Inferential Statistics Foundations

Inferential statistics is pivotal in statistical analysis and decision-making and involves drawing conclusions about populations based on samples. This module will introduce learners to the common probability distributions and how they are used to make statistically-sound, data-driven decisions.

• Experiments, Events, and Definition of Probability
• Introduction to Inferential Statistics
• Introduction to Probability Distributions (Random Variable, Discrete and Continuous Random Variables, Probability Distributions)
• Binomial Distribution
• Normal Distribution
• z-score

Estimation and Hypothesis Testing

Estimation involves determining likely values for population parameters from sample data, while hypothesis testing provides a framework for drawing conclusions from sample data to the broader population. This module covers the important concepts of central limit theorem and estimation theory that as vital for statistical analysis, and the framework for conducting hypothesis tests.

• Sampling
• Central Limit Theorem
• Estimation
• Introduction to Hypothesis Testing (Null and Alternative hypothesis, Typ-I and Type-II errors, alpha, critical region, p-value)
• Hypothesis Formulation and Performing a Hypothesis Test
• One-tailed and Two-tailed Tests
• Confidence Intervals and Hypothesis Testing

Common Statistical Tests

Hypothesis tests assess the validity of a claim or hypothesis about a population parameter through statistical analysis. This module introduces learners to the most commonly used hypothesis tests used in the world of Data Science and how to choose the right test for a given business claim depending on the associated context.

• Common Statistical Tests
• Test for one mean
• Test for equality of means (known standard deviation)
• Test for equality of means (Equal and unknown std dev)
• Test for equality of means (Unequal and unknown std dev)
• Test of independence
• One-way ANOVA

Intro to Supervised Learning – Linear Regression

Machine Learning (ML), a subset of Artificial Intelligence (AI), which focuses on developing algorithms capable of learning patterns in data and making predictions without being explicitly programmed to do so. Linear Regression is one of the most popular supervised ML algorithms that identifies the degree of linear relationship in data. This module introduces participants to ML and explores how linear regression can be used for predictive analysis.

• Introduction to learning from data
• Simple and Multiple Linear Regression
• Evaluating a regression model
• Pros and Cons of Linear Regression

Linear Regression Assumptions and Statistical Inference

The linear regression algorithm has a set of assumptions that need to be satisfied for the model to be statstically validated and to be able to draw inferences from it. This module walks participants through these assumptions, how to check them, what to do in case they are violated, and the statistical inferences that can be drawn based on the model’s output.

• Statistician vs ML Practitioner
• Linear Regression Assumptions
• Statistical Inferences from a Linear Regression Model

Logistic Regression

Logistic regression is a statistical modeling technique primarily used for modeling the probability of binary outcomes and it finds applications in various fields such as medicine, finance, and manufacturing. This module covers the theory behind the logistic regression model, how to asses its performance, and how to draw statistical inferences from it.

• Introduction to Logistic Regression
• Interpretation from a Logistic Regression model
• Changing the threshold of a Logistic Regression model
• Evaluation of a classification model
• Pros and Cons

Naive-Bayes, KNN

Bayes’ Rule is an important topic in probabilistic reasoning and decision-making. Distance metrics offer a handy way of measuring similarity between data points. This module provides participants with a comprehensive understanding of the Bayes Rule and Naive Bayes algorithm, its assumptions, different distance metrics, the K-Nearest Neighbors (KNN) algorithm, and its practical applications in classification and regression tasks.

• Bayes Rule
• Naive Bayes Algorithm
• Distance Metrics
• KNN Algorithm

Decision Tree

Decision trees are supervised ML algorithms that utilize a hierarchical structure for decision making and can be used for both classification and regression problems. This module dives into how a decison tree can be used to model complex, non-linear data and how to improve the performance of decision trees using pruning techniques.

• Introduction to Decision Tree
• How a Decision Tree is built
• Methods of pruning a Decision Tree
• Different impurity measures
• Regression Trees
• Pros and Cons

Bagging and Random Forest

Random forest is a popular ensemble learning technique that comprises of several decision trees, each using a subset of the data to understand patterns. The outputs of each tree are then aggregated to provide predictive performance. This module will explore how to train a random forest model to solve complex business problems.

• Introduction to Ensemble Techniques
• Bagging
• Random Forests

Boosting:

Boosting models are robust ensemble models that comprise of several sub-models, each of which are developed in a sequential manner to improve upon the errors made by the previous one. This modules will cover essential boosting algorithms like Adaboost and XGBoost that are widely used in the industry for accurate and robust predictions.

• Introduction to Boosting
• Bagging VS Boosting
• Different boosting techniques – AdaBoost, Gradient Boosting, XGBoost
• Stacking

Model Tuning

Model tuning is a crucial step in developing ML models and focuses on improving the performance of a model using different techniques like feature engineering, imbalance handling, regularization, and hyperparameter tuning to tweak the data and the model. This module covers the different techniques to tune the performance of an ML model to make it robust and generalized.

• K-fold cross validation
• Oversampling and Undersampling
• Regularization
• Data Leakage
• Hyperparameter Tuning
• GridSearchCV and RandomizedSearchCV

K-Means Clustering

K-means clustering is a popular unsupervised ML algorithm that is used for identifying patterns in unlabeled data and grouping it. This module dive into the working of the algorithm and the important points to keep in mind when implementing it in practical scenarios.

• Introduction to Clustering
• Types of Clustering
• K-means Clustering
• Importance of Scaling
• Silhouette Score
• Visual Analysis of Clustering

Hierarchical Clustering and PCA

Hierarchical clustering organizes data into a tree-like structure of nested clusters, while dimensionality reduction techniques are used to transform data into a lower-dimensional space while retaining the most important information in it. This module covers the business applications of hierarchical clustering and how to reduce the dimension of data using PCA to aid in visualization and feature selection of multivariate datasets.

• Hierarchical Clustering
• Cophenetic Correlation
• Introduction to Dimensionality Reduction
• Principal Component Analysis