> The Fundamental Limits of Machine Learning
Depends on the largely mathematical assumptions can bring to the data. What can be done with the variety of assumptions is illustrated with details beyond belief in the QA section of most research libraries.
For more, the OP has
> Almost all of the learning we expect our computers to do—and much of the learning we ourselves do —is about reducing information to underlying patterns, which can then be used to infer the unknown.
Ah, NOW I see! The OP has stated a relatively narrow problem.
E.g., consider arrivals at HN: Over each 30 minutes or so, they about have to be a sample path of a Poisson process. Why? The renewal theorem, as in W. Feller's second volume. Can say that without looking at "patterns" in the data, indeed, without looking at any data at all.
Then from knowing that the arrivals are a Poisson process, there is a nice stream of results can get right away, without the data and even more with the data. E.g., the sum of two independent Poisson processes is another Poisson process. Then more generally can have a continuous time, discrete state space Markov process subordinated to that or a related Poisson process. From that can have some, say, network queuing calculations good for capacity planning, optimization of capacity planning, stochastic optimal control, anomaly detection, etc. Have a good shot at using the strong law of large numbers and the martingale convergence theorem.
Can say nearly all of this, and more, without looking for "patterns" in the data or looking at the data at all. Again, looking at the data can say still more.
There's a lot in the QA section of the library!