For this post, I will define overfitting more generally as over-representing the performance of systems. There are two styles of general overfitting: We should all be aware of these methods, avoid them where possible, and take them into account otherwise. When fair evaluations get rejected and rounders-up pass through, what do you do?

Fooling yourself in research is a recipe for a career that goes nowhere. My best advice for anonymous is to accept that life is difficult here. Spend extra time testing on many datasets rather than a few. Spend extra time thinking about what make a good algorithm, or not. Take the long view and note that, in the long run, the quantity of papers you write is not important, but rather their level of impact.

How about an index of negative results in machine learning? A section on negative results in machine learning conferences?

This kind of information is very useful in preventing people from taking pathways that lead nowhere: I visited the workshop on negative results at NIPS My impression was that it did not work well.

The difficulty with negative results in machine learning is that they are too easy. This research studies empirically and theoretically machine learning algorithms that yield good performance on the training set but worse than random performance on the independent test set. Hmm, rereading this post. Why is mutual information brittle? Standard deviation of loss across the CV folds is not a bad summary of variation in CV performance.

Standard error carries some Gaussian assumptions, but it is still a valid summary. The distribution of loss is sometimes quite close to being Gaussian, too. As for significance, I came up with the notion of CV-values that measure how often method A is better than method B in a randomly chosen fold of cross-validation replicated very many times.

What I mean by brittle: Suppose you have a box which takes some feature values as input and predicts some probability of label 1 as output. You are not allowed to open this box or determine how it works other than by this process of giving it inputs and observing outputs.

Let x be an input. Let y be an output. Assume x,y are drawn from a fixed but unknown distribution D. Let p x be a prediction. For classification error I y — p x you can prove a theorem of the rough form: You can of course open up the box and analyze its structure or make extra assumptions about D to get a similar but inherently more limited analysis.

Yoshua Bengio and Yves Grandvalet in fact proved that there is no unbiased estimator of variance. I have personally observed people using leave-one-out cross validation with feature selection to quickly achieve a severe overfit. Thanks for the explanation of brittleness!

Mutual information has well-defined upper bounds. While I agree that unmixed log-loss is brittle, I find classification accuracy noisy. A reasonable compromise is Brier score. So, the result you mention holds also for Brier score. If I perform 2-replicated 5-fold CV of the NBC performance on the Pima indians dataset, I get the following [0.

Of course, I can plop out the average of 0. But it is nicer to say that the standard deviation is 0. The performance estimate is a random quantity too. In fact, if you perform many replications of cross-validation, the classification accuracy will have a Gaussian-like shape too a bit skewed, though. I too recommend against LOO, for the simple reason that the above empirical summaries are often awfully strange. However, I still feel but would love to be convinced otherwise that when the dataset is small and no additional data can be obtained, LOO-CV is the best among the admittedly non-ideal choices.

What do you suggest as a practical alternative for a small dataset? Even if I use a completely separately drawn validation set, which Bengio and Grandvalet show yield an unbiased estimtae of the variance of the prediction error, I can still easily overfit the validation set when doing feature selection, right?

This is my first post on your blog. Thanks so much for putting it up — a very nice resource! One reason why people consider log loss is that the optimal prediction is the probability. When we mix with the uniform distribution, this no longer becomes true. Mixing with the uniform distribution shifts all probabilistic estimates towards 0. David McAllester advocates truncation as a solution to the unboundedness. Even when we swallow the issues of bounding log loss, rates of convergence are typically slower than for classification, essentially because the dynamic range of the loss is larger.

Before trusing mutual information, etc…, I want to see rate of convergence bounds of the form I mentioned above. I consider reporting standard deviation of cross validation to be problematic. If it has a small deviation, this does not mean that I can expect the future error rate on i. It does not mean that if I cut the data in another way and the data is i. There are specific simple counterexamples to each of these intuitions. You may not encounter this problem on some problems, but the monsters are out there.

You are correct about the feature selection example being about using the same validation set multiple times. Developing good confidence on a small dataset is a hard problem. The simplest solution is to accept the need for a test set even though you have few examples.

In this case, it might be worthwhile to compute very exact confidence intervals code here. The theory approach, which has never yet worked well, is to very carefully use the examples for both purposes. A blend of these two approaches can be helpful, but the computation is a bit rough. And of course we should remember that all of this is only meaningful when the data is i.

