Monday, October 22, 2018

Discriminate for fairness

As machine learning methods come to be more widely used, there is a great deal of hand-wringing about whether they produce fair results.  For example, Pro Publica reported that a widely used program intended to assess the likelihood of criminal recidivism, that is whether a person in custody would be likely to commit an additional crime, tended to over-estimate the probability that a black person would commit an additional crime and under-estimate whether a white person would.  Amazon was said to have abandoned a machine learning system that evaluated resumes for potential hires, because that program under-estimated the likely success of women and therefore, recommended against hiring them.

I don’t want to deny that these processes are biased, but I do want to try to understand why they are biased and what we can do about it.  The bias is not an inherent property of the machine learning algorithms, and we would not find its source by investigating the algorithms that go into them. 

The usual explanation is that the systems are trained on the “wrong” data and merely perpetuate the biases of the past.  If they were trained on unbiased data, the explanation goes, they would achieve less biased results.  Bias in the training data surely plays a role, but I don’t think that it is the primary explanation for the bias.

Instead, it appears that the bias comes substantially from how we approach the notion of fairness itself.  We assess fairness as if it were some property that should emerge automatically, rather than a process that must be designed in. 

What do we mean by fairness?

In the Pro Publica analysis of recidivism, the unfairness derived largely from the fact that when errors are made, they tend to be in one direction for black defendants and in the other direction for white defendants.  This bias means that black defendants are denied bail when they really do not present a risk, and white defendants are given bail when they really should remain in custody.  That bias seems to be inherently unfair, but the race of the defendant is not even considered explicitly by the program that makes this prediction. 

In the case of programs like the Amazon hiring recommendation system, fairness would seem to imply that women and men with similar histories be recommended for hiring at similar rates.  But again, the gender of the applicant is not among the factors considered explicitly by the hiring system.
Race and gender are protected factors under US law (e.g., Title VII of the Civil Rights Act of 1964).  The law states that “It shall be an unlawful employment practice for an employer … to discriminate against any individual with respect to his compensation, terms, conditions, or privileges of employment, because of such individual’s race, color, religion, sex, or national origin.”

Although the recidivism system does not include race explicitly in its assessment, it does include such factors as whether the defendant has any family members who have ever been arrested, whether they have financial resources, etc.  As I understand it, practically every black person who might come before the court is likely to have at least one family member who has been arrested, but that is less often true for whites.  Black people are more likely than whites to be arrested, and once arrested, they are more likely than whites to be convicted and incarcerated.  Relative to their proportion in the population, they are substantially over-represented in the US prison system compared to whites.  These correlations may be the result of other biases, such as racism in the US, but they are not likely to be the result of any intentional bias being inserted into the recidivism machine learning system.  Black defendants are substantially more likely to be evaluated by the recidivism system and were more likely to be included in its training set because these same factors.  I don’t believe that anyone set out to make any of these systems biased.

The resumes written by men and women are often different.  Women tend to have more interruptions in their work history; they tend to be less assertive about seeking promotions; they use different language than men to talk about their accomplishments.  These tendencies, associated with gender are available to the system, even without any desire to impose a bias on the results.  Men are more likely to be considered for technical jobs at Amazon because they are more likely to apply for them.  Male resumes are also more likely to be used in the training set, because historically, men have filled a large majority of the technical jobs at Amazon.

One reason to be skeptical that imbalances in the training set are sufficient to explain the bias of these systems is that machine learning systems do not always learn what their designers think that they will learn.  Machine learning works by adjusting internal parameters (for example the weights of a neural network) to best realize a “mapping” from the inputs on which it is trained to the goal states that it is set.  If the system is trained to recognize cat photos versus photos of other things, it will adjust its internal parameters to most accurately achieve that result.  The system is shown a lot of labeled pictures, some of which contain cats, and some of which do not.  Modern machine learning systems are quite capable of learning distinctions like this, but there is no guarantee that they learn the same features that a person would learn.

For example, even given many thousand of training examples to classify photographs, a deep neural network system can still be “duped” into classifying a photo of a panda as a photo of a gibbon, even though both photos look to the human eye very much like a panda and not at all by a gibbon.  All it took to cause this system to misclassify the photo was to add a certain amount of apparently random visual noise to the photograph.  The misclassification of the picture when noise was added implies that the system learned features, in this case pixels, that were disrupted by the noise and not the features that a human used.

The recidivism and hiring systems, similarly, can learn to make quite accurate predictions without having to consider the same factors that a human might.  People find some features more important than others when classifying pictures.  Computers are free to choose whatever features will allow correct performance, whether a human would find them important or not.

In many cases, the features that it identifies are also applicable to other examples that it has not seen, but there is often a decrease in accuracy when a well-trained machine learning system is actually deployed by a business and applied to items (e.g., resumes) that were not drawn from the same group as the training set.  The bigger point is that for machine learning systems, the details can be more important than the overall gist and the details may be associated with the unfairness.

