MIT6036L01f 1

so we said we're trying to figure out what makes the hypothesis good and so far what we did was we said what makes a single prediction good so now I have to talk about what makes a whole how do we evaluate a whole hypothesis and so what makes the hypothesis great well the fact is that what makes a hypothesis good is its performance what we would really like is small loss on new data right so I always I always use studying in a class as my example for this right so um you might study really hard to get a hypothesis in your head that performs very well on your training data right so that's like learning the homework problems but the homework I tell you now it's the homework problems are not going to be on the test right so you have to learn a hypothesis then generalizes right you have to learn a hypothesis that's gonna perform well on questions that you have never seen before and so that's having a small loss on new data ok so good so we'd like to have a hypothesis that has small loss on new data but I don't know how to write down an objective function that a computer can optimize that says please optimize your performance on data but I don't know what it is all right so that's not easy thing I don't know how to write that problem down so generally speaking what we can do and and and this will not be the final answer this will be the answer that we work with for right now and then we'll sneak up on trying to make this more like that but in the short term a proxy for asking for hypothesis to have small loss on a new data is asking it to have small loss on the training day right so I'm writing this down as approximate but I want to say you know not the whole story this isn't really the right answer but it's part of the right answer and it's good enough for right now okay so small loss of training data this is a thing that we can least start to write down on the board right so we would say and so we might say well if I have n training examples I can define the training set error okay so this is a training scenario this is the sum over my training examples I said we had n training examples there XY pairs they come in pairs it's important to keep them together alright so we say okay how good is this hypothesis well I sum up over all my training examples and I say H of X I what is that H of X I that is the prediction that my hypothesis would make if it's given this input so this is the prediction that I make that's my guess and though Y is the actual and I say how sad am i that I made this prediction when that was the actual answer I add those all up divided by n that's my training error okay so we'll write write it this way so just so that we kind of establish the idea that there are these two quantities and they are not the same we can also talk about test error and our notation will be this and it's going to be the sum over some it's gonna look sort of like the same thing but it's summed over some let's say additional chunk of data right so you might have a big set of data you might say oh well these end-to-end plus and the data is data end-to-end prime are the ones that Oh n plus 1 to n prime if we're being careful line we're doing one indexing and plus 1 to n prime that's the data that my learning algorithm didn't get to see it's my testing data so really this is what I get to work with but but this is what I would like to optimize and and it'll be a theme in the class over and over we'll talk about how it is that optimizing this might or might not cause us to optimize that but we'll focus on the training error here for now yep yeah good ok so so that's a great question so what oh oh oh this oh yea that's a typo that's the reason why good I thought the question was why don't you could also ask why don't I average my training performance of my testing performance and the answer is well you could do that but that's not really a good estimate of how well you'll perform on the wild and brand-new data but no that was just a typo so thank you yes do please like I will make mistakes if I use slides it just becomes really boring and it doesn't give you a chance to find me catch me out so there aren't any slides no there's a there's written notes there's copious written notes there aren't any actual slides yeah ok so anyway if you find a mistake anywhere do let me know I love it when you find mistakes gives me faith that you were there