum
entropy problems concerning probability distributions, spectral densities and
covariance matrices. These include Burg's spectral estimation method and
Dempster's covariance completion, as well as various recent generalizations of
the above. We then apply this orthogonality principle to the new problem of
completing a block-circulant covariance matrix when an a priori estimate is
available.Comment: 22 page
Regularized Optimal Transport and the Rot Mover's Distance
This paper presents a unified framework for smooth convex regularization of
discrete optimal transport problems. In this context, the regularized optimal
transport turns out to be equivalent to a matrix nearness problem with respect
to Bregman divergences. Our framework thus naturally generalizes a previously
proposed regularization based on the Boltzmann-Shannon entropy related to the
Kullback-Leibler divergence, and solved with the Sinkhorn-Knopp algorithm. We
call the regularized optimal transport distance the rot mover's distance in
reference to the classical earth mover's distance. We develop two generic
schemes that we respectively call the alternate scaling algorithm and the
non-negative alternate scaling algorithm, to compute efficiently the
regularized optimal plans depending on whether the domain of the regularizer
lies within the non-negative orthant or not. These schemes are based on
Dykstra's algorithm with alternate Bregman projections, and further exploit the
Newton-Raphson method when applied to separable divergences. We enhance the
separable case with a sparse extension to deal with high data dimensions. We
also instantiate our proposed framework and discuss the inherent specificities
for well-known regularizers and statistical divergences in the machine learning
and information geometry communities. Finally, we demonstrate the merits of our
methods with experiments using synthetic data to illustrate the effect of
different regularizers and penalties on the solutions, as well as real-world
data for a pattern recognition application to audio scene classification
Differential Evolution with Population and Strategy Parameter Adaptation
Differential evolution (DE) is simple and effective in solving numerous real-world global optimization problems. However, its effectiveness critically depends on the appropriate setting of population size and strategy parameters. Therefore, to obtain optimal performance the time-consuming preliminary tuning of parameters is needed. Recently, different strategy parameter adaptation techniques, which can automatically update the parameters to appropriate values to suit the characteristics of optimization problems, have been proposed. However, most of the works do not control the adaptation of the population size. In addition, they try to adapt each strategy parameters individually but do not take into account the interaction between the parameters that are being adapted. In this paper, we introduce a DE algorithm where both strategy parameters are self-adapted taking into account the parameter dependencies by means of a multivariate probabilistic technique based on Gaussian Adaptation working on the parameter space. In addition, the proposed DE algorithm starts by sampling a huge number of sample solutions in the search space and in each generation a constant number of individuals from huge sample set are adaptively selected to form the population that evolves. The proposed algorithm is evaluated on 14 benchmark problems of CEC 2005 with different dimensionality
Flexible methods for blind separation of complex signals
One of the main matter in Blind Source Separation (BSS) performed with a neural network approach is the choice of the nonlinear activation function (AF). In fact if the shape of the activation function is chosen as the cumulative density function (c.d.f.) of the original source the problem is solved.
For this scope in this thesis a flexible approach is introduced and the shape of the
activation functions is changed during the learning process using the so-called “spline functions”.
The problem is complicated in the case of separation of complex sources where there is the problem of the dichotomy between analyticity and boundedness of the complex activation functions. The problem is solved introducing the “splitting function” model as activation function. The “splitting function” is a couple of “spline function” which wind off the real and the imaginary part of the complex activation function, each of one depending from the real and imaginary variable.
A more realistic model is the “generalized splitting function”, which is formed by a couple of two bi-dimensional functions (surfaces), one for the real and one for
the imaginary part of the complex function, each depending by both the real and imaginary part of the complex variable.
Unfortunately the linear environment is unrealistic in many practical applications.
In this way there is the need of extending BSS problem in the nonlinear environment: in this case both the activation function than the nonlinear distorting function are realized by the “splitting function” made of “spline function”.
The complex and instantaneous separation in linear and nonlinear environment allow us to perform a complex-valued extension of the well-known INFOMAX algorithm in several practical situations, such as convolutive mixtures, fMRI signal analysis and bandpass signal transmission.
In addition advanced characteristics on the proposed approach are introduced and deeply described. First of all it is shows as splines are universal nonlinear functions for BSS problem: they are able to perform separation in anyway. Then it is analyzed as the “splitting solution” allows the algorithm to obtain a phase recovery:
usually there is a phase ambiguity. Finally a Cramér-Rao lower bound for ICA is discussed.
Several experimental results, tested by different objective indexes, show the
effectiveness of the proposed approaches
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