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Robert Tibshirani

Bio: Robert Tibshirani is an academic researcher from Stanford University. The author has contributed to research in topics: Lasso (statistics) & Elastic net regularization. The author has an hindex of 147, co-authored 593 publications receiving 326580 citations. Previous affiliations of Robert Tibshirani include University of Toronto & University of California.


Papers
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Journal ArticleDOI
TL;DR: A simple method is proposed for the estimation of the minimum value of the cross-validation error which can be biased downward as an estimate of the test error at that samevalue of the tuning parameter.
Abstract: Tuning parameters in supervised learning problems are often estimated by cross-validation. The minimum value of the cross-validation error can be biased downward as an estimate of the test error at that same value of the tuning parameter. We propose a simple method for the estimation of this bias that uses information from the cross-validation process. As a result, it requires essentially no additional computation. We apply our bias estimate to a number of popular classifiers in various settings, and examine its performance.

103 citations

Journal ArticleDOI
TL;DR: Simulations and results on microarray data and the Netflix data show that these imputation techniques often outperform existing methods and offer a greater degree of flexibility.
Abstract: Missing data estimation is an important challenge with high-dimensional data arranged in the form of a matrix. Typically this data matrix is transposable, meaning that either the rows, columns or both can be treated as features. To model transposable data, we present a modification of the matrix-variate normal, the mean-restricted matrix-variate normal, in which the rows and columns each have a separate mean vector and covariance matrix. By placing additive penalties on the inverse covariance matrices of the rows and columns, these so-called transposable regularized covariance models allow for maximum likelihood estimation of the mean and nonsingular covariance matrices. Using these models, we formulate EM-type algorithms for missing data imputation in both the multivariate and transposable frameworks. We present theoretical results exploiting the structure of our transposable models that allow these models and imputation methods to be applied to high-dimensional data. Simulations and results on microarray data and the Netflix data show that these imputation techniques often outperform existing methods and offer a greater degree of flexibility.

102 citations

Journal ArticleDOI
TL;DR: Time‐dependent changes in fetal tissue gene expression in a rat model of in utero hypoxia compared with normoxic controls were investigated as an initial approach to understand molecular events underlying fetal development in response to Hypoxia.
Abstract: Molecular mechanisms underlying fetal growth restriction due to placental insufficiency and in utero hypoxia are not well understood In the current study, time-dependent (3 h-11 days) changes in fetal tissue gene expression in a rat model of in utero hypoxia compared with normoxic controls were investigated as an initial approach to understand molecular events underlying fetal development in response to hypoxia Under hypoxic conditions, litter size was reduced and IGFBP-1 was up-regulated in maternal serum and in fetal liver and heart Tissue-specific, distinct regulatory patterns of gene expression were observed under acute vs chronic hypoxic conditions Induction of glycolytic enzymes was an early event in response to hypoxia during organ development; consistently, tissue-specific induction of calcium homeostasis-related genes and suppression of growth-related genes were observed, suggesting mechanisms underlying hypoxia-related fetal growth restriction Furthermore, induction of inflammation-related genes in placentas exposed to long-term hypoxia (11 days) suggests a mechanism for placental dysfunction and impaired pregnancy outcome accompanying in utero hypoxia

101 citations

Posted Content
TL;DR: A simple algorithm, using a coordinate descent procedure for the lasso, is developed that solves a 1000 node problem in at most a minute, and is 30 to 4000 times faster than competing methods.
Abstract: We consider the problem of estimating sparse graphs by a lasso penalty applied to the inverse covariance matrix. Using a coordinate descent procedure for the lasso, we develop a simple algorithm| the Graphical Lasso| that is remarkably fast: it solves a 1000 node problem (» 500; 000 parameters) in at most a minute, and is 30 to 4000 times faster than competing methods. It also provides a conceptual link between the exact problem and the approximation suggested by Meinshausen & B˜ uhlmann (2006). We illustrate the method on some cell-signaling data from proteomics.

101 citations

Journal ArticleDOI
TL;DR: Clustering and statistical analysis supports the finding that malignant tumors generally show broad mis regulation of mitotic APC/C substrates not seen in benign tumors, suggesting that a "mitotic profile" in tumors may result from misregulation of the APC-C destruction pathway.
Abstract: The fidelity of cell division is dependent on the accumulation and ordered destruction of critical protein regulators. By triggering the appropriately timed, ubiquitin-dependent proteolysis of the mitotic regulatory proteins securin, cyclin B, aurora A kinase, and polo-like kinase 1, the anaphase promoting complex/cyclosome (APC/C) ubiquitin ligase plays an essential role in maintaining genomic stability. Misexpression of these APC/C substrates, individually, has been implicated in genomic instability and cancer. However, no comprehensive survey of the extent of their misregulation in tumors has been performed. Here, we analyzed more than 1600 benign and malignant tumors by immunohistochemical staining of tissue microarrays and found frequent overexpression of securin, polo-like kinase 1, aurora A, and Skp2 in malignant tumors. Positive and negative APC/C regulators, Cdh1 and Emi1, respectively, were also more strongly expressed in malignant versus benign tumors. Clustering and statistical analysis supports the finding that malignant tumors generally show broad misregulation of mitotic APC/C substrates not seen in benign tumors, suggesting that a “mitotic profile” in tumors may result from misregulation of the APC/C destruction pathway. This profile of misregulated mitotic APC/C substrates and regulators in malignant tumors suggests that analysis of this pathway may be diagnostically useful and represent a potentially important therapeutic target.

