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

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.

/pdf/regression-shrinkage-and-selection-via-the-lasso-6mx35txfr5.pdf

Regression Shrinkage and Selection via the Lasso

Introduction to a Transient World. Fourier Kingdom. Discrete Revolution. Time Meets Frequency. Frames. Wavelet Zoom. Wavelet Bases. Wavelet Packet and Local Cosine Bases. An Approximation Tour. Estimations are Approximations. Transform Coding. Appendix A: Mathematical Complements. Appendix B: Software Toolboxes.

http://ahvazdownload.persiangig.com/document/article/39.pdf

A wavelet tour of signal processing

Summary. We propose the elastic net, a new regularization and variable selection method. Real world data and a simulation study show that the elastic net often outperforms the lasso, while enjoying a similar sparsity of representation. In addition, the elastic net encourages a grouping effect, where strongly correlated predictors tend to be in or out of the model together.The elastic net is particularly useful when the number of predictors (p) is much bigger than the number of observations (n). By contrast, the lasso is not a very satisfactory variable selection method in the

/pdf/regularization-and-variable-selection-via-the-elastic-net-4z8q6j5o0i.pdf

Regularization and variable selection via the elastic net

MOTIVATION: Next-generation sequencing technologies generate millions of short sequence reads, which are usually aligned to a reference genome. In many applications, the key information required for downstream analysis is the number of reads mapping to each genomic feature, for example to each exon or each gene. The process of counting reads is called read summarization. Read summarization is required for a great variety of genomic analyses but has so far received relatively little attention in the literature. RESULTS: We present featureCounts, a read summarization program suitable for counting reads generated from either RNA or genomic DNA sequencing experiments. featureCounts implements highly efficient chromosome hashing and feature blocking techniques. It is considerably faster than existing methods (by an order of magnitude for gene-level summarization) and requires far less computer memory. It works with either single or paired-end reads and provides a wide range of options appropriate for different sequencing applications. AVAILABILITY AND IMPLEMENTATION: featureCounts is available under GNU General Public License as part of the Subread (http://subread.sourceforge.net) or Rsubread (http://www.bioconductor.org) software packages.

featureCounts: an efficient general-purpose program for assigning sequence reads to genomic features

Objectives: Autopsy studies show that prostate cancer begins in the 4th and 5th decade of life. We sought to determine if increasing age at the time of diagnosis is related to morphologic and clinical predictors of cancer progression.



Materials and Methods: We examined 7 morphologic variables known to impact progression of prostate cancer plus clinical stage and serum PSA in relation to increasing age. 981 untreated men undergoing radical prostatectomy were divided into 5 increasing age groups. Prostate size, which is known to increase with age, was used as a positive control. We compared the median and inter-quartile range for each grouping.



Results: Increase in prostate weight was highly significant at all age differences. The % Gleason grade 4/5 cancer and cancer volume showed the most statistically significant changes with ageing, followed by non-organ confined cancer and capsular penetration both of which are highly correlated with cancer volume. Serum PSA was significant at 12, 17, and 22 years of age differences, but may be related more to prostate size than to increasing cancer volume. The presence of positive lymph nodes, seminal vesicle invasion, and palpable cancer were unrelated to increasing age.



Conclusions: With the exception of increasing prostate size, % Gleason grade 4/5 cancer and cancer volume are the most significantly related variables to increasing age. Since % Gleason grade 4/5 cancer and cancer volume are also the primary determinants of failure to cure prostate cancer by radical prostatectomy, these age related changes suggest that detection of prostate cancer later in life will be accompanied by increased amounts of high grade cancer and larger tumor volumes. They also explain why, in so many younger men (age 45–60), the largest prostate cancer is often clinically insignificant (< 0.5 cc) at the time of radical prostatectomy.

