AI News, New to Machine Learning? Avoid these three mistakes

New to Machine Learning? Avoid these three mistakes

Machine learning is a field of computer science where algorithms improve their performance at a certain task as more data are observed.To do so, algorithms select a hypothesis that best explains the data at hand with the hope that the hypothesis would generalize to future (unseen) data.

Take the left panel in the figure in the header, the crosses denote the observed data projected in a two-dimensional space — in this case house prices and their corresponding size in square meters.

As the house’s size increases, so does its price in linear increments.” Now using this hypothesis, I can predict the price of an unseen datapoint based on its size.

As the dimensions of the data increase, the hypotheses that explain the data become more complex.However, given that we are using a finite sample of observations to learn our hypothesis, finding an adequate hypothesis that generalizes to unseen data is nontrivial.

In their 2008 paper in Nature, Johan Nyberg and colleagues used a 4-level artificial neural network to predict seasonal hurricane counts using two or three environmental variables.

The authors reported stellar accuracy in predicting seasonal North Atlantic hurricane counts, however their model violates Occam’s razor and most certainly doesn’t generalize to unseen data.

The razor was violated when the hypothesis or model selected to describe the relationship between environmental data and seasonal hurricane counts was generated using a four-layer neural network.

A four-layer neural network can model virtually any function no matter how complex and could fit a small dataset very well but fail to generalize to unseen data.

However, many fail to remove the test data before computing the anomalies and hence the anomalies carry some information about the data you want to predict since they influenced the mean and standard deviation before being removed.

Say you want to predict whether a tornado is going to originate at certain location based on two environmental conditions: wind shear and convective available potential energy (CAPE).

Being mindful of these limitations does not guarantee that your ML algorithm will solve all your problems, but it certainly reduces the risk of being disappointed when your model doesn’t generalize to unseen data.

New to Machine Learning? Avoid these three mistakes

Machine learning is a field of computer science where algorithms improve their performance at a certain task as more data are observed.To do so, algorithms select a hypothesis that best explains the data at hand with the hope that the hypothesis would generalize to future (unseen) data.

Take the left panel in the figure in the header, the crosses denote the observed data projected in a two-dimensional space — in this case house prices and their corresponding size in square meters.

As the house’s size increases, so does its price in linear increments.” Now using this hypothesis, I can predict the price of an unseen datapoint based on its size.

As the dimensions of the data increase, the hypotheses that explain the data become more complex.However, given that we are using a finite sample of observations to learn our hypothesis, finding an adequate hypothesis that generalizes to unseen data is nontrivial.

In their 2008 paper in Nature, Johan Nyberg and colleagues used a 4-level artificial neural network to predict seasonal hurricane counts using two or three environmental variables.

The authors reported stellar accuracy in predicting seasonal North Atlantic hurricane counts, however their model violates Occam’s razor and most certainly doesn’t generalize to unseen data.

The razor was violated when the hypothesis or model selected to describe the relationship between environmental data and seasonal hurricane counts was generated using a four-layer neural network.

A four-layer neural network can model virtually any function no matter how complex and could fit a small dataset very well but fail to generalize to unseen data.

However, many fail to remove the test data before computing the anomalies and hence the anomalies carry some information about the data you want to predict since they influenced the mean and standard deviation before being removed.

Say you want to predict whether a tornado is going to originate at certain location based on two environmental conditions: wind shear and convective available potential energy (CAPE).

Being mindful of these limitations does not guarantee that your ML algorithm will solve all your problems, but it certainly reduces the risk of being disappointed when your model doesn’t generalize to unseen data.

Model evaluation, model selection, and algorithm selection in machine learning

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.

After the machine learning algorithm fit a model to the training set, we evaluated it on the independent test set that we withheld from the machine learning algorithm during model fitting.

In this context, lazy learning (or instance-based learning) means that there is no training or model fitting stage: A k-nearest neighbors model literally stores or memorizes the training data and uses it only at prediction time.

nonparamtric models do not assume that the data follows certain probability distributions unlike parametric methods (exceptions of nonparametric methods that make such assumptions are Bayesian nonparametric methods).

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.

However, reusing the test set multiple times would introduce a bias and our final performance estimate and likely result in overly optimistic estimates of the generalization performance — we can say that “the test set leaks information.” To avoid this problem, we could use a three-way split, dividing the dataset into a training, validation, and test dataset.

“There ain’t no such thing as a free lunch.” The three-way holdout method for hyperparameter tuning and model selection is not the only — and certainly often not the best — way to approach this task.

However, before we move on to the probably most popular method for model selection, k-fold cross-validation (or sometimes also called “rotation estimation” in older literature), let us have a look at an illustration of the 3-way split holdout method:

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.

(If we use test data for fitting, we do not have data left to evaluate the model, unless we collect new data.) In real-world applications, having the “best possible” model is often desired – or in other words, we do not mind if we slightly underestimated its performance.

In each round, we split the dataset into k parts: one part is used for validation, and the remaining k-1 parts are merged into a training subset for model evaluation as shown in the figure below, which illustrates the process of 5-fold cross-validation:

Just as in the “two-way” holdout method, we use a learning algorithm with fixed hyperparameter settings to fit models to the training folds in each iteration — if we use the k-fold cross-validation method for model evaluation.

The idea behind this approach is to reduce the pessimistic bias by using more training data in contrast to setting aside a relatively large portion of the dataset as test data.

