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High Dimension (high + dimension)

Distribution by Scientific Domains
Mathematics and Statistics71%

Selected Abstracts

Maximum Likelihood Estimation of VARMA Models Using a State-Space EM Algorithm

JOURNAL OF TIME SERIES ANALYSIS, Issue 5 2007
Konstantinos Metaxoglou
Abstract., We introduce a state-space representation for vector autoregressive moving-average models that enables maximum likelihood estimation using the EM algorithm. We obtain closed-form expressions for both the E- and M-steps; the former requires the Kalman filter and a fixed-interval smoother, and the latter requires least squares-type regression. We show via simulations that our algorithm converges reliably to the maximum, whereas gradient-based methods often fail because of the highly nonlinear nature of the likelihood function. Moreover, our algorithm converges in a smaller number of function evaluations than commonly used direct-search routines. Overall, our approach achieves its largest performance gains when applied to models of high dimension. We illustrate our technique by estimating a high-dimensional vector moving-average model for an efficiency test of California's wholesale electricity market. [source]

SOLVING DYNAMIC WILDLIFE RESOURCE OPTIMIZATION PROBLEMS USING REINFORCEMENT LEARNING

NATURAL RESOURCE MODELING, Issue 1 2005
CHRISTOPHER J. FONNESBECK
ABSTRACT. An important technical component of natural resource management, particularly in an adaptive management context, is optimization. This is used to select the most appropriate management strategy, given a model of the system and all relevant available information. For dynamic resource systems, dynamic programming has been the de facto standard for deriving optimal state-specific management strategies. Though effective for small-dimension problems, dynamic programming is incapable of providing solutions to larger problems, even with modern microcomputing technology. Reinforcement learning is an alternative, related procedure for deriving optimal management strategies, based on stochastic approximation. It is an iterative process that improves estimates of the value of state-specific actions based in interactions with a system, or model thereof. Applications of reinforcement learning in the field of artificial intelligence have illustrated its ability to yield near-optimal strategies for very complex model systems, highlighting the potential utility of this method for ecological and natural resource management problems, which tend to be of high dimension. I describe the concept of reinforcement learning and its approach of estimating optimal strategies by temporal difference learning. I then illustrate the application of this method using a simple, well-known case study of Anderson [1975], and compare the reinforcement learning results with those of dynamic programming. Though a globally-optimal strategy is not discovered, it performs very well relative to the dynamic programming strategy, based on simulated cumulative objective return. I suggest that reinforcement learning be applied to relatively complex problems where an approximate solution to a realistic model is preferable to an exact answer to an oversimplified model. [source]

Modeling the operation of multireservoir systems using decomposition and stochastic dynamic programming

NAVAL RESEARCH LOGISTICS: AN INTERNATIONAL JOURNAL, Issue 3 2006
T.W. Archibald
Abstract Stochastic dynamic programming models are attractive for multireservoir control problems because they allow non-linear features to be incorporated and changes in hydrological conditions to be modeled as Markov processes. However, with the exception of the simplest cases, these models are computationally intractable because of the high dimension of the state and action spaces involved. This paper proposes a new method of determining an operating policy for a multireservoir control problem that uses stochastic dynamic programming, but is practical for systems with many reservoirs. Decomposition is first used to reduce the problem to a number of independent subproblems. Each subproblem is formulated as a low-dimensional stochastic dynamic program and solved to determine the operating policy for one of the reservoirs in the system. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006 [source]

High-dimensional data analysis: Selection of variables, data compression and graphics , Application to gene expression

BIOMETRICAL JOURNAL, Issue 2 2009
Jürgen Läuter
Abstract The paper presents effective and mathematically exact procedures for selection of variables which are applicable in cases with a very high dimension as, for example, in gene expression analysis. Choosing sets of variables is an important method to increase the power of the statistical conclusions and to facilitate the biological interpretation. For the construction of sets, each single variable is considered as the centre of potential sets of variables. Testing for significance is carried out by means of the Westfall-Young principle based on resampling or by the parametric method of spherical tests. The particular requirements for statistical stability are taken into account; each kind of overfitting is avoided. Thus, high power is attained and the familywise type I error can be kept in spite of the large dimension. To obtain graphical representations by heat maps and curves, a specific data compression technique is applied. Gene expression data from B-cell lymphoma patients serve for the demonstration of the procedures. [source]

Stability of bifurcating solutions of the problem about capillary-gravity surface waves in spatial layer of floating fluid

PROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2009
Artyom N. Andronov
In prolongation of our previous investigations on capillary-gravity surface waves in spatial fluid layers the stability of the bifurcating families of solutions in the horizontal layers of the floating (and without flotation) incompressible heavy capillary fluid is considered. The assumption about layer depth simplifies the proof of the existence of bifurcating solutions at the high dimensions of the linearized operator degeneracy, computation of their asymptotics and as the main subject of this communication the investigation of their stability, relative to perturbations with the same symmetry as bifurcating solutions. Group analysis methods of differential equations are used. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

Some notes on poisson limits for empirical point processes

THE CANADIAN JOURNAL OF STATISTICS, Issue 3 2009
André Dabrowski
Abstract The authors define the scaled empirical point process. They obtain the weak limit of these point processes through a novel use of a dimension-free method based on the convergence of compensators of multiparameter martingales. The method extends previous results in several directions. They obtain limits at points where the density may be zero, but has regular variation. The joint limit of the empirical process evaluated at distinct points is given by independent Poisson processes. They provide applications both to nearest-neighbour density estimation in high dimensions, and to the asymptotic behaviour of multivariate extremes such as those arising from bivariate normal copulas. The Canadian Journal of Statistics 37: 347,360; 2009 © 2009 Statistical Society of Canada Les auteurs définissent un processus ponctuel empirique normalisé. Ils obtiennent une limite faible de ces processus ponctuels grâce à l'utilisation novatrice d'une méthode indépendante de la dimension basée sur la convergence des compensateurs de martingales à plusieurs paramètres. La méthode généralise des résultats précédents de différentes façons. Ils obtiennent des limites à des points où la densité peut être égale à 0, mais qui est à variation régulière. La limite conjointe du processus empirique évalué à des points distincts est représentée par des processus de Poisson indépendants. Les auteurs présentent deux applications, l'une sur l'estimation de densité de dimension élevée basée sur le plus proche voisin et l'autre sur le comportement asymptotique des extrêmes multidimensionnels provenant de copules normales bidimensionnelles. La revue canadienne de statistique 37: 347,360; 2009 © 2009 Société statistique du Canada [source]

HIGH-DIMENSIONAL PARAMETRIC MODELLING OF MULTIVARIATE EXTREME EVENTS

AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, Issue 1 2009
Alec G. Stephenson
Summary Multivariate extreme events are typically modelled using multivariate extreme value distributions. Unfortunately, there exists no finite parametrization for the class of multivariate extreme value distributions. One common approach is to model extreme events using some flexible parametric subclass. This approach has been limited to only two or three dimensions, primarily because suitably flexible high-dimensional parametric models have prohibitively complex density functions. We present an approach that allows a number of popular flexible models to be used in arbitrarily high dimensions. The approach easily handles missing and censored data, and can be employed when modelling componentwise maxima and multivariate threshold exceedances. The approach is based on a representation using conditionally independent marginal components, conditioning on positive stable random variables. We use Bayesian inference, where the conditioning variables are treated as auxiliary variables within Markov chain Monte Carlo simulations. We demonstrate these methods with an application to sea-levels, using data collected at 10 sites on the east coast of England. [source]