Learning mathematics in machine learning is not about solving a mathematical problem, but rather about understanding the application of mathematics in ML algorithms
Machine learning is the latest in a long line of attempts to organize human knowledge and reason into a form suitable for building machines and engineering automated systems. As machine learning becomes more ubiquitous and its software packages become easier to use, it is natural and desirable that low-level technical details are abstracted and hidden from the practitioner. However, this presents the danger that practitioners are unaware of the limitations of design decisions and therefore of machine learning algorithms.
Machine learning refers to the design of algorithms to automatically extract useful information from data. The focus here is on “automatic”, i.e. machine learning, which involves a general methodology applied to many data sets and produces meaningful insights. Machine learning includes three concepts: data, models, and learning. Those interested in learning more about the magic behind successful machine learning algorithms are currently faced with an overwhelming number of knowledge prerequisites: programming languages, data analysis tools, large-scale computing, and the associated frameworks of mathematics and statistics and how machine learning builds on it.
In universities, introductory machine learning courses tend to spend the early parts of the course covering some of these prerequisites. For historical reasons, machine learning courses tend to be taught in the computer science department, where students are often trained in the first two knowledge areas, but not so much in math and statistics. Current machine learning textbooks mainly focus on machine learning algorithms and methods and assume that readers are proficient in math and statistics.
After teaching graduate and postgraduate courses, we find that the gap between graduate math and the level of math required to read a standard machine learning textbook is too big for many people. Machine learning draws on the language of mathematics to express concepts that seem intuitively obvious but are surprisingly difficult to formalize. Once properly formalized, we can have an overview of the task we want to solve.
A common complaint from math students around the world is that the topics covered seem to bear little relation to practical problems. Mathematics defines the concept behind ML algorithms and helps in choosing the right algorithm considering accuracy, training time, model complexity, number of features, etc. Computers understand data differently than humans; such that an image is seen as a 2D-3D matrix by a computer for which mathematics is necessary. Understanding the bias-variance trade-off helps us identify underfitting and overfitting issues that are major problems with ML models.
Essential math for machine learning includes linear algebra, multivariate calculus, probability theory, discrete math, statistics, algorithm and optimization, etc. I believe that machine learning is an obvious and direct motivation for people to learn math. Keen learners always wonder what is the need for math in machine learning because computers can solve math problems faster than humans. So the answer is that learning mathematics in machine learning is not about solving a mathematical problem, but rather about understanding the application of mathematics in ML algorithms and how they work.
The author is Professor and Head of Agricultural Statistics Division, Faculty of Horticulture, SKUAST-Kashmir
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