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Nested cross-validation when selecting classifiers is overzealous for most practical applications

arXiv.org Machine Learning

Abstract--When selecting a classification algorithm to be applied to a particular problem, one has to simultaneously select the best algorithm for that dataset and the best set of hyperparameters for the chosen model. The usual approach is to apply a nested cross-validation procedure; hyperparameter selection is performed in the inner crossvalidation, while the outer cross-validation computes an unbiased estimate of the expected accuracy of the algorithm with cross-validation based hyperparameter tuning. The alternative approach, which we shall call "flat cross-validation", uses a single cross-validation step both to select the optimal hyperparameter values and to provide an estimate of the expected accuracy of the algorithm, that while biased may nevertheless still be used to select the best learning algorithm. We tested both procedures using 12 different algorithms on 115 real life binary datasets and conclude that using the less computationally expensive flat crossvalidation procedure will generally result in the selection of an algorithm that is, for all practical purposes, of similar quality to that selected via nested cross-validation, provided the learning algorithms have relatively few hyperparameters to be optimised. A practitioner who builds a classification model has to select the best algorithm for that particular problem. There are hundreds of classification algorithms described in the literature, such as k-nearest neighbour [1], SVM [2], neural networks [3], naïve Bayes [4], gradient boosting machines [5], and so on.


Randomization as Regularization: A Degrees of Freedom Explanation for Random Forest Success

arXiv.org Machine Learning

Random forests remain among the most popular off-the-shelf supervised machine learning tools with a well-established track record of predictive accuracy in both regression and classification settings. Despite their empirical success as well as a bevy of recent work investigating their statistical properties, a full and satisfying explanation for their success has yet to be put forth. Here we aim to take a step forward in this direction by demonstrating that the additional randomness injected into individual trees serves as a form of implicit regularization, making random forests an ideal model in low signal-to-noise ratio (SNR) settings. Specifically, from a model-complexity perspective, we show that the mtry parameter in random forests serves much the same purpose as the shrinkage penalty in explicitly regularized regression procedures like lasso and ridge regression. To highlight this point, we design a randomized linear-model-based forward selection procedure intended as an analogue to tree-based random forests and demonstrate its surprisingly strong empirical performance. Numerous demonstrations on both real and synthetic data are provided.


Scalable and Efficient Hypothesis Testing with Random Forests

arXiv.org Machine Learning

Throughout the last decade, random forests have established themselves as among the most accurate and popular supervised learning methods. While their black-box nature has made their mathematical analysis difficult, recent work has established important statistical properties like consistency and asymptotic normality by considering subsampling in lieu of bootstrapping. Though such results open the door to traditional inference procedures, all formal methods suggested thus far place severe restrictions on the testing framework and their computational overhead precludes their practical scientific use. Here we propose a permutation-style testing approach to formally assess feature significance. We establish asymptotic validity of the test via exchangeability arguments and show that the test maintains high power with orders of magnitude fewer computations. As importantly, the procedure scales easily to big data settings where large training and testing sets may be employed without the need to construct additional models. Simulations and applications to ecological data where random forests have recently shown promise are provided.


Subsampling Winner Algorithm for Feature Selection in Large Regression Data

arXiv.org Machine Learning

Feature selection from a large number of covariates (aka features) in a regression analysis remains a challenge in data science, especially in terms of its potential of scaling to ever-enlarging data and finding a group of scientifically meaningful features. For example, to develop new, responsive drug targets for ovarian cancer, the actual false discovery rate (FDR) of a practical feature selection procedure must also match the target FDR. The popular approach to feature selection, when true features are sparse, is to use a penalized likelihood or a shrinkage estimation, such as a LASSO, SCAD, Elastic Net, or MCP procedure (call them benchmark procedures). We present a different approach using a new subsampling method, called the Subsampling Winner algorithm (SWA). The central idea of SWA is analogous to that used for the selection of US national merit scholars. SWA uses a "base procedure" to analyze each of the subsamples, computes the scores of all features according to the performance of each feature from all subsample analyses, obtains the "semifinalist" based on the resulting scores, and then determines the "finalists," i.e., the most important features. Due to its subsampling nature, SWA can scale to data of any dimension in principle. The SWA also has the best-controlled actual FDR in comparison with the benchmark procedures and the randomForest, while having a competitive true-feature discovery rate. We also suggest practical add-on strategies to SWA with or without a penalized benchmark procedure to further assure the chance of "true" discovery. Our application of SWA to the ovarian serous cystadenocarcinoma specimens from the Broad Institute revealed functionally important genes and pathways, which we verified by additional genomics tools. This second-stage investigation is essential in the current discussion of the proper use of P-values.


Clinical Trial and Evaluation of a Prototype Case-Based System for Planning Medical Imaging Work-up Strategies

AAAI Conferences

ISIS (Intelligent Selection of Imaging Studies) is a casebased decision support tool being developed to help physicians select appropriate radiological procedures (Kahn 1993; Kahn & Anderson 1994). Its goal is provide comprehensive computer-based expertise in the domain of diagnostic medical imaging procedures such as computed tomography (CT), ultrasound (US), magnetic resonance imaging (MRI). To better assess the applicability of CBR techniques to the problem of imaging procedure selection, we conducted a pilot study in a more limited domain, that of ultrasound and body CT. This report describes the construction, testing, and evaluation of ProtolSIS, a prototype version of ISIS.