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Naïve Bayes is a probabilistic data mining classifier which fits nicely into the MapReduce model and gives pretty good predictive performance for its simplicity. The Hadoop implementation uses a single map/reduce operation to calculate the mean and standard deviation of each attribute/class combination, as well as the global class distribution of the training dataset.

Some basic pseudo code:

instance = single row of training set
instance.class = class/target of row
instance.attributes = list of attributes

def map(key, instance):
	i = 0
	for attribute in instance.attributes:
		collect(instance.class + "_" + i, attribute)
		i++
 
	collect("target_" + instance.class, 1) # class distribution
 
def reduce(key, values):
	if key.startsWith("target_"): # reduce class dist keys
		sum = 0
		for v in values:
			sum += v
                collect(key,sum)
 
	else: # reduce attribute/class keys
		sum=0
		sumSq = 0
		count = 0
		for v in values:
			sum += v
			sumSq += v*v
			count++
 
		mean = sum/count
		collect(key + "_mean", mean)
		collect(key + "_stddev", sqrt(abs(sumSq - mean * sum) / count))

This will produce a file of means, standard deviations and a class distribution for which you can then load into a model (such as that found in Weka- weka.classifiers.bayes.NaiveBayes.distributionForInstance). This doesn’t support discrete attributes yet, only numeric/real ones. Working on it.

I was able to process a ~5GB file of ~200k rows/2000 attributes per row in 4 minutes on 30 nodes.