Month: September 2019

Can We Predict our Future in Chaos?

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“For human action we have no such model and may never have one. That makes the prediction problem massively harder.”

[How not to be wrong, Jordan Ellenberg]

In the weather, the very tiny scale of energy at a certain location can change the global outcome dramatically – we called this chaos. Edward Lorenz discovered this and wrote: “if the theory were correct, one flap of a sea gull’s wing would be enough to alter the course of the weather forever”. Even though we have an accurate mathematical model (or a data-driven model) for the weather forecast with tons of measured data, we can make only a short-range prediction.

Our behaviors in society are much more chaotic than the weather, leading to a failure of prediction of future outcomes. Moreover, we have no mathematical model to describe our behaviors effectively. Hence, it is really hard (or impossible) to find “right” causation from the massive data. In this chaotic system, we should keep in mind the followings: (1) don’t make any causation from your success (rather, say, just “lucky”); (2) don’t follow others’ successes (a tiny different condition makes a totally different outcome); (3) don’t prejudge the situation using “common sense” (no one can predict the outcome).

Improbable Things Happen All the Time

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“The universe is big, and if you’re sufficiently attuned to amazingly improbable occurrences, you’ll find them. Improbable things happen a lot.”

[How not to be wrong, Jordan Ellenberg]

You have a card deck and draw five cards from this. Surprisingly, five cards you drawn are spade A, 2, 3, 4, and 5. (Congrats! you made a straight flush). Then, you might think that this is a new card deck so it is not shuffled yet because drawing these five cards in a row might be improbable (or much lower probable). However, improbable things happen all the time. Please go to Las Vegas and check this!

When analyzing some results, we need to get used to a BIG number in our fields. Our field of interest is pretty big and you can see many improbable occurrences (we can see winners of the lottery every week). Hence, we should be careful not to make any causality from a chance occurrence. In data science, even though the data-driven model finds some patterns from Big Data, we should examine that this pattern can be made by randomness or not. (It may be improbable that millions of people read this post and like it but improbable things happen all the time!!)

The Past is in the Past: the Law of Large Numbers

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“That’s how the Law of Large Numbers works: not by balancing out what’s already happened, but by diluting what’s already happened with new data, until the past is so proportionally negligible that it can safely be forgotten.”

[How not to be wrong, Jordan Ellenberg]

You have a FAIR coin and toss it ten times. Surprisingly, ten heads in a row! Now, you should bet on head or tail. Where do you put your money? Fortunately, you had learned the law of large numbers which said that the average of large trials closer to the expected value. So, the next will be “tail” for balancing out by this law. BUT, it is not true, the probability of getting head or tail is still the same. We called this misconception as “Gambler’s Fallacy”. The law of large numbers CANNOT predict your future.

We often misunderstand that the previous independent results are highly related to the future result. Before you think like that, you should check first that previous results are really related to my future decision. If not, please forget about the past. Please don’t make the wrong causality using the law of large numbers. Even though you see that the average of repeated trials is far from normal, it cannot say anything about the future. Queen Elsa in Frozen says “Past is in the past” in her famous song ‘Let it go’.

Do You Want to Be a Nonlinear Thinker?

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“Nonlinearity is a real thing! … Thinking nonlinearly is crucial, because not all curves are lines.”

[How not to be wrong, Jordan Ellenberg]

Many people want to be a nonlinear thinker who does not follow the step-by-step progression but tries to find the solution outside of the box. Hence, the word ‘nonlinear thinking’ implies somewhat special ability but most of the curves are nonlinear (only a few are lines) in the real world. That is, becoming a nonlinear thinker means (maybe) being mediocre.

When predicting future behaviors from the past (like the predictive model in AI), we should keep in mind that almost all curves are not lines. We should consider all possibilities to make our prediction nonlinear. Moreover, if our case turns out the nonlinear prediction, our optimal decision depends on where we already lie on the nonlinear curve. However, a linear prediction gives us good advantages to quickly find the pattern from the past and efficiently predict the (near) future behaviors because ALL curves seem to be lines locally. Hence, the balance of linear and nonlinear thinking is highly required in the age of Big Data.

[Wrap up] Book Review: Weapons of Math Destruction

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NOW, we live in the age of Big Data and nobody can stop the invasion of artificial intelligence (AI) into our world. Many books about data science have shown the effectiveness, accuracy, and efficiency of the data-driven models in various fields such as economics, social science, and engineering. Do you agree with that data-driven models via mathematics/computer science/machine learning make a prosperous future?

THE author, Cathy O’Neil, based on her academical and industrial experiences, showed us the dark side of mathematical (or data-driven) models and called this ‘Weapons of Math Destruction’. The author said that WMDs have peculiar characteristics: (1) Opacity; (2) Scale; and (3) Damage. Through several examples that these characteristics of WMD have a negative effect on, the author called our attention to ‘fairness’ in Big Data and AI.

