Welcome back. This is the third and final course of this specialization, where you learn about probability and statistics. I've found that when I have a framework of thinking about probability and statistics, it helps me to design learning algorithms and make them work better. And it helps me to better interpret the outputs of learning algorithms. It helps me figure out why we do certain things in learning algorithms and how to adapt it if it's not quite working. So I'm thrilled that once again, we have Luis as our instructor for this course. Thank you. Yes, I'm very excited about this course. I think intuition of probability is something very important in the scientist toolkit, because a lot of these algorithms can be phrased as a probability, right? For example, a spam detection algorithm outputs the probability that the email is spam. Yeah. And then in fact, having that framework in mind often lets you do a better job taking the output of a spam classifier or whatever learning algorithm you're using, and then better figure out what to do with that output downstream, such as do you put in a spam folder or do you show it to the user? And even for much more complex learning algorithms, this is a key part of understanding what to do with the output of that learning algorithm. Yes, absolutely. And the spam detection example calculates the probability of spam given the words or other features. And that's exactly one of the most important theorems in probability, which is Bayes' theorem. Bayes' theorem tells you how to calculate a probability given certain events. And so one of our favorite examples of Bayes' theorem is this example where there's an illness and it's kind of rare, and you want to take a test to see if you have it and you test positive. And it turns out that it's not that likely that you have the illness because of that application of Bayes' theorem. Yeah, as I was saying, a positive test for a rare illness leads you to conclude that you probably still do not have that rare illness, and that's Bayes' theorem. Yes. And then one more topic that we cover is maximum likelihood estimation, which happens all over machine learning. When you want to train models, you want to find the model that most likely gave you your data. So you want to maximize the probability that the model gave you your data. And a lot of models can be seen this way. In fact, we often use squared error, linear regression squared error. Why squared error and not the error to the power of four or the absolute value of the error? It turns out this comes out of maximum likelihood estimation. Exactly. That comes out of maximum likelihood estimation because you are picking points out of a Gaussian distribution. The Gaussian distribution is also something we learned, which is one of the most popular distributions out there. And that one has a square. And it turns out that when you take the logarithm, the square comes down and that's the square error. I think that's really cool because it lets you figure out if the data is kind of Gaussian squared error is appropriate. But then you think maybe this isn't quite the right model. It actually gives you better guidance and better intuition for when squared error will work and when you might want to consider something else. I find these math probability intuitions very hopeful for helping me try to figure out, do I need to change my cost function or fiddle with my machine learning in some way to make it better? Exactly. And even things like regularization can come out of probability because when you start considering the probability of the model, not just the data given the model, but the actual model, there's another Gaussian there for the coefficients and then the squares of the regularization term come out too. Yeah, I thought it was very cool that L2 regularization comes from a Gaussian distribution assumption on the parameters. But all this will make sense when you go through this course. And then one last very cool and important topic that this also covers is hypothesis testing. Yes, hypothesis testing is super important for things. Do you want to check if a drug is helpful by sampling population and testing them? Or if you want to see if a particular feature in a web page actually helped you increase the viewership? For that, you use hypothesis testing. Yeah, I find a lot of people, because we use terms like confidence and confidence interval, there's a popular interpretation of these terms that isn't quite the mathematically precise ones. And so through this course, you also learn precisely what those terms confidence, confidence interval, p-value mean so that when you see maybe a scientific conclusion reported in the news, or when you're generating your own scientific conclusion, you'd be able to be very precise and accurate about the use of these concepts. Yes, you'll be precise and accurate and also confident about your answers. And so on that note, I'm excited to have you jump into this third and final course of math for machine learning and data science. So please go learn about probability and statistics. And let's go on to the next video.