If you are an aspiring data scientist, it is essential to be able to incorporate math into your workflows. Learning the basics of data science math will help you become a successful data scientist and understand how machines learn. This blog post will provide an overview on how to incorporate the core principles of math into your workflows, from probability and statistics to linear algebra and beyond.
Data Science Math: Data science utilizes probability and statistics in order to discover patterns or insights in a given dataset. By understanding the basics of probability and statistics, you will be able to develop and analyse models that can accurately interpret data. From understanding correlation to forecasting future trends, knowledge of probability and statistics will serve as your foundation for data science.
Linear Algebra: Linear algebra helps you understand relationships between multiple variables. For example, linear algebra can help you understand how changes in one variable affect all others. With knowledge of linear algebra, you can build predictive models that leverage these relationships among variables.
Calculus & Differential Equations: Calculus is used to create models that describe changes in a system over time. Differential equations are highly useful for model selection criteria related to dynamic systems such as population growth or predicting market trends over time. With calculus and differential equations, you can identify which model best represents the system being studied over time.
Optimization Techniques: Optimization techniques enable data scientists to uncover maximum or minimum values from any given set of parameters or inputs. This could be finding the MLE (maximum likelihood estimator) for a given set of input values or using gradient descent algorithms for training models with neural networks. Knowing optimization techniques allows aspiring data scientists to design their models in the most efficient way possible.
Graph algorithms, like many other algorithms applied in the field of computer science and artificial intelligence, allow us to solve complex problems by searching through a graph's data structure. A simple example of a graph algorithm, is one that can help you find the shortest path between two nodes in a graph. This type of algorithm could be useful in mapping applications when trying to determine the fastest route from point A to point B, or for any situation were looking for the quickest solution is necessary.
In addition to finding paths and routes, other graph algorithms have been developed that can help us with several different tasks. For instance, algorithms have been developed for routing protocols such as OSPF (Open Shortest Path First), which can be used in networking software systems when exchanging information between different networks over a distance. Graph algorithms are also utilized in mathematical optimization problems such as network flow models so they can identify optimal solutions more quickly and accurately than when using traditional mathematical methods.
For aspiring data scientists who are just getting started on their journey in machine learning, understanding graph theory & algorithms will inevitably become an important skill set they need to acquire along the way.
Vectors and matrices are fundamental mathematical objects used for various purposes such as storing datasets or representing linear functions in higher dimensions. Vectors represent a collection of numbers that can be thought of as a physical quantity such as displacement or velocity. Matrices are rectangular arrays containing multiple vectors which can be used to represent a system of linear equations. Linear equations such as y=mx+b can be represented by matrices which makes them easier to solve when dealing with large systems of equations.
Gradient descent is an important optimization algorithm used for finding local minima or maxima. It uses numerical methods to find the direction of steepest descent (or ascent) in multivariate calculus problems with multiple variables. This can be used for training a neural network or optimizing a cost function by taking ‘steps’ towards a global optimum solution.
Optimization algorithms are techniques that search for the best solution among multiple options using heuristics such as simulated annealing or genetic algorithms. These methods are useful when it is not possible to calculate an exact solution due to high computational complexity or limited search space. They are also useful when searching for nearby solutions rather than exact solutions since they may result in faster convergence than analytical methods like linear programming or dynamic programming.
Statistical Analysis is the practice of collecting data, analysing it, and drawing meaningful conclusions from it. With data sets that are large enough and properly collected, statistical analysis can be used to identify trends, predict future outcomes, and answer questions. It involves the use of descriptive statistics to summarize data, as well as inferential statistics which are used to interpret complex processes based on the available information.
Probability is a branch of mathematics that deals with the likelihood of certain events occurring. By studying probabilities, you can determine potential outcomes based on past data and information given. This knowledge can then be applied in machine learning algorithms such as Bayesian networks and deep neural networks in order to make accurate predictions about future outcomes.
Data Science is another important tool for ML applications. Data Science involves using Exploratory Data Analysis (EDA) techniques such as correlation analysis, regression modelling, parameter estimation, hypothesis testing and more in order to gain insight from large datasets. By leveraging these tools and techniques, you can identify patterns in data that can be used to make decisions or build models for machine learning applications.
Linear algebra and optimization techniques are essential elements of machine learning and data science. Aspiring data scientists need to understand the fundamentals of these two areas in order to undertake more advanced and powerful applications of machine learning. In this blog, we will explore the basics of vector and matrix operations, linear equations, gradient descent, optimization algorithms, regression techniques, convex and nonconvex functions, LaGrange multipliers, and quadratic programming.
Vectors and matrices are fundamental mathematical objects used for various purposes such as storing datasets or representing linear functions in higher dimensions. Vectors represent a collection of numbers that can be thought of as a physical quantity such as displacement or velocity. Matrices are rectangular arrays containing multiple vectors which can be used to represent a system of linear equations. Linear equations such as y=mx+b can be represented by matrices which makes them easier to solve when dealing with large systems of equations.
Gradient descent is an important optimization algorithm used for finding local minima or maxima. It uses numerical methods to find the direction of steepest descent (or ascent) in multivariate calculus problems with multiple variables. This can be used for training a neural network or optimizing a cost function by taking ‘steps’ towards a global optimum solution.
Optimization algorithms are techniques that search for the best solution among multiple options using heuristics such as simulated annealing or genetic algorithms. These methods are useful when it is not possible to calculate an exact solution due to high computational complexity or limited search space. They are also useful when searching for nearby solutions rather than exact solutions since they may result in faster convergence than analytical methods like linear programming or dynamic programming.
