The Rebirth of Confounding and Theory in Science?

Wired recently published an interesting article titled: The End of Theory: The Data Deluge Makes the Scientific Method Obsolete, where they roughly conclude that with enough data and processing correlation is all you need. While interesting I think it misses a few important points.

Confounding variables
At the end of the article they claimed: "Correlation supersedes causation, and science can advance even without coherent models, unified theories, or really any mechanistic explanation at all".

Correlation between two variables can give some information, and with a lot of data and computational horsepower you can find correlation relatively easily, but the danger is if correlation is interpreted as causation (and that can happen).

Example: Correlation between GDP and Children´s Weight
An example is the positive correlation between a country´s Gross Domestic Product (GDP) and the weight of its children, if that was interpreted as a causation the cheapest way to increase GDP for a country would be put kids on e.g. a Chankonabe diet (note: I am not saying that is a likely action). The GDP and weight correlation is an example of where a third confounding variable time was not accounted for.

Example: Correlation between substance X and your health
In the press you frequently see eating/drinking substance X is good for your health and makes you live longer, in several of those cases I believe correlation is reported and not the confounding variables, i.e. many of these substances are luxury goods and may not be affordable to most of the worlds population, so the confounding variable might be personal economy which is probably correlated with access to vaccines and medical care.

The value of theory
My personal hypothesis is that the likelihood of not finding confounding variables increases exponentially with the complexity or level of abstractness of the domain investigated for correlation (e.g. in medicine, farmacology, biology or physics) The useful information is more likely to be found when discovering confounding variables, and the correlation is primarily a signal that says that something exciting is underneath (there can be cases where correlation is sufficiently interesting in itself though). In order to find or propose confounding variables I believe the need for models and theories is still very much needed, probably even more than earlier (but the simplicity or complexity of models is another discussion, I tend to lean towards KISS).

Disclaimer: This posting (and all my others) represent only my personal views.

Annual Echo Chamber

Having blogged for a bit more than a year (April 2007), here are some rough stats and opinions of blog entries so far. Most read entries:

1. Pragmatic Classification with Python
2. Greenlet Python is concurrently alive and kicking
3. RPython GCLB Benchmark - Recursive
4. How to complete your PhD
5. Future number of programming languages - singularity or infinity?

In terms of self-eval (read: navel gazing..) of entries, the list would look like this:

• Increase Automation of Test-Driven Development
• PhD Subject in Computer Science?
• Pragmatic Classification: The very basics
• Pragmatic Classification of Classifiers
• Dining Philosophers and Quarreling Kids

As always this blog only expresses my personal opinions.

Pragmatic Classification of Classifiers

recap: In my previous machine learning related postings I have written about the basics of classification and given an overview of Python tools for classification (and also a machine learning dream team and how to increase automation of test-driven development).

In this posting I will "go meta" and say something about classes and characteristics of classifiers.



Informative vs Discriminative Classifiers
Informative classifiers model the densities of classes and select the class that most likely produce the features, in the naive bayes case this modeling involves counting (see here for an example with these data).

Discriminative classifiers have a different approach - they try to model class boundary and membership directly, e.g. in a simple 2-feature dimension case this could mean trying to finding the line that best separates the classes (in >3 feature dimensions case it would be looking for the hyperplane that best separate classes). Examples of discriminative classifiers are support vector machines (SVM) and ridge regression.

Classifier training methods
Many classifiers are batch-based, that means that they need to have access to all training data at the same time (including historic data in a re-training case). Online classifiers don't need all data for every training round, they supporting updating the classifier data incrementally. A related training method is decremental training, which is about dealing with classifier problems where there is concept drift (i.e. forgetting out-of-date examples). Other training methods include stochastic training which is about training using random samples of data.

Linear vs Non-Linear Classifiers
If you have a situation where one class is inside a circle and the other class is outside the circle (and surrounding the circle), it will be impossible to linearly separate the two classes (with a discriminative classifier), fortunately there are non-linear classifiers that can solve this (typically by transforming the problem into a more computationally heavier problem using a kernel trick, but at least the new problem is possible to solve).

Sequential vs Parallel Classifiers
Sequential classifier algorithms can typically utilize one core, cpu or machine, and parallel classifier algorithms are able to utilize more cores, cpus or machines (e.g. in order to handle more data or get faster results).

