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New algorithms for M-estimation of multivariate scatter and location

JOURNAL OF MULTIVARIATE ANALYSIS 2016年 144卷 200-217页

作者： Duembgen, Lutz Nordhausen, Klaus Schuhmacher, Heike Univ Bern CH-3012 Bern Switzerland Univ Turku SF-20500 Turku Finland

We present new algorithms for M-estimators of multivariate scatter and location and for symmetrized M-estimators of multivariate scatter. The new algorithms are considerably faster than currently used fixed-point and other algorithms. The main idea is to utilize a Taylor expansion of second order of the target functional and devise a partial Newton-Raphson procedure. In connection with symmetrized M-estimators we work with incomplete U-statistics to accelerate our procedures initially. (C) 2015 Elsevier Inc. All rights reserved.

关键词： fixed-point algorithm Matrix exponential function Newton-Raphson algorithm Taylor expansion

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Spatial independent component analysis of functional MRI time-series: To what extent do results depend on the algorithm used?

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HUMAN BRAIN MAPPING 2002年第3期16卷 146-157页

作者： Esposito, F Formisano, E Seifritz, E Goebel, R Morrone, R Tedeschi, G Di Salle, F Univ Naples Federico II Nuovo Policlin 2 Div Neuroradiol Dept Neurol Sci I-80127 Naples Italy Univ Naples 2 Inst Neurol Sci Naples Italy Maastricht Univ Dept Cognit Neurosci Maastricht Netherlands Univ Basel Dept Psychiat CH-4003 Basel Switzerland Morrone Diagnost Ctr Caserta Italy

Independent component analysis (ICA) has been successfully employed to decompose functional MRI (fMRI) time-series into sets of activation maps and associated time-courses. Several ICA algorithms have been proposed in the neural network literature. Applied to fMRI, these algorithms might lead to different spatial or temporal readouts of brain activation. We compared the two ICA algorithms that have been used so far for spatial ICA (sICA) of fMRI time-series: the Infomax (Bell and Sejnowski [1995]: Neural Comput 7:1004-1034) and the fixed-point (Hyvarinen [1999]: Adv Neural Inf Proc Syst 10:273-279) algorithms. We evaluated the Infomax- and fixed point-based sICA decompositions of simulated motor, and real motor and visual activation fMRI time-series using an ensemble of measures. Log-likelihood (McKeown et al. [1998]: Hum Brain Mapp 6:160-188) was used as a measure of how significantly the estimated independent sources fit the statistical structure of the data;receiver operating characteristics (ROC) and linear correlation analyses were used to evaluate the algorithms' accuracy of estimating the spatial layout and the temporal dynamics of simulated and real activations;cluster sizing calculations and an estimation of a residual gaussian noise term within the components were used to examine the anatomic structure of ICA components and for the assessment of noise reduction capabilities. Whereas both algorithms produced highly accurate results, the fixed-point outperformed the Infomax in terms of spatial and temporal accuracy as long as inferential statistics were employed as benchmarks. Conversely, the Infomax sICA was superior in terms of global estimation of the ICA model and noise reduction capabilities. Because of its adaptive nature, the Infomax approach appears to be better suited to investigate activation phenomena that are not predictable or adequately modelled by inferential techniques. (C) 2002 Wiley-Liss, Inc.

关键词： functional magnetic resonance imaging exploratory data-driven analysis independent component analysis fixed-point algorithm adaptive algorithm information maximization receiver operating characteristics Infomax algorithm

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Fast and precise independent component analysis for high field fMRI time series tailored using prior information on spatiotemporal structure

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HUMAN BRAIN MAPPING 2002年第1期15卷 54-66页

作者： Suzuki, K Kiryu, T Nakada, T Niigata Univ Brain Res Inst Dept Integrated Neurosci Niigata 9518585 Japan Niigata Univ Grad Sch Sci & Technol Niigata 95021 Japan Univ Calif Davis Dept Neurol Davis CA 95616 USA

Independent component analysis (ICA) has been shown as a promising tool for the analysis of functional magnetic resonance imaging (fMRI) time series. Each of these studies, however, used a general-purpose algorithm for performing ICA and the computational efficiency and accuracy of elicited neuronal activations have not been discussed in much detail. We have previously proposed a direct search method for improving computational efficiency. The method, which is based on independent component-cross correlation-sequential epoch (ICS) analysis, utilizes a form of the fixed-point ICA algorithm and considerably reduces the time required for extracting desired components. At the same time, it is shown that the accuracy of detecting physiologically meaningful components is much improved by tailoring the contrast function used in the algorithm. In this study, further improvement was made to this direct search method by integrating an optimal contrast function. Functional resolution of activation maps could be controlled with a suitable selection of the contrast function derived from prior knowledge of the spatial patterns of physiologically desired components. A simple skewness-weighted contrast function was verified to extract sufficiently precise activation maps from the fMRI time series acquired using a 3.0 Tesla MRI system. (C) 2001 Wiley-Liss, Inc.

