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We present a new restricted SVD-based CUR (RSVD-CUR) factorization for matrix triplets (A, B, G) that aims to extract meaningful information by providing a low-rank approximation of the three matrices using a subset of their rows and columns. The proposed method utilizes the discrete empirical interpolation method (DEIM) to select the subset of rows and columns from the orthogonal and nonsingular matrices obtained through an RSVD of the matrix triplet. We explore the relationships between a DEIM type RSVD-CUR factorization, a DEIM type CUR factorization, and a DEIM type generalized CUR decomposition and provide an error analysis that establishes the accuracy of the RSVD-CUR decomposition within a factor of the approximation error of the RSVD of the given matrices. The RSVD-CUR factorization can be used in applications that require approximating one data matrix relative to two other given matrices. We discuss two such applications, namely multiview dimension reduction and data perturbation problems where a correlated noise matrix is added to the input data matrix. Our numerical experiments demonstrate the advantages of the proposed method over the standard CUR approximation in these scenarios.

Model selection in linear regression models is a major challenge when dealing with high-dimensional data where the number of available measurements (sample size) is much smaller than the dimension of the parameter space. Traditional methods for model selection such as Akaike information criterion, Bayesian information criterion (BIC), and minimum description length are heavily prone to overfitting in the high-dimensional setting. In this regard, extended BIC (EBIC), which is an extended version of the original BIC, and extended Fisher information criterion (EFIC), which is a combination of EBIC and Fisher information criterion, are consistent estimators of the true model as the number of measurements grows very large. However, EBIC is not consistent in high signal-to-noise-ratio (SNR) scenarios where the sample size is fixed and EFIC is not invariant to data scaling resulting in unstable behaviour. In this article, we propose a new form of the EBIC criterion called EBIC-Robust, which is invariant to data scaling and consistent in both large sample sizes and high-SNR scenarios. Analytical proofs are presented to guarantee its consistency. Simulation results indicate that the performance of EBIC-Robust is quite superior to that of both EBIC and EFIC., QC 20230803

Model selection in linear regression models is a major challenge when dealing with high-dimensional data where the number of available measurements (sample size) is much smaller than the dimension of the parameter space. Traditional methods for model selection such as Akaike information criterion, Bayesian information criterion (BIC), and minimum description length are heavily prone to overfitting in the high-dimensional setting. In this regard, extended BIC (EBIC), which is an extended version of the original BIC, and extended Fisher information criterion (EFIC), which is a combination of EBIC and Fisher information criterion, are consistent estimators of the true model as the number of measurements grows very large. However, EBIC is not consistent in high signal-to-noise-ratio (SNR) scenarios where the sample size is fixed and EFIC is not invariant to data scaling resulting in unstable behaviour. In this article, we propose a new form of the EBIC criterion called EBIC-Robust, which is invariant to data scaling and consistent in both large sample sizes and high-SNR scenarios. Analytical proofs are presented to guarantee its consistency. Simulation results indicate that the performance of EBIC-Robust is quite superior to that of both EBIC and EFIC., QC 20230803

Model selection in linear regression models is a major challenge when dealing with high-dimensional data where the number of available measurements (sample size) is much smaller than the dimension of the parameter space. Traditional methods for model selection such as Akaike information criterion, Bayesian information criterion (BIC), and minimum description length are heavily prone to overfitting in the high-dimensional setting. In this regard, extended BIC (EBIC), which is an extended version of the original BIC, and extended Fisher information criterion (EFIC), which is a combination of EBIC and Fisher information criterion, are consistent estimators of the true model as the number of measurements grows very large. However, EBIC is not consistent in high signal-to-noise-ratio (SNR) scenarios where the sample size is fixed and EFIC is not invariant to data scaling resulting in unstable behaviour. In this article, we propose a new form of the EBIC criterion called EBIC-Robust, which is invariant to data scaling and consistent in both large sample sizes and high-SNR scenarios. Analytical proofs are presented to guarantee its consistency. Simulation results indicate that the performance of EBIC-Robust is quite superior to that of both EBIC and EFIC., QC 20230803

Model selection in linear regression models is a major challenge when dealing with high-dimensional data where the number of available measurements (sample size) is much smaller than the dimension of the parameter space. Traditional methods for model selection such as Akaike information criterion, Bayesian information criterion (BIC), and minimum description length are heavily prone to overfitting in the high-dimensional setting. In this regard, extended BIC (EBIC), which is an extended version of the original BIC, and extended Fisher information criterion (EFIC), which is a combination of EBIC and Fisher information criterion, are consistent estimators of the true model as the number of measurements grows very large. However, EBIC is not consistent in high signal-to-noise-ratio (SNR) scenarios where the sample size is fixed and EFIC is not invariant to data scaling resulting in unstable behaviour. In this article, we propose a new form of the EBIC criterion called EBIC-Robust, which is invariant to data scaling and consistent in both large sample sizes and high-SNR scenarios. Analytical proofs are presented to guarantee its consistency. Simulation results indicate that the performance of EBIC-Robust is quite superior to that of both EBIC and EFIC., QC 20230803

Model selection in linear regression models is a major challenge when dealing with high-dimensional data where the number of available measurements (sample size) is much smaller than the dimension of the parameter space. Traditional methods for model selection such as Akaike information criterion, Bayesian information criterion (BIC), and minimum description length are heavily prone to overfitting in the high-dimensional setting. In this regard, extended BIC (EBIC), which is an extended version of the original BIC, and extended Fisher information criterion (EFIC), which is a combination of EBIC and Fisher information criterion, are consistent estimators of the true model as the number of measurements grows very large. However, EBIC is not consistent in high signal-to-noise-ratio (SNR) scenarios where the sample size is fixed and EFIC is not invariant to data scaling resulting in unstable behaviour. In this article, we propose a new form of the EBIC criterion called EBIC-Robust, which is invariant to data scaling and consistent in both large sample sizes and high-SNR scenarios. Analytical proofs are presented to guarantee its consistency. Simulation results indicate that the performance of EBIC-Robust is quite superior to that of both EBIC and EFIC., QC 20230803

Extended Bayesian information criterion (EBIC) and extended Fisher information criterion (EFIC) are two popular criteria for model selection in sparse high-dimensional linear regression models. However, EBIC is inconsistent in scenarios when the signal-to-noise-ratio (SNR) is high but the sample size is small, and EFIC is not invariant to data scaling, which affects its performance under different signal and noise statistics. In this paper, we present a refined criterion called EBIC R where the ‘R’ stands for robust. EBIC R is an improved version of EBIC and EFIC. It is scale-invariant and a consistent estimator of the true model as the sample size grows large and/or when the SNR tends to infinity. The performance of EBIC R is compared to existing methods such as EBIC, EFIC and multi-beta-test (MBT). Simulation results indicate that the performance of EBIC R in identifying the true model is either at par or superior to that of the other considered methods., QC 20220516