Non-orthogonal Data
Non-orthogonality is handled by some classifiers, this can happen when there are repeated occurrences of training data.

Dependencies between features
Dealing with dependencies between features (e.g. correlations) is handled by some classifiers (this is sometimes a symptom of potential for improvement in feature representation).

Blogging is good for you..

Source: Blogging -- It's Good for You (Scientific American)

Scrum makes you smarter

Disclaimer: cartoon presents a free interpretation of this

Pragmatic Classification with Python

In my previous posting I wrote about classification basics, this posting will follow up and talk about Python tools for classification and give an example with one of the tools.

Open Source Python Tools for Classification

• Orange - machine learning tool which supports classification (including combining classifiers in ensembles), feature extraction, basic statistical analysis, regression and association rules. It also has an extension module which supports clustering and additional classifier algorithms. Note: Orange is probably the Python-based machine learning tool that is most similar to the more famous tool Weka (which is for Java, or Jython for that matter).

• Monte - less comprehensive than Orange, written purely in Python (i.e. no SWIGed C++). Looks interesting (has several classifiers algorithms), but the APIs seems to be in an early phase (relatively new tool in version 0.1.0)

• libsvm - Python API for most popular open source implementation of SVM. Note: libsvm is also included with Orange and PyML. (I used this tools during my PhD a few years ago)
  

• RPy - not exactly a classification tool, but it is quite useful with a statistics tool when you are doing classification (it has a nice plotting capability, not unlike matlabs), check out the demo.
  

• PyML - also less comprehensive than Orange (specialized towards classification and regression, it supports SVM/SMO, ANN and Ridge Regression), but it has a nice API. Example of use:
  

  
  from PyML import multi, svm, datafunc
  # read training data, last column has the class
  mydataset = datafunc.SparseDataSet('iris.data', labelsColumn = -1)
  myclassifier = multi.OneAgainstRest(svm.SVM())
  print "cross-validation results", myclassifier.cv(mydataset)
  

My recommendation is to either go with Orange or with PyML.

Pragmatic Classification: The very basics

Classification is an everyday task, it is about selecting one out of several outcomes based on their features. An example could be recycling of garbage where you select the bin based on the characteristics of the garbage, e.g. paper, metal, plastic or organic.

Classification with computers
For classification with computers the focus is frequently on the classifier - the function/algorithm that selects the class based on features (note: classifiers usually has to be trained to get fit for fight). Classifiers can be found in many flavors, and quite a few of them have impressive names (phrases with rough, kernel, vector, machine and reasoning aren't uncommon when naming them).

note: Garbage in leads to Garbage out - as (almost always) - same goes for classification.

The numerical baseline
Let us assume you have a data set with 1000 documents that shows to have 4 equally different categories (e.g. math, physics, chemistry and medicine). A simple classifier for a believe-to-be-similar-dataset could be the rule: "the class is math", which is likely to give a classification accuracy of about 25%. (Another classifier could be to pick a random category for every document). This can be used as a numerical baseline for comparison with when bringing in heavier classification machinery, e.g if you get 19% accuracy with the heavier machinery it probably isn't very good (or your feature representation isn't very good) for that particular problem. (Note: heavy classification machinery frequently has plenty of degrees of freedom, so fine tuning them can be a challenge, same goes for feature extraction and representation).

Combining classifiers
On the other hand, if the heavy machinery classifier gave 0% accuracy you could combine it with a random classifier to only randomly select from the 3 classes the heavy machinery classifier didn't suggest.

Question 1: What is the accuracy with these combined classifiers?

Baseline for unbalanced data sets
Quite frequently classification problems have to deal with unbalanced data sets, e.g. let us say you were to classify documents about soccer and casting (fishing), and your training data set contained about 99.99% soccer and 0.01% about casting, a baseline classifier for a similar dataset could be to say - "the article is about soccer". This would most likely be a very strong baseline, and probably hard to beat for most heavy machinery classifiers.

Silver bullet classifier and feature extraction method?

Q: My friend says that classifier algorithm X and feature extraction method Y are the best for all problems, is that the case?
A: No, tell him/her to read about the ugly duckling and no free lunch theorems which clearly says that there is no universally best classifier or feature extraction approach.

note: Just some of the basics this time, something more concrete next time (I think).