I think we have a case where the assumptions of applied machine learners differ from the assumptions of the theoretical machine learners. There is a good justification for mixing: I generally look at the histogram and eyeball it for gaussianity, as I have done in my example. I am saying that caution should be exercised in trusting it.

You are right to be skeptical about models, but the ordering of skepticism seems important. Models which make more assumptions and in particular which makes assumptions that are clearly false should be viewed with more skepticism. What is standard deviation of cross validation errors is supposed to describe? Could you discuss this in more detail, or provide a reference that would help me follow this up? The issue at hand is whether the standard deviation of CV errors is useful or not.

I can see two reasons for why one can be unhappy about it:. What could that mean? The standard deviation is a summary. If you provide a summary consisting of the first two moments, it does not mean that you believe in the Gaussian model — of course those statistics are not sufficient. It is a summary that roughly describes the variance of the classifier, inasmuch that the mean accuracy indicates its bias.

Yes, but the above summary relates to the question: Aleks, I regard the 0.

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Why should I care about this? Would you argue that reporting 0. Anyone surely knows that the classification accuracy cannot be more than 1. CV is the de facto standard method of evaluating classifiers, and many people trust the results that come out of this. Permutability is a weaker assumption than iid. Estimating Replicability of Classifier Learning Experiments. It is unfair to criticize CV on these grounds.

I am not trying to claim anything about the belief of the person making the application and certainly not trying to be arrogant. It seems that it has no interesting interpretation, and the obvious statistical interpretation is simply wrong. The parameter I care about is the accuracy, the probability that the classifier is correct. Since the true error rate can not go above 1this confidence interval must be constructed with respect to the wrong assumptions about the observation generating process.

In other words, it generates overconfidence. I do not have an interpretation of 0. Using this obvious interpretation routinely leads to overconfidence which is what this post was about. We do not care what the value of this hidden random variable is because a good confidence interval for accuracy works no matter what the datageneration process is. For example, tuning parameters might be reasonable.

What seems unreasonable is making confidence interval-like statements subject to known-wrong assumptions. I think you are correct: For example if you use Leave One Out cross-validation for feature selection, you might end up selecting suboptimal subset, even with infinite training sample. Te neural-nets FAQ talks about it: Experimentally, Ronny Kohavi and Breiman found independently that 10 is the best number of folds for CV.

Over here it says: It is quite rare in statistics to provide confidence intervals — usually one provides either the standard deviation of the distribution or the standard error of the estimate of the mean.

Still, I consider the 0. My level of agreement with the binomial model is about at the same level as your agreement with the Gaussian model. Probability of error is meaningless: Treating all these groups as one would be misleading. Regarding de Finetti, one has to be careful: When you have an infinite set, there is no difference between forming a finite sample by sampling-with-replacement bootstrap versus sampling-without-replacement cross-validation. How do you use it? On probability of error: Nevertheless, we like small pieces of information because we can better understand and use them.

Hence, such judgements will be more often wrong. I had assumed secrets of trading binary options were interested in infinite exchangeability because we are generally interested in what the data tells us about future not yet seen events.

Why bother to make a paper, at all? It is quite meaningless to try to assume any kind of average classification error across different data sets. Infinite exchangeability does not apply to a finite population. You cannot pretend robot on forex there are infinitely many cows in the farm. You can, however, wonder about the number of cows 2,5, 10, 25? I maintain that future is unknowable.

Any kind of a statement regarding the performance of a particular classifier trained from data should always be seen as relative to the data set. I can imagine using an error rate in decision making. I can imagine using a confidence interval on the error rate in decision making. But, I do not know how to use 0.

Your comment 100 world-famous stock market techniques richard j. maturi exchangeability makes more sense now. It seems to imply nothing about how the algorithm would perform for new problems or even for a new draw of the process generating the current training examples.

Why do we care about this very limited notion of stability? The NBC becomes highly stable beyond instances. On the other hand, C4. The difference equifax stock options expected hong kong government stock market intervention is negligible in amd stock market value calculator to the total amount of variation in performance.

How and why do you use 0. There should be a simple answer to this, just like there are simple answeres for 0. It quantifies the variance of the learned model.

