Part I
Data Science Fundamentals
Section 1.1
Introduction to Data Science
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Section 1.2
Data Fundamentals: Attributes & Objects
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Types of Data
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Data Quality
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Aggregation
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Sampling
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Dimensionality Reduction
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Section 1.8
Discretization & Binarization
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Attribute Transformation
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Section 1.10
Similarity & Dissimilarity
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Distance Metrics
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Similarity Metrics
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Section 1.13
Visualization (Jupyter Notebook)
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Part II
Hypothesis Testing
Section 2.1
Continuous Random Variables
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Central Limit Theorem
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Confidence Intervals
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t-Distribution
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Section 2.5
Hypothesis Testing (One Sample)
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Section 2.6
Hypothesis Testing (Two Samples)
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Effect Sizes & Cohen's d
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Mann-Whitney U, ANOVA, Correlations, ICC
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Markov & Chebyshev Inequalities
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Part III
High-Dimensional Geometry
Section 3.1
Geometry of High Dimensions
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Volume of the Unit Ball
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Sampling from the Unit Ball
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Section 3.4
Gaussians in High Dimensions
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Near Orthogonality
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Random Projections
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Johnson-Lindenstrauss Lemma
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Part IV
Matrix Decompositions & Dimensionality Reduction
Section 4.1
Singular Value Decomposition (SVD)
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Singular Values & Best-Fit Subspaces
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Another Interpretation of SVD
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Section 4.4
k-Rank Approximations
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To Center or Not to Center?
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Section 4.6
Principal Component Analysis (PCA)
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Effects of Feature Scale
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Part V
Machine Learning
Section 5.1
Introduction to Machine Learning
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Ordinary Least Squares (OLS)
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Logistic Regression
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Section 5.4
Performance Metrics
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Section 5.5
Training ML Models
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Cross Validation
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Regularization (Ridge, Lasso, ElasticNet)
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Hyperparameters
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Interpreting Linear Models
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Section 5.10
Decision Trees
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Decision Tree Ensembles (Bagging & Boosting)
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Part VI
Markov Processes
Section 6.1
Markov Chains
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Chapman-Kolmogorov Equation
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Stationary Distributions
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Section 6.4
Hidden Markov Models (HMM)
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Forward Algorithm (Likelihood)
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Viterbi Algorithm (Decoding)
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Forward-Backward / Baum-Welch (Learning)
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Section 6.8
Random Walks
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Markov Chain Monte Carlo (MCMC)
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Metropolis-Hastings & Gibbs Sampling
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Part VII
Time Series & Digital Signal Processing
Section 7.1
Time-Series Introduction
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Frequency Domain & Fourier Series
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Spectrograms
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Section 7.4
Digital Filters
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Finite Impulse Response (FIR)
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Infinite Impulse Response (IIR)
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Section 7.7
Time Series Segmentation
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Classical Time Series Features
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Spectral Features & MFCC
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Section 7.10
Deep Learning for Time Series
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CNNs for Time Series
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Sequences, Attention & Transformers
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