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feat: Added advanced tabular feature engineering sections (NLP, Time-Series, Target Leakage, AutoFE)

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	<!DOCTYPE html>
	<html lang="en">

	<head>
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	<title>Feature Engineering Explorer</title>

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	<body>
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	<!-- Sidebar Navigation -->
	<aside class="sidebar" id="sidebar">
	<h1 class="sidebar__title">🛠️ Feature Engineering</h1>
	<nav>
	<ul class="nav__list" id="navList">
	<li><a href="#intro" class="nav__link">🎯 Introduction</a></li>
	<li><a href="#missing-data" class="nav__link">🔍 Missing Data</a></li>
	<li><a href="#outliers" class="nav__link">📊 Outliers</a></li>
	<li><a href="#scaling" class="nav__link">⚖️ Scaling</a></li>
	<li><a href="#encoding" class="nav__link">🔢 Encoding</a></li>
	<li><a href="#feature-selection" class="nav__link">🎯 Feature Selection</a></li>
	<li><a href="#imbalanced-data" class="nav__link">⚖️ Imbalanced Data</a></li>
	<li><a href="#eda" class="nav__link">📈 EDA Overview</a></li>
	<li><a href="#feature-transformation" class="nav__link">🔄 Feature Transformation</a></li>
	<li><a href="#feature-creation" class="nav__link">🛠️ Feature Creation</a></li>
	<li><a href="#dimensionality-reduction" class="nav__link">📉 Dimensionality Reduction</a></li>
	<li><a href="#text-data" class="nav__link">📝 Text Data (NLP)</a></li>
	<li><a href="#time-series" class="nav__link">⏳ Time-Series</a></li>
	<li><a href="#target-leakage" class="nav__link">⚠️ Target Leakage</a></li>
	<li><a href="#automated-fe" class="nav__link">🤖 Automated FE</a></li>
	</nav>
	</aside>

	<!-- Main Content -->
	<main class="content" id="content">
	<!-- ============================ 1. INTRO ============================ -->
	<section id="intro" class="topic-section">
	<h2>Introduction to Feature Engineering</h2>
	<p>Feature Engineering is the process of transforming raw data into meaningful inputs that boost
	machine-learning model performance. A well-crafted feature set can improve accuracy by 10-30% without changing
	the underlying algorithm.</p>

	<div class="info-card">
	<strong>Key Idea:</strong> 💡 Thoughtful features provide the model with clearer patterns, like lenses
	sharpening a blurry picture.
	</div>

	<!-- Canvas Visual -->
	<div class="canvas-wrapper">
	<canvas id="canvas-intro" width="600" height="280"></canvas>
	</div>

	<div class="code-block" style="margin-top: 20px;">
	<div class="code-header">
	<span>setup.py - Pandas Basics</span>
	<button class="copy-btn" onclick="copyCode(this)">Copy</button>
	</div>
	<pre><code>import pandas as pd
	import numpy as np

	# Load the dataset
	df = pd.read_csv('housing_data.csv')

	# Inspect raw data types and missing values
	df.info()

	# View summary statistics
	display(df.describe())</code></pre>
	</div>
	</section>

	<!-- ====================== 2. HANDLING MISSING DATA ================== -->
	<section id="missing-data" class="topic-section">
	<h2>Handling Missing Data</h2>
	<p>Missing values come in three flavors: MCAR (Missing Completely At Random), MAR (Missing At Random), and MNAR
	(Missing Not At Random). Each demands different treatment to avoid bias.</p>

	<!-- Real-world Example -->
	<div class="info-card">
	<strong>Real Example:</strong> A hospital's patient records often have absent <em>cholesterol</em> values
	because certain tests were not ordered for healthy young adults.
	</div>

	<!-- Controls -->
	<div class="form-group">
	<button id="btn-mean-impute" class="btn btn--primary">Mean Imputation</button>
	<button id="btn-median-impute" class="btn btn--primary">Median Imputation</button>
	<button id="btn-knn-impute" class="btn btn--primary">KNN Imputation</button>
	</div>

	<!-- Canvas -->
	<div class="canvas-wrapper">
	<canvas id="canvas-missing-data" width="800" height="500"></canvas>
	</div>

	<!-- Callouts -->
	<div class="callout callout--insight">💡 Mean/Median work best when data is MCAR or MAR.</div>
	<div class="callout callout--mistake">⚠️ Using mean imputation on skewed data can distort distributions.</div>
	<div class="callout callout--tip">✅ Always impute <strong>after</strong> splitting into train and test to avoid
	leakage.</div>

