“Curiouser and curiouser!” cried Alice, for the cake made her larger and her head struck against the roof of the hall: in fact, she was now more than nine feet high, and she at once hurried off to the garden door. Poor Alice! It was as much as she could do, lying down on one side, to look through into the garden with one eye; but to get through was more hopeless than ever: she sat down and began to cry again, until there was a large pool all round her, about four inches deep and reaching half down the hall.

Once the effects of the cake started wearing off, Alice started to drown in her own pool of tears. Oh, the poor thing! She started to look around for help, and soon enough she saw a Mouse swimming along. Alice yelled as loudly as she could, “Mr. Mouse! Please help. Help please.”

The mouse gave a sudden leap.

In a few moments, the mouse calmed himself down. Alice started, “Good morning, Mr. Mouse. Really sorry to interrupt you.” For you see, by now, Alice had learned that people in Wonderland did not like to be interrupted much.

“No, no, dear.”, replied the mouse. “I am Thomas. I was just frightened that you were my wife. Which you statistically are not!”

“No, Mr. Thomas.”, assured Alice. “My name is Alice, and I’m stuck in this pool of my own tears. Can you please tell me what to do?”

“Yes, dear. I most definitely can. But before that, you will need to help me solve a very crucial problem.”, said the Mouse.

“I will do my best, Mr. Thomas.”, said Alice.

“Great! So, let me start with a secret that only a few people know. Can you keep a secret?”, he asked.

Alice was very good at keeping secrets. At least, she thought she was. In any case, she nodded vigorously.

“Here’s the secret: Nothing is certain in the wonderland. And when nothing is certain, everything is possible. And when everything is possible — there is only one way to talk about anything that is reasonable — and that is to talk about what is probable. Everything has a probability, and it is this distribution of probabilities that holds the secret to life, the universe, and everything.”

“Sorry to counter you, Mr. Thomas, but aren’t some things fixed? Like your name, or the shortest path from here to the shore?”, inquired Alice. For she never left any doubt until she fully understood everything, which was one of the things she was very proud of herself for.

“No, m’dear. These are just some events that have already happened. My name could have been anyone out of a million options, and the shortest distance would have depended on where you started out. And since there is no point in talking about the past, anything that is of vital importance is a probability distribution.”, replied Thomas the Mouse.

“That is indeed an interesting way to look at it.”, said Alice. “So Mr. Mouse, what is your crucial problem?”, because Alice was also in a hurry to get out of the pool and find the Duchess. She started feeling that everyone in the wonderland is always late and running.

“I need to find my students. They too got lost somewhere in this pool.”, started Thomas, “ — as you may be aware, I am a professor — and I had asked my students to do some research on human subjects and get back with their conclusions on probability today. We need to find Daphy the Duck, Duo the Dodo, Louie the Lory, Ellie the Eaglet, et al.”

Alice and the Mouse started searching for them, and, just as a formality, Alice asked Thomas the professor, “Mr. Mouse, Sir, would you tell me more about your students?”, for Alice knew very well that Computer Science professors revered formality.

Thomas jumped up at once, not because he was a mouse, but because of excitement! He stated:

“Well, first there’s Daphy the Duck. She is a third-month undergraduate. She’s the youngest of the lot, and the most quacky. One fine day, in her very first month, she came up to me and asked me to play a game! Do you know about the Monty Hall Problem, dear? Also, I forgot your name, dear. Can you remind me?”

Alice nodded and said “Yes, Mr. Thomas. I am Alice, and I know about it.”

“Great!”, continued the Mouse. “So, Daphy started playing the game with me. And to her utter surprise, I gave the correct answer! She asked me how I could get it right and how to explain the correct choice. That was when I told her about my last name.”

This led to a very awkward silence. Alice tried to match the mood on Thomas’s face, and play along. She learned that Computer Science professors also had a very curious habit — they assumed that people knew and were talking about them or their work. However, she contented herself by thinking about the beautiful Monty Hall problem and how it was explained using the Bayes Theorem. She asked about other students. The mouse was more than happy to introduce Duo the Dodo.

