40,028 research outputs found
Towards Machine Wald
The past century has seen a steady increase in the need of estimating and
predicting complex systems and making (possibly critical) decisions with
limited information. Although computers have made possible the numerical
evaluation of sophisticated statistical models, these models are still designed
\emph{by humans} because there is currently no known recipe or algorithm for
dividing the design of a statistical model into a sequence of arithmetic
operations. Indeed enabling computers to \emph{think} as \emph{humans} have the
ability to do when faced with uncertainty is challenging in several major ways:
(1) Finding optimal statistical models remains to be formulated as a well posed
problem when information on the system of interest is incomplete and comes in
the form of a complex combination of sample data, partial knowledge of
constitutive relations and a limited description of the distribution of input
random variables. (2) The space of admissible scenarios along with the space of
relevant information, assumptions, and/or beliefs, tend to be infinite
dimensional, whereas calculus on a computer is necessarily discrete and finite.
With this purpose, this paper explores the foundations of a rigorous framework
for the scientific computation of optimal statistical estimators/models and
reviews their connections with Decision Theory, Machine Learning, Bayesian
Inference, Stochastic Optimization, Robust Optimization, Optimal Uncertainty
Quantification and Information Based Complexity.Comment: 37 page
Self-adaptation of mutation distribution in evolutionary algorithms
This paper is posted here with permission from IEEE - Copyright @ 2007 IEEEThis paper proposes a self-adaptation method to control not only the mutation strength parameter, but also the mutation distribution for evolutionary algorithms. For this purpose, the isotropic g-Gaussian distribution is employed in the mutation operator. The g-Gaussian distribution allows to control the shape of the distribution by setting a real parameter g and can reproduce either finite second moment distributions or infinite second moment distributions. In the proposed method, the real parameter q of the g-Gaussian distribution is encoded in the chromosome of an individual and is allowed to evolve. An evolutionary programming algorithm with the proposed idea is presented. Experiments were carried out to study the performance of the proposed algorithm
Stochastic Block Coordinate Frank-Wolfe Algorithm for Large-Scale Biological Network Alignment
With increasingly "big" data available in biomedical research, deriving
accurate and reproducible biology knowledge from such big data imposes enormous
computational challenges. In this paper, motivated by recently developed
stochastic block coordinate algorithms, we propose a highly scalable randomized
block coordinate Frank-Wolfe algorithm for convex optimization with general
compact convex constraints, which has diverse applications in analyzing
biomedical data for better understanding cellular and disease mechanisms. We
focus on implementing the derived stochastic block coordinate algorithm to
align protein-protein interaction networks for identifying conserved functional
pathways based on the IsoRank framework. Our derived stochastic block
coordinate Frank-Wolfe (SBCFW) algorithm has the convergence guarantee and
naturally leads to the decreased computational cost (time and space) for each
iteration. Our experiments for querying conserved functional protein complexes
in yeast networks confirm the effectiveness of this technique for analyzing
large-scale biological networks
Motion Planning of Uncertain Ordinary Differential Equation Systems
This work presents a novel motion planning framework, rooted in nonlinear programming theory, that treats uncertain fully and under-actuated dynamical systems described by ordinary differential equations. Uncertainty in multibody dynamical systems comes from various sources, such as: system parameters, initial conditions, sensor and actuator noise, and external forcing. Treatment of uncertainty in design is of paramount practical importance because all real-life systems are affected by it, and poor robustness and suboptimal performance result if itâs not accounted for in a given design. In this work uncertainties are modeled using Generalized Polynomial Chaos and are solved quantitatively using a least-square collocation method. The computational efficiency of this approach enables the inclusion of uncertainty statistics in the nonlinear programming optimization process. As such, the proposed framework allows the user to pose, and answer, new design questions related to uncertain dynamical systems.
Specifically, the new framework is explained in the context of forward, inverse, and hybrid dynamics formulations. The forward dynamics formulation, applicable to both fully and under-actuated systems, prescribes deterministic actuator inputs which yield uncertain state trajectories. The inverse dynamics formulation is the dual to the forward dynamic, and is only applicable to fully-actuated systems; deterministic state trajectories are prescribed and yield uncertain actuator inputs. The inverse dynamics formulation is more computationally efficient as it requires only algebraic evaluations and completely avoids numerical integration. Finally, the hybrid dynamics formulation is applicable to under-actuated systems where it leverages the benefits of inverse dynamics for actuated joints and forward dynamics for unactuated joints; it prescribes actuated state and unactuated input trajectories which yield uncertain unactuated states and actuated inputs.
The benefits of the ability to quantify uncertainty when planning the motion of multibody dynamic systems are illustrated through several case-studies. The resulting designs determine optimal motion plansâsubject to deterministic and statistical constraintsâfor all possible systems within the probability space
Price decomposition in large-scale stochastic optimal control
We are interested in optimally driving a dynamical system that can be
influenced by exogenous noises. This is generally called a Stochastic Optimal
Control (SOC) problem and the Dynamic Programming (DP) principle is the natural
way of solving it. Unfortunately, DP faces the so-called curse of
dimensionality: the complexity of solving DP equations grows exponentially with
the dimension of the information variable that is sufficient to take optimal
decisions (the state variable). For a large class of SOC problems, which
includes important practical problems, we propose an original way of obtaining
strategies to drive the system. The algorithm we introduce is based on
Lagrangian relaxation, of which the application to decomposition is well-known
in the deterministic framework. However, its application to such closed-loop
problems is not straightforward and an additional statistical approximation
concerning the dual process is needed. We give a convergence proof, that
derives directly from classical results concerning duality in optimization, and
enlghten the error made by our approximation. Numerical results are also
provided, on a large-scale SOC problem. This idea extends the original DADP
algorithm that was presented by Barty, Carpentier and Girardeau (2010)
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