Extended Bayesian information criterion (EBIC) and extended Fisher information criterion (EFIC) are two popular criteria for model selection in sparse high-dimensional linear regression models. However, EBIC is inconsistent in scenarios when the signal-to-noise-ratio (SNR) is high but the sample size is small, and EFIC is not invariant to data scaling, which affects its performance under different signal and noise statistics. In this paper, we present a refined criterion called EBIC R where the ‘R’ stands for robust. EBIC R is an improved version of EBIC and EFIC. It is scale-invariant and a consistent estimator of the true model as the sample size grows large and/or when the SNR tends to infinity. The performance of EBIC R is compared to existing methods such as EBIC, EFIC and multi-beta-test (MBT). Simulation results indicate that the performance of EBIC R in identifying the true model is either at par or superior to that of the other considered methods., QC 20220516

Extended Bayesian information criterion (EBIC) and extended Fisher information criterion (EFIC) are two popular criteria for model selection in sparse high-dimensional linear regression models. However, EBIC is inconsistent in scenarios when the signal-to-noise-ratio (SNR) is high but the sample size is small, and EFIC is not invariant to data scaling, which affects its performance under different signal and noise statistics. In this paper, we present a refined criterion called EBIC R where the ‘R’ stands for robust. EBIC R is an improved version of EBIC and EFIC. It is scale-invariant and a consistent estimator of the true model as the sample size grows large and/or when the SNR tends to infinity. The performance of EBIC R is compared to existing methods such as EBIC, EFIC and multi-beta-test (MBT). Simulation results indicate that the performance of EBIC R in identifying the true model is either at par or superior to that of the other considered methods., QC 20220516

Extended Bayesian information criterion (EBIC) and extended Fisher information criterion (EFIC) are two popular criteria for model selection in sparse high-dimensional linear regression models. However, EBIC is inconsistent in scenarios when the signal-to-noise-ratio (SNR) is high but the sample size is small, and EFIC is not invariant to data scaling, which affects its performance under different signal and noise statistics. In this paper, we present a refined criterion called EBIC R where the ‘R’ stands for robust. EBIC R is an improved version of EBIC and EFIC. It is scale-invariant and a consistent estimator of the true model as the sample size grows large and/or when the SNR tends to infinity. The performance of EBIC R is compared to existing methods such as EBIC, EFIC and multi-beta-test (MBT). Simulation results indicate that the performance of EBIC R in identifying the true model is either at par or superior to that of the other considered methods., QC 20220516

Extended Bayesian information criterion (EBIC) and extended Fisher information criterion (EFIC) are two popular criteria for model selection in sparse high-dimensional linear regression models. However, EBIC is inconsistent in scenarios when the signal-to-noise-ratio (SNR) is high but the sample size is small, and EFIC is not invariant to data scaling, which affects its performance under different signal and noise statistics. In this paper, we present a refined criterion called EBIC R where the ‘R’ stands for robust. EBIC R is an improved version of EBIC and EFIC. It is scale-invariant and a consistent estimator of the true model as the sample size grows large and/or when the SNR tends to infinity. The performance of EBIC R is compared to existing methods such as EBIC, EFIC and multi-beta-test (MBT). Simulation results indicate that the performance of EBIC R in identifying the true model is either at par or superior to that of the other considered methods., QC 20220516

In cross-version defect prediction (CVDP), historical data is derived from the prior version of the same project to predict defects of the current version. Recent studies in CVDP focus on subset selection to deal with the changes of the data distributions. No prior study has focused on training data arriving in streaming fashion across the versions where the significant differences between versions make the prediction unreliable. We refer to this situation as Drift Propensity (DP). By identifying DP, necessary steps can be taken (e.g., updating or retraining the model) to improve the prediction performance. In this paper, we investigate the chronological defect datasets and identify DP in the datasets. The no-memory data management technique is employed to manage the data distributions and a DP detection technique is proposed. The idea behind the proposed DP detection technique is to monitor the algorithm's error-rate. The DP detector triggers DP, warning, and control flags to take necessary steps. The proposed technique is significantly superior in identifying the distribution differences (p-value < 0.05). The DP's identified in the data distributions achieve large effect sizes (Hedges' g ≥ 0.80) during the pair-wise comparisons. We observe that if the error-rate exponentially increases, it causes DP, resulting in prediction performance deterioration. We thus recommend researches and practitioners to address DP in the chronological datasets. Due to its potential effects in the datasets, the prediction models could be enhanced to get the best results in CVDP. © 2020 IEEE.

Multi-armed bandit (MAB) algorithms could be used to select a subset of the k most informative summary statistics, from a pool of m possible summary statistics, by reformulating the subset selection problem as a MAB problem. This is suggested by experiments that tested five MAB algorithms (Direct, Halving, SAR, OCBA-m, and Racing) on the reformulated problem and comparing the results to two established subset selection algorithms (Minimizing Entropy and Approximate Sufficiency). The MAB algorithms yielded errors at par with the established methods, but in only a fraction of the time. Establishing MAB algorithms as a new standard for summary statistics subset selection could therefore save numerous scientists substantial amounts of time when selecting summary statistics for approximate bayesian computation.

Multi-armed bandit (MAB) algorithms could be used to select a subset of the k most informative summary statistics, from a pool of m possible summary statistics, by reformulating the subset selection problem as a MAB problem. This is suggested by experiments that tested five MAB algorithms (Direct, Halving, SAR, OCBA-m, and Racing) on the reformulated problem and comparing the results to two established subset selection algorithms (Minimizing Entropy and Approximate Sufficiency). The MAB algorithms yielded errors at par with the established methods, but in only a fraction of the time. Establishing MAB algorithms as a new standard for summary statistics subset selection could therefore save numerous scientists substantial amounts of time when selecting summary statistics for approximate bayesian computation.

Regression is a statistical technique for modeling the relationship between a dependent variable Y and two or more predictor variables, also known as regressors. In the broad field of regression, there exists a special case in which the relationship between the dependent variable and the regressor(s) is linear. This is known as linear regression. The purpose of this paper is to create a useful method that effectively selects a subset of regressors when dealing with high dimensional data and/or collinearity in linear regression. As the name depicts it, high dimensional data occurs when the number of predictor variables is far too large to use commonly known methods. Collinearity, on the other hand, occurs when there exists a linear relationship amongst one or more pairs of independent variables. This paper is divided into three main section: an introduction, which reviews key concepts that are needed for a full understanding of the paper; the methodology, which guides the reader, step-by-step, through the process of the newly devised method; results, which thoroughly explain and analyze any findings and propose further ideas to be studied.

