88 research outputs found
Accelerated Proximal Algorithm for Finding the Dantzig Selector and Source Separation Using Dictionary Learning
In most of the applications, signals acquired from different sensors are composite and are corrupted by some noise. In the presence of noise, separation of composite signals into its components without losing information is quite challenging. Separation of signals becomes more difficult when only a few samples of the noisy undersampled composite signals are given. In this paper, we aim to find Dantzig selector with overcomplete dictionaries using Accelerated Proximal Gradient Algorithm (APGA) for recovery and separation of undersampled composite signals. We have successfully diagnosed leukemia disease using our model and compared it with Alternating Direction Method of Multipliers (ADMM). As a test case, we have also recovered Electrocardiogram (ECG) signal with great accuracy from its noisy version using this model along with Proximity Operator based Algorithm (POA) for comparison. With less computational complexity compared with ADMM and POA, APGA has a good clustering capability depicted from the leukemia diagnosis
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Penalised regression for high-dimensional data: an empirical investigation and improvements via ensemble learning
In a wide range of applications, datasets are generated for which the number of variables p exceeds the sample size n. Penalised likelihood methods are widely used to tackle regression problems in these high-dimensional settings. In this thesis, we carry out an extensive empirical comparison of the performance of popular penalised regression methods in high-dimensional settings and propose new methodology that uses ensemble learning to enhance the performance of these methods.
The relative efficacy of different penalised regression methods in finite-sample settings remains incompletely understood. Through a large-scale simulation study, consisting of more than 1,800 data-generating scenarios, we systematically consider the influence of various factors (for example, sample size and sparsity) on method performance. We focus on three related goals --- prediction, variable selection and variable ranking --- and consider six widely used methods. The results are supported by a semi-synthetic data example. Our empirical results complement existing theory and provide a resource to compare performance across a range of settings and metrics.
We then propose a new ensemble learning approach for improving the performance of penalised regression methods, called STructural RANDomised Selection (STRANDS). The approach, that builds and improves upon the Random Lasso method, consists of two steps. In both steps, we reduce dimensionality by repeated subsampling of variables. We apply a penalised regression method to each subsampled dataset and average the results. In the first step, subsampling is informed by variable correlation structure, and in the second step, by variable importance measures from the first step. STRANDS can be used with any sparse penalised regression approach as the ``base learner''. In simulations, we show that STRANDS typically improves upon its base learner, and demonstrate that taking account of the correlation structure in the first step can help to improve the efficiency with which the model space may be explored.
We propose another ensemble learning method to improve the prediction performance of Ridge Regression in sparse settings. Specifically, we combine Bayesian Ridge Regression with a probabilistic forward selection procedure, where inclusion of a variable at each stage is probabilistically determined by a Bayes factor. We compare the prediction performance of the proposed method to penalised regression methods using simulated data
Challenges of Big Data Analysis
Big Data bring new opportunities to modern society and challenges to data
scientists. On one hand, Big Data hold great promises for discovering subtle
population patterns and heterogeneities that are not possible with small-scale
data. On the other hand, the massive sample size and high dimensionality of Big
Data introduce unique computational and statistical challenges, including
scalability and storage bottleneck, noise accumulation, spurious correlation,
incidental endogeneity, and measurement errors. These challenges are
distinguished and require new computational and statistical paradigm. This
article give overviews on the salient features of Big Data and how these
features impact on paradigm change on statistical and computational methods as
well as computing architectures. We also provide various new perspectives on
the Big Data analysis and computation. In particular, we emphasis on the
viability of the sparsest solution in high-confidence set and point out that
exogeneous assumptions in most statistical methods for Big Data can not be
validated due to incidental endogeneity. They can lead to wrong statistical
inferences and consequently wrong scientific conclusions
Classification of gene expression autism data based on adaptive penalized logistic regression
The common issues of high-dimensional gene expression data are that many of genes may not be relevant to their diseases. Gene selection has been proved to be an effective way to improve the result of many classification methods. In this paper, an adaptive penalized logistic regression is proposed, with the aim of identification relevant genes and provides high classification accuracy of autism data, by combining the logistic regression with the weighted L1-norm. Experimental results show that the proposed method significantly outperforms two competitor methods in terms of classification accuracy, G-mean, and area under the curve. Thus, the proposed method can be useful for other cancer classification using DNA gene expression data in the real clinical practice
Feature selection when there are many influential features
Recent discussion of the success of feature selection methods has argued that
focusing on a relatively small number of features has been counterproductive.
