Despite his image as a bloody tyrant, Genghis was also forward thinking. His empire had the first international postal system, invented the concept of diplomatic immunity, and even allowed women in its councils. But more importantly, the Mongols were also unprecedented in their religious tolerance.
I think it's much more interesting to live not knowing than to have answers which might be wrong. I have approximate answers and possible beliefs and different degrees of uncertainty about different things, but I am not absolutely sure of anything and there are many things I don't know anything about, such as whether it means anything to ask why we're here. I don't have to know an answer. I don't feel frightened not knowing things, by being lost in a mysterious universe without any purpose, which is the way it really is as far as I can tell.
This competition is unique among Kaggle contests in that there is a history of submissions from previous years. My idea was to model not only the probability of each team winning each game, but also the competitors’ submissions. Combining these models, I searched for the submission with the highest chance of finishing with a prize (top 5 on the leaderboard). A schematic of my approach is below. The three main processes are shaded in blue: (1) A model of the probability of winning each game, (2) a model of what the competitors are likely to submit, and (3) an optimization of my submission based on these two models.
Finally, I used these models to come up with an optimal submission by simulating the bracket and the competitions’ submissions 10,000 times. This essentially gave me 10,000 simulated leaderboards of the competitors and my goal was to find the submission that most frequently showed up in the top 5 of the leaderboard. I tried to use a general-purpose optimizer, but it was very slow and it gave poor results. Instead, I sampled pairs of probabilities from the posterior many times, and chose the pair that was in the top 5 the most times. If I had naively used the posterior mean as a submission, my estimated probability of being in the top 5 would have been 15%, while my estimated probability of for the optimized submission (with two entries) went up to 25%.
The competitors’ submission model was trained on 2015 data. To assess the quality of the model, I have plotted the simulated distribution of the leaderboard losses for 2016 and 2017 and compared to the actual leaderboards. 2016 seems well in line, but 2017 had more submissions with lower losses than predicted. For both years, the actual 5th place loss was right in line with what was expected.
“I very frequently get the question: ‘What’s going to change in the next 10 years?’ And that is a very interesting question; it’s a very common one. I almost never get the question: ‘What’s not going to change in the next 10 years?’ And I submit to you that that second question is actually the more important of the two — because you can build a business strategy around the things that are stable in time. … [I]n our retail business, we know that customers want low prices, and I know that’s going to be true 10 years from now. They want fast delivery; they want vast selection. It’s impossible to imagine a future 10 years from now where a customer comes up and says, ‘Jeff I love Amazon; I just wish the prices were a little higher,’ [or] ‘I love Amazon; I just wish you’d deliver a little more slowly.’
The vast majority of human beings dislike and even actually dread all notions with which they are not familiar... Hence it comes about that at their first appearance innovators have generally been persecuted, and always derided as fools and madmen.
But Trump’s statements don’t necessarily come from anywhere, lead anywhere or have a permanent reality beyond his wish to be liked at any given instant.
We’ve got this perverse situation in which the vast analytic powers of the entire world are being spent trying to understand a guy whose thoughts are often just six fireflies beeping randomly in a jar.
“We badly want to understand Trump, to grasp him,” David Roberts writes in Vox. “It might give us some sense of control, or at least an ability to predict what he will do next. But what if there’s nothing to understand? What if there is no there there?”
And out of that void comes a carelessness that quite possibly betrayed an intelligence source, and endangered a country.