Data mining for significant variables (numerical): Where to start?

Question

I have a trading strategy on the foreign exchange market that I am attempting to improve upon.

I have a huge table (100k+ rows) that represent every possible trade in the market, the type of trade (buy or sell), the profit/loss after that trade closed, and 10 or so additional variables that represent various market measurements at the time of trade-opening.

I am trying to find out if any of these 10 variables are significantly related to the profits/losses.

For example, imagine that variable X ranges from 50 to -50. The average value of X for a buy order is 25, and for a sell order is -25.

If most profitable buy orders have a value of X > 25, and most profitable sell orders have a value of X < -25 then I would consider the relationship of X-to-profit as significant.

I would like a good starting point for this. I have installed RapidMiner 5 in case someone can give me a specific recommendation for that.

Answer 1

A Decision Tree is perhaps the best place to begin.

The tree itself is a visual summary of feature importance ranking (or significant variables as phrased in the OP).

• gives you a visual representation of the entire classification/regression analysis (in the form of a binary tree), which distinguishes it from any other analytical/statistical technique that i am aware of;

• decision tree algorithms require very little pre-processing on your data, no normalization, no rescaling, no conversion of discrete variables into integers (eg, Male/Female => 0/1); they can accept both categorical (discrete) and continuous variables, and many implementations can handle incomplete data (values missing from some of the rows in your data matrix); and

• again, the tree itself is a visual summary of feature importance ranking
  (ie, significant variables)--the most significant variable is the
  root node, and is more significant than the two child nodes, which in turn are more significant than their four combined children. "significance" here means the percent of variance explained (with respect to some response variable, aka 'target variable' or the thing you are trying to predict). One proviso: from a visual inspection of a decision tree you cannot distinguish variable significance from
  among nodes of the same rank.

If you haven't used them before, here's how Decision Trees work: the algorithm will go through every variable (column) in your data and every value for each variable and split your data into two sub-sets based on each of those values. Which of these splits is actually chosen by the algorithm--i.e., what is the splitting criterion? The particular variable/value combination that "purifies" the data the most (i.e., maximizes the information gain) is chosen to split the data (that variable/value combination is usually indicated as the node's label). This simple heuristic is just performed recursively until the remaining data sub-sets are pure or further splitting doesn't increase the information gain.

What does this tell you about the "importance" of the variables in your data set? Well importance is indicated by proximity to the root node--i.e., hierarchical level or rank.

One suggestion: decision trees handle both categorical and discrete data usually without problem; however, in my experience, decision tree algorithms always perform better if the response variable (the variable you are trying to predict using all other variables) is discrete/categorical rather than continuous. It looks like yours is probably continuous, in which case in would consider discretizing it (unless doing so just causes the entire analysis to be meaningless). To do this, just bin your response variable values using parameters (bin size, bin number, and bin edges) meaningful w/r/t your problem domain--e.g., if your r/v is comprised of 'continuous values' from 1 to 100, you might sensibly bin them into 5 bins, 0-20, 21-40, 41-60, and so on.

For instance, from your Question, suppose one variable in your data is X and it has 5 values (10, 20, 25, 50, 100); suppose also that splitting your data on this variable with the third value (25) results in two nearly pure subsets--one low-value and one high-value. As long as this purity were higher than for the sub-sets obtained from splitting on the other values, the data would be split on that variable/value pair.

RapidMiner does indeed have a decision tree implementation, and it seems there are quite a few tutorials available on the Web (e.g., from YouTube, here and here). (Note, I have not used the decision tree module in R/M, nor have i used RapidMiner at all.)

The other set of techniques i would consider is usually grouped under the rubric Dimension Reduction. Feature Extraction and Feature Selection are two perhaps the most common terms after D/R. The most widely used is PCA, or principal-component analysis, which is based on an eigen-vector decomposition of the covariance matrix (derived from to your data matrix).

One direct result from this eigen-vector decomp is the fraction of variability in the data accounted for by each eigenvector. Just from this result, you can determine how many dimensions are required to explain, e.g., 95% of the variability in your data

If RapidMiner has PCA or another functionally similar dimension reduction technique, it's not obvious where to find it. I do know that RapidMiner has an R Extension, which of course let's you access R inside RapidMiner.R has plenty of PCA libraries (Packages). The ones i mention below are all available on CRAN, which means any of the PCA Packages there satisfy the minimum Package requirements for documentation and vignettes (code examples). I can recommend pcaPP (Robust PCA by Projection Pursuit).

In addition, i can recommend two excellent step-by-step tutorials on PCA. The first is from the NIST Engineering Statistics Handbook. The second is a tutorial for Independent Component Analysis (ICA) rather than PCA, but i mentioned it here because it's an excellent tutorial and the two techniques are used for the similar purposes.