September 17, 2014

Heuristic Haystacks and the Messy Lesson

As an admitted and self-styled parsimony skeptic, I was interested to see a discussion in the blogosphere on the seductive allure of simple explanations [1]. This was in the context of economic policy and decision-making, with Paul Krugman even offering an H.L. Mencken quote: "For every complex problem there is an answer that is clear, simple, and wrong" [2]. Yet while parsimony was never brought up, I suspect that hypotheses and arguments related to the efficient markets hypothesis were always somewhat in mind.

There are, of course, broader parallels between seductive simplicity and parsimony. As I have pointed out before, I find parsimony to be a overly-seductive null model [3]. The simplest explanation often leads us not to the truth, but to what is most conceptually consistent. In some cases (where theory is well-established) this works out well. Intuition in support of serendipity and serendipity in support of discovery is an unassuming (and often underplayed) pillar of science [4]. However, in cases where our intuitions get in the way of objective analysis, this becomes problematic. And this seeming exception is actually quite common. In a related manner, this brings up an interesting problem of the relationship between parsimony as a decision-making criterion and the epistomology of a scientific phenomenon.

An appalling lack of faith in both Occam's and Einstein's worldviews. More horrifying details in my Ignite! talk on the topic.

This relationship, or more accurately inconsistency, is due to argumentatively-influenced judgments on a naturalistic search space. Even in children, it is observed that argumentation is rife with confirmation bias and logically arguing to absurd positions [5]. While argumentation allows us to build hypotheses, it also gets us stuck in a conceptual minimum (my own ad-hoc phrase). In a previous post, I pointed to recent work on how belief systems and associated systems of argumentation can shape our perception of reality. But, of course, this cannot will the natural world to our liking. In fact, it often serves to muddy the conceptual and theoretical waters [6]. Therefore, you often have a conceptual gap unrelated to problem incompleteness which we will flesh out in the rest of this post.

The first point to be made here is that such an inconsistency introduces two biases that shape how we think about the simplest explanation, and more generally about what is optimal. First of all, can we even find the true simplest explanation? Perhaps the simplest possible statement that can be constructed cannot capture the true complexity of a given situation. This is particularly true when there are competing dimensions (or layers or levels) of complexity. Secondly, and particularly in the face of complexity, simplicity can often be a foil to deep understanding. Unfortunately, this is often conceptualized of and practiced upon in a destructive way, favoring simple and homogeneous mental models over more subtle ones.

How to dream of complex sheep....

In the parlance of decision-making theory, parsimony is consistent with the notion of good-enough heuristics. In the work of Gigerenzer [7], such heuristics are claimed to be nearly optimal when compared to formal analysis of a problem. This can also be seen with statistical prediction rules that outperform human judgments in a number of everyday contexts [8]. But is this a statement of problem "wickedness", or a statement of superiority with respect to human cognition? When compared to problems that require needle in a haystack criteria, fast and frugal heuristics (and hence parsimony) is severely lacking.

So complexity introduces a secondary bias at best and serves as a severe limitation to achieving parsimony at worst. One might expect that experimentally verifying a prediction made in conjunction with Occam's Razor requires finding an exact analytical solution. Finding this proverbial "needle in a haystack" requires both a multi-criterion, algorithmically-friendly heuristic solution in addition to a formal strategy that often defies intuition. Seemingly, the simple solution cannot keep up.

I found it! It was quick, but I was also quite lucky,

[1] The Simplicity Paradox. Stumbling and Mumbling blog, September 9 (2014) AND Krugman, P.   Simply Unacceptable. The Conscience of a Liberal blog, September 5 (2014).

[2] This is not to equate parsimony with methodological snake oil -- in fact, I am arguing quite the opposite. But I am merely pointing out that parsimony is an incomplete hypothesis for acquiring knowledge.

[3] For more, please see this Synthetic Daisies post: Alicea, B.   Argument from Non-Optimality: what does it mean to be optimal? Synthetic Daisies blog, July 28 (2013).

[4] Kantorovich, A.   Scientific Discovery: Logic and Tinkering. SUNY Press, Albany (1993).

[5] I say "even" in children even though the latter (logically arguing to absurd conclusions) is often expected from children. But we see these things in adults as well, and such is the point of argumentation theory. For more, please see: Mercier, H.   Reasoning Serves Argumentation in Children. Cognitive Development, 26(3), 177–191 (2011).

[6] Wolchover, N.   Is Nature Unnatural? Quanta Magazine, May 24 (2013).

[7] While there are likely other (and perhaps better) examples, I am using a reference cited in [1]: Gigerenzer, G.   Bounded and Rational. In "Contemporary Debates in Cognitive Science", R.J. Stainton eds. Blackwell, Oxford, UK (2006).

[8] lukeprog   Statistical Prediction Rules Out-Perform Expert Human Judgments. LessWrong blog, January 18 (2011).

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