The following links are some quotations from the book with my thoughts.

(1) Make Your Crystal Ball Shine

(2) What Ingredients Do We Need for Yummy Data Soup?

(3) How to Make my Model Unspoiled?

(4) Am I the Same Person as I Was Yesterday?

(5) Some Numbers to Represent You

(6) The Whole is Different the Sum of its Parts

(7) Don’t put me in, Data

(8) Justice: What’s the Right Thing to Do in Data Science?

(9) As Human Beings, We are Flawed but We Learn

As Human Beings, We are Flawed but We Learn

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“But human decision making, while often flawed, has one chief virtue. It can evolve. As human beings learn and adapt, we change, and so do our processes.”

[Weapons of Math Destruction, Cathy O’neil]

We are flawed and vulnerable. We sometimes are blinded by prejudice. We are often apt to be emotional and fails to make the right decision. Yes, we are human beings. However, we have learned from our mistakes. We accepted the Copernican system. We changed our mind after Martin Luther King’s “I Have A Dream” speech. When we realized that there is something wrong, we can change all at once.

Automated systems, by contrast, CANNOT change their model immediately. The only thing they can do is an improvement of the model to add more parameters and correlations (like the eccentric and the epicycle in the Ptolemaic system). This makes the model more complex and complicated (not the right direction!). This shows the main role of human beings in the age of Big Data. Only we, human beings, stop and change the data-driven model immediately when it goes wrong.

Justice: What’s the Right Thing to Do in Data Science?

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“The model is optimized for efficiency and profitability, not for justice or the good of the “team”. This is, of course, the nature of capitalism.”

[Weapons of Math Destruction, Cathy O’neil]

Michel J Sandel’s magnum opus, Justice: What’s the Right Thing to Do?, called our attention to justice (and fairness) in a period of prosperity of capitalism. Data science acts in a similar fashion of capitalism. More data (money) is more powerful and the efficiency (profitability) is the most important factor for its success. Hence, in Data Science, we should consider that fairness and efficiency (and profitability) are compatible.

To take fairness into the consideration in data-driven models, we need to think over what we can do. First, we should double-check that our data are unbiased. Specifically, historical data are often biased due to different historical backgrounds. So when combining long-time history data, we need delicate effort to eliminate hidden bias. Moreover, we add “fairness” to the main objectives in data-driven models directly. Here, we have the problem of how to quantify fairness (also justice and morality). Hence, it is still challenging to make the fair model but it is not impossible.

Don’t Put Me in, Data

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“More times than not, birds of a feather do fly together. … Investors double down on scientific systems that can place thousands of people into what appear to be the correct buckets.”

[Weapons of Math Destruction, Cathy O’neil]

To enhance computational efficiency, data-driven models often create subgroups and predict future behaviors of these subgroups (not every single person). Under the premise that people who have similar characteristics may make a similar decision for specific problems (like doppelganger search). This prediction for the subgroups leads to an efficient and simple predictive model.

There are still some important questions about this efficient model. Are we in the correct subgroups? If so, is it true that all the people in the same subgroup always make the same (or very similar) decision? Data scientists should remind these questions. And then they check that our prediction results can be divided by some (finite) subgroups and the number of subgroups is enough to make the right prediction. Someone may want to say like “Don’t put me in any subgroups. I am so independent!”

The Whole is Different the Sum of its Parts

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“When a whole body of data displays one trend, yet when broken into subgroups, the opposite trend comes into view for each of those subgroups.”

[Weapons of Math Destruction, Cathy O’neil]

In statistics, Simpson’s paradox shows the difference in trends between the whole group and subgroups. This result shows that we often mislead the statistical result from the data-driven model, leading to the wrong causation for some phenomena in our world.

We pay particular attention to make a model to avoid this misconception. A general model often fails to predict the behavior of subgroups. And also, we CANNOT guarantee that the combination of specific models predicts the coarse-scale behavior of the whole system effectively. Hence, there should be a proper balance in the use of Big Data.

Some Numbers to Represent You

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“When you can create a model from proxies, it is far simpler for people to game it. This is because proxies are easier to manipulate than the complicated reality they represent.”

[Weapons of Math Destruction, Cathy O’neil]

This is NOT the story of “Numerology” (but somewhat related). Can you believe that there exist some numbers to represent your whole life? In data science, we called these numbers “proxies”. To make a model simpler, we often use some numbers instead of your characteristic, leading to an efficient prediction about you and your future.

The AI model for college admission may use only SAT scores (and the number of completed APs) for screening. The AI model for a personal loan may use only five numbers of your zip code. However, we should keep in mind that these proxies (numbers) cannot represent our life correctly.