If k is too small, though, we may increase the pessimistic bias of our estimate (since less training data is available for model fitting), and the variance of our estimate may increase as well since the model is more sensitive to how we split the data (later, we will discuss experiments that suggest k=10 as a good choice for k).

However, this statement would only be true if we perform the holdout method by rotating the training and validation set in two rounds (i.e., using exactly 50% data for training and 50% of the samples for validation in each round, swapping these sets, repeating the training and evaluation procedure, and eventually computing the performance estimate as the arithmetic mean of the two performance estimates on the validation sets).

Unfortunately, there is no Free Lunch though as shown by Yohsua Bengio and Yves Grandvalet in “No unbiased estimator of the variance of k-fold cross-validation.” The main theorem shows that there exists no universal (valid under all distributions) unbiased estimator of the variance of K-fold cross-validation.

For now, let’s conclude this section by looking at an interesting research project where Hawkins and others compared performance estimates via LOOCV to the holdout method and recommend the LOOCV over the latter — if computationally feasible.

The following table summarizes the finding in a comparison of different Ridge Regression models: In rows 1-4, Hawkins and others used 100-sample training sets to compare different methods of model evaluation.

The reported “mean” refers to the averaged difference between the true coefficiants of determination and the coefficients of determination obtained via LOOCV (here called q2) after repeating this procedure on different 100-sample training sets.

In rows 2-4, the researchers used the holdout method for fitting models to 100-sample training sets, and they evaluated the performances on holdout sets of sizes 10, 20, and 50 samples.

For instance, if we repeated a 5-fold cross-validation run 100 times, we would compute the performance estimate for 500 test folds report the cross-validation performance as the arithmetic mean of these 500 folds.

In addition, we can think of the LOOCV estimate as being approximately unbiased: the pessimistic bias of LOOCV (k=n) is intuitively lower compared k<n-fold cross-validation, since almost all (for instance, n-1) training samples are available for model fitting.

Remember that if we use the 0-1 loss function (the prediction is either correct or not), we could consider each prediction as a Bernoulli trial, and the number of correct predictions X is following a binomial distribution X \sim B(n, p), where n \in \mathbb{N} \text{ and } p \in [0,1];

and others, 2009) Or in other words, we can attribute the high variance to the well-known fact that the mean of highly correlated variables has a higher variance than the mean of variables that are not highly correlated.

Maybe, this can intuitively be explained by looking at the relationship between covariance (\text{cov}) and variance (\sigma^2): Proof: \text{Let } \mu = E(X), { then } \quad \text{cov}_{X, X} = E\left[(X - \mu)^2\right] = \sigma^{2}_{X} And the relationship between covariance \text{cov}_{X, Y} and correlation \rho_{X, Y} (X and Y are random variables) is defined as where and The large variance that is often associated with LOOCV has also been observed in empirical studies — for example, I really recommend reading the excellent paper A Study of Cross-Validation and Bootstrap for Accuracy Estimation and Model Selection (Kohavi, 1995) by Ron Kohavi.

Before moving on to model selection, let’s summarize this discussion of the bias-variance trade-off by listing the general trends when increasing the number of folds or k: Previously, we used k-fold cross-validation for model evaluation.

Aside from computational efficiency concerns, we only use deep learning algorithms when we have relatively large sample sizes anyway, scenarios where we don’t have to worry about high variance — due to sensitivity of our estimates towards how we split the dataset for training, validation, and testing — so much.

Or to say it with other words, using one of my favorite quotes: “Everything should be made as simple as possible, but not simpler.” — Albert Einstein In model selection practice, we can apply Occam’s razor using the one-standard error method as follows: Although, we may prefer simpler models for several reasons, Pedro Domingos made a good point regarding the performance of “complex” models.

Some of the most powerful learning algorithms output models that seem gratuitously elaborate — sometimes even continuing to add to them after they’ve perfectly fit the data — but that’s how they beat the less powerful ones.

To see how the one-standard error method works in practice, let us apply it to a simple toy dataset: 300 datapoints, concentric circles, and a uniform class distribution (150 samples from class 1 and 150 samples from class 2).

Say we want to optimize the Gamma hyperparameter of a Support Vector Machine (SVM) with a non-linear Radial Basis Function-kernel (RBF-kernel), where \gamma is the free parameter of the Gaussian RBF: (Intuitively, we can think of the Gamma as a parameter that controls the influence of single training samples on the decision boundary.) When I ran the RBF-kernel SVM algorithm with different Gamma values over the training set, using stratified 10-fold cross-validation, I obtained the following performance estimates, where the error bars are the standard errors of the cross-validation estimates:

In fact, \gamma=0.1 seems like a good trade-off between the two aforementioned models — the performance of the corresponding model falls within one standard error of the best performing model with \gamma=0 or \gamma=10.

Assuming that no candidate has a clue about how stocks work, and everyone was guessing randomly, the probability that at least one of the candidates got 8 out of 10 predictions correct is: So, shall we assume that a candidate who got 8 out of 10 predictions correct was not simply guessing randomly?

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.

Model Selection and Train/Validation/Test Sets

In the past decade, machine learning has given us self-driving cars, practical speech recognition, effective web search, and a vastly improved understanding of the human genome.

More importantly, you'll learn about not only the theoretical underpinnings of learning, but also gain the practical know-how needed to quickly and powerfully apply these techniques to new problems.

The course will also draw from numerous case studies and applications, so that you'll also learn how to apply learning algorithms to building smart robots (perception, control), text understanding (web search, anti-spam), computer vision, medical informatics, audio, database mining, and other areas.

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