![]() The optimization problem is to find the parameters that give the best value of a function known as the “objective function”. Since regression, root finding, and optimization are the same, the optimization problem is a good one to use to describe the twists in the road that affects all of these problems. Usually getting the exact answer to the wrong problem started out being a way to get an approximate answer to the right problem, but somewhere along the line we lost our way and forgot which problem we were actually trying to solve. We often have the choice to either solve the right problem approximately or the wrong problem exactly. This exemplifies a common pattern of error worth mentioning. Many businesses have ridden bad forecasts into bankruptcy not even realizing that they were depending on a linear model to describe a nonlinear environment. And lots of things are linear, but the most interesting things are not "steady as she goes!" Part of the data scientist's job is to know which cheats are being used and what the impact of those cheats are. For instance, in regression problems we usually restrict the model we fit to. Typically, there is some kind of a cheat. If you can solve any of these problems, you can solve all of them. ![]() Optimization is key to data science because it is how the enterprise transforms situational understanding into effective decisions. So root finding is key to situational understanding. Root finding is needed to find the boundaries of those regimes. One of the most important enterprise questions is whether we are operating in a stable regime or an unstable one. Those questions often take the form of "when does this thing equal that thing?" As a trivial example, a phase space in which a system operates is often partitioned into stable and unstable regimes. Root finding comes up in analytics where we answer enterprise questions. Regression is how the enterprise gets its situational awareness. It’s the bread-and-butter of data fusion. The regression problem is obviously crucial to data science. By some miracle of Nature, or cosmic mathematical coincidence, there are three extremely important problems that end up being identical:įinding the best fit to a set of data (regression),įinding the places where the a system or function takes a certain value (root finding),įinding the minimum or maximum value of a system or function (optimization). But we promised, at the end, to illuminate the distinctions between optimization and control, starting with a more structured discussion of optimization.
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