	<div class="info-card" style="margin-top: 20px; border-left-color: #9900ff;">
	<h3 style="margin-top: 0; color: #9900ff;">🧠 Under the Hood: Imputation Math</h3>
	<p><strong>KNN Imputation</strong> predicts missing values by finding the $k$ closest neighbors using a
	distance metric like Euclidean distance. For two samples $x$ and $y$ with $n$ features, ignoring missing
	dimensions:</p>
	<div
	style="background: rgba(0,0,0,0.2); padding: 15px; border-radius: 8px; text-align: center; margin: 15px 0; font-size: 1.1em; color: #e4e6eb;">
	$$ d(x, y) = \sqrt{\sum_{i=1}^{n} w_i (x_i - y_i)^2} $$
	</div>
	<p style="margin-bottom: 0;">Once the $k$ neighbors are found, their values are averaged (or weighted by
	distance) to fill the missing slot. This preserves local cluster distributions better than global mean
	imputation.</p>
	</div>

	<div class="code-block" style="margin-top: 20px;">
	<div class="code-header">
	<span>missing_data.py - Scikit-Learn Imputers</span>
	<button class="copy-btn" onclick="copyCode(this)">Copy</button>
	</div>
	<pre><code>from sklearn.impute import SimpleImputer, KNNImputer

	# 1. Simple Imputation (Mean/Median/Most Frequent)
	# Good for MCAR (Missing Completely At Random)
	mean_imputer = SimpleImputer(strategy='mean')
	df['age_imputed'] = mean_imputer.fit_transform(df[['age']])

	# 2. KNN Imputation (Distance-based)
	# Good for MAR (Missing At Random) when variables are correlated
	knn_imputer = KNNImputer(n_neighbors=5, weights='distance')
	df_imputed = knn_imputer.fit_transform(df)

	# Note: Tree-based models like XGBoost can handle NaNs natively!</code></pre>
	</div>
	</section>

	<!-- ======================= 3. HANDLING OUTLIERS ===================== -->
	<section id="outliers" class="topic-section">
	<h2>Handling Outliers</h2>
	<p>Outliers are data points that deviate markedly from others. Detecting and treating them prevents skewed
	models.</p>

	<div class="form-group">
	<button id="btn-detect-iqr" class="btn btn--primary">IQR Method</button>
	<button id="btn-detect-zscore" class="btn btn--primary">Z-Score Method</button>
	<button id="btn-winsorize" class="btn btn--primary">Winsorization</button>
	</div>

	<div class="canvas-wrapper">
	<canvas id="canvas-outliers" width="600" height="300"></canvas>
	</div>

	<div class="callout callout--insight">💡 The IQR method is robust to non-normal data.</div>
	<div class="callout callout--mistake">⚠️ Removing legitimate extreme values can erase important signals.</div>

	<div class="info-card" style="margin-top: 20px; border-left-color: #9900ff;">
	<h3 style="margin-top: 0; color: #9900ff;">🧠 Under the Hood: Outlier Math</h3>
	<p><strong>Z-Score</strong> measures how many standard deviations $\sigma$ a point is from the mean $\mu$. It
	assumes the data is normally distributed:</p>
	<div
	style="background: rgba(0,0,0,0.2); padding: 15px; border-radius: 8px; text-align: center; margin: 15px 0; font-size: 1.1em; color: #e4e6eb;">
	$$ z = \frac{x - \mu}{\sigma} \quad \text{(Threshold: } \|z\| > 3 \text{)} $$
	</div>
	<p style="margin-bottom: 0;"><strong>IQR (Interquartile Range)</strong> is non-parametric. It defines fences
	based on the 25th ($Q1$) and 75th ($Q3$) percentiles: $[Q1 - 1.5 \times \text{IQR},\ Q3 + 1.5 \times
	\text{IQR}]$. <em>Winsorization</em> caps values at these percentiles instead of dropping them.</p>
	</div>

	<div class="code-block" style="margin-top: 20px;">
	<div class="code-header">
	<span>outliers.py - Z-Score and Winsorization</span>
	<button class="copy-btn" onclick="copyCode(this)">Copy</button>
	</div>
	<pre><code>import numpy as np
	from scipy import stats

	# 1. Z-Score Method (Dropping Outliers)
	z_scores = np.abs(stats.zscore(df['income']))
	# Keep only rows where z-score is less than 3
	df_clean = df[z_scores < 3]

	# 2. IQR Method (Winsorization / Capping)
	# Capping at 5th and 95th percentiles to retain data points
	lower_limit = df['income'].quantile(0.05)
	upper_limit = df['income'].quantile(0.95)

	df['income_capped'] = np.clip(df['income'], lower_limit, upper_limit)</code></pre>
	</div>
	</section>

	<!-- ========================== 4. SCALING ============================ -->
	<section id="scaling" class="topic-section">
	<h2>Feature Scaling</h2>
	<p>Algorithms that rely on distance, like KNN, demand comparable feature magnitudes.</p>

