|
You can never step into the same river twice, said Heraclitus; no two events are ever exactly the same. Even Einstein thought it a miracle that we perceive order in the universe. But to survive, we must find order and make predictions. Otherwise, we would be unable to tell friend from foe, food from poison, and cheap from dear.
But how do we generalize from our unique and finite experiences? Somehow we have the capacity to connect the dots, induce from the scattered data we gather daily a general pattern from which we can extrapolate and forecast.
Connecting the dots is a complex undertaking. There can be infinite ways to do it, and it requires you to make assumptions either explicitly or implicitly. And if the assumptions don’t match the reality you are trying to model, your decisions can fall way off the mark. Consider this progression: 1, 2, 3. What comes next, 4 or 5? It depends on whether we are counting integers or primes. With all the possibilities, it is amazing that biological learning systems have generally arrived at the right learning laws and rules of extrapolating.
Learning Laws
A learning law is a set of rules or algorithms that determine how known instances or experiences become functional concepts or models. A law comprises two main components: how to generalize or extend from instances (modeling forms) and how to accommodate new and existing information (methods of determining parameters).
The methods you use in generalizing from specifics often contain many assumptions, sometimes implicit, about the real world.
The simplest and most common presupposition is that things exist or will continue in a straight-line relation. The black line in Figure 1 (page 26) is a linear projection of coal use, based on the years 1850 to 1910. Notice now, although the original data is finite, coal use for any of a continuum of dates can now be imputed. But as you can see, with the wrong model the forecasted values can differ greatly from the actual. I show a little later how this sort of feedback is invaluable to model improvement.
Just as important to survival as generalization is the ability to adapt so as to respond correctly to a changing world. Without this ability, we might get stuck with dead, outdated views, become an old dog with no new tricks or—even worse—an adult with a child’s view of the world. So we must value history as an indicator of the future but allow new understandings to replace old ways when appropriate.
In Figure 1, the purple line is a linear fit now based on data from 1850 to 1940. Compare the purple line to the red line, which forecasts one period ahead at a time on a rolling basis using a polynomial chosen so as to best fit the previous four data points. In certain circumstances, a regularly updated and flexible model can provide many advantages.
To accommodate new information, you need to decide whether only timely data is important and, if so, what timely is; whether some experiences are more salient than others; and whether only incremental change can occur or catastrophic revisions of views might be required.
FIGURE 1 All models connect the dots, but only some are responsive enough to forecast a changing world.
Stephen Grossberg of Boston University speaks to the need to define a learning law in any intelligent system meant to model reality:
“The selection of a learning law thus needs to be done in parallel with the design of the information processing architecture in which it lives. This proposal runs counter to beliefs that are still held in cognitive science and AI, wherein it is often thought that an information processing architecture can be designed first, and that learning can be tacked on later. Many examples now show that learning laws that might be suitable in one type of architecture might be the wrong laws for a different type of architecture. For example, the learning laws for sensory and cognitive processes,…are often computationally complementary to the learning laws for spatial and motor processes…”(Birth of a Learning Law INNS/ENNS/JNNS Newsletter, 21, 1-4, 1998).
As our data-mining software gets more complex, we often forget that selective learning laws are hidden in the algorithms and software we choose to use, such as the type of logistics function used in a neural network or the nature of the probability distribution used to calculate the value of derivatives.
The human brain’s success comes not from the speed at which it calculates (computers are much faster), but rather from the rightness and subtle appropriateness of the computations it makes and results it gets for the problem at hand. In any knowledge management problem, retrieval is the easiest part. Queries, such as key-word searches on the Internet, often bring unmanageably large results. It is the assimilation of the information that is complex and costly—so, getting exactly the right information is of major value.
Feedback—Knowing How You Are Doing
With any of these kinds of problems, it’s not only the initial data, but also feedback about your conclusions that gives the learning law the essential information needed to model, change, and adapt so as to offer the most appropriate answers.
