AI News, Bagging, boosting and stacking in machine learning

Bagging, boosting and stacking in machine learning

The idea behind bagging is that when you OVERFIT with a nonparametric regression method (usually regression or classification trees, but can be just about any nonparametric method), you tend to go to the high variance, no (or low) bias part of the bias/variance tradeoff.

This is because an overfitting model is very flexible (so low bias over many resamples from the same population, if those were available) but has high variability (if I collect a sample and overfit it, and you collect a sample and overfit it, our results will differ because the non-parametric regression tracks noise in the data).

Like all nonparametric regression or classification approaches, sometimes bagging or boosting works great, sometimes one or the other approach is mediocre, and sometimes one or the other approach (or both) will crash and burn.

Nonparametric regression

Nonparametric regression is a category of regression analysis in which the predictor does not take a predetermined form but is constructed according to information derived from the data.

Nonparametric regression requires larger sample sizes than regression based on parametric models because the data must supply the model structure as well as the model estimates.

Kernel regression estimates the continuous dependent variable from a limited set of data points by convolving the data points' locations with a kernel function—approximately speaking, the kernel function specifies how to 'blur' the influence of the data points so that their values can be used to predict the value for nearby locations.

key biological feature of an NPMR model is that failure of an organism to tolerate any single dimension of the predictor space results in overall failure of the organism.

Note further that in this simple example, the second condition listed above is probably true: the response of the plant to moisture probably depends on temperature and vice versa.

By 'local model' we mean the way that data points near a target point in the predictor space are combined to produce an estimate for the target point.

In words, the estimate of the response is a local estimate (for example a local mean) of the observed values, each value weighted by its proximity to the target point in the predictor space, the weights being the product of weights for individual predictors.

Instead, one can control overfitting by setting a minimum average neighborhood size, minimum data:predictor ratio, and a minimum improvement required to add a predictor to a model.

Thus, NPMR with cross-validation in the model fitting phase already penalizes the measure of fit, such that the error rate of the training data set is expected to approximate the error rate in a validation data set.

Overfitting and Underfitting With Machine Learning Algorithms

The cause of poor performance in machine learning is either overfitting or underfitting the data.

Supervised machine learning is best understood as approximating a target function (f) that maps input variables (X) to an output variable (Y).

Induction refers to learning general concepts from specific examples which is exactly the problem that supervised machine learning problems aim to solve.

There is a terminology used in machine learning when we talk about how well a machine learning model learns and generalizes to new data, namely overfitting and underfitting.

This is good terminology to use in machine learning, because supervised machine learning algorithms seek to approximate the unknown underlying mapping function for the output variables given the input variables.

calculating the residual errors), but some of these techniques assume we know the form of the target function we are approximating, which is not the case in machine learning.

Overfitting happens when a model learns the detail and noise in the training data to the extent that it negatively impacts the performance of the model on new data.

If we train for too long, the performance on the training dataset may continue to decrease because the model is overfitting and learning the irrelevant detail and noise in the training dataset.

The sweet spot is the point just before the error on the test dataset starts to increase where the model has good skill on both the training dataset and the unseen test dataset.

This is often not useful technique in practice, because by choosing the stopping point for training using the skill on the test dataset it means that the testset is no longer “unseen”

Overfitting is such a problem because the evaluation of machine learning algorithms on training data is different from the evaluation we actually care the most about, namely how well the algorithm performs on unseen data.

There are two important techniques that you can use when evaluating machine learning algorithms to limit overfitting: The most popular resampling technique is k-fold cross validation.

It allows you to train and test your model k-times on different subsets of training data and build up an estimate of the performance of a machine learning model on unseen data.

After you have selected and tuned your machine learning algorithms on your training dataset you can evaluate the learned models on the validation dataset to get a final objective idea of how the models might perform on unseen data.

An Introduction to Recursive Partitioning: Rationale, Application and Characteristics of Classification and Regression Trees, Bagging and Random Forests

As described in the previous sections, single classification trees are easily interpretable, both intuitively at first glance and descriptively when looking in detail at the tree structure.

In the latter case, permuting the variable results only in a small random decrease in prediction accuracy, or the permutation of an irrelevant variable can even lead to a small increase in the prediction accuracy (if, by chance, the permutated variable happens to be slightly better suited for splitting than the original one).

Note also that in our simple example the two relevant predictor variables friends_smoke and alcohol_per_month are correctly identified by the permutation variable importance of both bagging and random forests, even though the positions of the variables vary more strongly in random forests (cf.

In real data applications, however, the random forest variable importance may reveal higher importance scores for variables working in complex interactions, that may have gone unnoticed in single trees and bagging (as well as in parametric regression models, where modeling high-order interactions is usually not possible at all).

(Note that VI (t)(Xj) = 0 by definition, if variable Xj is not in tree t.) The raw importance score for each variable is then computed as the average importance over all trees From this raw importance score a standardized importance score can be computed with the following rationale: The individual importance scores VI (t)(xj) are computed from ntree bootstrap samples, that are independent given the original sample, and are identically distributed.

As already mentioned, the main advantage of the random forest permutation accuracy importance, as compared to univariate screening methods, is that it covers the impact of each predictor variable individually as well as in multivariate interactions with other predictor variables.

(2004) find that genetic markers relevant in interactions with other markers or environmental variables can be detected more efficiently by means of random forests than by means of univariate screening methods like Fisher’s exact test.

This, together with its applicability to problems with many predictor values, also distinguishes the random forest variable importance from the otherwise appealing approach of Azen, Budescu, and Reiser (2001) and advanced in Azen and Budescu (2003) for assessing the criticality of a predictor variable, termed “dominance analysis”: The authors suggest employing bootstrap sampling and select the best regression model from all possible models for each bootstrap sample in order to estimate the empirical probability distribution of all possible models.

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