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Reading list

Machine Learning Basics for a Newbie
6 Steps of Machine learning Lifecycle Introduction to Predictive Modeling
Introduction to Exploratory Data Analysis & Data Insights Descriptive Statistics Inferential Statistics How to Understand Population Distributions?
Reading Data Files into Python Different Variable Datatypes
Probability for Data Science Basic Concepts of Probability Axioms of Probability Conditional Probability
Central Tendencies for Continuous Variables Spread of Data KDE plots for Continuous Variable Overview of Distribution for Continuous variables Normal Distribution Skewed Distribution Skeweness and Kurtosis Distribution for Continuous Variable
Central Tendencies for Categorical Variables Understanding Discrete Distributions Performing EDA on Categorical Variables
Dealing with Missing Values Understanding Outliers Identifying Outliers in Data Outlier Detection in Python Outliers Detection Using IQR, Z-score, LOF and DBSCAN
Sample and Population Central Limit Theorem Confidence Interval and Margin of Error
Bivariate Analysis Introduction
Covariance Pearson Correlation Spearman's Correlation & Kendall's Tau Correlation versus Causation Tabular and Graphical methods for Bivariate Analysis Performing Bivariate Analysis on Continuous-Continuous Variables
Tabular and Graphical methods for Continuous-Categorical Variables Introduction to Hypothesis Testing P-value Two sample Z-test T-test T-test vs Z-test Performing Bivariate Analysis on Continuous-Catagorical variables
Chi-Squares Test Bivariate Analysis on Categorical Categorical Variables
Multivariate Analysis A Comprehensive Guide to Data Exploration The Data Science behind IPL
Supervised Learning vs Unsupervised Learning Reinforcement Learning Generative and Descriminative Models Parametric and Non Parametric model
Machine Learning Pipeline Preparing Dataset Build a Benchmark Model: Regression Build a Benchmark Model: Classification
Evaluation Metrics for Machine Learning Everyone should know Confusion Matrix Accuracy Precision and Recall AUC-ROC Log Loss R2 and Adjusted R2
Dealing with Missing Values Replacing Missing Values Imputing Missing Values in Data Working with Categorical Variables Working with Outliers Preprocessing Data for Model Building
Understanding Cost Function Understanding Gradient Descent Math Behind Gradient Descent Assumptions of Linear Regression Implement Linear Regression from Scratch Train Linear Regression in Python Implementing Linear Regression in R Diagnosing Residual Plots in Linear Regression Models Generalized Linear Models Introduction to Logistic Regression Odds Ratio Implementing Logistic Regression from Scratch Introduction to Scikit-learn in Python Train Logistic Regression in python Multiclass using Logistic Regression How to use Multinomial and Ordinal Logistic Regression in R ? Challenges with Linear Regression Introduction to Regularisation Implementing Regularisation Ridge Regression Lasso Regression
Introduction to K Nearest Neighbours Determining the Right Value of K in KNN Implement KNN from Scratch Implement KNN in Python
Bias Variance Tradeoff Introduction to Overfitting and Underfitting Visualizing Overfitting and Underfitting Selecting the Right Model What is Validation? Hold-Out Validation Understanding K Fold Cross Validation
Introduction to Feature Selection Feature Selection Algorithms Missing Value Ratio Low Variance Filter High Correlation Filter Backward Feature Elimination Forward Feature Selection Implement Feature Selection in Python Implement Feature Selection in R
Introduction to Decision Tree Purity in Decision Tree Terminologies Related to Decision Tree How to Select Best Split Point in Decision Tree? Chi-Squares Information Gain Reduction in Variance Optimizing Performance of Decision Tree Train Decision Tree using Scikit Learn Pruning of Decision Trees