Statistical model selection is a great challenge when the number of accessible measurements is much smaller than the dimension of the parameter space. We study the problem of model selection in the context of subset selection for high-dimensional linear regressions. Accordingly, we propose a new model selection criterion with the Fisher information that leads to the selection of a parsimonious model from all the combinatorial models up to some maximum level of sparsity. We analyze the performance of our criterion as the number of measurements grows to infinity, as well as when the noise variance tends to zero. In each case, we prove that our proposed criterion gives the true model with a probability approaching one. Additionally, we devise a computationally affordable algorithm to conduct model selection with the proposed criterion in practice. Interestingly, as a side product, our algorithm can provide the ideal regularization parameter for the Lasso estimator such that Lasso selects the true variables. Finally, numerical simulations are included to support our theoretical findings., QC 20180824

Statistical model selection is a great challenge when the number of accessible measurements is much smaller than the dimension of the parameter space. We study the problem of model selection in the context of subset selection for high-dimensional linear regressions. Accordingly, we propose a new model selection criterion with the Fisher information that leads to the selection of a parsimonious model from all the combinatorial models up to some maximum level of sparsity. We analyze the performance of our criterion as the number of measurements grows to infinity, as well as when the noise variance tends to zero. In each case, we prove that our proposed criterion gives the true model with a probability approaching one. Additionally, we devise a computationally affordable algorithm to conduct model selection with the proposed criterion in practice. Interestingly, as a side product, our algorithm can provide the ideal regularization parameter for the Lasso estimator such that Lasso selects the true variables. Finally, numerical simulations are included to support our theoretical findings., QC 20180824

Statistical model selection is a great challenge when the number of accessible measurements is much smaller than the dimension of the parameter space. We study the problem of model selection in the context of subset selection for high-dimensional linear regressions. Accordingly, we propose a new model selection criterion with the Fisher information that leads to the selection of a parsimonious model from all the combinatorial models up to some maximum level of sparsity. We analyze the performance of our criterion as the number of measurements grows to infinity, as well as when the noise variance tends to zero. In each case, we prove that our proposed criterion gives the true model with a probability approaching one. Additionally, we devise a computationally affordable algorithm to conduct model selection with the proposed criterion in practice. Interestingly, as a side product, our algorithm can provide the ideal regularization parameter for the Lasso estimator such that Lasso selects the true variables. Finally, numerical simulations are included to support our theoretical findings., QC 20180824

Most of the computer vision methods assume that data will be labeled and available beforehand in order to train a good recognition model. However, it becomes infeasible and unrealistic to know all the labels beforehand with the huge corpus of visual data being generated on a daily basis. In most image and video analysis tasks, selection of the most informative samples from a huge pool of training data in order to learn a good recognition model is an active research problem. Furthermore, it is also useful to reduce the annotation cost, as it is time-consuming to annotate unlabeled samples. In this thesis, we aim to design information-theoretic approaches which exploit inter-relationships between data instances in order to find informative samples in image or videos. Moreover, in recent years, the advent of high-tech journaling tools facilitates an image to be forged in a way that can easily evade state-of-the-art image tampering detection approaches. The recent success of the deep learning approaches in different recognition tasks inspires us to develop a high-confidence detection framework which can localize forged/manipulated regions in an image. Unlike semantic object segmentation where all meaningful regions (objects) are segmented, the localization of image forgery focuses only the possible tampered region which makes the problem even more challenging.We present two distinct information-theoretic approaches for selecting samples to learn recognition models, and a deep learning based method for localizing manipulation from images. In first approach, we show how models for joint scene and object classification can be learned online. A major motivation for this approach is to exploit the hierarchical relationships between scenes and objects, represented as a graphical model, in an active learning framework. To select the samples on graph, which need to be labeled by a human, we formulate an optimization function that reduces the joint entropy of scene and object va

Most of the computer vision methods assume that data will be labeled and available beforehand in order to train a good recognition model. However, it becomes infeasible and unrealistic to know all the labels beforehand with the huge corpus of visual data being generated on a daily basis. In most image and video analysis tasks, selection of the most informative samples from a huge pool of training data in order to learn a good recognition model is an active research problem. Furthermore, it is also useful to reduce the annotation cost, as it is time-consuming to annotate unlabeled samples. In this thesis, we aim to design information-theoretic approaches which exploit inter-relationships between data instances in order to find informative samples in image or videos. Moreover, in recent years, the advent of high-tech journaling tools facilitates an image to be forged in a way that can easily evade state-of-the-art image tampering detection approaches. The recent success of the deep learning approaches in different recognition tasks inspires us to develop a high-confidence detection framework which can localize forged/manipulated regions in an image. Unlike semantic object segmentation where all meaningful regions (objects) are segmented, the localization of image forgery focuses only the possible tampered region which makes the problem even more challenging.We present two distinct information-theoretic approaches for selecting samples to learn recognition models, and a deep learning based method for localizing manipulation from images. In first approach, we show how models for joint scene and object classification can be learned online. A major motivation for this approach is to exploit the hierarchical relationships between scenes and objects, represented as a graphical model, in an active learning framework. To select the samples on graph, which need to be labeled by a human, we formulate an optimization function that reduces the joint entropy of scene and object va

Statistical model selection is a great challenge when the number of accessible measurements is much smaller than the dimension of the parameter space. We study the problem of model selection in the context of subset selection for high-dimensional linear regressions. Accordingly, we propose a new model selection criterion with the Fisher information that leads to the selection of a parsimonious model from all the combinatorial models up to some maximum level of sparsity. We analyze the performance of our criterion as the number of measurements grows to infinity, as well as when the noise variance tends to zero. In each case, we prove that our proposed criterion gives the true model with a probability approaching one. Additionally, we devise a computationally affordable algorithm to conduct model selection with the proposed criterion in practice. Interestingly, as a side product, our algorithm can provide the ideal regularization parameter for the Lasso estimator such that Lasso selects the true variables. Finally, numerical simulations are included to support our theoretical findings., QC 20180824

Statistical model selection is a great challenge when the number of accessible measurements is much smaller than the dimension of the parameter space. We study the problem of model selection in the context of subset selection for high-dimensional linear regressions. Accordingly, we propose a new model selection criterion with the Fisher information that leads to the selection of a parsimonious model from all the combinatorial models up to some maximum level of sparsity. We analyze the performance of our criterion as the number of measurements grows to infinity, as well as when the noise variance tends to zero. In each case, we prove that our proposed criterion gives the true model with a probability approaching one. Additionally, we devise a computationally affordable algorithm to conduct model selection with the proposed criterion in practice. Interestingly, as a side product, our algorithm can provide the ideal regularization parameter for the Lasso estimator such that Lasso selects the true variables. Finally, numerical simulations are included to support our theoretical findings., QC 20180824

Let B be a set of n axis-parallel boxes in d-dimensions such that each box has a corner at the origin and the other corner in the positive quadrant, and let k be a positive integer. We study the problem of selecting k boxes in B that maximize the volume of the union of the selected boxes. The research is motivated by applications in skyline queries for databases and in multicriteria optimization, where the problem is known as the hypervolume subset selection problem. It is known that the problem can be solved in polynomial time in the plane, while the best known algorithms in any dimension d>2 enumerate all size-k subsets. We show that: * The problem is NP-hard already in 3 dimensions. * In 3 dimensions, we break the enumeration of all size-k subsets, by providing an n^O(sqrt(k)) algorithm. * For any constant dimension d, we give an efficient polynomial-time approximation scheme.