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It describes that the estimate of classification accuracy across test sets of a certain size is not a number, it is a distribution. I get my distribution of expected classification accuracy through sampling, and the only assumption is the fixed choice of the relative size of the training and test set.

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The purpose of 0. I know what 0. How is this information supposed to affect the choices that we make? The central question is whether or not 0. Instead, it is the implication. The assumption is iid samples. In particular, cutting up the data in several different ways and learning different classifiers with different observed test belajar menjadi broker forex rates cannot disprove the independence assumption.

The weatherman tells us can you earn money from hubpages subjective probability of rain tomorrow is 0.

Now suppose we know something about the prior he current exchange rate aud sgd to come up with the indian stock market participants. Does that change the way we use the number?

It concerns the estimation of risk, second-order probability probability-of-probabilityetc. The issue is that you cannot characterize the error rate reliably, and must therefore use a probability distribution. This is the same pattern as with introducing error rate because you cannot say whether a a classifier is always correct or always wrong. A more practical utility is comparing two classifiers in two cases.

In one case, the classifier A gets the classification accuracy of 0. Now consider another experiment, where you get 0. How would you even do that given this information? I would generally rather make a weighted integration of predictions. If pressed for computational reasons, I might choose the classifier with the smallest cross validation or validation set error rate.

You give examples of 0. How do you use the how franchisors make money. But you dislike model selection, so obviously these tools and tricks may indeed seem useless. Instead, it may usually be better. Probability captures the uncertainty inherent to making such a choice. The probability of 0. What do you do? Regarding the purpose of model selection. I train SVM, I train classification foreign exchange investing basics, I train NBC, I train many other things.

Eventually, I would like to give them a 60 second binary option ebook crash nicely presented model. They cannot evaluate or teach this ensemble of models. So the nitty-gritty reality of practical machine learning has quite an explicit model complexity cost. And one way of dealing with model complexity is model selection. The above probability is a way of quantifying how unjustified or arbitrary it is in a particular case.

I am just trying to justify its importance to applied data analysis. Why are probabilities required? The extreme example mentioned in this post shows you can get 1. If I wanted to know roughly how well I might reasonably expect to hmm stock market prediction in the future and thought the data was i. For each of these experiments, we obtain a particular error rate. For a particular experiment, A might be better than B, but for a different experiment B would be better than A.

Both probability and the standard deviations are ways of modelling the uncertainty that comes with this. If I cannot make a sure choice, and if modelling uncertainty is not too expensive, why not model it?

Still, I would stress that cross-validation is to be replicated multiple times, with several different permutations of the fold-assignment vector. Otherwise, the results are excessively dependent on a particular assignment to folds. If something affects your results, and if you are unsure about it, then you should not keep it fixed, but vary it.

In the extreme, this argument can be used to justify anything. There are some things which are more robust than other things, and it seems obvious that we should prefer the more robust things. If you use confidence intervals, this nasty example will not result in nonsense numbers, as it does with the empirical variance approach. You may try to counterclaim that there are examples where confidence intervals fail, but the empirical variance approach works.

If so, state them. If not, the confidence interval approach at least provides something reasonable subject to a fairly intuitive assumption. No such statement holds for the empirical variance approach. I agree about bbut continue to disagree about a. The argument behind it is somewhat intricate. Cross-validation is a bit like that: Does it make sense? No, it does not. Cross validation makes samples which are in analogy more likely to be the same than independent samples.

I was arguing for cross-validation compared to random splitting into the training and test set. In some cases, i. These two stances should be kept apart and not mixed, as seems to be the fashion.

What should be a challenge is to study learning in the latter case. We do not and cannot fully know how much smaller this variance is. If you want to argue that cross-validation is a good idea because it removes variance, I can understand that. If you want to argue that the individual runs with different held out folds are experiments, I disagree. This really is like averaging the position of wheels on a race car. It reduces variance i. If you want more experiments, you should not share examples between runs of the learning algorithm.

Incompatible means that assuming i. I try to be agnostic with respect to evaluation protocols, and adapt to the problem at hand. Yes, the experiments are not independent. Why should they be? Would it be less silly than sampling just one tire and compute a bound based on that single measurement, as any additional measure could be dependent?

As an example, suppose you have data from wall street and are trying to predict stock performance. If you try to use cross validation, you will simply solve the wrong problem.

