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Model selection by resampling penalization  [PDF]
Sylvain Arlot
Mathematics , 2007,
Abstract: We present a new family of model selection algorithms based on the resampling heuristics. It can be used in several frameworks, do not require any knowledge about the unknown law of the data, and may be seen as a generalization of local Rademacher complexities and $V$-fold cross-validation. In the case example of least-square regression on histograms, we prove oracle inequalities, and that these algorithms are naturally adaptive to both the smoothness of the regression function and the variability of the noise level. Then, interpretating $V$-fold cross-validation in terms of penalization, we enlighten the question of choosing $V$. Finally, a simulation study illustrates the strength of resampling penalization algorithms against some classical ones, in particular with heteroscedastic data.
Model selection by resampling penalization  [PDF]
Sylvain Arlot
Mathematics , 2009, DOI: 10.1214/08-EJS196
Abstract: In this paper, a new family of resampling-based penalization procedures for model selection is defined in a general framework. It generalizes several methods, including Efron's bootstrap penalization and the leave-one-out penalization recently proposed by Arlot (2008), to any exchangeable weighted bootstrap resampling scheme. In the heteroscedastic regression framework, assuming the models to have a particular structure, these resampling penalties are proved to satisfy a non-asymptotic oracle inequality with leading constant close to 1. In particular, they are asympotically optimal. Resampling penalties are used for defining an estimator adapting simultaneously to the smoothness of the regression function and to the heteroscedasticity of the noise. This is remarkable because resampling penalties are general-purpose devices, which have not been built specifically to handle heteroscedastic data. Hence, resampling penalties naturally adapt to heteroscedasticity. A simulation study shows that resampling penalties improve on V-fold cross-validation in terms of final prediction error, in particular when the signal-to-noise ratio is not large.
Finite sample penalization in adaptive density deconvolution  [PDF]
Fabienne Comte,Yves Rozenholc,Marie-Luce Taupin
Mathematics , 2006,
Abstract: We consider the problem of estimating the density $g$ of identically distributed variables $X\_i$, from a sample $Z\_1, ..., Z\_n$ where $Z\_i=X\_i+\sigma\epsilon\_i$, $i=1, ..., n$ and $\sigma \epsilon\_i$ is a noise independent of $X\_i$ with known density $ \sigma^{-1}f\_\epsilon(./\sigma)$. We generalize adaptive estimators, constructed by a model selection procedure, described in Comte et al. (2005). We study numerically their properties in various contexts and we test their robustness. Comparisons are made with respect to deconvolution kernel estimators, misspecification of errors, dependency,... It appears that our estimation algorithm, based on a fast procedure, performs very well in all contexts.
Reduced rank regression via adaptive nuclear norm penalization  [PDF]
Kun Chen,Hongbo Dong,Kung-Sik Chan
Statistics , 2012,
Abstract: Adaptive nuclear-norm penalization is proposed for low-rank matrix approximation, by which we develop a new reduced-rank estimation method for the general high-dimensional multivariate regression problems. The adaptive nuclear norm of a matrix is defined as the weighted sum of the singular values of the matrix. For example, the pre-specified weights may be some negative power of the singular values of the data matrix (or its projection in regression setting). The adaptive nuclear norm is generally non-convex under the natural restriction that the weight decreases with the singular value. However, we show that the proposed non-convex penalized regression method has a global optimal solution obtained from an adaptively soft-thresholded singular value decomposition. This new reduced-rank estimator is computationally efficient, has continuous solution path and possesses better bias-variance property than its classical counterpart. The rank consistency and prediction/estimation performance bounds of the proposed estimator are established under high-dimensional asymptotic regime. Simulation studies and an application in genetics demonstrate that the proposed estimator has superior performance to several existing methods. The adaptive nuclear-norm penalization can also serve as a building block to study a broad class of singular value penalties.
Variable Selection in Causal Inference Using Penalization  [PDF]
Ashkan Ertefaie,Masoud Asgharian,David A. Stephens
Statistics , 2013,
Abstract: In the causal adjustment setting, variable selection techniques based on either the outcome or treatment allocation model can result in the omission of confounders or the inclusion of spurious variables in the propensity score. We propose a variable selection method based on a penalized likelihood which considers the response and treatment assignment models simultaneously. The proposed method facilitates confounder selection in high-dimensional settings. We show that under some conditions our method attains the oracle property. The selected variables are used to form a double robust regression estimator of the treatment effect. Simulation results are presented and economic growth data are analyzed.