Selecting an optimal subset of k out of d features for linear regression models given n training instances is often considered intractable for feature spaces with hundreds or thousands of dimensions. We propose an efficient massively-parallel implementation for selecting such optimal feature subsets in a brute-force fashion for small k. By exploiting the enormous compute power provided by modern parallel devices such as graphics processing units, it can deal with thousands of input dimensions even using standard commodity hardware only. We evaluate the practical runtime using artificial datasets and sketch the applicability of our framework in the context of astronomy.

Astronomy light curves are sparse, gappy, and heteroscedastic. As a result standard time series methods regularly used for financial and similar datasets are of little help and astronomers are usually left to their own instruments and techniques to classify light curves. A common approach is to derive statistical features from the time series and to use machine learning methods, generally supervised, to separate objects into a few of the standard classes. In this work, we transform the time series to two-dimensional light curve representations in order to classify them using modern deep learning techniques. In particular, we show that convolutional neural networks based classifiers work well for broad characterization and classification. We use labeled datasets of periodic variables from CRTS survey and show how this opens doors for a quick classification of diverse classes with several possible exciting extensions.

Considering two classes of vehicles, we aim to identify the physical elements of the vehicles with the most impact on identifying the class of the vehicle in synthetic aperture radar (SAR) images. We classify vehicles using features, from polarimetric SAR images, corresponding to the structure of physical elements. We demonstrate a method which determines the most impactful features to classification by applying subset selection on the features. Determination of the most impactful elements of the vehicles is beneficial to the development of low observables, target models, and automatic target recognition (ATR) algorithms. We show how previous work with features from individual pixels is applied to a greater number of target states. At a greater number of target states, the previous work has poor classification performance. Additionally, the nature of the features from pixels limits the identification of the most impactful elements of vehicles. We apply concepts from optical sensing to reduce the limitation on identification of physical elements. We draw from optical sensing feature extraction with the use of Histogram of Oriented Gradients (HOG). From the cells of HOG, we form features from frequency and polarization attributes of SAR images. Using a subset set of features, we achieve a classification performance of 96.10 percent correct classification. Using the features from HOG and the cells, we identify the features with the most impact. Using backward selection, a process for subset selection, we identify the features with the most impact to classification. The execution of backward selection removes the features which induce the most error, The original document contains color images.

The correct diagnosis of cancer patients conventionally depends on the pathologist's experience and ability to distinguish cancer tissue from normal tissue under a microscope. Advances in technology for measuring the abundance of, e.g., proteins and mRNAs in tissue samples make it interesting to search for an optimal subset of these for classification of samples as cancer or normal. We discuss issues of identification of biomarkers that provide distinct signatures for prediction of tissues as cancer or normal, exemplified by our recent study of cancer signalling signatures in human colon cancer characterised with regards to protein abundance using high sensitivity isoelectric focusing. We show that the optimal subset for separation of cancer tissues from normal tissues does not contain any of the proteins in the top quintile in terms of significant difference between the groups according to Mann-Whitney U-test or correlation to the diagnosis. Actually, one of the proteins belongs to the tertile with the lowest significance and correlation. This highlights the weakness of the practice of only looking for significant differences in the abundance of individual proteins and raises the question of how many lifesaving discoveries that have been missed due to it. We also demonstrate how Monte Carlo simulations of the separation with random class assignment can be used to calculate p-values for observing any specific separation by chance and selection of the optimal number of proteins in the subset based on these p-values. Both selection of the optimal number of biomarkers and calculation of p-values corrected for multiple hypothesis testing are essential to obtain a subset of biomarkers that yield robust predictions for clinical use.

Ballistocardiogram (BCG) artifact remains a major challenge that renders electroencephalographic (EEG) signals hard to interpret in simultaneous EEG and functional MRI (fMRI) data acquisition. Here, we propose an integrated learning and inference approach that takes advantage of a commercial high-density EEG cap, to estimate the BCG contribution in noisy EEG recordings from inside the MR scanner. To estimate reliably the full-scalp BCG artifacts, a near-optimal subset (20 out of 256) of channels first was identified using a modified recording setup. In subsequent recordings inside the MR scanner, BCG-only signal from this subset of channels was used to generate continuous estimates of the full-scalp BCG artifacts via inference, from which the intended EEG signal was recovered. The reconstruction of the EEG was performed with both a direct subtraction and an optimization scheme. We evaluated the performance on both synthetic and real contaminated recordings, and compared it to the benchmark Optimal Basis Set (OBS) method. In the challenging non-event-related-potential (non-ERP) EEG studies, our reconstruction can yield more than fourteen-fold improvement in reducing the normalized RMS error of EEG signals, compared to OBS.

Ballistocardiogram (BCG) artifact remains a major challenge that renders electroencephalographic (EEG) signals hard to interpret in simultaneous EEG and functional MRI (fMRI) data acquisition. Here, we propose an integrated learning and inference approach that takes advantage of a commercial high-density EEG cap, to estimate the BCG contribution in noisy EEG recordings from inside the MR scanner. To estimate reliably the full-scalp BCG artifacts, a near-optimal subset (20 out of 256) of channels first was identified using a modified recording setup. In subsequent recordings inside the MR scanner, BCG-only signal from this subset of channels was used to generate continuous estimates of the full-scalp BCG artifacts via inference, from which the intended EEG signal was recovered. The reconstruction of the EEG was performed with both a direct subtraction and an optimization scheme. We evaluated the performance on both synthetic and real contaminated recordings, and compared it to the benchmark Optimal Basis Set (OBS) method. In the challenging non-event-related-potential (non-ERP) EEG studies, our reconstruction can yield more than fourteen-fold improvement in reducing the normalized RMS error of EEG signals, compared to OBS.

