We live in a complex world with diverse people, firms, and governments whose behaviors aggregate to produce novel, unexpected phenomena. We see political uprisings, market crashes, and a never ending array of social trends. How do we make sense of it? Models. Evidence shows that people who think with models consistently outperform those who don't. And, moreover people who think with lots of models outperform people who use only one. Why do models make us better thinkers? Models help us to better organize information - to make sense of that fire hose or hairball of data (choose your metaphor) available on the Internet. Models improve our abilities to make accurate forecasts. They help us make better decisions and adopt more effective strategies. They even can improve our ability to design institutions and procedures. In this class, I present a starter kit of models: I start with models of tipping points. I move on to cover models explain the wisdom of crowds, models that show why some countries are rich and some are poor, and models that help unpack the strategic decisions of firm and politicians. The models covered in this class provide a foundation for future social science classes, whether they be in economics, political science, business, or sociology. Mastering this material will give you a huge leg up in advanced courses. They also help you in life. Here's how the course will work. For each model, I present a short, easily digestible overview lecture. Then, I'll dig deeper. I'll go into the technical details of the model. Those technical lectures won't require calculus but be prepared for some algebra. For all the lectures, I'll offer some questions and we'll have quizzes and even a final exam. If you decide to do the deep dive, and take all the quizzes and the exam, you'll receive a Course Certificate. If you just decide to follow along for the introductory lectures to gain some exposure that's fine too. It's all free. And it's all here to help make you a better thinker!
Linear Models
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来自 University of Michigan 的课程
模型思维
1136 个评分
从本节课中
Learning Models: Replicator Dynamics & Prediction and the Many Model Thinker
In this section, we cover replicator dynamics and Fisher's fundamental theorem. Replicator dynamics have been used to explain learning as well as evolution. Fisher's theorem demonstrates how the rate of adaptation increases with the amount of variation. We conclude by describing how to make sense of both Fisher's theorem and our results on six sigma and variation reduction. The readings for this section are very short. The second reading on Fisher's theorem is rather technical. Both are excerpts from Diversity and Complexity.
与讲师见面
Scott E. PageProfessor of Complex Systems, Political Science, and Economics
Center for the Study of Complex Systems
Hi, in this lecture, we're going to talk about prediction.
And what we're going to do is, we're going to go back and
look at some of the models we learned earlier in the class.
We're going to look at the category models we looked at, and
the linear models we looked at.
And we're going to show how those were in fact predictive models.
And how they enabled us to get estimates of something that was going to
happen in the real world.
So first, let's just talk about a basic predictive task.
Suppose I said to you, predict the height of the Saturn V rocket.
Now what you'd typically do is, you might think,
well, the Saturn V rocket is like blank, something else.
And if you thought of the Saturn V rocket like, let's say a water tower,
you might guess that it's 100 feet high.
Or alternatively, you might say the Saturn V rocket is like the Statue of Liberty,
and then you might guess that it's about 400 feet high.
Or you might even think the Saturn V rocket is like the Empire State Building,
and you might guess it's 1,000 feet high.
So different people are going to use different categories and
therefore make different predictions.
Now this idea that people put things in different categories,
we talked about before in terms of the phrase, lump to live.
To use these categories to make sense of the world.
And then making sense of the world literally is predicting.
So let's go back to the example used in class, about different food items.
Like apples, pears, cakes, pies, those sort of things, and
they all have different calories.
Well, if we just sort of think, how much calories do food have,
there's a lot of variation in there.
And we can compute the variation in total calories here, remember,
we got this massive number that the total variation's 53,000.
But when we think about things like bananas,
we think about them differently than cake.
We put them in different categories, and
these categories enable us to make better predictions.
So for example, we created a fruit category and
we created a dessert category.
And when we did that, we could then make predictions about how many calories fruits
have, and how many calories desserts have, and we reduce the variation.
So for example, our fruit had a mean of a hundred 100,
and our desserts had a mean of 300, then the variations were only 200 and 5,000.
And so what we got was, initial variation was 53,000.
But afterwards, we only had 5200 in variation left over, so
we explained a lot of the variation.
And we described that comes of R squared,
which is the percent of variation explained, and in this case, that was 90%.
So let me talk about, just to review what we did, let me talk about what this needs.
You create categories, these categories reduce variation.
The less variation you have, the better you are predicting.
If different people use different categorizations,
then they're going to make different predictions.
And that's what we want to think about in this set of lectures.
Not only how people create these categories and make predictions.
We want to think about accurate individual categorizations, and
we want to think about accurate collective categorizations, that's the idea.
But categories weren't the only way we thought about proving predictions.
Remember, we also talked about people using linear models.
Let's see how people can use a linear model to predict.
So remember, linear model, we just sort of say, Z = ax + by + cz + a constant.
And this z is called the dependent variable, and x, y, and
z are called independent variables.
And the idea is, x, y, and z vary, and they determine the value of Z.
So let's suppose I asked you to figure out how many calories there are in a sub.
Well, you could write a linear model of the calories in the sub.
You'd say that calories in the sub depends on the bun, the mayo, the ham, the cheese,
the onion, the tomato, all those sorts of things.
And you just decompose the total calories into all the things that comprise the sub.
Now, this is a very different approach than categorization.
Categorization would say, well, a sub is sort of like cake, and
cake has 400 calories, or a sub is like a banana, and a banana has 100 calories.
This is a different approach, it's a different model.
So what we're going to see is, different models can end up being useful.
But let's think about this just for a second.
You're going to make this assumption that the calories in the sub are just the sum
of the parts.
And sub calories are linear, there's no interactions in terms of calories.
So if we do this, we're going to get that the bun has possibly 300 calories.
The mayo has 200, the ham has 50, and so on, and we get a total of 665.
Now it's interesting, I had my students do this in a class I was teaching.
And we got this number, 665, and then we looked up how many calories were
in a sub from a local sub shop, and the answer was 683.
So our model was really, really accurate, which was cool.
So that's the idea I want in the back of your mind as we move forward.
The idea that you could reason by categories, and
people could have different categories.
You could reason by linear models, and people could have different linear models.
But we make these predictions, and these predictions have some level of accuracy.
In the case of categorical models, we think of that accuracy in terms of R
squared, the percentage of the variation explained.
In the case of linear models,
we do the same thing in terms of percentage of the variation explained.
When we try and understand the wisdom of crowds,
which is where we're going to go next, we're going to ask, sort of how much
variation is there in the crowd's predication, how far off is the crowd?
Okay, but a crowd, we want to think of it as, consists of people, and
those people have models, and those models can differ.
And the reason they can differ is because people use different categorizations,
people use different models.
Some people use linear models, some people might use Markov models,
some people might use percolation models.
In a set model diversity, this can end up being so useful, all right, thank you.
