Statistics For Machine Learning

Preface

Introduction to Statistics 

• Population and Sample
• Introduction to Random Variables
• Other variables
• Introduction to Descriptive Statistics
• Visualizations
• Conclusion

Descriptive Statistics

• Measures of Central Tendency
• Measures of dispersion
• The Strength of the relationship between variables
• Conclusion

Random Variables

• Random Variables
• Discrete Random Variables
• Continuous Random Variables
• Joint Distributions
• Independent Random Variables
• Marginal and Conditional Distributions
• Definition of Mathematical Expectation
• Properties of Mathematical Expectation
• Chebyshev’s Inequality
• Law of large numbers
• Conclusion

Probability

• Introduction
• Properties of probability
• Some other terminologies
• Conditional probability
• Bayes’s theorem
• Probability distributions
• Conclusion

Parameter Estimation

• Parameter estimation
• Point estimate – The mathematics way
• Sampling distributions
• Central Limit Theorem
• Estimators having bias component
• The variance of a point estimate
• Standard Error of Estimator
• Mean Squared Error of Estimator
• Methods to Determine Point Estimates
• Confidence Intervals
• Conclusion

Hypothesis Testing

• Hypothesis
• Hypothesis Testing
• Confidence Interval
• Types of Hypothesis
• Null Hypothesis
• Alternative Hypothesis
• P-Value
• Steps in hypothesis testing
• Use Case
• Z-test
• T-test
• One-sample T-test
• Two-sample T-test
• Paired T-test
• Chi-Square test
• Test of Goodnessoffit
• Independence test
• Conclusion

Analysis of Variance

• Introduction to ANOVA
• One-way ANOVA test
• Calculation of Mean Square due to Error
• Calculation of Mean Square due to Treatment
• Decision Rule
• Tukey test
• Two-way ANOVA
• Main Effects
• Interaction Effects
• Multivariate Analysis of Variance (MANOVA)
• Wilks’ Lambda test
• Lawley Hotelling Trace
• Pillai’s Trace
• Roy’s Largest Root
• Conclusion

Regression

• Simple Linear Regression
• Finding the Values of β0 and β1
• Standard Error
• Confidence Intervals
• Unimportant Variable
• Accuracy of Prediction
• Data Pre-processing
• Multiple Linear Regression
• Polynomial Regression
• Subset Selection Method
• Ridge Regression
• Lasso Regression
• ElasticNet Regression
• Logistic Regression
• Estimation of Parameters
• Understanding Residuals
• Patterns of Residuals
• Multicollinearity
• Conclusion

Data Analysis Using Python

• Pandas
• Importing and Reading a CSV Sheet
• Basic Exploration of Data
• Converting a Python Data Structure to Data Frame
• Numerical Description of a Data Frame
• Adding Conditions in Pandas
• Extending Extractions – loc and iloc
• Understanding the iloc() Function
• Understanding the loc() Function
• Tackling Null Values
• Concatenating Data Frames
• Merging Data Frames
• Left Join
• Right Join
• Outer Join
• Inner Join
• Reading and Writing Excel Sheets
• Exploring Groupby
• Binning in Pandas
• Pandas Series
• NumPy
• Creating Null Vector
• Indexing
• Reshaping a Numpy Array
• Generating Random Values Using Numpy
• Descriptive statistics using Numpy
• Mathematical Operations Using Numpy
• Other important features in Numpy
• Conclusion

Non-Parametric Statistics

• The test for randomness
• Sign Tests
• One-sample Sign Test
• Wilcoxon Test
• Mann Whitney Test
• Spearman Rank Correlation Test
• Kruskal Wallis test
• Conclusion

Introduction to Machine Learning

• Machine Learning
• Supervised Learning
• K-Nearest Neighbour
• Naive Bayes Theorem
• Decision trees
• Ensemble trees
• Support Vector Machines
• Python application
• Unsupervised Learning
• K-Means Clustering
• Hierarchical Clustering
• Principal Component Analysis
• Conclusion