Introduction to Feature Engineering Feature Transformation Feature Scaling Feature Engineering Frequency Encoding Automated Feature Engineering: Feature Tools
Introduction to Naive Bayes Conditional Probability and Bayes Theorem Introduction to Bayesian Adjustment Rating: The Incredible Concept Behind Online Ratings! Working of Naive Bayes Math behind Naive Bayes Types of Naive Bayes Implementation of Naive Bayes
Understanding how to solve Multiclass and Multilabled Classification Problem Evaluation Metrics: Multi Class Classification
Introduction to Ensemble Techniques Basic Ensemble Techniques Implementing Basic Ensemble Techniques Finding Optimal Weights of Ensemble Learner using Neural Network Why Ensemble Models Work well?
Introduction to Stacking Implementing Stacking Variants of Stacking Implementing Variants of Stacking Introduction to Blending Bootstrap Sampling Introduction to Random Sampling Hyper-parameters of Random Forest Implementing Random Forest Out-of-Bag (OOB) Score in the Random Forest IPL Team Win Prediction Project Using Machine Learning Introduction to Boosting Gradient Boosting Algorithm Math behind GBM Implementing GBM in python Regularized Greedy Forests Extreme Gradient Boosting Implementing XGBM in python Tuning Hyperparameters of XGBoost in Python Implement XGBM in R/H2O Adaptive Boosting Implementing Adaptive Boosing LightGBM Implementing LightGBM in Python Catboost Implementing Catboost in Python
Different Hyperparameter Tuning methods Implementing Different Hyperparameter Tuning methods GridsearchCV RandomizedsearchCV Bayesian Optimization for Hyperparameter Tuning Hyperopt
Understanding SVM Algorithm SVM Kernels In-depth Intuition and Practical Implementation SVM Kernel Tricks Kernels and Hyperparameters in SVM Implementing SVM from Scratch in Python and R
Introduction to Principal Component Analysis Steps to Perform Principal Compound Analysis Computation of Covariance Matrix Finding Eigenvectors and Eigenvalues Implementing PCA in python Visualizing PCA A Brief Introduction to Linear Discriminant Analysis Introduction to Factor Analysis
Introduction to Clustering Applications of Clustering Evaluation Metrics for Clustering Understanding K-Means Implementation of K-Means in Python Implementation of K-Means in R Choosing Right Value for K Profiling Market Segments using K-Means Clustering Hierarchical Clustering Implementation of Hierarchial Clustering DBSCAN Defining Similarity between clusters Build Better and Accurate Clusters with Gaussian Mixture Models
Understand Basics of Recommendation Engine with Case Study
8 Ways to Improve Accuracy of Machine Learning Models
Introduction to Dask Working with CuML
Introduction to Machine Learning Interpretability Framework and Interpretable Models model Agnostic Methods for Interpretability Implementing Interpretable Model Understanding SHAP Out-of-Core ML Introduction to Interpretable Machine Learning Models Model Agnostic Methods for Interpretability Game Theory & Shapley Values
Introduction to Machine Learning Interpretability Framework and Interpretable Models model Agnostic Methods for Interpretability Implementing Interpretable Model Understanding SHAP Out-of-Core ML Introduction to Interpretable Machine Learning Models Model Agnostic Methods for Interpretability Game Theory & Shapley Values
Introduction to AutoML Implementation of MLBox Introduction to PyCaret TPOT Auto-Sklearn EvalML
Pickle and Joblib Introduction to Model Deployment
Deploying Machine Learning Model using Streamlit Deploying ML Models in Docker Deploy Using Streamlit Deploy on Heroku Deploy Using Netlify Introduction to Amazon Sagemaker Setting up Amazon SageMaker Using SageMaker Endpoint to Generate Inference Deploy on Microsoft Azure Cloud Introduction to Flask for Model Deploying ML model using Flask
Model Deployment in Android Model Deployment in Iphone

