Contents

Embedded bias

  • How to deal with words in mathematical models?

represent words with numbers!

Method 1: bag-of-words

  • make list of occurring words and give them numbers ordered by frequency

    • ‘the’ -> 1

    • ‘it’ -> 2

    • …

    • ‘embedding’ -> 23579

  • Problems:

    • huge one-hot-vectors

    • hard to train

    • no context embedded

Method 2: Unsupervised word-vectors

  • use word and its context in reduced vector space (e.g. 300 dim.)

    • train model such that similar context leads to similar vectors

  • Pro: Semantics partly encoded in numbers

  • Problems:

    • large and very clean corpora necessary

    • computational hard

General problems

  • No result for out-of-corpus words

  • Bad for specific language of e.g. scientific terms

  • Word embeddings are based on contemporary texts

  • If specific words occur in a limited set of contexts, bias translates from text to numbers

    • ‘man’ occurs with ‘doctor’, but ‘woman’ occurs with ‘nurse’

    • ‘black’ occurs with ‘criminal’

    • ‘muslim’ with ‘radical’

Showing the embedded biasword

Based on the blog post:

import numpy as np

The GloVe dataset contains lines with words and their vectors. You have to download the dataset from the source page: Source

Choose the smallest dataset, since this is already around 800MB.

def read_glove_vecs(glove_file):
    with open(glove_file, 'r', encoding='utf8') as f:
        words = set()
        word_to_vec_map = {}
        
        for line in f:
            line = line.strip().split()
            curr_word = line[0]
            words.add(curr_word)
            word_to_vec_map[curr_word] = np.array(line[1:], dtype=np.float64)
            
    return words, word_to_vec_map

words, word2vectors = read_glove_vecs('../data/glove.6B.50d.txt')

One way to compare vectors is to calculate their cosine similarity (wikipedia):

  • similar vectors point in similar directions, the angle between them is small

  • equal vectors have cosine equals one

  • exactly opposite vectors have cosine equals minus one

  • unrelated vectors can have cosine equal zero

Formular:

\(\cos(\theta) = \frac{\textbf{U} \cdot \textbf{V}}{||\textbf{U}|| \cdot || \textbf{V}|| }\)

Using numpy package we can encode this as a function.

The parameters disp and multi allow to change the output or input format. If disp=True the function will print a string with the input words and the calculated value, if its off (default) only the calculated similarity is returned. If multi=True the input is expected as two lists, with two words each. The word vectors are then substracted from each other and the similarity of the new values is calculated.

def cosine_similarity(word1, word2, disp=False, multi=False):
    if multi:
        u = word2vectors[word1[1].lower()] - word2vectors[word1[0].lower()]
        v = word2vectors[word2[1].lower()] - word2vectors[word2[0].lower()]
    else:
        u = word2vectors[word1.lower()]
        v = word2vectors[word2.lower()]
    cossim = np.dot(u, v) / (np.sqrt(np.sum(u**2)) * np.sqrt(np.sum(v**2)))
    if disp:
        return print('cos_sim({0}, {1}) = {2}'.format(word1, word2, cossim))
    return cossim

Working with word vectors

  • Experiment with the function!

  • How does the similarity of (father,mother) compares to e.g. (rocket,cake)?

  • Calculate the similarity for [‘rome’,’italy’] and [‘france’,’paris’].

  • Why does the sign change for [‘rome’,’italy’],[‘paris’,’france’] ?

cosine_similarity(???,???,disp=True)

cosine_similarity(???,???,disp=True)

cosine_similarity([???,???], [???,???], disp=True, multi=True)

Are there semantics captured ?

To have a look at semantics, we have to be able to analyse relations like

Man is to woman as king is to X (e.g. queen)

Since words are now encoded as vectors, we can calculate (woman - man), which forms a new vector. Since we are looking for a word X such that (X - king) is similar to (woman - man), we can iteratively scan all words of the corpus.

If the cosine similarity of cos_sim((woman-man),(X-king)) for a target word X is larger then the similarity of the word before, we take not of the word and the similarity and repeat.

In the end, the word with the largest similarity is returned. If disp=True the input words are printed as well.

def complete_analogy(word1, word2, word3, disp=True):
    word1, word2, word3 = word1.lower(), word2.lower(), word3.lower()
    words = word2vectors.keys()
    max_cosine_sim = -100              # Initialize max_cosine_sim to a large negative number
    best_word = None                   # Initialize best_word with None, it will help keep track of the word to output
    for w in words:           
        if w in [word1, word2, word3] :
            continue
        cosine_sim = cosine_similarity([word1,word2], [word3,w], multi=True)
        # If the cosine_sim is more than the max_cosine_sim seen so far,
            # then: set the new max_cosine_sim to the current cosine_sim and the best_word to the current word
        if cosine_sim > max_cosine_sim:
            max_cosine_sim = cosine_sim
            best_word = w
    if disp:
        return print ('{0} -> {1} :: {2} -> {3}'.format(word1,word2,word3, best_word ))
    return best_word

Basics:

  • Test if embeddings can capture semantics

  • What is the best word for the trio (italy, italian, spain) ?

  • And for (germany,berlin,austria) ?

What about bias?

  • What is the best word for (woman, nurse, man)?

  • And for (christian, civilians, muslim)?

  • Discuss these findings

complete_analogy(???,???,???, disp=True)

Is there a gender vector?

Take for example the difference between woman and man. Does this encode a “gender” vector?

def vecCosSimilarity(u,v):
    cossim = np.dot(u, v) / (np.sqrt(np.sum(u**2)) * np.sqrt(np.sum(v**2)))
    return cossim

g = word2vectors['woman'] - word2vectors['man']
print(g)

  • Check for a range of names if there is a common trend in male or female names.

print ('List of names and their similarities with constructed vector:')
name_list = ['john','eve','priya']
for w in name_list:
    print (w, vecCosSimilarity(word2vectors[w], g))

  • Do the same for charged words, e.g. fashion, guns, etc.

  • Do you see a trend?

print('Other words and their similarities:')
word_list = ['actor','actress','doctor','nurse']
for w in word_list:
    print (w, vecCosSimilarity(word2vectors[w], g))

How to change this ?

Not shown, but a simple projection works, if we assume that gender is indeed encoded in g.

Basic idea, source deeplearning.ai

Can we use ML to detect bias ?

  • Pre-process Tucholsky corpus with NLP tools

  • Train GloVe on Tucholsky

  • Exercise:

    • Can we see a bias in Tucholsky’s language?

Outlook: Intellectual dept of software

We have stepped in the area of unknown software and silently started using programs without understanding them

This has lots of interesting implications and philosophical dimensions!

  • Cory Doctorow Blog-Post

    • Technology on top of other technology hides technological dept

  • Jonathan Zittrain New Yorker Article

    • Main argument: AI is applied science and limits basic research

  • Tyler Vigen Collection of Correlations

    • More data creates also more spurious correlations

Training a new spacy model for Tucholsky