In this thesis, inference of biological networks from in vivo data generated by perturbation experiments is considered, i.e. deduction of causal interactions that exist among the observed variables. Knowledge of such regulatory influences is essential in biology. A system property–interampatteness–is introduced that explains why the variation in existing gene expression data is concentrated to a few “characteristic modes” or “eigengenes”, and why previously inferred models have a large number of false positive and false negative links. An interampatte system is characterized by strong INTERactions enabling simultaneous AMPlification and ATTEnuation of different signals and we show that perturbation of individual state variables, e.g. genes, typically leads to ill-conditioned data with both characteristic and weak modes. The weak modes are typically dominated by measurement noise due to poor excitation and their existence hampers network reconstruction. The excitation problem is solved by iterative design of correlated multi-gene perturbation experiments that counteract the intrinsic signal attenuation of the system. The next perturbation should be designed such that the expected response practically spans an additional dimension of the state space. The proposed design is numerically demonstrated for the Snf1 signalling pathway in S. cerevisiae. The impact of unperturbed and unobserved latent state variables, that exist in any real biological system, on the inferred network and required set-up of the experiments for network inference is analysed. Their existence implies that a subnetwork of pseudo-direct causal regulatory influences, accounting for all environmental effects, in general is inferred. In principle, the number of latent states and different paths between the nodes of the network can be estimated, but their identity cannot be determined unless they are observed or perturbed directly. Network inference is recognized as a variable/model selection problem an, Denna avhandling behandlar inferens av biologiskanätverk från in vivo data genererat genom störningsexperiment, d.v.s. bestämning av kausala kopplingar som existerar mellan de observerade variablerna. Kunskap om dessa regulatoriska influenser är väsentlig för biologisk förståelse. En system egenskap—förstärksvagning—introduceras. Denna förklarar varför variationen i existerande genexpressionsdata är koncentrerat till några få ”karakteristiska moder” eller ”egengener” och varför de modeller som konstruerats innan innehåller många falska positiva och falska negativa linkar. Ett system med förstärksvagning karakteriseras av starka kopplingar som möjliggör simultan FÖRSTÄRKning och förSVAGNING av olika signaler. Vi demonstrerar att störning av individuella tillståndsvariabler, t.ex. gener, typiskt leder till illakonditionerat data med både karakteristiska och svaga moder. De svaga moderna domineras typiskt av mätbrus p.g.a. dålig excitering och försvårar rekonstruktion av nätverket. Excitationsproblemet löses med iterativdesign av experiment där korrelerade störningar i multipla gener motverkar systemets inneboende försvagning av signaller. Följande störning bör designas så att det förväntade svaret praktiskt spänner ytterligare en dimension av tillståndsrummet. Den föreslagna designen demonstreras numeriskt för Snf1 signalleringsvägen i S. cerevisiae. Påverkan av ostörda och icke observerade latenta tillståndsvariabler, som existerar i varje verkligt biologiskt system, på konstruerade nätverk och planeringen av experiment för nätverksinferens analyseras. Existens av dessa tillståndsvariabler innebär att delnätverk med pseudo-direkta regulatoriska influenser, som kompenserar för miljöeffekter, generellt bestäms. I princip så kan antalet latenta tillstånd och alternativa vägar mellan noder i nätverket bestämmas, men deras identitet kan ej bestämmas om de inte direkt observeras eller störs. Nätverksinferens behandlas som ett variabel-/modelselektionsproblem och löses geno, QC 20130508

In this thesis, inference of biological networks from in vivo data generated by perturbation experiments is considered, i.e. deduction of causal interactions that exist among the observed variables. Knowledge of such regulatory influences is essential in biology. A system property–interampatteness–is introduced that explains why the variation in existing gene expression data is concentrated to a few “characteristic modes” or “eigengenes”, and why previously inferred models have a large number of false positive and false negative links. An interampatte system is characterized by strong INTERactions enabling simultaneous AMPlification and ATTEnuation of different signals and we show that perturbation of individual state variables, e.g. genes, typically leads to ill-conditioned data with both characteristic and weak modes. The weak modes are typically dominated by measurement noise due to poor excitation and their existence hampers network reconstruction. The excitation problem is solved by iterative design of correlated multi-gene perturbation experiments that counteract the intrinsic signal attenuation of the system. The next perturbation should be designed such that the expected response practically spans an additional dimension of the state space. The proposed design is numerically demonstrated for the Snf1 signalling pathway in S. cerevisiae. The impact of unperturbed and unobserved latent state variables, that exist in any real biological system, on the inferred network and required set-up of the experiments for network inference is analysed. Their existence implies that a subnetwork of pseudo-direct causal regulatory influences, accounting for all environmental effects, in general is inferred. In principle, the number of latent states and different paths between the nodes of the network can be estimated, but their identity cannot be determined unless they are observed or perturbed directly. Network inference is recognized as a variable/model selection problem an, Denna avhandling behandlar inferens av biologiskanätverk från in vivo data genererat genom störningsexperiment, d.v.s. bestämning av kausala kopplingar som existerar mellan de observerade variablerna. Kunskap om dessa regulatoriska influenser är väsentlig för biologisk förståelse. En system egenskap—förstärksvagning—introduceras. Denna förklarar varför variationen i existerande genexpressionsdata är koncentrerat till några få ”karakteristiska moder” eller ”egengener” och varför de modeller som konstruerats innan innehåller många falska positiva och falska negativa linkar. Ett system med förstärksvagning karakteriseras av starka kopplingar som möjliggör simultan FÖRSTÄRKning och förSVAGNING av olika signaler. Vi demonstrerar att störning av individuella tillståndsvariabler, t.ex. gener, typiskt leder till illakonditionerat data med både karakteristiska och svaga moder. De svaga moderna domineras typiskt av mätbrus p.g.a. dålig excitering och försvårar rekonstruktion av nätverket. Excitationsproblemet löses med iterativdesign av experiment där korrelerade störningar i multipla gener motverkar systemets inneboende försvagning av signaller. Följande störning bör designas så att det förväntade svaret praktiskt spänner ytterligare en dimension av tillståndsrummet. Den föreslagna designen demonstreras numeriskt för Snf1 signalleringsvägen i S. cerevisiae. Påverkan av ostörda och icke observerade latenta tillståndsvariabler, som existerar i varje verkligt biologiskt system, på konstruerade nätverk och planeringen av experiment för nätverksinferens analyseras. Existens av dessa tillståndsvariabler innebär att delnätverk med pseudo-direkta regulatoriska influenser, som kompenserar för miljöeffekter, generellt bestäms. I princip så kan antalet latenta tillstånd och alternativa vägar mellan noder i nätverket bestämmas, men deras identitet kan ej bestämmas om de inte direkt observeras eller störs. Nätverksinferens behandlas som ett variabel-/modelselektionsproblem och löses geno, QC 20130508