“Duo was a first-month master’s student. He was trying to understand the reasons behind the extinction of the Solitaire bird, in order to help their own species not get extinct.

One day during his undergrad, Duo the Dodo came running to me, yelling “Eureka! Eureka!”, and he pronounced that he had found the reason. He said that the reason was the deadly nightshade bush. Eating it was causing the solitaires to fight amongst each other and eventually kill each other.

Unfortunately, removing the nightshade bushes didn’t help, and the Dodos all died except Duo who was working with me in the lab.

We later delved deeper into what really happened. And it turns out that Duo’s reasoning was incorrect. While there was a Correlation between eating the nightshade and the fights, there was no Statistical Causality. It was their increasing population, leading to an increased demand for food. A reduced supply made them all very hungry, which was the cause behind both of the activities — them eating the nightshade in desperation, and them fighting with each other. Without the nightshade, they just fought with each other and died.

This led to Duo getting very serious about Causality. He read the famous book called Causality: Models, Reasoning, and Inference by Judea Pearl. He read about Causal Graphs and Causal Bayesian Networks, and how they can serve as a powerful quantitative tool to measure the unfairness in any dataset, and how to deal with it. He also read about some recent Transformer-based and RL-based approaches for learning the inherent causal structure from data.”

Alice had read about Bayesian Inference, and how we could update the posterior probability of a model’s parameters through the prior probability and a likelihood function using the Bayes’ Rule. Thomas also talked about some terms like d-separation and do-calculus, which Alice did not understand. But she made a mental note of reading about them when she got out of there.

“Then”, continued the Mouse, “there’s Ellie the Eaglet. Ellie’s my favorite student. She’s a Ph.D. student working on Statistical Modeling. And she loves paradoxes. Zeno’s, Liar’s, Barber’s, Grandfather’s, you name it and she’ll recite it to you with such zeal! And her favorite was the Simpson’s Paradox. Have you heard of it, m’dear?”

Alice shook her head.

“You’ll love it too. I taught it to Ellie, and now I’ll teach it to you.”, said the Mouse. Alice noticed that Computer Science professors always made a list of everything they did — almost like a log.

And then he ventured to describe Alice a situation which can much better be depicted through this figure:

Oops, sorry. This one:

Name/Day	Games Won	Games Played	Win Percentage
Alice, Day 1	7	8	87.5%
Alice, Day 2	1	2	50%
Alice, Total	8	10	80%
Thomas, Day 1	2	2	100%
Thomas, Day 2	5	8	62.5%
Thomas, Total	7	10	70%

“So,”, he said, “the Simpson’s Paradox occurs when different groups of data show a particular trend individually, but the trend reverses when the groups are combined.”

For instance, in Figure 7, even though Alice won a higher percentage of games on both Day 1 and Day 2, her overall winning percentage is lesser. Alice did not show it, but she couldn’t fully understand why it was called a “paradox”, because there was nothing here that felt odd. But then she was odd, she thought, and so only normal things would feel odd to her.

Thomas the Mouse also told Alice about Louie the Lorry, but she didn’t understand any of it at all — simply because she wasn’t paying any attention. She was thinking about why we should use the Bayesian approach at all. How it could be better than the usual supervised deep learning framework. Here’s what she could think of:

• Bayesian models would have far fewer parameters and would train faster, and inference would be very fast too.
• They would be inherently probabilistic, thereby being better at capturing the intrinsic nature of a lot of data.
• They would be more robust to adversarial attacks and fair across all sorts of things that could create bias.
• It would be much easier to talk about the confidence of the prediction since the outputs are direct probability estimates.
• Interpretation of the model would be very straightforward and meaningful.

Another interesting thing that happened simultaneously was that as Alice got to know about all of the Mouse’s students, slowly they all started appearing at different parts of the pool, and started swimming towards her. In just a few seconds, all of them were around Alice and Thomas. Thomas pointed the shortest path to the shore. Fortunately, all of them were very good at swimming.

Alice led the way, and the whole party swam to the shore.