The Math Skills that make Machine Learning easy (and how you can learn it)

So, I've been a data scientist for around 10 years and I've taught machine learning to many cohorts and bootcamps in different countries, so I've seen hundreds of students with different backgrounds struggle or excel at machine learning and data science. And I believe this one skill has more influence on what camp you will fall into than any other. The good news is that I think you can learn this skill regardless of your background, but of course it will be easier for some than for others. In this video I will try to show you how exactly to go about acquiring the skill, no matter your background, to make you a much better data scientist or machine learning engineer. Some of the bootcamps I taught at had fairly different syllabuses, so I was able to see what types of skills ended up producing better data scientists. What I would see often is that people memorize machine learning algorithms and learn how to use tools like scikit-learn and get really amazing accuracies in their projects, but then get total nonsense when trying to apply what they learned to the real world. The reason is that students will blindly use the tools without having a good intuition on what the algorithms are meant for and how they work. So they end up overfitting to their training data, which makes the algorithm completely fall apart when feeding it real world data. They don't understand why some models work for some problems but not others. That's why the one skill that will make machine learning insanely easy for you is mathematical intuition for certain concepts, in particular from statistics. This doesn't mean that you need to know all of math or be a math genius to become a good data scientist, although that would surely help. It means truly understanding the core mathematical concepts that most machine learning algorithms are built on instead of memorizing them. I will now give you a list of mathematical concepts that I consider to be essential for becoming a great data scientist or machine learning engineer, including what I consider to be the single most important concept in machine learning. I believe if you truly understand this concept, you will be better at machine learning than 95% of your peers. At the end of the video, I will share my favorite resources that I use to learn the most important math concepts for machine learning, completely for free. The most important mathematical branches for machine learning in my opinion are in order of importance statistics and probability, linear algebra, in particular if you want to get into neural networks, calculus, a few special concepts from machine learning. I believe that statistics is the most important branch because having a really good grasp on statistics will instantly make you 10 times better at machine learning and save you a ton of time by not picking the wrong algorithms for your problem. This does not mean that you need to know all of statistics, but that you get a good understanding and intuition for some core principles and ideas. While I always loved math, I actually used to hate statistics. But the good news is that when learning machine learning, I got over my fear of statistics and once this happened, my understanding of machine learning exploded. At the end of the video, I will share the free online resource I use to get over my fear of statistics. Statistical intuition will help you pick the right algorithm for the right problem and the data at hand. Accuracy isn't all that matters. Many problems can be solved with simple algorithms if you have a good intuition for what's needed. That will not only save you lots of time, but also make your model much more interpretable and the insights much more actionable, which in a business setting is sometimes the most important thing, and it will make your model much more generalizable and work better on unseen data. Additionally, if you truly understand the math behind your algorithms, you will have a very good understanding of what your hyperparameters do for each algorithm, which will help you fine-tune your model much more quickly than blindly searching the entire hyperparameter space, which again can lead to overfitting if you don't have enough data to cross-validate your hyperparameter search. And yes, you can tune too much, which will be obvious when your understanding of statistics improves. I do understand why math isn't taught more in many bootcamps. It's because it takes time and bootcamps are short, and they want you to get started with the tools quickly, sometimes to the detriment of your understanding. So usually it will be up to you to learn on your own, but it will be worth it, I promise. Before I share the list of concepts, I want to share a little trick with you. I want you to think about math a bit differently. Instead of just memorizing equations and formulas, try to understand what the formulas are trying to do. Very commonly, math or machine learning teachers will simply throw an equation on the screen and tell you, for example, this is the loss function for this algorithm, and simply expect you to accept it. Instead of just accepting the formula, I would try to ask myself, what is the point of this formula? What is it trying to do? You can even write it out in natural language. A good example might be linear regression. You're trying to find the line that best represents some data points. What does best even mean? In linear regression, best means that the points are as close to the line as possible. So if you try out different lines, what is the best line? One metric could be the vertical distance of the points to the line. How do we measure that? We could simply subtract the true value of y of a data point from the predicted value of y, which is the y value of the line at same value of x for that data point. In this case, y is the salary of a person, either actually measured by the data point or predicted by the regression line, and x is the experience of a person, for example in years. But if we want the distance from the line, truly we don't want negative values, we just want the distance. So we can just square the difference to make it always positive. What if we want to do that for all points? We sum up all the squares of the differences. That leads us to our formula. We are trying to minimize the sum of squared residuals, also called residual sum of squares or RSS. It's not about memorizing formulas, but trying to understand the purpose of the formula. There's often more than one way to solve a problem. This approach will also give you an intuition on what the different hyperparameters in different models stand for and thus help you fine-tune your models much better and pick the right model for the right problem. Mathematical formulas just help us communicate our goals with the computer. Minimizing the RSS is just the mathematical way of saying, I want the line to be close to the points, which allows us to put that into a computer program. Almost all formulas you might come across were thought up by a human trying to put an idea like that into formal mathematical language, which can be understood by a computer. Here my list of topics and concepts. Probability and statistics. Random variables. Probability distributions. Different types of plots for data and distributions and their interpretation. Populations and samples. And the law of large numbers. The mean, the median, and expected values, variance, and covariance. Correlation. The central limit theorem. And the normal distribution. The standard deviation, statistical significance, z-scores, and hypothesis testing. Specificity, sensitivity, and confusion matrices. The multiple comparisons problem and solutions, for example, Bonferroni correction. Conditional probability and Bayes theorem. Linear algebra. Vectors and matrices. Matrix operations. Addition, subtraction, multiplication, inverse, transpose. Matrix rank and linear independence. Calculation and meaning of basic trigonometric terms, like vector norms, cosine, and sine. Calculus, derivatives, and their meaning. Basic rules like the chain rule. Machine learning. Specific concepts. Lost functions. Gradient descent. Regularization. Truly understand the meaning of train, test, validation, set. Here your statistical intuition will help a lot. Truly and fully understand at least linear regression. Labels, weights, parameters, hyperparameters. Validation and cross-validation. Overfitting and underfitting. In my opinion, the single most important concept in machine learning. Truly understand bias and variance and the bias-variance trade-off. Your intuition here will be formed mostly by a deep intuition about statistics and statistical significance. The size and quality of your data set. Proper model selection and so on. This is truly at the core of being a good data scientist. If you want me to make a video on any specific topic from this list, please let me know in the comments. Also let me know if I forgot anything important. Here are the free resources I used to learn these skills from scratch. I will also leave links in the description. Khan Academy has amazing and very beginner-friendly content on statistics, linear algebra and calculus. Completely for free. I would start here. I will leave links in the description for machine learning specific topics. I then read the book An Introduction to Statistical Learning. Also available for free on the website of the authors, who also made an amazing video series based on the book, which is also available for free on YouTube. I will leave links to both in the description as well. The YouTube channel 3 Blue1Brown has amazing videos on some specific topics with truly incredible visuals that help you understand some of the more complicated concepts of math and machine learning. Like the central limit theorem, neural networks, calculus and probability distributions. In my opinion the single best math education content available on the internet. If you want to now dive into the most important machine learning algorithms or get a roadmap to how to learn machine learning, check out my videos on that on this channel. I will also leave links in the description. If you found this video helpful, share it with someone who you think might also like it and get started on one of the tutorials in the description or on this very channel. 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