The Mathematics Behind Machine Learning – Kashmir Reader – Kashmir Reader

Learning mathematics in machine learning is not about solving a maths problem, but rather understanding the application of maths in ML algorithms

Machine learning is the latest attempt in a long line to organise human knowledge and reason into a suitable form for the construction of machinery and the engineering of automated systems. As machine learning becomes more ubiquitous and its software packages become easier to use, it is natural and desirable that the low-level technical details are abstracted away and hidden from the practitioner. However, this poses the danger that practitioners do not know the limitations of designing decisions and thus machine learning algorithms.
Machine learning refers to the design of algorithms to automatically extract useful information from data. The emphasis is placed here on “automatic,” i.e., machine learning, which involves general methodology applied to many datasets and produces meaningful information. Machine learning consists of three concepts: data, models, and learning. Those interested in learning more about the magic behind successful machine learning algorithms are currently confronted with a daunting number of prerequisites of knowledge: programming languages, data analysis tools, large-scale computation, and the associated frameworks of mathematics and statistics and how machine learning builds on it.
At universities, introductory courses on machine learning tend to spend the early parts of the course covering some of these prerequisites. For historical reasons, courses in machine learning tend to be taught in the computer science department, where students are often trained in the first two areas of knowledge, but not so much in mathematics and statistics. Current manuals on machine learning mainly focus on algorithms and methods of machine learning and assume that readers have skills in mathematics and statistics.
Having taught graduate and post-graduate courses, we find that the gap between graduate/post-graduate mathematics and the mathematics level required to read a standard machine learning textbook is too big for many people. Machine learning builds upon the language of mathematics to express concepts that seem intuitively obvious but that are surprisingly difficult to formalise. Once formalised properly, we can gain insights into the task we want to solve.
One common complaint of students of mathematics around the globe is that the topics covered seem to have little relevance to practical problems. Mathematics defines the concept behind the ML algorithms and helps in choosing the right algorithm by considering accuracy, training time, the complexity of the model, number of features, etc. Computers understand data differently than humans; such as an image is seen as a 2D-3D matrix by a computer for which mathematics is required. Understanding the Bias-Variance trade-off helps us identify underfitting and overfitting issues that are the main issues in ML models.
Essential Mathematics for Machine Learning includes Linear algebra, Multivariate Calculus, Probability Theory, Discrete Mathematics, Statistics, Algorithm & Optimization, and others. I believe that machine learning is an obvious and direct motivation for people to learn mathematics. There is always a question in enthusiast learners what is the need for mathematics in machine learning, as computers can solve mathematics problems faster than humans. So, the answer is, that learning mathematics in machine learning is not about solving a maths problem, but rather understanding the application of maths in ML algorithms and their working.

The writer is Professor and Head, Division of Agricultural Statistics, Faculty of Horticulture, SKUAST-Kashmir

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