In this thesis, inference of biological networks from in vivo data generated by perturbation experiments is considered, i.e. deduction of causal interactions that exist among the observed variables. Knowledge of such regulatory influences is essential in biology. A system property–interampatteness–is introduced that explains why the variation in existing gene expression data is concentrated to a few “characteristic modes” or “eigengenes”, and why previously inferred models have a large number of false positive and false negative links. An interampatte system is characterized by strong INTERactions enabling simultaneous AMPlification and ATTEnuation of different signals and we show that perturbation of individual state variables, e.g. genes, typically leads to ill-conditioned data with both characteristic and weak modes. The weak modes are typically dominated by measurement noise due to poor excitation and their existence hampers network reconstruction. The excitation problem is solved by iterative design of correlated multi-gene perturbation experiments that counteract the intrinsic signal attenuation of the system. The next perturbation should be designed such that the expected response practically spans an additional dimension of the state space. The proposed design is numerically demonstrated for the Snf1 signalling pathway in S. cerevisiae. The impact of unperturbed and unobserved latent state variables, that exist in any real biological system, on the inferred network and required set-up of the experiments for network inference is analysed. Their existence implies that a subnetwork of pseudo-direct causal regulatory influences, accounting for all environmental effects, in general is inferred. In principle, the number of latent states and different paths between the nodes of the network can be estimated, but their identity cannot be determined unless they are observed or perturbed directly. Network inference is recognized as a variable/model selection problem an, Denna avhandling behandlar inferens av biologiskanätverk från in vivo data genererat genom störningsexperiment, d.v.s. bestämning av kausala kopplingar som existerar mellan de observerade variablerna. Kunskap om dessa regulatoriska influenser är väsentlig för biologisk förståelse. En system egenskap—förstärksvagning—introduceras. Denna förklarar varför variationen i existerande genexpressionsdata är koncentrerat till några få ”karakteristiska moder” eller ”egengener” och varför de modeller som konstruerats innan innehåller många falska positiva och falska negativa linkar. Ett system med förstärksvagning karakteriseras av starka kopplingar som möjliggör simultan FÖRSTÄRKning och förSVAGNING av olika signaler. Vi demonstrerar att störning av individuella tillståndsvariabler, t.ex. gener, typiskt leder till illakonditionerat data med både karakteristiska och svaga moder. De svaga moderna domineras typiskt av mätbrus p.g.a. dålig excitering och försvårar rekonstruktion av nätverket. Excitationsproblemet löses med iterativdesign av experiment där korrelerade störningar i multipla gener motverkar systemets inneboende försvagning av signaller. Följande störning bör designas så att det förväntade svaret praktiskt spänner ytterligare en dimension av tillståndsrummet. Den föreslagna designen demonstreras numeriskt för Snf1 signalleringsvägen i S. cerevisiae. Påverkan av ostörda och icke observerade latenta tillståndsvariabler, som existerar i varje verkligt biologiskt system, på konstruerade nätverk och planeringen av experiment för nätverksinferens analyseras. Existens av dessa tillståndsvariabler innebär att delnätverk med pseudo-direkta regulatoriska influenser, som kompenserar för miljöeffekter, generellt bestäms. I princip så kan antalet latenta tillstånd och alternativa vägar mellan noder i nätverket bestämmas, men deras identitet kan ej bestämmas om de inte direkt observeras eller störs. Nätverksinferens behandlas som ett variabel-/modelselektionsproblem och löses geno, QC 20130508

In this thesis, inference of biological networks from in vivo data generated by perturbation experiments is considered, i.e. deduction of causal interactions that exist among the observed variables. Knowledge of such regulatory influences is essential in biology. A system property–interampatteness–is introduced that explains why the variation in existing gene expression data is concentrated to a few “characteristic modes” or “eigengenes”, and why previously inferred models have a large number of false positive and false negative links. An interampatte system is characterized by strong INTERactions enabling simultaneous AMPlification and ATTEnuation of different signals and we show that perturbation of individual state variables, e.g. genes, typically leads to ill-conditioned data with both characteristic and weak modes. The weak modes are typically dominated by measurement noise due to poor excitation and their existence hampers network reconstruction. The excitation problem is solved by iterative design of correlated multi-gene perturbation experiments that counteract the intrinsic signal attenuation of the system. The next perturbation should be designed such that the expected response practically spans an additional dimension of the state space. The proposed design is numerically demonstrated for the Snf1 signalling pathway in S. cerevisiae. The impact of unperturbed and unobserved latent state variables, that exist in any real biological system, on the inferred network and required set-up of the experiments for network inference is analysed. Their existence implies that a subnetwork of pseudo-direct causal regulatory influences, accounting for all environmental effects, in general is inferred. In principle, the number of latent states and different paths between the nodes of the network can be estimated, but their identity cannot be determined unless they are observed or perturbed directly. Network inference is recognized as a variable/model selection problem an, Denna avhandling behandlar inferens av biologiskanätverk från in vivo data genererat genom störningsexperiment, d.v.s. bestämning av kausala kopplingar som existerar mellan de observerade variablerna. Kunskap om dessa regulatoriska influenser är väsentlig för biologisk förståelse. En system egenskap—förstärksvagning—introduceras. Denna förklarar varför variationen i existerande genexpressionsdata är koncentrerat till några få ”karakteristiska moder” eller ”egengener” och varför de modeller som konstruerats innan innehåller många falska positiva och falska negativa linkar. Ett system med förstärksvagning karakteriseras av starka kopplingar som möjliggör simultan FÖRSTÄRKning och förSVAGNING av olika signaler. Vi demonstrerar att störning av individuella tillståndsvariabler, t.ex. gener, typiskt leder till illakonditionerat data med både karakteristiska och svaga moder. De svaga moderna domineras typiskt av mätbrus p.g.a. dålig excitering och försvårar rekonstruktion av nätverket. Excitationsproblemet löses med iterativdesign av experiment där korrelerade störningar i multipla gener motverkar systemets inneboende försvagning av signaller. Följande störning bör designas så att det förväntade svaret praktiskt spänner ytterligare en dimension av tillståndsrummet. Den föreslagna designen demonstreras numeriskt för Snf1 signalleringsvägen i S. cerevisiae. Påverkan av ostörda och icke observerade latenta tillståndsvariabler, som existerar i varje verkligt biologiskt system, på konstruerade nätverk och planeringen av experiment för nätverksinferens analyseras. Existens av dessa tillståndsvariabler innebär att delnätverk med pseudo-direkta regulatoriska influenser, som kompenserar för miljöeffekter, generellt bestäms. I princip så kan antalet latenta tillstånd och alternativa vägar mellan noder i nätverket bestämmas, men deras identitet kan ej bestämmas om de inte direkt observeras eller störs. Nätverksinferens behandlas som ett variabel-/modelselektionsproblem och löses geno, QC 20130508

