Fast and Flexible ADMM Algorithms for Trend Filtering

Ramdas, Aaditya; Tibshirani, Ryan J.

doi:10.1080/10618600.2015.1054033

Cited by 97 publications

(115 citation statements)

References 20 publications

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“…Piecewise linear fits are better-suited to this type of relationship. The problem of estimating piecewise trends of any order between a single predictor and response has been previously explored [Kim et al, 2009, Ramdas and Tibshirani, 2014, Tibshirani, 2014]. We leave the extension of FLAM to this setting to future work.…”

Section: Discussionmentioning

confidence: 99%

Fused Lasso Additive Model

Petersen¹,

Witten²,

Simon³

2016

Journal of Computational and Graphical Statistics

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We consider the problem of predicting an outcome variable using p covariates that are measured on n independent observations, in a setting in which additive, flexible, and interpretable fits are desired. We propose the fused lasso additive model (FLAM), in which each additive function is estimated to be piecewise constant with a small number of adaptively-chosen knots. FLAM is the solution to a convex optimization problem, for which a simple algorithm with guaranteed convergence to a global optimum is provided. FLAM is shown to be consistent in high dimensions, and an unbiased estimator of its degrees of freedom is proposed. We evaluate the performance of FLAM in a simulation study and on two data sets. Supplemental materials are available online, and the R package flam is available on CRAN.

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Section: Discussionmentioning

confidence: 99%

Fused Lasso Additive Model

Petersen¹,

Witten²,

Simon³

2016

Journal of Computational and Graphical Statistics

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“…Using Bowtie (Langmead et al 2009) default parameters, 5 ′ -and 3 ′ -end reads were aligned to corresponding genomes and converted to single nucleotide read-end pileups. To identify significant read peaks, we simultaneously inferred the size and locations of constant backgrounds using first-order Poisson trend filtering with outlier detection as described (Ramdas and Tibshirani 2016;Supplemental Methods). RNA-seq and Ribo-seq library preparation was performed as previously described (McManus et al 2014;Spealman et al 2016), except that S. uvarum libraries were produced using the ART-seq kit (Illumina) (for full details, see Supplemental Materials).…”

Section: Methodsmentioning

confidence: 99%

Conserved non-AUG uORFs revealed by a novel regression analysis of ribosome profiling data

et al. 2017

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Upstream open reading frames (uORFs), located in transcript leaders (5′ UTRs), are potent cis-acting regulators of translation and mRNA turnover. Recent genome-wide ribosome profiling studies suggest that thousands of uORFs initiate with non-AUG start codons. Although intriguing, these non-AUG uORF predictions have been made without statistical control or validation; thus, the importance of these elements remains to be demonstrated. To address this, we took a comparative genomics approach to study AUG and non-AUG uORFs. We mapped transcription leaders in multiple Saccharomyces yeast species and applied a novel machine learning algorithm (uORF-seqr) to ribosome profiling data to identify statistically significant uORFs. We found that AUG and non-AUG uORFs are both frequently found in Saccharomyces yeasts. Although most non-AUG uORFs are found in only one species, hundreds have either conserved sequence or position within Saccharomyces. uORFs initiating with UUG are particularly common and are shared between species at rates similar to that of AUG uORFs. However, non-AUG uORFs are translated less efficiently than AUG-uORFs and are less subject to removal via alternative transcription initiation under normal growth conditions. These results suggest that a subset of non-AUG uORFs may play important roles in regulating gene expression.

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“…However, the authors claim that in practice the interior-point method converges in tens of iterations, in which case the general running time for solving the optimization problem will still be O ( N ). The other specialized optimization method for trend filtering problem is recently proposed by A. Ramdas et al [28]. They introduced a specialized alternating direction method of multipliers (ADMM), and they showed that their method has better scalability and faster convergence rate for large scale problems compared to the interior-point based method, while on the small sample sizes they have similar performance to the interior-point based method proposed by Kim et al [22].…”

Section: Methodsmentioning

confidence: 99%

“…The resulting optimization program will be equivalent to the recently proposed ℓ 1 trend filtering signal approximation method [22]. It uses recently proposed alternating direction method of multipliers (ADMM) based optimization method to find a collection of a piecewise linear calibration mappings [28]. Finally, it uses the AICc scoring measure [5] to combine the predictions made by these models to yield more robust calibrated predictions for each of the test instances.…”

Section: Related Workmentioning

confidence: 99%

Binary Classifier Calibration Using an Ensemble of Linear Trend Estimation

Naeini¹,

Cooper²

2016

Proceedings of the 2016 SIAM International Conference on Data Mining

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Learning accurate probabilistic models from data is crucial in many practical tasks in data mining. In this paper we present a new non-parametric calibration method called ensemble of linear trend estimation (ELiTE). ELiTE utilizes the recently proposed ℓ1 trend ltering signal approximation method [22] to find the mapping from uncalibrated classification scores to the calibrated probability estimates. ELiTE is designed to address the key limitations of the histogram binning-based calibration methods which are (1) the use of a piecewise constant form of the calibration mapping using bins, and (2) the assumption of independence of predicted probabilities for the instances that are located in different bins. The method post-processes the output of a binary classifier to obtain calibrated probabilities. Thus, it can be applied with many existing classification models. We demonstrate the performance of ELiTE on real datasets for commonly used binary classification models. Experimental results show that the method outperforms several common binary-classifier calibration methods. In particular, ELiTE commonly performs statistically significantly better than the other methods, and never worse. Moreover, it is able to improve the calibration power of classifiers, while retaining their discrimination power. The method is also computationally tractable for large scale datasets, as it is practically O(N log N) time, where N is the number of samples.

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Fast and Flexible ADMM Algorithms for Trend Filtering

Cited by 97 publications

References 20 publications

Fused Lasso Additive Model

Fused Lasso Additive Model

Conserved non-AUG uORFs revealed by a novel regression analysis of ribosome profiling data

Binary Classifier Calibration Using an Ensemble of Linear Trend Estimation

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