It is essential to understand this in considering methods for looking at your performance. For your second point, I agree with the idea of reducing variance via cross validation see second paragraph of comment 42 when the data is IID. What I disagree with is making confidence interval-like statements about the error rate based upon these nonindependent tests. If you want to know that one race car is better than another, you run them both on different tracks and observe the outcome.

Well, of course neither cross-validation nor bootstrap makes sense when the assumption of instance exchangeability is clearly not justified. It was very funny to see R. Kalman make this mistake in http: Although you might do that, the crux of my message is that finite exchangeability FEX exercised by CV is different from infinite exchangeability iid exercised by bootstrap. Finite exchangeability has value on its own, not just as an approximation to infinite exchangeability. I hope that I understand you correctly.

Until then, it would be unfair to dismiss empirical work assuming FEX in some places just because most theory work assumes IID. The details change, but not the basic message w.

For this conversation to be further constructive, I think you need to a state a theorem and b argue that it is relevant. Pharmaceutical companies make predictions about the effects of their drugs and then conduct blind clinical studies to determine their effect. Unfortunately, they have also been caught using some of the more advanced techniques for cheating here: Organization — jl Name Method Explanation Remedy Traditional overfitting Train a complex predictor on too-few examples.

Hold out pristine examples for testing. Use a simpler predictor.

Get more training examples. Integrate over many predictors. Reject papers which do this. Parameter tweak overfitting Use a learning algorithm with many parameters. Choose the parameters based on the test set performance.

For example, choosing the features so as to optimize test set performance can achieve this. Brittle measure Use a measure of performance which is especially brittle to overfitting. This is particularly severe when used in conjunction with another approach. Prefer less brittle measures of performance. Bad statistics Misuse statistics to overstate confidences.

One common example is pretending that cross validation performance is drawn from an i. Cross validation errors are not independent. Another standard method is to make known-false assumptions about some system and then derive excessive confidence. Choice of measure Choose the best of Accuracy, error rate, A ROC, F1, percent improvement on the previous best, percent improvement of error rate, etc. For bonus points, use ambiguous graphs.

This is fairly common and tempting. Use canonical performance measures. For example, the performance measure directly motivated by the problem. Incomplete Prediction Instead of say making a multiclass prediction, make a set of binary predictions, then compute the optimal multiclass prediction.

This is subtle and comes in many forms. One example is a human using a clustering algorithm on training and test examples to guide learning algorithm choice. Make sure test examples are not available to the human. Data set selection Chose to report results on some subset of datasets where your algorithm performs well.

The reason why we test on natural datasets is because we believe there is some structure captured by the past problems that helps on future problems. Data set selection subverts this and is very difficult to detect. Use comparisons on standard datasets. Select datasets without using the test set. Reprobleming Alter the problem so that your performance improves. For example, take a time series dataset and use cross validation.

This can be completely unintentional, for example when someone uses an ill-specified UCI dataset. Discount papers which do this.

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Make sure problem specifications are clear. Old datasets Create an algorithm for the purpose of improving performance on old datasets. After a dataset has been released, algorithms can be made to perform well on the dataset using a process of feedback design, indicating better performance than we might expect in the future.

Some conferences have canonical datasets that have been used for a decade… Prefer simplicity in algorithm design. Weight newer datasets higher in consideration.

Making test examples not publicly available for datasets slows the feedback design process but does not eliminate it. Overfitting by review 10 people submit a paper to a conference. The one with the best result is accepted. This is a systemic problem which is very difficult to detect or eliminate. We want to prefer presentation of good results, but doing so can result in overfitting.

Be more pessimistic of confidence statements by papers at high rejection rate conferences. Some people have advocated allowing the publishing of methods with poor performance. I have doubts this would work. I have personally observed all of these methods in action, and there are doubtless others.

Details A modest proposal How to Contribute a Post Who? Why did my comment not appear? Big News on W 3,r! Machine Learning the Future Class. A computational linguistic farce in three acts. COLT accepted papers. Use a learning algorithm with many parameters. Choose the best of Accuracy, error rate, A ROC, F1, percent improvement on the previous best, percent improvement of error rate, etc. Instead of say making a multiclass prediction, make a set of binary predictions, then compute the optimal multiclass prediction.

Some conferences have canonical datasets that have been used for a decade…. Prefer simplicity in algorithm design.