Mathematics for Data Science

Janvi Kumari
Janvi Kumari Last Updated : 14 Jun, 2024
4 min read

Introduction

Mathematics is a way of uncovering possible insights or information from data as done in the field of Data Science. So data science is a vast and a type of mixed field of statistical analysis, computer science, and domain expertise. But it is still the underlying mathematics used in data science that provides essential techniques and tools for working with, and learning from, data. In this article we will cover Math needed for Data Science So, let’s start.

Mathematics for Data Science

Overview

  • Master statistics concepts like mean, median, mode, variance, and standard deviation.
  • Understand inferential statistics for drawing conclusions beyond collected data.
  • Learn about probability, random variables, and probability distributions.
  • Gain insights into linear algebra, including vectors, matrices, and operations like transpose and inverse.
  • Explore calculus topics such as differentiation, integration, and their applications in data science.

Table of contents

Statistics

Statistics provide the first datagnosis for the data science Datagnosis that is a sophisticated tool and technique of Data Analysis, Data Collection, And Data Interpretation.

Let us now explore types of statistics.

Descriptive Statistics

This includes few parameters to consider. Let us explore them:

  • Mean: The MEAN is the arithmetic average of the data points and is defined as the SUM of all data points of the given list of data points divided by the number of data points.
  • Median: The middle value in the sorted data set.
  • Mode: The highest frequency in the data set.
  • Variance and standard deviation: variance and standard deviation tell us about the spread of our data points in the dataset. They are measures of the data dispersion.

Example:

Consider this the dataset: [2,3,4,4,5,5,7,9]

Mean= (2+3+4+4+5+5+7+9)/8 = 4.875

Median = 4.5 (4+5)/2

Mode= 4

Inferential Statistics

Inferential statistics provides conclusions that extend beyond the data collected in the study. The key idea here is this:

  • Statistical Hypothesis: To test assumptions regarding the population parameter.
  • Confidence Interval: Interval of values within the population parameter is expected to be found.
  • Regression Analysis: Relation between the dependent and independent variables are modeled.

Example:

Using a t-test to check if the mean of a sample is significantly different from a known population mean

Probability

Probability is a fundamental concept in data science, involving uncertainty and randomness. It is crucial for understanding events and outcomes in datasets. The Central Limit Theorem explains this. Probability distributions like binomial, Poisson, and normal are essential for modeling real-world phenomena and making statistical inferences.

Random Variables (Discrete & Continuous)

  • Discrete random variable: A random variable which can only take some certain, particular values is known as a discrete random variable. For example, the quantity of students in the classroom.
  • Continuous Random Variable: The value of a continuous random variable is immeasurable, example of continuous random variable is a waiting time between two phone calls. For Example: A person’s Height

Central Limit Theorem

The main general purpose theorem behind this is Central Limit Theorem (CLT) which states that the distribution of sum of large number of independent, identically distributed random variables approaches normal distribution with mean of distribution equal to summation of mean of random variables and variance equals to summation of variances of random variables.

Probability Distributions

The person should be also familiar with the other distributions because Binomial, Poisson, Normal Distribution.

Linear Algebra

Apart from these points, it is also useful for the data scientists to know about linear algebra that enables him to understand the data structure and algorithms underpinning machine learning.

  • Vectors: An ordered list of numbers.
  • Matrix: The set of numbers in an array, placed in rows and columns. Matrices are a whole new topic in itself and so if you are taking this tip, you better learn most of the matrices; like transpose, inverse, trace, determinant, and dot product of the matrix.

Calculus

Differential Calculus, Integral Calculus, Maxima, Minima, the Mean value theorem, the Product rule, the chain rule, Taylor’s series, derivatives, the gradients of matrices, Backpropagation, The Gradient Descent algorithm, higher-order derivatives, the Multivariate Taylor series, the Fourier transformations, area under the curve in Calculus.

Geometry and Graph

You need to know how to handle the angles, measurements, and proportions of regular objects and also be familiar with multiple types of plots.

Conclusion

Thus with this article, we can have an idea on what Mathematics is required to master data science. These were the few basic concepts of mathematics which is the backbone of data science one should have a really good understanding of these topics in order to learn data science.

Frequently Asked Questions

Q1. What is the role of statistics in data science?

A. Statistics provides tools for data analysis, including measures like mean, median, mode, variance, and standard deviation to understand and interpret data.

Q2. What are the types of statistics used in data science?

A. Descriptive statistics (mean, median, mode, variance, standard deviation) and inferential statistics (hypothesis testing, confidence intervals, regression analysis) are commonly used.

Q3. Why is probability important in data science?

A. Probability helps quantify uncertainty and randomness in data, essential for making predictions and decisions based on data analysis.

Janvi Kumari
Janvi Kumari

Hi, I am Janvi, a passionate data science enthusiast currently working at Analytics Vidhya. My journey into the world of data began with a deep curiosity about how we can extract meaningful insights from complex datasets.

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