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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: In this article, the authors discuss a strategy for polychotomous classification that involves estimating class probabilities for each pair of classes, and then coupling the estimates together, similar to the Bradley-Terry method for paired comparisons.
Abstract: We discuss a strategy for polychotomous classification that involves estimating class probabilities for each pair of classes, and then coupling the estimates together. The coupling model is similar to the Bradley-Terry method for paired comparisons. We study the nature of the class probability estimates that arise, and examine the performance of the procedure in real and simulated data sets. Classifiers used include linear discriminants, nearest neighbors, adaptive nonlinear methods and the support vector machine.

1,569 citations

Journal ArticleDOI
TL;DR: A penalized matrix decomposition (PMD), a new framework for computing a rank-K approximation for a matrix, and establishes connections between the SCoTLASS method for sparse principal component analysis and the method of Zou and others (2006).
Abstract: SUMMARY We present a penalized matrix decomposition (PMD), a new framework for computing a rank-K approximation for a matrix. We approximate the matrix X as ˆ X = � K=1 dkukv T , where dk, uk, and

1,540 citations

Journal ArticleDOI
Trevor Hastie1, Robert Tibshirani
TL;DR: In this paper, a class of regression and generalized regression models in which the coefficients are allowed to vary as smooth functions of other variables is explored and general algorithms are presented for estimating the models flexibly and some examples are given.
Abstract: We explore a class of regression and generalized regression models in which the coefficients are allowed to vary as smooth functions of other variables. General algorithms are presented for estimating the models flexibly and some examples are given. This class of models ties together generalized additive models and dynamic generalized linear models into one common framework. When applied to the proportional hazards model for survival data, this approach provides a new way of modelling departures from the proportional hazards assumption

1,509 citations

Journal ArticleDOI
TL;DR: It is suggested that prostate tumors can be usefully classified according to their gene expression patterns, and these tumor subtypes may provide a basis for improved prognostication and treatment stratification.
Abstract: Prostate cancer, a leading cause of cancer death, displays a broad range of clinical behavior from relatively indolent to aggressive metastatic disease. To explore potential molecular variation underlying this clinical heterogeneity, we profiled gene expression in 62 primary prostate tumors, as well as 41 normal prostate specimens and nine lymph node metastases, using cDNA microarrays containing ≈26,000 genes. Unsupervised hierarchical clustering readily distinguished tumors from normal samples, and further identified three subclasses of prostate tumors based on distinct patterns of gene expression. High-grade and advanced stage tumors, as well as tumors associated with recurrence, were disproportionately represented among two of the three subtypes, one of which also included most lymph node metastases. To further characterize the clinical relevance of tumor subtypes, we evaluated as surrogate markers two genes differentially expressed among tumor subgroups by using immunohistochemistry on tissue microarrays representing an independent set of 225 prostate tumors. Positive staining for MUC1, a gene highly expressed in the subgroups with “aggressive” clinicopathological features, was associated with an elevated risk of recurrence (P = 0.003), whereas strong staining for AZGP1, a gene highly expressed in the other subgroup, was associated with a decreased risk of recurrence (P = 0.0008). In multivariate analysis, MUC1 and AZGP1 staining were strong predictors of tumor recurrence independent of tumor grade, stage, and preoperative prostate-specific antigen levels. Our results suggest that prostate tumors can be usefully classified according to their gene expression patterns, and these tumor subtypes may provide a basis for improved prognostication and treatment stratification.

1,315 citations

Journal ArticleDOI
TL;DR: Evidence is provided that widespread DNA copy number alteration can lead directly to global deregulation of gene expression, which may contribute to the development or progression of cancer.
Abstract: Genomic DNA copy number alterations are key genetic events in the development and progression of human cancers. Here we report a genome-wide microarray comparative genomic hybridization (array CGH) analysis of DNA copy number variation in a series of primary human breast tumors. We have profiled DNA copy number alteration across 6,691 mapped human genes, in 44 predominantly advanced, primary breast tumors and 10 breast cancer cell lines. While the overall patterns of DNA amplification and deletion corroborate previous cytogenetic studies, the high-resolution (gene-by-gene) mapping of amplicon boundaries and the quantitative analysis of amplicon shape provide significant improvement in the localization of candidate oncogenes. Parallel microarray measurements of mRNA levels reveal the remarkable degree to which variation in gene copy number contributes to variation in gene expression in tumor cells. Specifically, we find that 62% of highly amplified genes show moderately or highly elevated expression, that DNA copy number influences gene expression across a wide range of DNA copy number alterations (deletion, low-, mid- and high-level amplification), that on average, a 2-fold change in DNA copy number is associated with a corresponding 1.5-fold change in mRNA levels, and that overall, at least 12% of all the variation in gene expression among the breast tumors is directly attributable to underlying variation in gene copy number. These findings provide evidence that widespread DNA copy number alteration can lead directly to global deregulation of gene expression, which may contribute to the development or progression of cancer.

1,258 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