99 citations


Cited by
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Journal Article
TL;DR: Scikit-learn is a Python module integrating a wide range of state-of-the-art machine learning algorithms for medium-scale supervised and unsupervised problems, focusing on bringing machine learning to non-specialists using a general-purpose high-level language.
Abstract: Scikit-learn is a Python module integrating a wide range of state-of-the-art machine learning algorithms for medium-scale supervised and unsupervised problems. This package focuses on bringing machine learning to non-specialists using a general-purpose high-level language. Emphasis is put on ease of use, performance, documentation, and API consistency. It has minimal dependencies and is distributed under the simplified BSD license, encouraging its use in both academic and commercial settings. Source code, binaries, and documentation can be downloaded from http://scikit-learn.sourceforge.net.

47,974 citations

Journal ArticleDOI
TL;DR: This work presents DESeq2, a method for differential analysis of count data, using shrinkage estimation for dispersions and fold changes to improve stability and interpretability of estimates, which enables a more quantitative analysis focused on the strength rather than the mere presence of differential expression.
Abstract: In comparative high-throughput sequencing assays, a fundamental task is the analysis of count data, such as read counts per gene in RNA-seq, for evidence of systematic changes across experimental conditions. Small replicate numbers, discreteness, large dynamic range and the presence of outliers require a suitable statistical approach. We present DESeq2, a method for differential analysis of count data, using shrinkage estimation for dispersions and fold changes to improve stability and interpretability of estimates. This enables a more quantitative analysis focused on the strength rather than the mere presence of differential expression. The DESeq2 package is available at http://www.bioconductor.org/packages/release/bioc/html/DESeq2.html .

47,038 citations

Journal ArticleDOI
TL;DR: A new method for estimation in linear models called the lasso, which minimizes the residual sum of squares subject to the sum of the absolute value of the coefficients being less than a constant, is proposed.
Abstract: SUMMARY We propose a new method for estimation in linear models. The 'lasso' minimizes the residual sum of squares subject to the sum of the absolute value of the coefficients being less than a constant. Because of the nature of this constraint it tends to produce some coefficients that are exactly 0 and hence gives interpretable models. Our simulation studies suggest that the lasso enjoys some of the favourable properties of both subset selection and ridge regression. It produces interpretable models like subset selection and exhibits the stability of ridge regression. There is also an interesting relationship with recent work in adaptive function estimation by Donoho and Johnstone. The lasso idea is quite general and can be applied in a variety of statistical models: extensions to generalized regression models and tree-based models are briefly described.

40,785 citations

Proceedings ArticleDOI
07 Jun 2015
TL;DR: Inception as mentioned in this paper is a deep convolutional neural network architecture that achieves the new state of the art for classification and detection in the ImageNet Large-Scale Visual Recognition Challenge 2014 (ILSVRC14).
Abstract: We propose a deep convolutional neural network architecture codenamed Inception that achieves the new state of the art for classification and detection in the ImageNet Large-Scale Visual Recognition Challenge 2014 (ILSVRC14). The main hallmark of this architecture is the improved utilization of the computing resources inside the network. By a carefully crafted design, we increased the depth and width of the network while keeping the computational budget constant. To optimize quality, the architectural decisions were based on the Hebbian principle and the intuition of multi-scale processing. One particular incarnation used in our submission for ILSVRC14 is called GoogLeNet, a 22 layers deep network, the quality of which is assessed in the context of classification and detection.

40,257 citations

Book
18 Nov 2016
TL;DR: Deep learning as mentioned in this paper is a form of machine learning that enables computers to learn from experience and understand the world in terms of a hierarchy of concepts, and it is used in many applications such as natural language processing, speech recognition, computer vision, online recommendation systems, bioinformatics, and videogames.
Abstract: Deep learning is a form of machine learning that enables computers to learn from experience and understand the world in terms of a hierarchy of concepts. Because the computer gathers knowledge from experience, there is no need for a human computer operator to formally specify all the knowledge that the computer needs. The hierarchy of concepts allows the computer to learn complicated concepts by building them out of simpler ones; a graph of these hierarchies would be many layers deep. This book introduces a broad range of topics in deep learning. The text offers mathematical and conceptual background, covering relevant concepts in linear algebra, probability theory and information theory, numerical computation, and machine learning. It describes deep learning techniques used by practitioners in industry, including deep feedforward networks, regularization, optimization algorithms, convolutional networks, sequence modeling, and practical methodology; and it surveys such applications as natural language processing, speech recognition, computer vision, online recommendation systems, bioinformatics, and videogames. Finally, the book offers research perspectives, covering such theoretical topics as linear factor models, autoencoders, representation learning, structured probabilistic models, Monte Carlo methods, the partition function, approximate inference, and deep generative models. Deep Learning can be used by undergraduate or graduate students planning careers in either industry or research, and by software engineers who want to begin using deep learning in their products or platforms. A website offers supplementary material for both readers and instructors.

38,208 citations