	<div class="form-group">
	<button id="btn-minmax" class="btn btn--primary">Min-Max Scaling</button>
	<button id="btn-standardize" class="btn btn--primary">Standardization</button>
	<button id="btn-robust" class="btn btn--primary">Robust Scaler</button>
	</div>

	<div class="canvas-wrapper">
	<canvas id="canvas-scaling" width="600" height="300"></canvas>
	</div>

	<div class="info-card" style="margin-top: 20px; border-left-color: #9900ff;">
	<h3 style="margin-top: 0; color: #9900ff;">🧠 Under the Hood: Scaling Math</h3>
	<p><strong>Min-Max Scaling (Normalization)</strong> scales data to a fixed range, usually $[0, 1]$:</p>
	<div
	style="background: rgba(0,0,0,0.2); padding: 15px; border-radius: 8px; text-align: center; margin: 15px 0; font-size: 1.1em; color: #e4e6eb;">
	$$ X_{norm} = \frac{X - X_{min}}{X_{max} - X_{min}} $$
	</div>
	<p><strong>Standardization (Z-Score Scaling)</strong> centers the data around a mean of 0 with a standard
	deviation of 1. It does not bound data to a specific range, handling outliers better than Min-Max:</p>
	<div
	style="background: rgba(0,0,0,0.2); padding: 15px; border-radius: 8px; text-align: center; margin: 15px 0; font-size: 1.1em; color: #e4e6eb;">
	$$ X_{std} = \frac{X - \mu}{\sigma} $$
	</div>
	<p style="margin-bottom: 0;"><strong>Robust Scaling</strong> uses statistics that are robust to outliers, like
	the median and Interquartile Range (IQR): $X_{robust} = \frac{X - \text{median}}{Q3 - Q1}$.</p>
	</div>

	<div class="code-block" style="margin-top: 20px;">
	<div class="code-header">
	<span>scaling.py - Scikit-Learn Scalers</span>
	<button class="copy-btn" onclick="copyCode(this)">Copy</button>
	</div>
	<pre><code>from sklearn.preprocessing import MinMaxScaler, StandardScaler, RobustScaler

	# 1. Min-Max Scaler (Best for Neural Networks/Images)
	minmax = MinMaxScaler()
	df[['age_minmax', 'income_minmax']] = minmax.fit_transform(df[['age', 'income']])

	# 2. Standard Scaler (Best for PCA, SVM, Logistic Regression)
	standard = StandardScaler()
	df_scaled = standard.fit_transform(df)

	# 3. Robust Scaler (Best when dataset has many outliers)
	robust = RobustScaler()
	df_robust = robust.fit_transform(df)</code></pre>
	</div>
	</section>

	<!-- ========================== 5. ENCODING =========================== -->
	<section id="encoding" class="topic-section">
	<h2>Data Encoding</h2>
	<p>Transform categorical variables into numbers so models can interpret them.</p>

	<div class="form-group">
	<button id="btn-label-encode" class="btn btn--primary">Label Encoding</button>
	<button id="btn-onehot-encode" class="btn btn--primary">One-Hot Encoding</button>
	<button id="btn-target-encode" class="btn btn--primary">Target Encoding</button>
	</div>

	<div class="canvas-wrapper">
	<canvas id="canvas-encoding" width="600" height="300"></canvas>
	</div>

	<div class="info-card" style="margin-top: 20px; border-left-color: #9900ff;">
	<h3 style="margin-top: 0; color: #9900ff;">🧠 Under the Hood: Target Encoding Math</h3>
	<p><strong>One-Hot Encoding</strong> creates $N$ sparse binary columns for $N$ categories, which can cause the
	"Curse of Dimensionality" for high-cardinality features.</p>
	<p><strong>Target Encoding</strong> replaces a categorical value with the average target value for that
	category. To prevent overfitting (especially on rare categories), a <em>Bayesian Smoothing</em> average is
	applied:</p>
	<div
	style="background: rgba(0,0,0,0.2); padding: 15px; border-radius: 8px; text-align: center; margin: 15px 0; font-size: 1.1em; color: #e4e6eb;">
	$$ S = \lambda \cdot \bar{y}_{cat} + (1 - \lambda) \cdot \bar{y}_{global} $$
	</div>
	<p style="margin-bottom: 0;">Where $\bar{y}_{cat}$ is the mean of the target for the specific category,
	$\bar{y}_{global}$ is the global target mean, and $\lambda$ is a weight between 0 and 1 determined by the
	category's frequency.</p>
	</div>

