Machine learning (ML) and artificial intelligence (AI) have been working hand-in-hand with the Internet to continue changing our lives. From the computer scientists working for big firms to 13-year-old smartphone users, there’s hardly anyone whose life has not been affected by these two concepts. And if you have heard the term “algorithm,” you too are already aware of an important aspect of ML and AI.
ML is a part of AI that implies the study of computer algorithms and their gradual improvements through data and continued experience. It is built on a mathematical prerequisite powered by the essential combination of statistics, discrete maths, calculus, probability, and linear algebra.
What Is the Use of Mathematical Calculations When Working with Modern Technologies?
Selecting the right algorithm includes careful consideration, accuracy, training time, use of parameters, understanding bias-variance trade offs, and correct computational formulas in programming. These parameters are built on the five pillars of ML, namely:
- Statistics
- Linear algebra
- Probability theory
- Calculus
- Discrete mathematics
Statistics
When studying mathematics in ML, you’ll find that statistics is ML’s backbone. Statistics, of course, is the practice or science of collecting and analyzing numerical data distributions to infer representations as a whole or as an individual sample.
Statistics allows us to draw logical conclusions from a data set. In AI, statistics is a key factor in determining the growth and development of an organization through two subcategories—descriptive and inferential statistics.
Descriptive Statistics
Descriptive statistics uses three basic measurement tools—mean, median, and mode. It also requires variability tools, including variance, standard deviation, and range.
Descriptive statistics data is used in ML to:
- Distribute and summarize the target population
- Implement the formula on small data sets
- Create pictorial representations to depict results
Inferential Statistics
Inferential statistics, meanwhile, uses measurement tools that include sampling distributions, variance analyses, and others.
The data obtained from inferential statistics is used in ML to:
- Make predictions about a population based on a given information sample
- Implement a formula on a large set of data
- Use probability scores to depict results
- Predict future outcomes by testing and comparing with previous data
- Make hypothetical predictions even beyond the available data
Calculus
This branch of mathematics helps balance the performance of algorithms. Calculus also helps in studying the rate at which quantities change, depending on the variables used. If you struggled a little with college calculus problems, you might be thankful to note that the concepts you learned are not necessary for ML. However, getting calculus online help can immediately get you refamiliarized with the study’s basic structures and principles.
Some necessary topics to ace the calculus arm of ML are:
- Differential and integral calculus
- Partial derivatives
- Vector-values functions
- Directional gradients
Within a few days of constructive learning, you might be able to learn and implement these concepts. It is also important to learn gradient descent derivatives and backpropagation in relation to neural networks.
Linear Algebra
This branch of computer mathematics concerns linear equations and their representations in vector spaces and matrices. It is commonly referred to as the “mathematics of the 21st century.”
Understanding the construction of linear equations is fundamental to developing central algorithms used to distribute and analyze collected data.
Here are some of the applications of linear algebra in ML:
- Loss functions
- Regularization
- Covariance matrices
- Singular value decomposition
- Matrix operations
- Symmetric matrices
- Eigenvalues and eigenvectors
- Support vector machine classification
With linear algebra, users can analyze massive amounts of data at once. Without the possibility of this large-scale operation, ML methods cannot be deployed, and complex data structures cannot be handled. With linear algebra, you can build better data intuition and kickstart your career in data science.
Probability
You have probably been encountering this topic since high school. Probability is the extent to which an event is likely to occur, measured by the ratio of favorable cases to the entire number of possible causes.
To conveniently work through ML, probability is important. It is calculated as:
P(Event) = Possible outcomes % Total Outcomes
The probability concepts you need to know are:
- Joint, marginal, and conditional probability
- Distributions of probability
- Density estimations
- Maximum likelihood estimations
- Regression with maximum likelihood
- Bayes theorem
In the real world, decisions have to be made based on incomplete information. It doesn’t matter, though, if your data is incomplete so long as the predictions you make from them are correct. Probability provides a way to quantify uncertainties and make meaningful predictions and possible outcomes. The applications of probability in ML include:
- Sampling
- Pattern recognition
- Training
- Developing specific algorithms
- Model evaluation
- Hyperparameter optimization
Discrete Maths
In this branch of mathematics, data is characterized by integers and is used to describe objects and problems in computer science. It may include computer algorithms, programming languages, and even software development. In ML, only the fundamentals of discrete maths are enough to get by, except you choose to go into certain domains like:
- Graphical models
- Combinatorial problems
- Structured predictions
Conclusion
It might take you a few months to learn the mathematical concepts above, but it is a joyride after that. The data science industry is growing exponentially every day, and this knowledge would prove very useful should you venture into a related career.
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