We are just beginning to realize the great value of differing kinds of feedback, for example:
• Immediate user feedback in Internet shopping or Q&A systems—as with eHNC’s automated online query system, SelectResponse, where the appropriateness of answers is automatically improved
• Bottom-up feedback on top-down corporate plans—as with Adaytum Software’s planning, budgeting, and forecasting software, e.planning, where data and projections by front-line workers can be used by management to reevaluate strategies.
• A subject’s ongoing behavior—as with Orbital Software’s knowledge management software Organik, where the text and email individuals have viewed or answered in the past are used to more effectively give them what they want in the future.
Frank R. Wilson argues that the very evolution of the human brain was influenced by feedback from the evolving human hand. See his book The Hand: How Its Use Shapes the Brain, Language, and Human Culture (Pantheon Books, 1998).
Joeseph LeDoux argues in his book The Emotional Brain: The Mysterious Underpinnings of Emotional Life (Touchstone Books, 1998) that the human brain’s complex wiring delivers a wide-ranging variety of emotional feedback throughout its network. Emotions may very well not be ancillary to reason, but much to the contrary, offer the essential evaluative feedback needed for reason to operate successfully.
Modeling and Survival
When results in feedback are very different from expected or forecasted values, then it is certainly time to reevaluate your model. Today many corporate contingencies and uncertainties are being modeled with options theory. In the example that follows, you will see how the choice of the right model can determine the very survival of a corporation.
In modeling option prices, the commonly used Black-Scholes approach uses a normal distribution—the mathematical equivalent of presupposing that securities move in a random walk. Some traders, such as Christina Ray, prefer an exponential distribution, positing that securities have momentum. The exponential distribution has fatter tails (because when things with momentum get going out of normal ranges they really get going), and thus predicts extreme events are far more common than a normal distribution would foretell. (See Figure 2, page 26.) This model change makes a major difference in attributing value. For more details, see her book The Bond Market : Trading and Risk Management (Irwin Professional, 1992).
FIGURE 2 The exponential probability distribution models events with momentum—with fatter tails, extreme events are less rare than with a random walk or the normal distribution.
For example, in predicting hurricanes, Ray’s model is vastly more accurate. Extreme hurricanes are three times more likely than a random walk would indicate and, on top of that, they tend to occur in runs. Inaccurate modeling has led to tremendous underpricing of hurricane insurance, which is why so many Florida insurance companies folded recently after two very bad years in a row…and why many Florida homeowners can no longer get insurance at any price. Bad modeling assumptions directly hurt business. With tens of trillions of dollars at stake in outstanding contingent business claim contracts, getting these models right makes quite a big difference in who wins or loses.
Learning How to Learn
Let me give you an example of model updating now. Next issue, I’ll discuss how a learning law that accomplishes this kind of updating might look.
Lucy was two when she first visited Boston. The first lobsters she had ever seen were on the dinner table. “Bugs!,” she exclaimed. Her father explained that lobsters are much bigger, you can eat them, and so forth. Lucy smiled, “Lobster, like a bug only bigger.” Lucy clearly figured something out. With a little tutelage, the father hoped to update the child’s generalization—a lobster is a kind of bug—to better approximate the distinction adults use. With a little help from her father, Lucy may discover how adults use this term and others. We’ll see what happens next time she visits New England. And I’ll discuss next time what Lucy can teach us adults about model building.
Barry Grushkin (bgrushkin@dsslab.com) is the senior lab researcher at the DSS Lab (www.dsslab.com) founded by Erik Thomsen in Cambridge, Mass.
RESOURCESFeedback planning: Adaytum, e.planning Automated Q&A: eHNC, SelectResponse Knowledge management: Orbital Software, Organik Financial instrument valuing software: www.thi.com/de/financial_software/quant_cashflow_func.jhtml Neural Network: SPSS, Clementine |
|
|
|
| |||||||||||||||||||||||||||||||
