Tags: #◇Computer Science #◇CSMODEL #◇Data Science #◇Machine Learning #◇Reviewer #◇Finals

CSMODEL Comprehensive Finals Reviewer

◇Overview

This reviewer synthesizes Statistical Modeling and Simulation (CSMODEL). Core areas include exploratory data analysis (EDA), data cleaning and preprocessing (imputation, normalization, one-hot encoding), linear and multiple regression (Ordinary Least Squares, $R^2$ , MSE, residual analysis), classification models (Logistic Regression, Decision Trees), unsupervised clustering (K-Means, Hierarchical Agglomerative Clustering, distance metrics: Euclidean, Manhattan, Cosine), Association Rule Mining (Apriori algorithm, Support, Confidence, Lift), Graph Data Modeling (NetworkX, centrality measures: Degree, Betweenness, Closeness, PageRank), and Linear Programming (Simplex method, SciPy optimization).

◇1. Master Metric & Modeling Matrix

Technique / Model	Core Objective	Key Mathematical Metrics	Libraries / Functions
Linear Regression	Predict continuous target $y$	$MSE = \frac{1}{n} \sum (y_i - \hat{y}_i)^2$ , $R^2 = 1 - \frac{SS_{res}}{SS_{tot}}$	`sklearn.linear_model.LinearRegression`
Logistic Regression	Binary classification probability	Sigmoid: $\sigma(z) = \frac{1}{1 + e^{-z}}$ , Binary Cross-Entropy	`sklearn.linear_model.LogisticRegression`
K-Means Clustering	Partition into $K$ spherical clusters	Inertia (WCSS) = $\sum_{k} \sum_{x \in C_k} \\|x - \mu_k\\|^2$	`sklearn.cluster.KMeans` (Elbow method)
Association Rules	Discover co-occurrence in transactions	$\text{Support}(X \implies Y) = \frac{freq(X \cup Y)}{N}$ $\text{Confidence} = \frac{freq(X \cup Y)}{freq(X)}$ $\text{Lift} = \frac{Support(X \cup Y)}{Support(X) \times Support(Y)}$	`mlxtend.frequent_patterns.apriori`
Graph Centrality	Quantify node importance in network	Degree, Betweenness (shortest paths passing through), PageRank	`networkx`
Linear Programming	Maximize/minimize objective subject to linear constraints	$\min \mathbf{c}^T \mathbf{x} \text{ s.t. } A \mathbf{x} \le \mathbf{b}, \mathbf{x} \ge \mathbf{0}$	`scipy.optimize.linprog`

◇2. Association Rule Mining Metrics

Support: Proportion of total transactions containing both $X$ and $Y$ .
Confidence: Conditional probability that a transaction contains $Y$ given that it contains $X$ ( $P(Y \mid X)$ ).
Lift: Ratio of observed co-occurrence to expected co-occurrence if independent:
- $\text{Lift} > 1$ : Positive correlation (items co-occur more than by chance).
- $\text{Lift} = 1$ : Independent (no relationship).
- $\text{Lift} < 1$ : Negative correlation (substitutes).

◇3. High-Yield Exam Checklist

Does an $R^2$ of 0.85 mean that 85% of the variance in $y$ is explained by the model? YES.
For K-Means, should features always be standardized (e.g. StandardScaler) beforehand? YES, because Euclidean distance is sensitive to feature scale!
In graph centrality, what does Betweenness Centrality measure? The fraction of all shortest paths in the graph that pass through a given vertex.
If Lift is less than 1, are the items positively associated? NO, Lift $< 1$ indicates negative association.
In Linear Programming, where does the optimal solution always lie? At a vertex (corner point) of the feasible polygon/polyhedron!

Previous Topic: ◇CSMATH2, ◇STT101A
Next Topic: None
Prerequisites: ◇Statistical Modeling, Regression, Clustering, Graph Analytics, Optimization
Cross-Curricular Connections: ◇CSINTSY

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