Essential Math for Data Science: Take Control of Your Data with Fundamental Linear Algebra, Probability, and Statistics

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Basic algebra — variables, coefficients, equations, functions — linear, exponential, logarithmic, and so on. Good question. I say this in the last chapter of my book, but what you learn has to be prioritized. I can’t tell you how a regular expression compiles but I am very good at using them. I have no reason to go down that rabbit hole unless my job suddenly needs me to become a subject matter expert on the ins and outs of regular expressions… and that’s the key determining factor! I am going to focus on technical data jobs that require expertise in at least one programming language. So in this article, I'll lay out some of the first steps you should take to learn Data Science or Machine Learning. The Three Pillars of Data Science and Machine Learning Source: wiplane.com

Figure 4 shows two different situations to illustrate the cross-entropy. On the left, you have two identical distributions P(x) (in blue) and Q(x) (in red). Their cross-entropy is equal to the entropy because the information of Q(x) is weighted according to the distribution of P(x), which is similar to Q(x). Each of these transformed probabilities is weighted by the corresponding raw probability. If an outcome occurs frequently, it will give more weight into the entropy of the distribution. This means that a low probability (like 0.1 in Figure 2) gives a large amount of information (3.32 bits) but has less influence on the final result. A larger probability (like 0.4 in Figure 2) is associated with less information (1.32 bits as shown in Figure 2) but has more weight. You also need to be able to quantify uncertainty, and this is an extremely valuable skill that is highly regarded at any data company. Knowing the chances of success in any experiment/decision is critical for all businesses. Basic statistics to know for Data Science and Machine Learning:Chapter 5: Linear Regression The chapter on linear regression is well-structured and covers key aspects, including finding the best-fit line, correlation coefficients, and prediction intervals. Including stochastic gradient descent is a valuable addition, providing readers with a practical understanding of the topic. Integrate and build upon incremental knowledge of calculus, probability, statistics, and linear algebra, and apply it to regression models including neural networks

However, in the right panel, P(x) and Q(x) are different. This results in a larger cross-entropy, because probabilities associated with a large quantity of information have a small weight, while probabilities associated with a small quantity of information have large weights.

Future Scope of Data Science

Understand techniques like linear regression, logistic regression, and neural networks in plain English, with minimal mathematical notation and jargon Everything was good until a few developers pointed out that there are too many resources and many of them are expensive. Python programming was the only branch that had a number of really good courses but it ends right there for beginners. However, vectors refer to various concepts according to the field they are used in. In the context of data science, they are a way to store values from your data. For instance, take the height and weight of people: since they are distinct values with different meanings, you need to store them separately, for instance using two vectors. You can then do operations on vectors to manipulate these features without losing the fact that the values correspond to different attributes.

In linear algebra, the information concerning a linear transformation can be represented as a matrix. Moreover, every linear transformation can be expressed as a matrix. Bits represent variables that can take two different states (0 or 1). For instance, 1 bit is needed to encode the outcome of a coin flip. If you flip two coins, you’ll need at least two bits to encode the result. For instance, 00 for HH, 01 for HT, 10 for TH, and 11 for TT. You could use other codes, such as 0 for HH, 100 for HT, 101 for TH, and 111 for TT. However, this code uses a larger number of bits on average (considering that the probability distribution of the four events is uniform, as you’ll see) What’s funny about academics and people with PhDs is they often are hyper specialized in their own rabbit holes. Many are much better writing papers on the HOW rather than the WHY. They can fill a whole whiteboard full of Greek symbols and impressive math equations, but handwave over the silliness it is an algorithm to separate pictures of hot dogs from dachshunds wearing hot dog costumes. What value does this create? So you have to take the academic gravitas with a grain of salt, but there are exceptionally talented academics of course who do valuable work. There are a few I look up to.And there you have it. Every beginner-level data science enthusiast should focus on these three pillars before diving into any core data science or ML courses. Resources to Learn Data Science and Machine Learning Fundamentals https://www.freecodecamp.org/news/data-science-learning-roadmap/ As you saw in Essential Math for Data Science and Essential Math for Data Science, being able to manipulate vectors and matrices is critical to create machine learning and deep learning pipelines, for instance for reshaping your raw data before using it with machine learning libraries. Chapter 1: Basic Mathematics and Calculus The book starts with an introduction to basic mathematics and calculus. This chapter serves as a refresher for those new to mathematical concepts. It covers topics like limits and derivatives, making it accessible for beginners while providing a valuable review for others. The use of coding exercises helps reinforce understanding. Machines only understand numbers. For instance, if you want to create a spam detector, you have first to convert your text data into numbers (for instance, through word embeddings). Data can then be stored in vectors, matrices, and tensors. For instance, images are represented as matrices of values between 0 and 255 representing the luminosity of each color for each pixel. It is possible to leverage the tools and concepts from the field of linear algebra to manipulate these vectors, matrices, and tensors.