Instead, it is suggested, the number of significant features can be in the
thousands or tens of thousands, rather than (as is commonly supposed at
present) approximately in the range from five to fifty. This change, in orders
of magnitude, in the number of influential features, necessitates alterations
to the way in which we choose features and to the manner in which the success
of feature selection is assessed. In this paper, we suggest a general approach
that is suited to cases where the number of relevant features is very large,
and we consider particular versions of the approach in detail. We propose ways
of measuring performance, and we study both theoretical and numerical
properties of the proposed methodology.Comment: Published in at http://dx.doi.org/10.3150/13-BEJ536 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
Robust and sparse estimation of high-dimensional precision matrices via bivariate outlier detection
Robust estimation of Gaussian Graphical models in the high-dimensional setting is becoming increasingly important since large and real data may contain outlying observations. These outliers can lead to drastically wrong inference on the intrinsic graph structure. Several procedures apply univariate transformations to make the data Gaussian distributed. However, these transformations do not work well under the presence of structural bivariate outliers. We propose a robust precision matrix estimator under the cellwise contamination mechanism that is robust against structural bivariate outliers. This estimator exploits robust pairwise weighted correlation coefficient estimates, where the weights are computed by the Mahalanobis distance with respect to an affine equivariant robust correlation coefficient estimator. We show that the convergence rate of the proposed estimator is the same as the correlation coefficient used to compute the Mahalanobis distance. We conduct numerical simulation under different contamination settings to compare the graph recovery performance of different robust estimators. Finally, the proposed method is then applied to the classification of tumors using gene expression data. We show that our procedure can effectively recover the true graph under cellwise data contamination.Acknowledgements: the authors acknowledge financial support from the Spanish Ministry of Education and Science, research project MTM2013-44902-P
An efficient gene selection method for high-dimensional microarray data based on sparse logistic regression
Gene selection in high-dimensional microarray data has become increasingly important in cancer classification. The high dimensionality of microarray data makes the application of many expert classifier systems difficult.To simultaneously perform gene selection and estimate the gene coefficientsin the model, sparse logistic regression using L1-norm was successfully applied in high-dimensional microarray data. However, when there are highcorrelation among genes, L1-norm cannot perform effectively. To addressthis issue, an efficient sparse logistic regression (ESLR) is proposed. Extensive applications using high-dimensional gene expression data show that ourproposed method can successfully select the highly correlated genes. Furthermore, ESLR is compared with other three methods and exhibits competitiveperformance in both classification accuracy and Youdens index. Thus, wecan conclude that ESLR has significant impact in sparse logistic regressionmethod and could be used in the field of high-dimensional microarray datacancer classification
High-dimensional Measurement Error Models for Lipschitz Loss
Recently emerging large-scale biomedical data pose exciting opportunities for
scientific discoveries. However, the ultrahigh dimensionality and
non-negligible measurement errors in the data may create difficulties in
estimation. There are limited methods for high-dimensional covariates with
measurement error, that usually require knowledge of the noise distribution and
focus on linear or generalized linear models. In this work, we develop
high-dimensional measurement error models for a class of Lipschitz loss
functions that encompasses logistic regression, hinge loss and quantile
regression, among others. Our estimator is designed to minimize the norm
among all estimators belonging to suitable feasible sets, without requiring any
knowledge of the noise distribution. Subsequently, we generalize these
estimators to a Lasso analog version that is computationally scalable to higher
dimensions. We derive theoretical guarantees in terms of finite sample
statistical error bounds and sign consistency, even when the dimensionality
increases exponentially with the sample size. Extensive simulation studies
demonstrate superior performance compared to existing methods in classification
and quantile regression problems. An application to a gender classification
task based on brain functional connectivity in the Human Connectome Project
data illustrates improved accuracy under our approach, and the ability to
reliably identify significant brain connections that drive gender differences
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