In [1,§3.2], [David Freedman](https://en.wikipedia.org/wiki/David_A._Freedman) suggests an essentially *negative* answer to your question. That is, **no (mere) statistical model or algorithm could solve John Snow's problem.** Snow's problem was to develop a critical argument supporting his theory that cholera is a water-borne infectious disease, against the prevailing [miasma theory](https://en.wikipedia.org/wiki/Miasma_theory) of his day. (Chapter 3 in [1], titled “Statistical Models and Shoe Leather,” is also available in previously published form [2] [here](http://psychology.okstate.edu/faculty/jgrice/psyc5314/Freedman_1991A.pdf).)
In these few short pages [1, pp.47–53], much of which is an extended quote from John Snow himself, Freedman argues that "what Snow actually did in 1853–54 is even more interesting than the fable [of the Broad Street Pump]." As far as marshalling *statistical evidence* (other preliminaries such as index case identification, etc., are discussed besides), Snow *exploited natural variation* to effect a truly remarkable quasi-experiment.
It turns out that at an earlier time, there was a vigorous competition among water supply companies in London, and this resulted in spatial mixing of the water supply that was (in Snow's words) "of the most intimate kind."
> The pipes of each Company go down all the streets, and into nearly all the courts and alleys. A few houses are supplied by one Company and a few by the other, according to the decision of the owner or occupier at that time when the Water Companies were in active competition.
>
> ...
>
> As there is no difference whatever in the houses or the people receiving the supply of the two Water Companies, or in any of the physical conditions with which they are surrounded, it is obvious that no experiment could have been devised which would more thoroughly test the effect of water supply on the progress of cholera than this, which circumstances placed ready made before the observer.
>
> —John Snow
Another critically important bit of 'natural variation' John Snow exploited in this quasi-experiment was that one water company had its water intake on the Thames *downstream of sewage discharges*, whereas the other had a few years before relocated its intake *upstream*. I'll let you guess which was which from John Snow's data table!
<pre>
| Number of | Cholera | Deaths per
Company | houses | deaths | 10,000 houses
----------------------------------------------------------
Southwark & Vauxhall | 40,046 | 1263 | 315
Lambeth | 26,107 | 98 | 37
Rest of London | 256,423 | 1422 | 59
</pre>
As Freedman notes witheringly,
> As a piece of statistical technology, [the above table] is by no means remarkable. But the story it tells is very persuasive. The force of the argument results from the clarity of the prior reasoning, the bringing together of many different lines of evidence, and the amount of shoe leather Snow was willing to use to get the data. [1, p.51]
One further point of natural variation exploited by Snow occurred in the *time* dimension: the abovementioned water intake relocation occurred *between* two epidemics, enabling Snow to compare the same company's water with and without added sewage. (Thanks to Philip B. Stark, one author of [1], for this info [via Twitter](https://twitter.com/philipbstark/status/900454312081477632). See [this online lecture](https://www.stat.berkeley.edu/~stark/SticiGui/Text/experiments.htm#cholera) of his.)
---
This matter also provides an instructive study in the contrast between *deductivism* and *inductivism*, as discussed in [this answer](https://stats.stackexchange.com/a/271091/41404).
1. Freedman D, Collier D, Sekhon JS, Stark PB. *Statistical Models and Causal Inference: A Dialogue with the Social Sciences.* Cambridge ; New York: Cambridge University Press; 2010.
2. Freedman DA. Statistical Models and Shoe Leather. *Sociological Methodology*. 1991;21:291-313. doi:10.2307/270939. [Full text](http://psychology.okstate.edu/faculty/jgrice/psyc5314/Freedman_1991A.pdf)