![]() ![]() Single variable world, and there are similarities Maximize your function, so how do you go about finding that? Well, this is perhaps the core observation in well, calculus, not just The values of the inputs that you should put in to Mountain in the entire area, and you're looking for the input value, the point on the xy-planeĭirectly below that peak, 'cause that tells you The height of this graph, and if you're looking to maximize it, basically, what you'reįinding is this peak, kind of the tallest It's something that hasĪ two-variable input that we're thinking of as the xy-plane, and then its output is So, first of all, on a conceptual level, let's just think about what it means to be finding the maximum Ways to basically apply these techniques, but really Then applying the techniques that I'm about to teach you to have the computer minimize that, and a lot of time and research has gone into figuring out Science of machine learning and artificial intelligenceĬomes down to, well, one finding this cost function and actually describing difficult tasks in terms of a function, but ![]() Of the flip side, right? Instead of finding the maximum, to minimize a certain function, and if it minimizes this cost function, that means that it'sĭoing a really good job at whatever task you've assigned it, so a lot of the art and Just need to tell the computer to Minimize, so that's kind What you do, is you find a function that basically tells it how wrong it is when it makes a guess,Īnd if you do a good job designing that function, you Is you assign something called a cost function to a task, so maybe you're trying to teach a computer how to understand audio or Another very common setting, more and more important these days, is that of machine learningĪnd artificial intelligence, where often what you do ![]() I'm about to teach you, that you can use to maximize this. That you maximize profits, you maximize the thing,Īnd if you have a function that models these relationships, there are techniques, which Values should you give to those choices such You raise for capital, all sorts of choices that you might make, and you wanna know what Where you're considering all the choices you can make, like the wages you give your employees or the prices of your goods, or the amount of debt that Profits of a company, maybe this is a function ![]() Represents something, so maybe it represents It's not just for fun and for dealing with abstract symbols, it's 'cause it actually Now this actually comes upĪll the time in practice 'cause usually when you're dealing with a multivariable function, Maximize it, and what this means is you're looking for the input points, the values of x and y andĪll of its other inputs, such that the output, f, is as Outputting a single number, a very common thing you wanna do with an animal like this is Maximize it. Multiple different input values and let's say it's just The divergence is the trace of the hessian matrix, which is related to its determinant but not quite the same (trace is the sum of the diagonal entries of a matrix).Ī multivariable function, something that takes in But after applying that test, you can find if it's a max or min just by using one partial derivative, so there's no need for the divergence anymore. So you need to apply the second derivative test first, with the hessian matrix's determinant. Saddle points can have nonzero divergence of the gradient. Once you've found an extremum, can you use the divergence of the gradient to determine whether it is a maximum or minimum? It's much easier to just let the gradient be 0. You were trying to find the maximum of something, and you do that by finding the maximum of something else? Okay. How do you find the maximum of the divergence of the gradient of the function? You can find the maximum of the divergence of the gradient of the divergence of the gradient of the function. I guess, but if you want to do that, you'll need to find the maximum of the divergence of the gradient of the function. ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |