Relative frequency of words in tree of documents
There are two reasons for the poor performance of the code in the post: first, it performs much unnecessary work, and, second, the operations that it does perform are carried out using inefficient data structures.

Let's look at the inefficient data structures first. The problem here is that the documents are represented as lists, and the occurrence of a word in a document is determined using Python's in operator: word in doc. But the in operator is not efficient for lists: Python has to potentially compare word with every element of doc in order to determine if it is there or not. For an efficient membership test we would need to convert the documents to use Python's set data structure. But as I'll try to demonstrate below, by careful organization of the work, we can avoid having to test words for membership of documents at all.

Now for the unnecessary work.


The main body of the function is a loop over the list of documents belonging to the child node:

for doc in child.documents:
    # Update occurlist[i] for all the words in doc
    for word in doc:
        # Update ratio_dict[word]


Much of this work is wasted because words are likely to occur in multiple documents, and only in the case of the last document containing the word will we get the ratio we want. (All previous computations of this ratio were wrong, but when the last document is reached the wrong ratio gets overwritten by the correct ratio.) To avoid the wasted work we can restructure the code like this:

for doc in child.documents:
    # Update occurlist[i] for all the words in doc
for word in occurlist[i]:
    # Update ratio_dict[word]


In this version of the code we only compute the ratio once for each word.
In this loop the code counts how many documents each word occurs in:

for word in wordSet:
    if word in doc:
        occurlist[i][word]+=1


but some of this will be wasted because not every word in wordSet will occur in doc. This waste could be avoided by only looking at the words that occur in doc:

for word in set(doc):
    occurlist[i][word] += 1


The use of set here ensures that we only count unique words.
Looking at the overall structure of the algorithm in word_frequency, we can see that if a node has \$k\$ children, then we will be computing ratio dictionaries for each of those \$k\$ children, and that will mean counting the occurrences of the words in the \$k-1\$ siblings. But this means that the documents for each child have to be counted \$k\$ times: once for its own ratios, and again for the ratios of each of its siblings.

We can avoid this duplicate work by counting the occurrences for each node just once, and storing the counts in the node. The natural way to implement this would be to add a property to the class of node objects, like this:

from collections import Counter

class Node(object):
    # ... other methods here ...

    @property
    def occurrence(self):
        """Mapping from words to number of documents at this node that contain
        the word.

        """
        if not hasattr(self, '_occurrence'):
            self._occurrence = Counter()
            for doc in self.documents:
                self._occurrence.update(set(doc))
        return self._occurrence


Here I've used collections.Counter, which is a specialized data structure for counting things. Notice the convenience of being able to call the update method instead of having to write a loop.

The occurrence property is a cached property, by which I mean that after computing the result, it caches the answer in a private attribute (self._ocurrence) and then on subsequent calls it returns the answer previously computed, instead of computing it again.

(There are libraries that help you simplify the writing of cached properties, for example, in Python 3 you would use functools.lru_cache, and in Python 2.7 there's a backport package.)
Now that we have an occurrence mapping for each node, we can compute the sibling occurrences by summing the occurrence mappings for the siblings of each node. This is easily done because in my implementation above these occurrence mappings are Counter objects, and when you add two Counter objects you get a new Counter object with the sum of the counts. (See the section starting "several mathematical operations..." in the Counter documentation.)

Then having summed the siblings, we can use this sum to compute the ratios. Again, it would make sense for the ratios to be a cached property on the class of node objects, like this:

from __future__ import division
from collections import Counter

class Node(object):
    # ... other methods here ...

    @property
    def ratio(self):
        """Mapping from words to the ratio of the occurrences of the word in
        documents at this node to the occurrences of the word in
        documents at the siblings of this node.

        """
        if not hasattr(self, '_ratio'):
            self._ratio = {}
            documents = len(self.documents)
            sibs_occurrence = sum((sib.occurrence for sib in self.siblings),
                                  Counter())
            sibs_documents = sum(len(sib.documents) for sib in self.siblings)
            for word, count in self.occurrence.items():
                sibs_count = sibs_occurrence[word]
                if sibs_count == 0:
                    r = 1e6 * count / documents
                else:
                    r = count * sibs_documents / (sibs_count * documents)
                self._ratio[word] = r
        return self._ratio


Notes: (i) I've used the __future__ module to get Python-3-style division. This avoids the need to call float in each division. (ii) I didn't implement the feature where you adjust the ratio so that it's negative if it was less than one. In comments you indicated that you didn't care about these ratios, so I think there's no point in adjusting them. If you don't want to store these ratios at all, you could add a guard like if r &gt;= 1: before storing them. (iii) I did fix the bug whereby if the ratio was 1 exactly then it would not be stored.

Now there is no remaining need for the word_frequency function. When you need the word frequency ratio mapping for node, then you write node.ratio and this computes it if needed, or returns the cached result if not, and there is little remaining duplicated work.


Summary. The code in the post computes the same intermediate results many times. The code can be sped up by organizing the work so that each result is computed just once. A convenient way to ensure this is to cache the results when they are computed.

Exercise. After making the changes suggested in this answer, which intermediate results are still computed many times, and how could this be avoided?