There is an overall skepticism in the job market with regard to machine learning engineers and their deep understanding of mathematics. The fact is, all machine learning algorithms are essentially mathematical frameworks — support-vector machines formulated as a dual optimization problem, principal component analysis as spectral decomposition filtering, or neural networks as a composition of successive non-linear functions — and only a thorough mathematical understanding will allow you to truly grasp them.
Various Python libraries facilitate the usage of advanced algorithms to simple steps, _e.g. _Scikit-learn library with KNN, K-means, decision trees, etc., or Keras, that lets you build neural network architectures without necessarily understanding the details behind CNNs or RNNs. However, becoming a good machine learning engineer requires much more than that, and interviews for such positions often include questions on, for example, the implementation of KNN or decision trees from scratch or deriving the matrix closed-form solution of linear regression or softmax back-propagation equations.
In this article, we will review some fundamental concepts of calculus — such as derivatives for uni- and multi-dimensional functions, including gradient, **Jacobian and Hessian **— to get you started with your interview preparation and, simultaneously, help you build a good foundation to successfully dive deeper into the exploration of mathematics behind machine learning, especially for neural networks.
These concepts will be demonstrated with 5 examples of derivatives that you should absolutely have in your pocket for interviews:
- Derivative of a Composed Exponential Function —f(x)= eˣ ²
- Derivative of a Variable Base and Variable Exponent Function — f(x)= xˣ
- Gradient of Multi-Dimensional Input Function — f(x,y,z) = 2ˣʸ+zcos(x)
- Jacobian of a Multi-Dimensional Function — f(x,y) = [2x², x √y]
- Hessian of a Multi-Dimensional Input Function — f(x,y) = x ²y³
Derivative 1: Composed Exponential Function
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