In this set of notes we’re going to

  1. Motivate the idea of Learning From Data
  2. Expand upon the idea of the Conditional Expectation Function

Matt Levine from Bloomberg can really write. Over the past couple of years, Matt has written multiple articles referencing Jim Simons, the former Harvard & MIT Mathematics Professor who founded the Hedge Fund Renaissance Technologies. Rentec, as its referred to, has a Medallion fund which under Jim’s leadership made a lot of money over the years:

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“Since 1988, his flagship Medallion fund has generated average annual returns of 66% before charging hefty investor fees—39% after fees—racking up trading gains of more than $100 billion” - https://www.wsj.com/articles/the-making-of-the-worlds-greatest-investor-11572667202?mod=hp_lead_pos8

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One thing I like about Matt’s account of Jim’s life is that it highlights the length of time it took for things to click for Jim. I think we often have an expectation that things should just click immediately. But sometimes, it takes time.

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“He launched his fund in 1978 and it didn’t really click until about 1990—but he absolutely achieved his dream of making money without doing anything.” - https://www.bloomberg.com/view/articles/2019-11-04/jim-simons-achieved-the-dream-of-not-managing-his-hedge-fund

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The other part I like is Matt’s description of Jim’s unique combination of skills.

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“Every obituary of Simons mentions the key facts of his career, which are that he knew (1) a lot about math and (2) nothing about finance. This seems to have been a very fruitful combination. If you can program computers to analyze data with, as it were, an open mind, they will pick out signals from the data that work, and then you can trade on those signals and make an enormous fortune. If you insist on the signals making sense to you, you will just get in the way.” - https://www.bloomberg.com/opinion/articles/2024-05-13/gamestop-is-back

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This a fantastic paragraph. It’s funny, yes. But it also lays out the essence of Jim’s strategy. He is arguably better at learning from data than the rest of us. Or at least better at assembling a team of really smart people to learn from data to make money than the rest of us.

For the rest of the semester, we’re going to grapple with the question of what does it mean to learn from data. How can we do it “better”? What does “better” even mean in this context? We’re certainly not going to get to the level of Jim and Renaissance technologies. But we’re at least going to get to somewhere.


A lot of learning from data problems can either be thought of as trying to estimate a either a Conditional Distribution, $\mathbb{p}_{Y\vert X}(y\vert x)$, or a Conditional Expectation Function, $\mathbb{E}[\text{Y} \vert X]$, given some data.

We’ll focus on the Conditional Expectation Function, although there is a lot of interesting work being done at the moment on conditional distributions regarding text which we’ll touch on at the end of the semester if we have time. https://youtu.be/YR9EztOF0R8?t=555

To motivate our interest in the Conditional Expectation Function, let’s say that you work at Apple and you are given some data about customer service phone calls regarding Apple’s credit card. Your project might be to estimate the expected number of phone calls on a given day of the month to help Apple better staff the phone lines. How might you go about this? How could you use your understanding of how to work with data and Python to generate some business insight?