关键词： fMRI independent component analysis fixed-point algorithm contrast function sequential epoch analysis overcomplete representation

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Compositions and convex combinations of averaged nonexpansive operators

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JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 2015年第1期425卷 55-70页

作者： Combettes, Patrick L. Yamada, Isao Univ Paris 06 Sorbonne Univ Lab Jacques Louis Lions UMR 7598 F-75005 Paris France Tokyo Inst Technol Dept Commun & Comp Engn Tokyo 1528550 Japan

Properties of compositions and convex combinations of averaged nonexpansive operators are investigated and applied to the design of new fixed point algorithms in Hilbert spaces. An extended version of the forward backward splitting algorithm for finding a zero of the sum of two monotone operators is obtained. (C) 2014 Elsevier Inc. All rights reserved.

关键词： Averaged operator fixed-point algorithm Forward-backward splitting Monotone operator Nonexpansive operator

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Real-time independent component analysis of fMRI time-series

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NEUROIMAGE 2003年第4期20卷 2209-2224页

作者： Esposito, F Seifritz, E Formisano, E Morrone, R Scarabino, T Tedeschi, G Cirillo, S Goebel, R Di Salle, F Univ Naples Federico II Dept Neurol Sci Poliklin Nouvo Policlin 2 I-80131 Naples Italy Univ Naples 2 Div Neurol 2 I-80138 Naples Italy Univ Basel Dept Psychiat CH-4025 Basel Switzerland Maastricht Univ Dept Cognit Neurosci NL-6200 MD Maastricht Netherlands Morrone Diagnost Ctr I-81100 Caserta Italy IRCCS Casa Sollievo Sofferenza Dept Neuroradiol I-71013 San Giovanni Rotondo Italy Univ Naples 2 Dept Neuroradiol I-80138 Naples Italy

Real-time functional magnetic resonance imaging fMRI) enables one to monitor a subject's brain activity during an ongoing session. The availability of online information about brain activity is essential for developing and refining interactive fMRI paradigms in research and clinical trials and for neurofeedback applications. Data analysis for real-time fMRI has traditionally been based on hypothesis-driven processing methods. Off-line data analysis, conversely, may be usefully complemented by data-driven approaches, such as independent component analysis (ICA), which can identify brain activity without a priori temporal assumptions on brain activity. However, ICA is commonly considered a time-consuming procedure and thus unsuitable to process the high flux of fMRI data while they are acquired. Here, by specific choices regarding the implementation, we exported the ICA framework and implemented it into real-time fMRI data analysis. We show that, reducing the ICA input to a few points within a time-series in a sliding-window approach, computational times become compatible with real-time settings. Our technique produced accurate dynamic readouts of brain activity as well as a precise spatiotemporal history of quasistationary patterns in the form of cumulative activation maps and time courses. Results from real and simulated motor activation data show comparable performances for the proposed ICA implementation and standard linear regression analysis applied either in a sliding-window or in a cumulative mode. Furthermore, we demonstrate the possibility of monitoring transient or unexpected neural activities and suggest that real-time ICA may provide the fMRI researcher with a better understanding and control of subjects' behaviors and performances. (C) 2003 Elsevier Inc. All rights reserved.

关键词： functional magnetic resonance imaging fMRI real-time analysis exploratory data-driven analysis descriptive statistics sliding-window analysis independent component analysis fixed-point algorithm receiver operating characteristics

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Optimal inclusion probabilities for balanced sampling

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JOURNAL OF STATISTICAL PLANNING AND INFERENCE 2011年第2期141卷 984-994页

作者： Chauvet, G. Bonnery, D. Deville, J. -C. Ecole Natl Stat & Anal Informat F-35170 Bruz France

When auxiliary information is available at the design stage, samples may be selected by means of balanced sampling. The variance of the Horvitz-Thompson estimator is then reduced, since it is approximately given by that of the residuals of the variable of interest on the balancing variables. In this paper, a method for computing optimal inclusion probabilities for balanced sampling on given auxiliary variables is studied. We show that the method formerly suggested by Title and Favre (2005) enables the computation of inclusion probabilities that lead to a decrease in variance under some conditions on the set of balancing variables. A disadvantage is that the target optimal inclusion probabilities depend on the variable of interest. If the needed quantities are unknown at the design stage, we propose to use estimates instead (e.g., arising from a previous wave of the survey). A limited simulation study suggests that, under some conditions, our method performs better than the method of Title and Favre (2005). (C) 2010 Elsevier B.V. All rights reserved.