Simpson’s paradox and unfairness

A phenomenon related to this bias is called Simpson’s paradox, and one of the most commonly cited examples of this so-called paradox concerns the appearance of bias in the acceptance rate of men versus women to the University of California graduate school. 

The admission figures for the Berkeley campus for 1973 showed that 8442 men applied, of which 44% were accepted, and 4321 women applied, of which only 35% were accepted.  The difference between 44% and 35% acceptance is substantial and could be a violation of Title VII.

The difference in proportions would seem to indicate that the admission process was unfairly biased toward men.  But when the departments were considered individually, the results looked much different.  Graduate admission decisions are made by the individual departments, such as English, or Psychology.  The graduate school may administer the process, but it plays no role in deciding who gets in.  On deeper analysis it was found (P. J. Bickel, E. A. Hammel, J. W. O'Connell, 1975) that 6 of the 85 departments showed small bias toward admitting women and only four of them showed a small bias toward admitting men.  Although the acceptance rate for women was substantially lower than for men, individual departments were slightly more likely to favor women than men. This is the apparent paradox, departments are not biased against women, but the overall performance of the graduate school seems to be.

Rather, according to Bickel and associates, the apparent mismatch derived from the fact that women applied to different departments on average than the men did.  Women were more likely to apply to departments that had more competition for their available slots and men were more likely to apply to departments that had relatively more slots per applicant. In those days, the “hard” sciences attracted more male applicants than female, but they were also better supported with teaching assistantships and so on than the humanities departments that women were more likely to apply to. Men applied on average to departments with high rates of admission and women tended to apply to departments with low rates.  The bias in admissions was apparently not caused by the graduate school, but by the prior histories of the women, which biased them away from the hard sciences and toward the humanities.

A lot has been written about Simpson’s paradox and even whether it is a paradox at all.  The Berkeley admissions study as well as the gender bias and recidivism bias can all be explained by the correlation between a factor of interest (gender or race) and some other variable.  Graduate applications were correlated with patterns of department selection, gender bias in resume analysis is correlated with such factors as work history, language used to describe work, and so on.  Recidivism predictors are correlated with race.  Although these examples all show large discrepancies in the size of the two groups of interest (many more men applied to graduate school, many more of the defendants being considered were black rather than white, and many more the Amazon applicants were men), these differences will not disappear if all we do is add training examples. 

These systems are considered unfair, presumably because we do not think that gender or race should play a causal role in whether people are admitted, hired, or denied bail (e.g., Title VII).  Yet, gender and race are apparently correlated with factors that do affect these decisions.  Statisticians call these correlated variables confounding variables.  The way to remove them from the prediction is to treat them separately (hold them fixed).  If the ability to predict recidivism is still accurate when considering just blacks or just whites, then it may have some value.  If hiring evaluations are made for men and women separately, then there can be no unintentional bias.  Differences between men and women then, cannot explain or cause the bias because that factor is held constant for any predictions within a gender.  Women do not differ from women in general in gender-related characteristics, and so these characteristics are not able to contribute to a hiring bias toward men.
We detect unfairness by ignoring a characteristic, for example, race or gender, during the training process and then examining it during a subsequent evaluation process.  In machine learning, that is often a recipe for disaster.  Ignoring a feature during training means that that feature is uncontrolled in the result.  As a result, it would be surprising if the computer were able to produce fair results.

Hiring managers may or may not be able to ignore gender.  The evidence is pretty clear that they cannot really do it, but the US law requires that they do.  In an attempt to make these programs consistent with laws like Title VII, their designers have explicitly avoided including gender or race among the factors that are considered.  In reality, however, gender and race are still functionally present in the factors that correlate with them.  Putting a man’s name on a woman’s resume, does not make it into a male resume, but including the questions about the number of a defendant’s siblings that have been arrested does provide information about the person’s race.  The system can learn about them.  But what really causes the bias, I think, is that these factors are not included as part of the system’s goals.  

If fairness is really a goal of our machine learning system, then it should be included as a criterion by which the success of the system is judged.  Program designers leave these factors out of the evaluation because they mistakenly (in my opinion) believe that the law requires them to leave them out, but machines are unlikely to learn about them unless they are included.  I am not a lawyer, but I believe that the law concerns the outcome of the process, not the means by which that outcome is achieved.  If these factors are left out of the training evaluation, then any resemblance of a machine learning process to a fair one is entirely coincidental.  By explicitly evaluating for fairness, fairness can be achieved. That is what I think is missing from these processes. 

The goals of machine learning need not be limited to just the accuracy of a judgment.  Other criteria, including fairness can be part of the goal for which the machine learning process is being optimized.  The same kind of approach of explicitly treating factors that must be treated fairly can be used in other areas where fairness is a concern, including mapping of voting districts (gerrymandering), college admissions, and grant allocations.  Fairness can be achieved by discriminating among the factors that we use to assess fairness and including these factors directly and explicitly in our models.  By discriminating we are much more likely to achieve fairness than by leaving these factors to chance in a world where factors are not actually independent of one another.

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