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.

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Scikit-learn: Machine Learning in Python

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

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.

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Regression Shrinkage and Selection via the Lasso

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.

/pdf/going-deeper-with-convolutions-1yobw2o2ds.pdf

Going deeper with convolutions

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 this http URL.

We missed an important reference in Section 3.4. In page 309 we stated that ‘. . . which is based on the recently proposed algorithm LARS of Efron et al. (2004). They proved that, starting from zero, the lasso solution paths grow piecewise linearly in a predictable way. They proposed a new algorithm called LARS to solve the entire lasso solution path efficiently by using the same order of computations as a single OLS fit. . . .’ The following sentence should have been included. The piecewise linearity of the lasso solution path was first proved by Osborne et al. (2000), who also described an efficient algorithm for calculating the complete lasso solution path. Reference Osborne, M. R., Presnell, B. and Turlach, B. A. (2000) A new approach to variable selection in least squares problems. IMA J. Numer. Anal., 20, 389–403.

https://web.stanford.edu/~hastie/Papers/B67.5%20(2005)%20768%20Correction.pdf

Addendum: Regularization and variable selection via the elastic net

SUMMARY The elements of a multivariate data set are often curves rather than single points. Functional principal components can be used to describe the modes of variation of such curves. If one has complete measurements for each individual curve or, as is more common, one has measurements on a fine grid taken at the same time points for all curves, then many standard techniques may be applied. However, curves are often measured at an irregular and sparse set of time points which can differ widely across individuals. We present a technique for handling this more difficult case using a reduced rank mixed effects framework.

Principal component models for sparse functional data

We propose a new method for class prediction in DNA microarray studies based on an enhancement of the nearest prototype classifier. Our technique uses "shrunken" centroids as prototypes for each class to identify the subsets of the genes that best characterize each class. The method is general and can be applied to the other high-dimensional classification problems. The method is illustrated on data from two gene expression studies: lymphoma and cancer cell lines.

Class Prediction by Nearest Shrunken Centroids, with Applications to DNA Microarrays

A kernel smoother is an intuitive estimate of a regression function or conditional expectation; at each point $x_0$ the estimate of $E(Y\mid x_0)$ is a weighted mean of the sample $Y_i$, with observations close to $x_0$ receiving the largest weights. Unfortunately this simplicity has flaws. At the boundary of the predictor space, the kernel neighborhood is asymmetric and the estimate may have substantial bias. Bias can be a problem in the interior as well if the predictors are nonuniform or if the regression function has substantial curvature. These problems are particularly severe when the predictors are multidimensional. A variety of kernel modifications have been proposed to provide approximate and asymptotic adjustment for these biases. Such methods generally place substantial restrictions on the regression problems that can be considered; in unfavorable situations, they can perform very poorly. Moreover, the necessary modifications are very difficult to implement in the multidimensional case. Local regression smoothers fit lower-order polynomials in $x$ locally at $x_0$, and the estimate of $f(x_0)$ is taken from the fitted polynomial at $x_0$. They automatically, intuitively and simultaneously adjust for both the biases above to the given order and generalize naturally to the multidimensional case. They also provide natural estimates for the derivatives of $f$, an approach more attractive than using higher-order kernel functions for the same purpose.

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Local Regression: Automatic Kernel Carpentry

Correspondence analysis is an exploratory multivariate technique that converts a data matrix into a particular type of graphical display in which the rows and columns are depicted as points. The method has a long and varied history and has appeared in different forms in the psychometric and ecological literature, among others. In this article we review the geometry of correspondence analysis and its geometric interpretation. We also discuss various extensions of correspondence analysis to multivariate categorical data (multiple correspondence analysis) and a variety of other data types.

Trevor Hastie

Papers

Addendum: Regularization and variable selection via the elastic net

Principal component models for sparse functional data

Class Prediction by Nearest Shrunken Centroids, with Applications to DNA Microarrays

Local Regression: Automatic Kernel Carpentry

The Geometric Interpretation of Correspondence Analysis