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22
On Differential Variability of Expression Ratios: Improving . . .
 JOURNAL OF COMPUTATIONAL BIOLOGY
, 2001
"... We consider the problem of inferring fold changes in gene expression from cDNA microarray data. Standard procedures focus on the ratio of measured fluorescent intensities at each spot on the microarray, but to do so is to ignore the fact that the variation of such ratios is not constant. Estimates o ..."
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Cited by 195 (6 self)
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We consider the problem of inferring fold changes in gene expression from cDNA microarray data. Standard procedures focus on the ratio of measured fluorescent intensities at each spot on the microarray, but to do so is to ignore the fact that the variation of such ratios is not constant. Estimates of gene expression changes are derived within a simple hierarchical model that accounts for measurement error and fluctuations in absolute gene expression levels. Significant gene expression changes are identified by deriving the posterior odds of change within a similar model. The methods are tested via simulation and are applied to a panel of Escherichia coli microarrays.
Blind Minimax Estimation
"... We consider the linear regression problem of estimating an unknown, deterministic parameter vector based on measurements corrupted by colored Gaussian noise. We present and analyze blind minimax estimators (BMEs), which consist of a bounded parameter set minimax estimator, whose parameter set is its ..."
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Cited by 11 (10 self)
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We consider the linear regression problem of estimating an unknown, deterministic parameter vector based on measurements corrupted by colored Gaussian noise. We present and analyze blind minimax estimators (BMEs), which consist of a bounded parameter set minimax estimator, whose parameter set is itself estimated from measurements. Thus, one does not require any prior assumption or knowledge, and the proposed estimator can be applied to any linear regression problem. We demonstrate analytically that the BMEs strictly dominate the leastsquares estimator, i.e., they achieve lower meansquared error for any value of the parameter vector. Both Stein’s estimator and its positivepart correction can be derived within the blind minimax framework. Furthermore, our approach can be readily extended to a wider class of estimation problems than Stein’s estimator, which is defined only for white noise and nontransformed measurements. We show through simulation that the BMEs generally outperform previous extensions of Stein’s technique.
Blind minimax estimators: Improving on least squares estimation
 IEEE WORKSHOP STATISTICAL SIGNAL PROCESSING (SSP
, 2005
"... We consider the linear regression problem of estimating an unknown, deterministic parameter vector based on measurements corrupted by colored Gaussian noise. We present and analyze estimators based on the blind minimax approach, a technique whereby a parameter set is estimated from measurements and ..."
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Cited by 7 (7 self)
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We consider the linear regression problem of estimating an unknown, deterministic parameter vector based on measurements corrupted by colored Gaussian noise. We present and analyze estimators based on the blind minimax approach, a technique whereby a parameter set is estimated from measurements and then used to construct a minimax estimator. We demonstrate analytically that the obtained estimators strictly dominate the leastsquares estimator (LSE), i.e., they achieve lower meansquared error for any value of the parameter vector. Simulations show that these estimators outperform Bock’s estimator, which also dominates the LSE.
Computational Models of Consciousness: An Evaluation
, 1999
"... This paper aims at evaluating existing computational (mechanistic) models of cognition in relation to the study of consciousness, on the basis of psychological and philosophical theories and data. It first critiques various mechanistic explanations of consciousness, especially existing computational ..."
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Cited by 4 (1 self)
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This paper aims at evaluating existing computational (mechanistic) models of cognition in relation to the study of consciousness, on the basis of psychological and philosophical theories and data. It first critiques various mechanistic explanations of consciousness, especially existing computational cognitive models. It then explores the issue of the functional roles of consciousness and examines various views in this regard, in relation to the mechanistic explanation of consciousness. In these examinations, the paper argues in favor of the explanation based on the distinction between localist (symbolic) representation and distributed representation (the ideas of which have been put forth in the connectionist literature). Serving as a basis for the discussions, a model of the conscious/unconscious interaction, utilizing the representational dierence explanation of consciousness, is briefly described. The paper also advances a proposal regarding the synergistic interaction between the co...
Computation, Reduction, and Teleology of Consciousness
, 2001
"... This paper aims to explore mechanistic and teleological explanations of consciousness. In terms of mechanistic explanations, it critiques various existing views, especially those embodied by existing computational cognitive models. In this regard, the paper argues in favor of the explanation based o ..."
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Cited by 4 (0 self)
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This paper aims to explore mechanistic and teleological explanations of consciousness. In terms of mechanistic explanations, it critiques various existing views, especially those embodied by existing computational cognitive models. In this regard, the paper argues in favor of the explanation based on the distinction between localist (symbolic) representation and distributed representation (as formulated in the connectionist literature), which reduces the phenomenological difference to a mechanistic difference. Furthermore, to establish a teleological explanation of consciousness, the paper discusses the issue of the functional role of consciousness on the basis of the aforementioned mechanistic explanation. A proposal based on synergistic interaction between the conscious and the unconscious is advanced that encompasses various existing views concerning the functional role of consciousness. This twostep deepening explanation has some empirical support, in the form of a cognitive model...
A new approach to fitting linear models in high dimensional spaces
, 2000
"... This thesis presents a new approach to fitting linear models, called “pace regression”, which also overcomes the dimensionality determination problem. Its optimality in minimizing the expected prediction loss is theoretically established, when the number of free parameters is infinitely large. In th ..."
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Cited by 4 (0 self)
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This thesis presents a new approach to fitting linear models, called “pace regression”, which also overcomes the dimensionality determination problem. Its optimality in minimizing the expected prediction loss is theoretically established, when the number of free parameters is infinitely large. In this sense, pace regression outperforms existing procedures for fitting linear models. Dimensionality determination, a special case of fitting linear models, turns out to be a natural byproduct. A range of simulation studies are conducted; the results support the theoretical analysis. Through the thesis, a deeper understanding is gained of the problem of fitting linear models. Many key issues are discussed. Existing procedures, namely OLS, AIC, BIC, RIC, CIC, CV(d), BS(m), RIDGE, NNGAROTTE and LASSO, are reviewed and compared, both theoretically and empirically, with the new methods. Estimating a mixing distribution is an indispensable part of pace regression. A measurebased minimum distance approach, including probability measures and nonnegative measures, is proposed, and strongly consistent estimators are produced. Of all minimum distance methods for estimating a mixing distribution, only the
Combining fossil and sunspot data: committee predictions
 in: International Conference on Neural Networks (ICNN97
, 1997
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Intrinsic estimation
 Bayesian Statistics 7
, 2003
"... In this paper the problem of parametric point estimation is addressed from an objective Bayesian viewpoint. Arguing that pure statistical estimation may be appropriately described as a precise decision problem where the loss function is a measure of the divergence between the assumed model and the e ..."
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Cited by 2 (0 self)
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In this paper the problem of parametric point estimation is addressed from an objective Bayesian viewpoint. Arguing that pure statistical estimation may be appropriately described as a precise decision problem where the loss function is a measure of the divergence between the assumed model and the estimated model, the informationbased intrinsic discrepancy is proposed as an appropriate loss function. The intrinsic estimator is then defined as that minimizing the expected loss with respect to the reference posterior distribution. The resulting estimators are shown have attractive invariance properties. As demonstrated with illustrative examples, the proposed theory either leads to new, arguably better estimators, or provides a new perspective on wellestablished solutions. Keywords: