Bias: can’t live with it, couldn’t survive without it.
Bias is a word that has different connotations depending on who you are. In the common world, when we hear the word “bias”, it might conjure up negative images of stereotyping and discrimination. It might be used to describe teachers favouring students on a course, or bias against a particular group of people based on the colour of their skin.
On the other hand, if you operate in the world of statistics and probability, or machine learning, you might know that bias can also be helpful. In this field, there is a well-known phenomenon known as the bias-variance trade-off, which tells us that the more we fine-tune a model, the more we constrain it, then the more efficiently it might be able to learn, but the worse the consequences when the assumptions we make are incorrect.
It is the same as when we teach school children about chemistry. In school, you might learn the model of electrons orbiting around an atom. This model might be very effective at helping us to understand and solve a wide variety of problems in our school years it isn’t a difficult model to understand. The unfortunate and ugly reality is that the model is actually a lie. The truth is that electrons aren’t these idealised little spheres of charge that float around a sun-like nucleus. Rather, a better view would be to describe them as probability clouds. Why do we lie to the students then? It is because it is much easier to teach them the simpler model that will work for most situations, than the more realistic model that works in all situations (e.g. the interesting phenomenon of electron tunnelling), but requires a lot more mental effort to understand and use.
The problem of machine learning is the problem of choosing a sufficiently complex model that will run correctly on the data we feed it, but one that isn’t overly complex. In fact, if we make the model too complex, this can actually be a bad thing, since our model might simply memorise the examples we pass it. The analogy is a student memorising the answers to a maths test that they know they need to pass, rather than actually understanding the more generally applicable underlying material, which might actually require less mental effort because it involves remembering just a few basic rules, rather than remembering answers to two decimal places for 30 different questions. The student also cannot use the knowledge they have learnt about the exam anywhere other than the exam setting — so it is pretty useless for other purposes. The student’s mental model which involved memorising the exam questions was very biased towards a particular setting, and so when the questions in the exam came up, there would be little deviation in the answers. However, it would only be applicable to the exam setting. Had the student learnt the theory necessary to solve the problem themselves, they might have admittedly had a bit more variation on the day of the exam, but they could apply what they had learnt to a wider variety of problems. This is the bias-variance trade-off, the variance here being the variance in the outcome of learning. If you give a model, or a student, more freedom to understand things in the way they see fit, they’ll probably learn more general rules. Give them too much freedom and they might not be able to latch on to anything. Give them too little freedom and they will just rote learn.
This bias-variance tradeoff happens all the time, and is based on the number of assumptions we hold at any particular time (our bias). When we get stuck in a rut of thinking, if we can’t understand something, it is usually because there is something about our current mental model of the world that involves an incorrect assumption. These assumptions are generated by our minds all the time because they are convenient. We can’t operate in the world without making assumptions. If we were completely unbiased about everything, then we would have to be completely agnostic about everything we saw on a day to day basis — we couldn’t assume the sun would come up every day, and we would have to reassess the threat that a tiger possessed every time we saw a new one. In the extreme case, every time we saw the same tiger, we couldn’t make the reasonable assumption that the tiger may still be ferocious and hostile, even if it had nearly eaten us alive the last time we saw it. Assumptions are necessary for our survival and are based on the idea that in the real world, things are often steady through time: things which happen in the past are unlikely to happen in a very different way in the future: there is a certain level of stability in the world. Therefore, we can predict the future and do something crucial: planning.
Ironically, the problem with assumptions is actually a larger assumption — the assumption that when one thing implies a second, the second thing must also imply the first. This is association and it can lead to the odd, or in some cases dark side of assumptions: if we have had negative experiences in the past, we are likely to associate aspects of those experiences, regardless of whether they were even necessarily relevant to the situations, with negative traits. It’s how many irrational fears develop, and how Pavlov conditioned his dog to salivate when a bell was rung. This implication by association can also be called the halo effect.
Racism, sexism, and all the other -isms and -phobias that we so strongly condemn in the world are unfortunate consequences of this spurious association. For example, in the case of bias against Brexiteers as disliking immigrants. Simply due to the experience of a few vocal Brexiteers, some assume that the reasoning of all must be that they simply hate immigrants. This might even become a self-fulfilling prophecy, leading those who support Brexit for other reasons to dissociate themselves.
This highlights the interesting observation that the words we choose to use can both affect and be affected by their frequent bedfellows. If there are particularly emotional or strong experiences that cause two words to become connected, society can unconsciously change the meaning of the words, conflating the two. That is — the word Brexiteer can become unconsciously associated with the concept of xenophobia, even though its technical meaning is “somebody who supports Britain’s departure from the European Union”.
A simple example can highlight why we go wrong so frequently. Consider a room full of librarians and politicians. There are 460 politicians, and 40 librarians. You go up to another one of the people in the room and she seems to be a quiet person. Would you say that this person is a librarian or a politician? You go up to another wearing a badge saying he is a librarian. Do you expect them to be a quiet person? What would be a reasonable assumption in each case? The answer might surprise you.
Let’s say 200 people are quiet by nature, meaning 300 are loud. Among the quiet people, 30 are them are librarians.
From this, we can deduce that most of the librarians (75%) are quiet by nature. On the other hand, out of the 200 people who were quiet, 160 were politicians (80%).
Therefore, the right assumption is that the first person, the quiet person, was a politician, and the second person, the librarian, was a quiet person.
This seems a bit strange, but it is only strange because of the strong association our minds form between quietness and librarians. Because most librarians we see are quiet, we assume that if we see a quiet person, they are likely to be a librarian, which is completely statistically false.
Interestingly, the evidence we are presented with and the language the media uses to describe society can influence our perceptions without us even knowing it. News corporations might choose different words to describe the same things happening to different people, simply because of the connotations they bring about. “Activists” might be storming parliament, but “insurgents” might be uprooting foreign governments, for example. Though both the “activists” and the “insurgents” might be using similar methods to fight for their causes, through constant conditioning, we can become used to thinking negatively about one, and positively about another group, through association.
Bias is present in everyone, and it is in our best interests to think about it when we navigate our everyday lives. Contrary to what many might say, I would disagree that it is the fault of an individual for assuming certain things. It is simply a product of the human brain’s machinery doing its job. Like every amazing machine, there are errors that slip in — nothing is perfect. Evolution, as evidenced by the example of avoiding the uncomfortable experience of being swallowed whole by a wild animal, has built us to judge things quickly, to save on time, which can be costly when trying to survive in the real world.
In learning and in prejudice, we need to realise that the most common cause or error is bias. When we don’t understand something new, it’s probably because we have an incorrect assumption that is difficult to get over, rather than the material being inherently difficult. When we dislike a certain thing, person, or idea, we have to think about whether our dislike is grounded in reason, or in spurious association. If we look deeply at the things we think about, very often we can find surprises and realise that our assumptions are so deeply rooted that we take them for granted. These assumptions begin to be built up from the moment we are born, and we are even born with many due to evolution tuning our brains to minimise the amount of learning effort necessary to go from babies to fully functioning adults (instinct). The key is to use these assumptions to our advantage, and to work to resist and reject those assumptions that harm us or those around us unnecessarily. It’s easy to find patterns, but hard to break them. Differences in our mental models, our biases, our assumptions, are what create misunderstandings between humans, and are what stop us from understanding new ideas that we are taught.
Originally published at http://plaee.wordpress.com on March 27, 2021.