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.

A Study of Error Variance Estimation in Lasso Regression

Abstract: Variance estimation in the linear model when $p > n$ is a difficult problem. Standard least squares estimation techniques do not apply. Several variance estimators have been proposed in the literature, all with accompanying asymptotic results proving consistency and asymptotic normality under a variety of assumptions. It is found, however, that most of these estimators suffer large biases in finite samples when true underlying signals become less sparse with larger per element signal strength. One estimator seems to be largely neglected in the literature: a residual sum of squares based estimator using Lasso coefficients with regularisation parameter selected adaptively (via cross-validation). In this paper, we review several variance estimators and perform a reasonably extensive simulation study in an attempt to compare their finite sample performance. It would seem from the results that variance estimators with adaptively chosen regularisation parameters perform admirably over a broad range of sparsity and signal strength settings. Finally, some intial theoretical analyses pertaining to these types of estimators are proposed and developed.

Disease-specific genomic analysis

Abstract: Motivation: Genomic high-throughput technology generates massive data, providing opportunities to understand countless facets of the functioning genome. It also raises profound issues in identifying data relevant to the biology being studied. Results: We introduce a method for the analysis of pathologic biology that unravels the disease characteristics of high dimensional data. The method, disease-specific genomic analysis (DSGA), is intended to precede standard techniques like clustering or class prediction, and enhance their performance and ability to detect disease. DSGA measures the extent to which the disease deviates from a continuous range of normal phenotypes, and isolates the aberrant component of data. In several microarray cancer datasets, we show that DSGA outperforms standard methods. We then use DSGA to highlight a novel subdivision of an important class of genes in breast cancer, the estrogen receptor (ER) cluster. We also identify new markers distinguishing ductal and lobular breast cancers. Although our examples focus on microarrays, DSGA generalizes to any high dimensional genomic/proteomic data. Contact: [email protected] Supplementary information: Supplementary data are available at Bioinformatics online.

Proliferation tracing with single-cell mass cytometry optimizes generation of stem cell memory-like T cells.

Abstract: Selective differentiation of naive T cells into multipotent T cells is of great interest clinically for the generation of cell-based cancer immunotherapies. Cellular differentiation depends crucially on division state and time. Here we adapt a dye dilution assay for tracking cell proliferative history through mass cytometry and uncouple division, time and regulatory protein expression in single naive human T cells during their activation and expansion in a complex ex vivo milieu. Using 23 markers, we defined groups of proteins controlled predominantly by division state or time and found that undivided cells account for the majority of phenotypic diversity. We next built a map of cell state changes during naive T-cell expansion. By examining cell signaling on this map, we rationally selected ibrutinib, a BTK and ITK inhibitor, and administered it before T cell activation to direct differentiation toward a T stem cell memory (TSCM)-like phenotype. This method for tracing cell fate across division states and time can be broadly applied for directing cellular differentiation.

Molecular subtyping for clinically defined breast cancer subgroups.

Abstract: Breast cancer is commonly classified into intrinsic molecular subtypes. Standard gene centering is routinely done prior to molecular subtyping, but it can produce inaccurate classifications when the distribution of clinicopathological characteristics in the study cohort differs from that of the training cohort used to derive the classifier. We propose a subgroup-specific gene-centering method to perform molecular subtyping on a study cohort that has a skewed distribution of clinicopathological characteristics relative to the training cohort. On such a study cohort, we center each gene on a specified percentile, where the percentile is determined from a subgroup of the training cohort with clinicopathological characteristics similar to the study cohort. We demonstrate our method using the PAM50 classifier and its associated University of North Carolina (UNC) training cohort. We considered study cohorts with skewed clinicopathological characteristics, including subgroups composed of a single prototypic subtype of the UNC-PAM50 training cohort (n = 139), an external estrogen receptor (ER)-positive cohort (n = 48) and an external triple-negative cohort (n = 77). Subgroup-specific gene centering improved prediction performance with the accuracies between 77% and 100%, compared to accuracies between 17% and 33% from standard gene centering, when applied to the prototypic tumor subsets of the PAM50 training cohort. It reduced classification error rates on the ER-positive (11% versus 28%; P = 0.0389), the ER-negative (5% versus 41%; P < 0.0001) and the triple-negative (11% versus 56%; P = 0.1336) subgroups of the PAM50 training cohort. In addition, it produced higher accuracy for subtyping study cohorts composed of varying proportions of ER-positive versus ER-negative cases. Finally, it increased the percentage of assigned luminal subtypes on the external ER-positive cohort and basal-like subtype on the external triple-negative cohort. Gene centering is often necessary to accurately apply a molecular subtype classifier. Compared with standard gene centering, our proposed subgroup-specific gene centering produced more accurate molecular subtype assignments in a study cohort with skewed clinicopathological characteristics relative to the training cohort.

CFH and ARMS2 genetic risk determines progression to neovascular age-related macular degeneration after antioxidant and zinc supplementation.

Abstract: We evaluated the influence of an antioxidant and zinc nutritional supplement [the Age-Related Eye Disease Study (AREDS) formulation] on delaying or preventing progression to neovascular AMD (NV) in persons with age-related macular degeneration (AMD). AREDS subjects (n = 802) with category 3 or 4 AMD at baseline who had been treated with placebo or the AREDS formulation were evaluated for differences in the risk of progression to NV as a function of complement factor H (CFH) and age-related maculopathy susceptibility 2 (ARMS2) genotype groups. We used published genetic grouping: a two-SNP haplotype risk-calling algorithm to assess CFH, and either the single SNP rs10490924 or 372_815del443ins54 to mark ARMS2 risk. Progression risk was determined using the Cox proportional hazard model. Genetics-treatment interaction on NV risk was assessed using a multiiterative bootstrap validation analysis. We identified strong interaction of genetics with AREDS formulation treatment on the development of NV. Individuals with high CFH and no ARMS2 risk alleles and taking the AREDS formulation had increased progression to NV compared with placebo. Those with low CFH risk and high ARMS2 risk had decreased progression risk. Analysis of CFH and ARMS2 genotype groups from a validation dataset reinforces this conclusion. Bootstrapping analysis confirms the presence of a genetics-treatment interaction and suggests that individual treatment response to the AREDS formulation is largely determined by genetics. The AREDS formulation modifies the risk of progression to NV based on individual genetics. Its use should be based on patient-specific genotype.

Scikit-learn: Machine Learning in Python

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.

Moderated estimation of fold change and dispersion for RNA-seq data with DESeq2

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 .

Regression Shrinkage and Selection via the Lasso

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.

Going deeper with convolutions

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.

Deep Learning

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.