Generalization

And then finally, another generalization.

Expectation maximization is a probabilistic generalization of k means.

And gives you the best generalization error out of these options.

This is a fairly complicated generalization of what we just saw.

There is no generalization at all from one task to another in robotics.

Not surprisingly the best complexity is obtained where the generalization error is minimum.

However, in reality your generalization error on unknown data tends to go like this.

For a neural network our cost function is going to be a generalization of this.

It is now really easy to explain expectation maximization as a generalization of K means.

And this generalization holds true of the testimony of authorities as much as of anything else.

and Bob Mills put forward, 50 years ago, this generalization of Maxwell's equations, with a new symmetry.

If you really wish to understand this math, it happens to be just a generalization of the math

Insertion is another strategy. This is the generalization of the solution that I gave for the find the second best example before.

This question involves function generalization in reinforcement learning, and we're operating in a 1 dimensional environment of squares, and we're going to consider a state generalization function, that is a function that takes a state such as this and condenses it into some features to represent that state.

So a tempting generalization for a child, for an adult, for a computer is that any verb that can appear in the construction,

It's not clear, by the way, since then, whether that is an accurate generalization, but the data at the time seemed to support that.

Which is a generalization of the Vaucouleurs profile, that log of a surface brightness goes as the radius to the minus 1 over n.

The cost function we use for the neural network is going to be a generalization of the one that we use for logistic regression.

EM is a probabilistic generalization that also allows you to find clusters but also modifies the shapes of the clusters by modifying the covariance matrix.

So we need to be able to recover that. The generalization of albedo of course is color, but color as in the pigmentation of the object.

But if you see a couple of examples and you see a pattern there you can often extrapolate and get to a kind of broader generalization.

When you implement this, I recommend you use the function arctan2, which is the generalization of arctangent that takes as input delta y and then delta x.

And so we've now saved a way the test set and we can use the test set to measure or to estimate the generalization error of the model that was selected by this algorithm.

So what we want to be able to do is find some generalization, so that these 2 states look the same, and what I learn for this state that learning can transfer over into this state.

And the other generalization that I want to mention is that it's particularly hard for a society to make quote unquote good decisions when there is a conflict involving strongly held values that are good in many circumstances but are poor in other circumstances.

Namely, we chose the value of d that gave us the best possible performance on the test set, and so, the performance of my parameter vector theta five on the test set, that's likely to be to be an overly optimistic estimate of generalization error.

But before that I first want to tell you in the next set of videos, the first want to tell you about a generalization of the gradient descent algorithm that will make it much more powerful and I guess I will tell you about that in the next video.

In this world, agents and Bad guys can move one Square at a time, and the agent tries to get to the goal without encountering Bad guys, and for the agent to do that, which is a more useful generalization function to use over these states F or G?

Now let's be a little careful here because Sudoku as it's typically designed, doesn't really have an input size all the inputs are of the same size. but you can imagine a generalization of Sudoku where you have a bigger grid and maybe more symbols and the same kind of verification procedure works.

So, in addition to learning some useful geometry, the child has been exposed to some pretty sophisticated science strategies, like reduction, which is the art of transforming a complex problem into a simple one, or generalization, which is at the heart of any scientific discipline, or the fact that some properties are invariant under some transformations.

And the more general principal is that, once your parameters were fit to some set of data maybe the training set, maybe something else then the error of your hypothesis as measured on that same data set, such as the training error, that's unlikely to be a good estimate of your actual generalization error, that is, of how well the hypothesis will generalize to new examples.

learning as of this practice today, there are many people that will do that early thing that I talked about, and said that isn't such a good idea of selecting your model using the test set and they're using the same test set to report the error, as though selecting your degree of polynomial on the test set, and then reporting the error on the test set as though that were good estimate of generalization error.