Quantifying selection in immune receptor repertoires  [PDF]
Yuval Elhanati,Anand Murugan,Curtis G. Callan Jr.,Thierry Mora,Aleksandra M. Walczak
Quantitative Biology , 2014, DOI: 10.1073/pnas.1409572111
Abstract: The efficient recognition of pathogens by the adaptive immune system relies on the diversity of receptors displayed at the surface of immune cells. T-cell receptor diversity results from an initial random DNA editing process, called VDJ recombination, followed by functional selection of cells according to the interaction of their surface receptors with self and foreign antigenic peptides. To quantify the effect of selection on the highly variable elements of the receptor, we apply a probabilistic maximum likelihood approach to the analysis of high-throughput sequence data from the $\beta$-chain of human T-cell receptors. We quantify selection factors for V and J gene choice, and for the length and amino-acid composition of the variable region. Our approach is necessary to disentangle the effects of selection from biases inherent in the recombination process. Inferred selection factors differ little between donors, or between naive and memory repertoires. The number of sequences shared between donors is well-predicted by the model, indicating a purely stochastic origin of such "public" sequences. We find a significant correlation between biases induced by VDJ recombination and our inferred selection factors, together with a reduction of diversity during selection. Both effects suggest that natural selection acting on the recombination process has anticipated the selection pressures experienced during somatic evolution.
Genome-Wide Stochastic Adaptive DNA Amplification at Direct and Inverted DNA Repeats in the Parasite Leishmania  [PDF]
Jean-Michel Ubeda equal contributor,Frédéric Raymond equal contributor,Angana Mukherjee equal contributor,Marie Plourde,Hélène Gingras,Gaétan Roy,Andréanne Lapointe,Philippe Leprohon,Barbara Papadopoulou,Jacques Corbeil,Marc Ouellette
PLOS Biology , 2014, DOI: 10.1371/journal.pbio.1001868
Abstract: Gene amplification of specific loci has been described in all kingdoms of life. In the protozoan parasite Leishmania, the product of amplification is usually part of extrachromosomal circular or linear amplicons that are formed at the level of direct or inverted repeated sequences. A bioinformatics screen revealed that repeated sequences are widely distributed in the Leishmania genome and the repeats are chromosome-specific, conserved among species, and generally present in low copy number. Using sensitive PCR assays, we provide evidence that the Leishmania genome is continuously being rearranged at the level of these repeated sequences, which serve as a functional platform for constitutive and stochastic amplification (and deletion) of genomic segments in the population. This process is adaptive as the copy number of advantageous extrachromosomal circular or linear elements increases upon selective pressure and is reversible when selection is removed. We also provide mechanistic insights on the formation of circular and linear amplicons through RAD51 recombinase-dependent and -independent mechanisms, respectively. The whole genome of Leishmania is thus stochastically rearranged at the level of repeated sequences, and the selection of parasite subpopulations with changes in the copy number of specific loci is used as a strategy to respond to a changing environment.
Natural selection and adaptive evolution of leptin
Guo Zou,YaPing Zhang,Li Yu
Chinese Science Bulletin , 2013, DOI: 10.1007/s11434-012-5635-8
Abstract: Leptin is an adiposity-secreted hormone that is pivotal in regulating feeding behavior, energy metabolism and body mass. The study of leptin has been of crucial importance for public health and pharmaceutical intervention given its role in obesity. Generally, leptin is highly conserved due to its functional importance. However, episodes of rapid sequence evolution and positive selection have been observed in some mammalian species, indicating that the leptin functions in these animals may have undergone adaptive modification to their environments. In this article, we review the adaptive evolution of leptin and its potential functional consequences. This review is expected to guide future research of molecular evolution and functional assays of this gene, and also to provide a theoretical foundation for the use of leptin in therapeutic applications.
Adaptive Observer-Based Fault Estimation for Stochastic Markovian Jumping Systems
Shuping He,Fei Liu
Abstract and Applied Analysis , 2012, DOI: 10.1155/2012/176419
Abstract: This paper studies the adaptive fault estimation problems for stochastic Markovian jump systems (MJSs) with time delays. With the aid of the selected Lyapunov-Krasovskii functional, the adaptive fault estimation algorithm based on adaptive observer is proposed to enhance the rapidity and accuracy performance of fault estimation. A sufficient condition on the existence of adaptive observer is presented and proved by means of linear matrix inequalities techniques. The presented results are extended to multiple time-delayed MJSs. Simulation results illustrate that the validity of the proposed adaptive faults estimation algorithms.
SVR with Adaptive Error Penalization

Chen Xiao-feng,Wang Shi-tong,Cao Su-qun,

电子与信息学报 , 2008,
Abstract: A novel support vector regression method AEPSVR is proposed in this paper. First, an approximate regression function is obtained using -SVR method, and then a new adaptive error penalization function is introduced to enhance the robust performance of SVR such that a robust support vector regression is derived. Because the proposed AEPSVR here is based on -SVR, so various optimization methods for SVR can be used. Experimental results show that the proposed AEPSVR can reduce the affect of outliers, and have the very good generalization capability.
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