关键词： Balanced sampling Calibration Cube method fixed-point algorithm Variance approximation

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An Invitation to Pharmacostatics

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BULLETIN OF MATHEMATICAL BIOLOGY 2019年第9期81卷 3642-3654页

作者： Gnacadja, Gilles Amgen Inc San Francisco CA 94080 USA

Pharmacology, the study of interactions between biological processes and therapeutic agents, is traditionally presented as consisting of two subdisciplines: pharmacokinetics, which is about the distribution and metabolism of drugs in organisms, and pharmacodynamics, which is about the organisms' response to drugs. In discovery-stage pharmacology however, one primary concern is what we call pharmacostatics, the characterization of equilibrium parameters and states of core interactions of physiologic and therapeutic interest. This usually takes the form of studying dose-response curves, without consideration for the relevant qualitative properties of the underlying reaction networks, e.g., the existence, multiplicity and asymptotic stability of steady states. Furthermore, steady-state calculations customarily employ manually derived closed-form expressions based on approximating assumptions. While these formulas may seem adequate most of the time, the assumptions need not apply, and there are genuine though seemingly uncommon cases where this approach is not feasible and/or fails to explain non-monotone dose-response curves. It is this paper's aim to stimulate interest in mathematical problems arising in pharmacostatics. We specifically pose two problems about a particular relevant class of networks of reversible binding reactions. The first problem is to exploit a certain fixed-point formulation of the equilibrium equation to devise an algorithmic method that would be compellingly preferable to current practice in the pharmacostatics context. The second problem is to explicitly anticipate the possibility of non-monotone dose-response curves from network topology. Addressing these problems would positively impact biopharmaceutical research, and they have inherent mathematical interest.

关键词： Pharmacostatics Receptor pharmacology Non-monotone dose-response curve Equilibrium calculation Polynomial system solving fixed-point algorithm

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On the Hicksian laws of comparative statics for the Hicksian case: the path-following approach using an alternative homotopy

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Computational Economics 1998年第1期12卷 25-33页

作者： Shiomura, Takashi Faculty of Informatics Kansai University Takatsuki Osaka Japan

The paper discusses an approach to comparative statics in the large by making use of a homotopy continuation method. This is based on the path-following approach presented by the author which is in turn due to the fixed-point algorithm explored by Garcia and Zangwill. We investigate from a global viewpoint the Hicksian laws of comparative statics for the Hicksian case which is a key to the first Hicksian law at least locally, and obtain the first Hicksian law in the large. Global results for the dominant diagonal case and the G1-Metzlerian case are also obtained.

关键词： Comparative statics fixed-point algorithm Homotopy

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Interpretation and improvement of an iterative wavelet-based denoising method

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IEEE SIGNAL PROCESSING LETTERS 2003年第8期10卷 239-241页

作者： Ranta, R Heinrich, C Louis-Dorr, V Wolf, D CRAN UMR CNRS INPL 7039 F-54516 Vandoeuvre Les Nancy France Univ Strasbourg 1 UMR CNRS 7005 LSIIT F-67400 Illkirch Graffenstaden France

The goal of this letter is to shed new light on a wavelet-based denoising method developed by Hadjileontiadis et al, which is derived from an iterative denoising algorithm by Coifman and Wickerhauser. The underlying algorithm is revisited and interpreted as a fixed-point algorithm. This allows to derive a new version of the algorithm largely increasing computational efficiency.

关键词： denoising fixed-point algorithm orthogonal wavelet transform

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INFINITE RETROGRESSION IN THE EAVES-SAIGAL algorithm

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MATHEMATICAL PROGRAMMING 1980年第3期19卷 313-327页

作者： BROOKS, PS Stanford University Stanford CA USA

For certain functionsf fromRn toRn, the Eaves—Saigal algorithm computes a path inRn × (0, 1] which converges to a zero off. In this case, it is shown that even whenf is of classC∞ and has a unique zero, the con... 详细信息

关键词： Retrogressing Paths Homotopy Method fixed-point algorithm

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