The correct use of model evaluation, model selection, and algorithm selection techniques is vital in academic machine learning research as well as in many industrial settings. This article reviews different techniques that can be used for each of these three subtasks and discusses the main advantages and disadvantages of each technique with references to theoretical and empirical studies. Further, recommendations are given to encourage best yet feasible practices in research and applications of machine learning. Common methods such as the holdout method for model evaluation and selection are covered, which are not recommended when working with small datasets. Different flavors of the bootstrap technique are introduced for estimating the uncertainty of performance estimates, as an alternative to confidence intervals via normal approximation if bootstrapping is computationally feasible. Common cross-validation techniques such as leave-one-out cross-validation and k-fold cross-validation are reviewed, the bias-variance trade-off for choosing k is discussed, and practical tips for the optimal choice of k are given based on empirical evidence. Different statistical tests for algorithm comparisons are presented, and strategies for dealing with multiple comparisons such as omnibus tests and multiple-comparison corrections are discussed. Finally, alternative methods for algorithm selection, such as the combined F-test 5x2 cross-validation and nested cross-validation, are recommended for comparing machine learning algorithms when datasets are small.

In contrast to k-nearest neighbors, a simple example of a parametric method would be logistic regression, a generalized linear model with a fixed number of model parameters: a weight coefficient for each feature variable in the dataset plus a bias (or intercept) unit. While the learning algorithm optimizes an objective function on the training set (with exception to lazy learners), hyperparameter optimization is yet another task on top of it; here, we typically want to optimize a performance metric such as classification accuracy or the area under a Receiver Operating Characteristic curve. Thinking back of our discussion about learning curves and pessimistic biases in Part II, we noted that a machine learning algorithm often benefits from more labeled data; the smaller the dataset, the higher the pessimistic bias and the variance -- the sensitivity of our model towards the way we partition the data. We start by splitting our dataset into three parts, a training set for model fitting, a validation set for model selection, and a test set for the final evaluation of the selected model.

Almost every machine learning algorithm comes with a large number of settings that we, the machine learning researchers and practitioners, need to specify. These tuning knobs, the so-called hyperparameters, help us control the behavior of machine learning algorithms when optimizing for performance, finding the right balance between bias and variance. Hyperparameter tuning for performance optimization is an art in itself, and there are no hard-and-fast rules that guarantee best performance on a given dataset. In Part I and Part II, we saw different holdout and bootstrap techniques for estimating the generalization performance of a model. We learned about the bias-variance trade-off, and we computed the uncertainty of our estimates. In this third part, we will focus on different methods of cross-validation for model evaluation and model selection. We will use these cross-validation techniques to rank models from several hyperparameter configurations and estimate how well they generalize to independent datasets. Previously, we used the holdout method or different flavors of bootstrapping to estimate the generalization performance of our predictive models.

Al, Walid Abdullah, Yun, Il Dong

With the advents of deep learning, improved image classification with complex discriminative models has been made possible. However, such deep models with increased complexity require a huge set of labeled samples to generalize the training. Such classification models can easily overfit when applied for medical images because of limited training data, which is a common problem in the field of medical image analysis. This paper proposes and investigates a reinforced classifier for improving the generalization under a few available training data. Partially following the idea of reinforcement learning, the proposed classifier uses a generalization-feedback from a subset of the training data to update its parameter instead of only using the conventional cross-entropy loss about the training data. We evaluate the improvement of the proposed classifier by applying it on three different classification problems against the standard deep classifiers equipped with existing overfitting-prevention techniques. Besides an overall improvement in classification performance, the proposed classifier showed remarkable characteristics of generalized learning, which can have great potential in medical classification tasks.

A single-PDF version of Model Evaluation parts 1-4 is available on arXiv: https://arxiv.org/abs/1811.12808 This final article in the series Model evaluation, model selection, and algorithm selection in machine learning presents overviews of several statistical hypothesis testing approaches, with applications to machine learning model and algorithm comparisons. This includes statistical tests based on target predictions for independent test sets (the downsides of using a single test set for model comparisons was discussed in previous articles) as well as methods for algorithm comparisons by fitting and evaluating models via cross-validation. Lastly, this article will introduce nested cross-validation, which has become a common and recommended a method of choice for algorithm comparisons for small to moderately-sized datasets. Then, at the end of this article, I provide a list of my personal suggestions concerning model evaluation, selection, and algorithm selection summarizing the several techniques covered in this series of articles. There are several different statistical hypothesis testing frameworks that are being used in practice to compare the performance of classification models, including conventional methods such as difference of two proportions (here, the proportions are the estimated generalization accuracies from a test set), for which we can construct 95% confidence intervals based on the concept of the Normal Approximation to the Binomial that was covered in Part I. Performing a z-score test for two population proportions is inarguably the most straight-forward way to compare to models (but certainly not the best!): In a nutshell, if the 95% confidence intervals of the accuracies of two models do not overlap, we can reject the null hypothesis that the performance of both classifiers is equal at a confidence level of (or 5% probability).