In this thesis, inference of biological networks from in vivo data generated by perturbation experiments is considered, i.e. deduction of causal interactions that exist among the observed variables. Knowledge of such regulatory influences is essential in biology. A system property–interampatteness–is introduced that explains why the variation in existing gene expression data is concentrated to a few “characteristic modes” or “eigengenes”, and why previously inferred models have a large number of false positive and false negative links. An interampatte system is characterized by strong INTERactions enabling simultaneous AMPlification and ATTEnuation of different signals and we show that perturbation of individual state variables, e.g. genes, typically leads to ill-conditioned data with both characteristic and weak modes. The weak modes are typically dominated by measurement noise due to poor excitation and their existence hampers network reconstruction. The excitation problem is solved by iterative design of correlated multi-gene perturbation experiments that counteract the intrinsic signal attenuation of the system. The next perturbation should be designed such that the expected response practically spans an additional dimension of the state space. The proposed design is numerically demonstrated for the Snf1 signalling pathway in S. cerevisiae. The impact of unperturbed and unobserved latent state variables, that exist in any real biological system, on the inferred network and required set-up of the experiments for network inference is analysed. Their existence implies that a subnetwork of pseudo-direct causal regulatory influences, accounting for all environmental effects, in general is inferred. In principle, the number of latent states and different paths between the nodes of the network can be estimated, but their identity cannot be determined unless they are observed or perturbed directly. Network inference is recognized as a variable/model selection problem an, Denna avhandling behandlar inferens av biologiskanätverk från in vivo data genererat genom störningsexperiment, d.v.s. bestämning av kausala kopplingar som existerar mellan de observerade variablerna. Kunskap om dessa regulatoriska influenser är väsentlig för biologisk förståelse. En system egenskap—förstärksvagning—introduceras. Denna förklarar varför variationen i existerande genexpressionsdata är koncentrerat till några få ”karakteristiska moder” eller ”egengener” och varför de modeller som konstruerats innan innehåller många falska positiva och falska negativa linkar. Ett system med förstärksvagning karakteriseras av starka kopplingar som möjliggör simultan FÖRSTÄRKning och förSVAGNING av olika signaler. Vi demonstrerar att störning av individuella tillståndsvariabler, t.ex. gener, typiskt leder till illakonditionerat data med både karakteristiska och svaga moder. De svaga moderna domineras typiskt av mätbrus p.g.a. dålig excitering och försvårar rekonstruktion av nätverket. Excitationsproblemet löses med iterativdesign av experiment där korrelerade störningar i multipla gener motverkar systemets inneboende försvagning av signaller. Följande störning bör designas så att det förväntade svaret praktiskt spänner ytterligare en dimension av tillståndsrummet. Den föreslagna designen demonstreras numeriskt för Snf1 signalleringsvägen i S. cerevisiae. Påverkan av ostörda och icke observerade latenta tillståndsvariabler, som existerar i varje verkligt biologiskt system, på konstruerade nätverk och planeringen av experiment för nätverksinferens analyseras. Existens av dessa tillståndsvariabler innebär att delnätverk med pseudo-direkta regulatoriska influenser, som kompenserar för miljöeffekter, generellt bestäms. I princip så kan antalet latenta tillstånd och alternativa vägar mellan noder i nätverket bestämmas, men deras identitet kan ej bestämmas om de inte direkt observeras eller störs. Nätverksinferens behandlas som ett variabel-/modelselektionsproblem och löses geno, QC 20130508

Thesis (Ph.D.)--University of Rochester. School of Medicine and Dentistry. Dept. of Biostatistics and Computational Biology, 2008., Identifying those genes that are differentially expressed in individuals with cancer could lead to new avenues of treatment or prevention. Gene array information can be collected for an individual and paired with information about a specific outcome. We consider binary and censored time to event survival outcomes. Improved construction of prognostic gene signatures − risk scores based on groups of genes that can relatively accurately predict an individual’s outcome or risk thereof − would be a step forward in gene array research. We consider the problem of selecting which variables (genes) to include in a prognostic gene signature with high dimensional data in the logistic regression model and the Cox proportional hazards model frameworks. Constructing a prognostic gene signature from gene array data is very difficult because the number of candidate genes greatly outnumbers the sample size available in most studies. In this case, commonly used statistical techniques perform poorly at choosing genes that accurately predict the endpoint of interest. We propose a search algorithm that lies between forward selection and searching over all subsets. This method uses an evolving subgroup paradigm to intelligently select variables over a relatively large model space. We show that our method applied to the Cox proportional hazards model for censored survival time data or the logistic regression model for binary data can yield significant improvements in the number of predictive variables selected and the prediction error compared with the LASSO method, forward selection, and univariate selection, as demonstrated with a simulation study. We also investigate validation methods. Censored survival time data confounds many of the common validation methods because the outcome is not always observed, and splitting a data set can lead to a lack of uncensored observations in some partitions. We pursue validation with the goal of selecting the ideal number of variables to include. We

When inspecting food quality, CT Scanning is among the primary tools used to gain insight. It provides valuable volumetric data using a process, which leaves the product unspoiled and untouched. However, volumetric data is merely a measure of density and therefore contains no appearance information (such as color, translucency, reflective properties). One way of reintroducing this lost information back to the volume data is to synthesize an appropriate texture and apply this to the volume data. A recent method within the field of texture synthesis is called Texture Optimization presented by Kopf et al. in 2007. This method accepts a number of 2D input exemplars, from which it generates a solid texture volume. The volume is iteratively improved via an expectation maximization algorithm. The bottleneck of Texture Optimization occurs during a nearest neighbor search, between texture patches from the 2D input exemplars and the generated texture volume. We examine the current procedures for minimizing the bottleneck and present a novel approach which increases the speed of the synthesis algorithm while minimizing loss of quality. The nearest neighbor search is performed in a high dimensional space. Applying a principal component analysis on the texture patches originating from the synthesized solid accelerates the process. These patches are then reduced in dimensionality until ”only” 95% of their original variance remains. This usually results in a dimension reduction from 192 to about 60-80. The reduction in dimensionality speeds up the convergence of the Texture Optimization method considerably. We examine the impacts of reducing the dimensionality further by tweaking the parameters as well as introducing an alternative method to reducing the dimensionality. Additionally, we study the possibility of selecting only a subsample of the neighborhoods available from the input exemplar without significantly impacting the overall synthesis quality.

