So, what is cross validation? Recalling my post about model selection, where we saw that it may be necessary to split data into three different portions, one for training, one for validation (to choose among models) and eventually measure the true accuracy through the last data portion. This procedure is one viable way to choose the best among several models. Cross validation (CV) is not too different from this idea, but deals with the model training/validation in quite a smart way. For CV we use a larger combined training and validation data set, followed by a testing dataset.
Cross-validation is used to evaluate machine learning models on a limited data sample.It estimates the skill of a machine learning model on unseen data. The techniques creates and validates given model multiple times. We have 2–4 types of cross validation like Stratified, LOOCV, K-Fold etc. Here, we will study K-Fold technique. Let's split data 70:30, train model and test the given data-set to get accuracy.
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.
K-fold cross-validation is one of the most used cross-validation methods. In this method, k represents the number of experiments(or fold) that I want to try in order to test and train my data. For example, suppose that we want to make 5 experiments(or performance) with our data composed of 1000 records. So during the first experiment, we test or validate the first 200 records and then we train the remaining 800 records. When the first experiment is finished I obtain a certain accuracy.
The k-fold cross-validation procedure is a standard method for estimating the performance of a machine learning algorithm or configuration on a dataset. A single run of the k-fold cross-validation procedure may result in a noisy estimate of model performance. Different splits of the data may result in very different results. Repeated k-fold cross-validation provides a way to improve the estimated performance of a machine learning model. This involves simply repeating the cross-validation procedure multiple times and reporting the mean result across all folds from all runs.
Super learner algorithm can be applied to combine results of multiple base learners to improve quality of predictions. The default method for verification of super learner results is by nested cross validation. It has been proposed by Tsamardinos et al., that nested cross validation can be replaced by resampling for tuning hyper-parameters of the learning algorithms. We apply this idea to verification of super learner and compare with other verification methods, including nested cross validation. Tests were performed on artificial data sets of diverse size and on seven real, biomedical data sets. The resampling method, called Bootstrap Bias Correction, proved to be a reasonably precise and very cost-efficient alternative for nested cross validation.
We study the problem of out-of-sample risk estimation in the high dimensional regime where both the sample size $n$ and number of features $p$ are large, and $n/p$ can be less than one. Extensive empirical evidence confirms the accuracy of leave-one-out cross validation (LO) for out-of-sample risk estimation. Yet, a unifying theoretical evaluation of the accuracy of LO in high-dimensional problems has remained an open problem. This paper aims to fill this gap for penalized regression in the generalized linear family. With minor assumptions about the data generating process, and without any sparsity assumptions on the regression coefficients, our theoretical analysis obtains finite sample upper bounds on the expected squared error of LO in estimating the out-of-sample error. Our bounds show that the error goes to zero as $n,p \rightarrow \infty$, even when the dimension $p$ of the feature vectors is comparable with or greater than the sample size $n$. One technical advantage of the theory is that it can be used to clarify and connect some results from the recent literature on scalable approximate LO.
Cross-validation (CV) is a popular approach for assessing and selecting predictive models. However, when the number of folds is large, CV suffers from a need to repeatedly refit a learning procedure on a large number of training datasets. Recent work in empirical risk minimization (ERM) approximates the expensive refitting with a single Newton step warm-started from the full training set optimizer. While this can greatly reduce runtime, several open questions remain including whether these approximations lead to faithful model selection and whether they are suitable for non-smooth objectives. We address these questions with three main contributions: (i) we provide uniform non-asymptotic, deterministic model assessment guarantees for approximate CV; (ii) we show that (roughly) the same conditions also guarantee model selection performance comparable to CV; (iii) we provide a proximal Newton extension of the approximate CV framework for non-smooth prediction problems and develop improved assessment guarantees for problems such as l1-regularized ERM.
We consider the problem of estimating the parameters of the covariance function of a Gaussian process by cross-validation. We suggest using new cross-validation criteria derived from the literature of scoring rules. We also provide an efficient method for computing the gradient of a cross-validation criterion. To the best of our knowledge, our method is more efficient than what has been proposed in the literature so far. It makes it possible to lower the complexity of jointly evaluating leave-one-out criteria and their gradients.