This is an attempt to organize the broad research programs related to machine learning currently underway. This isn’t easy—this map is partial, the categories often overlap, and there are many details left out. Nevertheless, it is (perhaps) helpful to have some map of what is happening where. The word ‘typical’ should not be construed narrowly here.
- Learning Theory Focuses on analyzing mathematical models of learning, essentially no experiments. Typical conference: COLT.
- Bayesian Learning Bayes law is always used. Focus on methods of speeding up or approximating integration, new probabilistic models, and practical applications. Typical conferences: NIPS,UAI
- Structured learning Predicting complex structured outputs, some applications. Typiical conferences: NIPS, UAI, others
- Reinforcement Learning Focused on ‘agent-in-the-world’ learning problems where the goal is optimizing reward. Typical conferences: ICML
- Unsupervised Learning/Clustering/Dimensionality Reduction Focused on simpiflying data. Typicaly conferences: Many (each with a somewhat different viewpoint)
- Applied Learning Worries about cost sensitive learning, what to do on very large datasets, applications, etc.. Typical conference: KDD
- Supervised Leanring Chief concern is making practical algorithms for simpler predictions. Many applications. Typical conference: ICML
Please comment on any missing pieces—it would be good to build up a better understanding of what are the focuses and where they are.
“Overfitting” is traditionally defined as training some flexible representation so that it memorizes the data but fails to predict well in the future. For this post, I will define overfitting more generally as over-representing the performance of systems. There are two styles of general overfitting: overrepresenting performance on particular datasets and (implicitly) overrepresenting performance of a method on future datasets.
We should all be aware of these methods, avoid them where possible, and take them into account otherwise. I have used “reproblem” and “old datasets”, and may have participated in “overfitting by review”—some of these are very difficult to avoid.
||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.
||Same as above.
||Use a measure of performance which is especially brittle to overfitting.
||“entropy”, “mutual information”, and leave-one-out cross-validation are all surprisingly brittle. This is particularly severe when used in conjunction with another approach.
||Prefer less brittle measures of performance.
||Misuse statistics to overstate confidences.
||One common example is pretending that cross validation performance is drawn from an i.i.d. gaussian, then using standard confidence intervals. Cross validation errors are not independent. Another standard method is to make known-false assumptions about some system and then derive excessive confidence.
||Don’t do this. Reject papers which do this.
|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 your method. 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.
||Instead of (say) making a multiclass prediction, make a set of binary predictions, then compute the optimal multiclass prediction.
||Sometimes it’s tempting to leave a gap filled in by a human when you don’t otherwise succeed.
|| Reject papers which do this.
||Use a human as part of a learning algorithm and don’t take into account overfitting by the entire human/computer interaction.
||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. Good Contest performance can’t be faked this way.
||Alter the problem so that your performance improves.
||For example, take a time series dataset and use cross validation. Or, ignore asymmetric false positive/false negative costs. This can be completely unintentional, for example when someone uses an ill-specified UCI dataset.
||Discount papers which do this. Make sure problem specifications are clear.
||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.
Edit: a repost on kdnuggets.
One way to organize learning theory is by assumption (in the assumption = axiom sense), from no assumptions to many assumptions. As you travel down this list, the statements become stronger, but the scope of applicability decreases.
- No assumptions
- Online learning There exist a meta prediction algorithm which compete well with the best element of any set of prediction algorithms.
- Universal Learning Using a “bias” of 2– description length of turing machine in learning is equivalent to all other computable biases up to some constant.
- Reductions The ability to predict well on classification problems is equivalent to the ability to predict well on many other learning problems.
- Independent and Identically Distributed (IID) Data
- Performance Prediction Based upon past performance, you can predict future performance.
- Uniform Convergence Performance prediction works even after choosing classifiers based on the data from large sets of classifiers.
- IID and partial constraints on the data source
- PAC Learning There exists fast algorithms for learning when all examples agree with some function in a function class (such as monomials, decision list, etc…)
- Weak Bayes The Bayes law learning algorithm will eventually reach the right solution as long as the right solution has a positive prior.
- Strong Constraints on the Data Source
- Bayes Learning When the data source is drawn from the prior, using Bayes law is optimal
This doesn’t include all forms of learning theory, because I do not know them all. If there are other bits you know of, please comment.
Let’s define a learning problem as making predictions given past data. There are several ways to attack the learning problem which seem to be equivalent to solving the learning problem.
- Find the Invariant This viewpoint says that learning is all about learning (or incorporating) transformations of objects that do not change the correct prediction. The best possible invariant is the one which says “all things of the same class are the same”. Finding this is equivalent to learning. This viewpoint is particularly common when working with image features.
- Feature Selection This viewpoint says that the way to learn is by finding the right features to input to a learning algorithm. The best feature is the one which is the class to predict. Finding this is equivalent to learning for all reasonable learning algorithms. This viewpoint is common in several applications of machine learning. See Gilad’s and Bianca’s comments.
- Find the Representation This is almost the same as feature selection, except internal to the learning algorithm rather than external. The key to learning is viewed as finding the best way to process the features in order to make predictions. The best representation is the one which processes the features to produce the correct prediction. This viewpoint is common for learning algorithm designers.
- Find the Right Kernel The key to learning is finding the “right” kernel. The optimal kernel is the one for which K(x, z)=1 when x and z have the same class and 0 otherwise. With the right kernel, an SVM(or SVM-like optimization process) can solve any learning problem. This viewpoint is common for people who work with SVMs.
- Find the Right Metric The key to learning is finding the right metric. The best metric is one which states that features with the same class label have distance 0 while features with different class labels have distance 1. With the best metric, the nearest neighbor algorithm can solve any problem.
Each of these viewpoints seems to be “right”, and each seems to have some utility in it’s context. It also seems important to realize that these are just different versions of the same problem. One consequence of this observation is that “wrapper methods” which try to automatically find a subset of features to feed into a learning algorithm in order to improve learning performance are simply trying to repair weaknesses in the learning algorithm.
All branches of machine learning seem to be united in the idea of using data to make predictions. However, people disagree to some extent about what this means. One way to categorize these different goals is on an axis, where one extreme is “tools to aid a human in using data to do prediction” and the other extreme is “tools to do prediction with no human intervention”. Here is my estimate of where various elements of machine learning fall on this spectrum.
||Human partially necessary
|Clustering, data visualization
||Bayesian Learning, Probabilistic Models, Graphical Models
||Kernel Learning (SVM’s, etc..)
The exact position of each element is of course debatable. My reasoning is that clustering and data visualization are nearly useless for prediction without a human in the loop. Bayesian/probabilistic models/graphical models generally require a human to sit and think about what is a good prior/structure. Kernel learning approaches have a few standard kernels which often work on simple problems, although sometimes significant kernel engineering is required. I’ve been impressed of late how ‘black box’ decision trees or boosted decision trees are. The goal of reinforcement learning (rather than perhaps the reality) is designing completely automated agents.
The position in this spectrum provides some idea of what the state of progress is. Things at the ‘human necessary’ end have been succesfully used by many people to solve many learning problems. At the ‘human unnecessary’ end, the systems are finicky and often just won’t work well.
I am most interested in the ‘human unnecessary’ end.