Open course ware

Let's review what we've done this week. We've seen that the work done by a force along a trajectory from point A to point B can be written as the integral of the dot product of that force, with the displacement going from point A to point B, where we note that this integral, in general, must be evaluated over the particular path taken from point A to point B. This is called a line integral or a path integral. And again, I want to emphasize the value of this integral depends, in general, on the path taken from point A to point B. And you could understand that if you considered the fact that, in general, the force is a function of position. And so if you go along different paths, the dot product of the force with a particular path may be different, even though you're going between the same end points. Now, the reason that the work is a useful concept is that it allows us to understand how the kinetic energy of an object-- so the kinetic energy is 1/2mv squar...

DAVID SONTAG: So we're done with our segment on causal inference and reinforcement learning. And for the next week, today and Tuesday's lecture, we'll be talking about disease progression modeling and disease subtyping. This is, from my perspective, a really exciting field. It's one which has really a richness of literature going back to somewhat simple approaches from a couple of decades ago up to some really state of the art methods, including one which is in one of your readings for today's lecture. And I could spent a few weeks just talking about this topic. But instead, since we have a lot to cover in this course, what I'll do today is give you a high-level overview of one approach to try to think through these questions. The methods in today's lecture will be somewhat simple. They're meant to illustrate how simple methods can go a long way. And they're meant to illustrate, also, how one could learn something really significant abo...