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In [1,§3.2], David 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 of his day. (Chapter 3 in [1], titled “Statistical Models and Shoe Leather,” is also available in previously published form [2] here.)

In [1,§3.2], David 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 of his day. (Chapter 3 in [1], titled “Statistical Models and Shoe Leather,” is also available in previously published form [2] here.)

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. See this online lecture of his.)

1. Freedman D, Pisani R, Purves R. Statistics, 4th Edition. 4th edition. New York: W. W. Norton & Company; 2007.

2. Freedman DA. Statistical Models and Shoe Leather. Sociological Methodology. 1991;21:291-313. doi:10.2307/270939. Full text

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