Differences Between Machine Learning and Mathematics

Machine learning, often regarded as a powerful tool in data science, is fundamentally different from traditional mathematical modeling. Understanding these differences can help in deciding which method is most appropriate for a given problem. This article explores the distinctions between machine learning, specifically deep learning, and mathematical modeling, highlighting the advantages and limitations of each approach.

Machine Learning: Fitting Functions to Data

Machine learning, particularly deep learning, is a technique used to fit a function that maps input-output pairs. This function can have numerous parameters, providing it with a high degree of freedom to learn to predict outputs based on inputs. However, it is important to note that machine learning does not inherently understand the problem; it merely identifies non-linear correlations within the data. As a result, the machine learning model may not be able to learn a perfect function with no errors. Predictions made on unseen input data can lead to interpolation and extrapolation, both of which are challenging to control due to the high dimensionality of potential outcomes.

Limitations of Machine Learning

Machine learning models, especially deep learning architectures, face several limitations. They are susceptible to adversarial attacks, making them unsafe for critical systems. Additionally, while machine learning can perform well in many cases, it is not universally applicable. Theoretical mathematical bounds cannot be derived, which can limit its effectiveness in certain scenarios.

Mathematical Modeling: Precise Problem Solving

Mathematical modeling, on the other hand, is a precise and accurate method for problem solving. It is based on understanding the functional operations of the problem, rather than relying solely on finding correlations in the data as in machine learning. Mathematical models are typically written as a set of equations that represent the relationships between variables. This makes it easier to derive theoretical mathematical bounds, which can lead to more reliable results.

Limited Scope of Mathematical Modeling

While mathematical modeling is highly effective for problems with well-defined relationships, it may struggle with highly complex problems involving numerous variables or high levels of randomness, such as turbulence or stochastic systems. In such cases, the mathematical relationships can become too intricate to model accurately.

Machine Learning vs. Mathematics: A Cloud for Data Scientists

Many data scientists and machine learning practitioners might not immediately recognize the importance of mathematics in their work. In reality, while applied machine learning heavily relies on data, it is not entirely devoid of mathematical principles. Machine learning requires a combination of statistical and mathematical understanding, computer knowledge, and domain-specific expertise. Without these components, even the most sophisticated algorithms may not perform optimally.

Key Components of Machine Learning

For effective machine learning, several key components are essential:

Statistics/Mathematics: Understanding the implementation of algorithms and tuning them for better accuracy. Computer Knowledge: Implementing algorithms using tools like Python, R, or other programming languages. Domain Knowledge: Understanding the intricacies of the domain to interpret data correctly.

While it is true that many data scientists may not use advanced mathematics in their daily work, a foundational knowledge of statistics and mathematical concepts is crucial for developing and improving machine learning models.

Conclusion

Both machine learning and mathematical modeling have their strengths and weaknesses. Machine learning is highly versatile and can handle complex datasets, but it lacks the precision and theoretical boundaries provided by mathematical modeling. Conversely, mathematical modeling offers accuracy and predictability, but it may struggle with highly variable and stochastic systems.

To draw the best from both worlds, data scientists should leverage the strengths of both methodologies. Understanding the fundamental principles of both approaches can lead to more robust and reliable machine learning solutions.