Calculus is a huge topic, and the crossing of calculus in machine learning is also vast. but once you understand step-by-step it will be very easy for you. Also, in this article, I have provided a basic knowledge of differentiation and integration and completing them in python programming.
Also, calculus is a part of mathematics that deals with the rate of change of any quantity. It also called slope or tan at a particular moment of time.
Calculus is divided into 2 parts:-
- Integral calculus
2 dx=2x(integration)
- Differential calculus
ddx2x=2 (differentiation)
From the above two examples, we are clear that they are somehow opposite of one another. Further, check this out!!
Where f’(t) represents the differentiation of f(t). Hope you understood the above figure.
However, The word Calculus comes from Latin word meaning “small stone”,
Because it is like recognizing something by looking at small pieces.
Differential calculus – basically we can say, it divides something in small pieces and analyzes the change at instant or on average in independent axis i.e time, in most of the cases.
Integral calculus – Moreover, it joins or integrates the small pieces together and analyzes it to get how much total is there.
Additionally, I will recommend you to watch this video for complete understanding of the basics of calculus. What is calculus??
fundamentals of calculus : –
Theorem 1
Theorem 2
Remember That,Understanding calculus is somehow central to understanding machine learning! You can think of calculus as a set of tools that analyze the relationship between functions and their domain (valid inputs). In machine learning, we also find inputs which best match the data.
Let’s implement differentiation and integration functions in python via jupyter notebook.
Here is my Jupyter link-tap here to run the functions.
These packages are necessary for implementing the functions.
These are four pillars of machine learning without knowing these things you can’t move forward to the journey of a machine learning developer.
Calculus in used in many stuffs in machine learning-
1. Gradient computations
Gradients analyze how much change occurs in output if you perform an infinitesimal small change in input. Again, calculus plays a major role in computations.
2.Numerical Optimization
This is used to train models, given a dataset, that will be used to perform anything from inference to data generation and other related stuff.
3.Bayesian Methods using probability density functions
One must use integration to calculate these types functions.
4.Variational Inference and related techniques
The whole concept of variational inference is based on variational calculus, so it is another use of calculus.
5.Generative Adversarial Networks
Lot of theories are based on game theory, so again calculus is used here.
That’s all for this article, hope you enjoyed the reading.
Article by: Satyam Roy
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