Effect of Ageing on Morphologic and Clinical Predictors of Prostate Cancer Progression

Shannon’s Rate-Distortion Theory describes the number of bits needed to approximately represent typical realizations of a stochastic process X = (X(t) : t ∈ T ), while Kolmogorov’s ǫ-entropy describes the number of bits needed to approximately represent an arbitrary member f = (f(t) : t ∈ T ) of a functional class F . For many stochastic processes a great deal is known about the behavior of the rate distortion function, while for few functional classes F has there been success in determining, say, the precise asymptotics of the ǫ-entropy. Let W 2,0(γ) denote the class of functions f(t) on T = [0, 2π) with periodic boundary conditions and 1 2π ∫ 2π 0 f(t)dt + 1 2π ∫ 2π 0 f (t)dt ≤ γ. We show that for approximating functions of this class in L norm we have the precise asymptotics of the Kolmogorov ǫentropy: Hǫ(W m 2,0(γ)) ∼ 2m(log2 e)(γ/2ǫ) , ǫ → 0. (0.1) This follows from a connection between the Shannon and Kolmogorov theories, which allows us to exploit the powerful formalism of Shannon’s Rate-Distortion theory to obtain information about the Kolmogorov ǫ-entropy. In fact, the Kolmogorov ǫ-entropy is asymptotically equivalent, as ǫ → 0, to the maximum Rate-Distortion R(D,X) over all stochastic processes X with sample paths in W 2,0(γ), where we make the calibration D = ǫ . There is a family of Gaussian processes X∗ D which asymptotically, as D → 0, take realizations in W 2,0(γ), and for which the process at index D has essentially the highest rate-distortion R(D,X) of all processes X living in W 2,0(γ). We evaluate the rate-distortion function of members of this family, giving formula (0.1). These results strongly parallel a key result in modern statistical decision theory, Pinsker’s theorem. This points to a connection between theories of statistical estimation and data compression, which will be the theme of these Lectures.

Wald Lecture I: Counting Bits with Kolmogorov and Shannon

Economic endpoints have been increasingly included in long-term clinical trials, but they pose several methodologic challenges, including how best to collect, describe, analyse and interpret medical cost data. Cost of care can be measured by converting billed charges, performing detailed micro-costing studies, or by measuring use of key resources and assigning cost weights to each resource. The latter method is most commonly used, with cost weights based either on empirical regression models or administratively determined reimbursement rates. In long-term studies, monetary units should be adjusted to reflect cost inflation and discounting. The temporal pattern of accumulating costs can be described using a modification of the Kaplan-Meier curve. Regression analyses to evaluate factors associated with cost are best performed on the log of costs due to their typically skewed distribution.Cost-effectiveness analysis attempts to measure the value of a new therapy by calculating the difference in cost between the new therapy and the standard therapy, divided by the difference in benefit between the new therapy and the standard therapy. The cost-effectiveness ratio based on the results of a randomized trial may change substantially with longer follow-up intervals, particularly for therapies that are initially expensive but eventually improve survival. A model that projects long-term patterns of cost and survival expected beyond the end of completed follow-up can provide an important perspective in the setting of limited trial duration.

Economic evaluation in long-term clinical trials

Roy’s largest root is a common test in multivariate analysis of variance (MANOVA), with applications in several other problems, such as signal detection in noise. In this paper, assuming multivariate Gaussian observations, we derive a simple yet accurate approximation for the distribution of Roy’s largest root test, in the extreme case of concentrated non-centrality, where the signal or difference between groups is concentrated in a single direction. Our main result is that in the MANOVA setting, up to centering and scaling, Roy’s largest root test approximately follows a non-central F distribution whereas in the signal detection application, it approximately follows a modified central F distribution (of the form (s + χ2a)/χ 2 b). Our results allow power calculations for Roy’s test, as well as estimates of sample size required to detect a given (rank-one) group difference by this test, both of which are important quantities in hypothesis-driven research.

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On the distribution of roy's largest root test in manova and in signal detection in noise

We study principal components analyses in multivariate random and mixed effects linear models, assuming a spherical-plus-spikes structure for the covariance matrix of each random effect. We characterize the behavior of outlier sample eigenvalues and eigenvectors of MANOVA variance components estimators in such models under a high-dimensional asymptotic regime. Our results show that an aliasing phenomenon may occur in high dimensions, in which eigenvalues and eigenvectors of the MANOVA estimate for one variance component may be influenced by the other components. We propose an alternative procedure for estimating the true principal eigenvalues and eigenvectors that asymptotically corrects for this aliasing problem.

Iain M. Johnstone

Papers

Effect of Ageing on Morphologic and Clinical Predictors of Prostate Cancer Progression

Wald Lecture I: Counting Bits with Kolmogorov and Shannon

Economic evaluation in long-term clinical trials

On the distribution of roy's largest root test in manova and in signal detection in noise

Spiked covariances and principal components analysis in high-dimensional random effects models