When inspecting food quality, CT Scanning is among the primary tools used to gain insight. It provides valuable volumetric data using a process, which leaves the product unspoiled and untouched. However, volumetric data is merely a measure of density and therefore contains no appearance information (such as color, translucency, reflective properties). One way of reintroducing this lost information back to the volume data is to synthesize an appropriate texture and apply this to the volume data. A recent method within the field of texture synthesis is called Texture Optimization presented by Kopf et al. in 2007. This method accepts a number of 2D input exemplars, from which it generates a solid texture volume. The volume is iteratively improved via an expectation maximization algorithm. The bottleneck of Texture Optimization occurs during a nearest neighbor search, between texture patches from the 2D input exemplars and the generated texture volume. We examine the current procedures for minimizing the bottleneck and present a novel approach which increases the speed of the synthesis algorithm while minimizing loss of quality. The nearest neighbor search is performed in a high dimensional space. Applying a principal component analysis on the texture patches originating from the synthesized solid accelerates the process. These patches are then reduced in dimensionality until ”only” 95% of their original variance remains. This usually results in a dimension reduction from 192 to about 60-80. The reduction in dimensionality speeds up the convergence of the Texture Optimization method considerably. We examine the impacts of reducing the dimensionality further by tweaking the parameters as well as introducing an alternative method to reducing the dimensionality. Additionally, we study the possibility of selecting only a subsample of the neighborhoods available from the input exemplar without significantly impacting the overall synthesis quality.

We consider selecting a regression model, using a variant of Gets, when there are more variables than observations, in the special case that the variables are impulse dummies (indicators) for every observation. We show that the setting is unproblematic if tackled appropriately, and obtain the finite-sample distribution of estimators of the mean and variance in a simple location-scale model under the null that no impulses matter. A Monte Carlo simulation confirms the null distribution, and shows power against an alternative of interest.

We consider selecting a regression model, using a variant of Gets, when there are more variables than observations, in the special case that the variables are impulse dummies (indicators) for every observation. We show that the setting is unproblematic if tackled appropriately, and obtain the finite-sample distribution of estimators of the mean and variance in a simple location-scale model under the null that no impulses matter. A Monte Carlo simulation confirms the null distribution, and shows power against an alternative of interest.

We consider selecting a regression model, using a variant of Gets, when there are more variables than observations, in the special case that the variables are impulse dummies (indicators) for every observation. We show that the setting is unproblematic if tackled appropriately, and obtain the finite-sample distribution of estimators of the mean and variance in a simple location-scale model under the null that no impulses matter. A Monte Carlo simulation confirms the null distribution, and shows power against an alternative of interest.

When building a Kriging model, the general intuition is that using more data will always result in a better model. However, we show that when we have a large non-uniform dataset, using a uniform subset can have several advantages. Reducing the time necessary to fit the model, avoiding numerical inaccuracies and improving the robustness with respect to errors in the output data are some aspects which can be improved by using a uniform subset. We furthermore describe several new and current methods for selecting a uniform subset. These methods are tested and compared on several artificial datasets and one real life dataset. The comparison shows how the selected subsets affect different aspects of the resulting Kriging model. As none of the subset selection methods performs best on all criteria, the best method to choose depends on how the different aspects are valued. The comparison made in this paper can be used to facilitate the user in making a good choice.

This paper revisits the topic of how linear functions of observations having zero expectation, play an important role in our statistical understanding of the effect of addition or deletion of a set of observations in the general linear model. The effect of adding or dropping a group of parameters is also explained well in this manner. Several sets of update equations were derived by previous researchers in various special cases of the general set-up that we consider here. The results derived here bring out the common underlying principles of these update equations and help integrate these ideas. These results also provide further insights into recursive residuals, design of experiments, deletion diagnostics and selection of subset models. © 2007 Elsevier B.V. All rights reserved.

This paper revisits the topic of how linear functions of observations having zero expectation, play an important role in our statistical understanding of the effect of addition or deletion of a set of observations in the general linear model. The effect of adding or dropping a group of parameters is also explained well in this manner. Several sets of update equations were derived by previous researchers in various special cases of the general set-up that we consider here. The results derived here bring out the common underlying principles of these update equations and help integrate these ideas. These results also provide further insights into recursive residuals, design of experiments, deletion diagnostics and selection of subset models. © 2007 Elsevier B.V. All rights reserved.

This paper revisits the topic of how linear functions of observations having zero expectation, play an important role in our statistical understanding of the effect of addition or deletion of a set of observations in the general linear model. The effect of adding or dropping a group of parameters is also explained well in this manner. Several sets of update equations were derived by previous researchers in various special cases of the general set-up that we consider here. The results derived here bring out the common underlying principles of these update equations and help integrate these ideas. These results also provide further insights into recursive residuals, design of experiments, deletion diagnostics and selection of subset models. © 2007 Elsevier B.V. All rights reserved.

We consider selecting a regression model, using a variant of Gets, when there are more variables than observations, in the special case that the variables are impulse dummies (indicators) for every observation. We show that the setting is unproblematic if tackled appropriately, and obtain the finite-sample distribution of estimators of the mean and variance in a simple location-scale model under the null that no impulses matter. A Monte Carlo simulation confirms the null distribution, and shows power against an alternative of interest

We consider selecting a regression model, using a variant of Gets, when there are more variables than observations, in the special case that the variables are impulse dummies (indicators) for every observation. We show that the setting is unproblematic if tackled appropriately, and obtain the finite-sample distribution of estimators of the mean and variance in a simple location-scale model under the null that no impulses matter. A Monte Carlo simulation confirms the null distribution, and shows power against an alternative of interest

We consider selecting a regression model, using a variant of Gets, when there are more variables than observations, in the special case that the variables are impulse dummies (indicators) for every observation. We show that the setting is unproblematic if tackled appropriately, and obtain the finite-sample distribution of estimators of the mean and variance in a simple location-scale model under the null that no impulses matter. A Monte Carlo simulation confirms the null distribution, and shows power against an alternative of interest

We consider selecting a regression model, using a variant of Gets, when there are more variables than observations, in the special case that the variables are impulse dummies (indicators) for every observation. We show that the setting is unproblematic if tackled appropriately, and obtain the finite-sample distribution of estimators of the mean and variance in a simple location-scale model under the null that no impulses matter. A Monte Carlo simulation confirms the null distribution, and shows power against an alternative of interest

There is an increasing interest in remote sensed vision systems for surveillance, object recognition, target identification, and cartography. Other fields that could benefit from such systems are land use and land cover administration, estimation of water sedimentation, and the creation of maps. Of particular interest are automatic systems that are robust with respect to analyst's knowledge in areas such as image analysis and computer vision. Remote Sensed image analysis focuses on obtaining information from radar, multi spectral and hyperspectral images. Hyperspectral data enables the analyst to detect more materials, objects. and regions with more accuracy than previously possible. As the number of bands of high spectral resolution data increases, the capability to detect more detailed classes should also increase and the classification accuracy should increase as well. The curse of dimensionality has been known for more than three decades. There is a need for the development of algorithms for detection, and classification that utilize the amount of information and separability that hyperdimensional data offers while simultaneously avoiding the difficulties inherent in hyperdimensional space. The present report will summarize the research done in the areas of clustering, parameter estimation of hyperspectral data, band subset selection, data compression, and unsupervised decision fusion mechanism., Original contains color plates: All DTIC reproductions will be in black and white.