	<div class="code-block" style="margin-top: 20px;">
	<div class="code-header">
	<span>encoding.py - Category Encoders</span>
	<button class="copy-btn" onclick="copyCode(this)">Copy</button>
	</div>
	<pre><code>import pandas as pd
	from sklearn.preprocessing import OneHotEncoder
	from category_encoders import TargetEncoder

	# 1. One-Hot Encoding (Best for nominal variables with few categories)
	ohe = OneHotEncoder(sparse_output=False, drop='first') # drop='first' avoids multicollinearity
	color_encoded = ohe.fit_transform(df[['color']])

	# Pandas alternative (easy but not ideal for pipelines):
	# pd.get_dummies(df, columns=['color'], drop_first=True)

	# 2. Target Encoding (Best for high-cardinality nominal variables like zipcodes)
	# Requires 'category_encoders' library
	te = TargetEncoder(smoothing=10) # Higher smoothing pulls estimates closer to global mean
	df['zipcode_encoded'] = te.fit_transform(df['zipcode'], df['target'])</code></pre>
	</div>
	</section>

	<!-- ===================== 6. FEATURE SELECTION ======================= -->
	<section id="feature-selection" class="topic-section">
	<h2>Feature Selection</h2>
	<p>Pick features that matter, drop those that don't.</p>

	<div class="form-group">
	<button id="btn-backward-elim" class="btn btn--primary">Backward Elimination</button>
	<button id="btn-forward-select" class="btn btn--primary">Forward Selection</button>
	<button id="btn-rfe" class="btn btn--primary">RFE</button>
	</div>

	<div class="canvas-wrapper">
	<canvas id="canvas-selection" width="600" height="300"></canvas>
	</div>

	<div class="info-card" style="margin-top: 20px; border-left-color: #9900ff;">
	<h3 style="margin-top: 0; color: #9900ff;">🧠 Under the Hood: Selection Math</h3>
	<p>Feature selection can be filter-based, wrapper-based, or intrinsic.</p>
	<p><strong>Filter Method (ANOVA F-Value):</strong> Scikit-Learn's `f_classif` computes the ANOVA F-value
	between numerical features and a categorical target. The F-statistic measures the ratio of variance
	<em>between</em> groups to the variance <em>within</em> groups:
	</p>
	<div
	style="background: rgba(0,0,0,0.2); padding: 15px; border-radius: 8px; text-align: center; margin: 15px 0; font-size: 1.1em; color: #e4e6eb;">
	$$ F = \frac{\text{Between-group variability}}{\text{Within-group variability}} $$
	</div>
	<p style="margin-bottom: 0;"><strong>Wrapper Method (RFE):</strong> Recursive Feature Elimination fits a model
	(e.g., Logistic Regression or Random Forest), ranks features by importance coefficients, drops the weakest
	feature, and repeats until the desired $N$ features remain.</p>
	</div>

	<div class="code-block" style="margin-top: 20px;">
	<div class="code-header">
	<span>selection.py - Feature Selection</span>
	<button class="copy-btn" onclick="copyCode(this)">Copy</button>
	</div>
	<pre><code>from sklearn.feature_selection import SelectKBest, f_classif, RFE
	from sklearn.linear_model import LogisticRegression

	X = df.drop('target', axis=1)
	y = df['target']

	# 1. Filter Method: SelectKBest (ANOVA F-value)
	# Keeps the 5 features with the highest ANOVA F-scores
	selector = SelectKBest(score_func=f_classif, k=5)
	X_top_5 = selector.fit_transform(X, y)
	selected_columns = X.columns[selector.get_support()]

	# 2. Wrapper Method: Recursive Feature Elimination (RFE)
	# Uses a model's intrinsic feature importance assigning to prune
	estimator = LogisticRegression()
	rfe = RFE(estimator, n_features_to_select=5, step=1)
	X_rfe = rfe.fit_transform(X, y)
	rfe_columns = X.columns[rfe.support_]</code></pre>
	</div>
	</section>

	<!-- =================== 7. IMBALANCED DATA =========================== -->
	<section id="imbalanced-data" class="topic-section">
	<h2>Handling Imbalanced Data</h2>
	<p>Class imbalance leads to biased predictions. Balancing techniques can fix this.</p>

	<div class="form-group">
	<button id="btn-rus" class="btn btn--primary">Random Under-Sampling</button>
	<button id="btn-ros" class="btn btn--primary">Random Over-Sampling</button>
	<button id="btn-smote" class="btn btn--primary">SMOTE</button>
	</div>

	<div class="canvas-wrapper">
	<canvas id="canvas-imbalanced" width="600" height="300"></canvas>
	</div>

	<div class="info-card" style="margin-top: 20px; border-left-color: #9900ff;">
	<h3 style="margin-top: 0; color: #9900ff;">🧠 Under the Hood: SMOTE Math</h3>
	<p><strong>SMOTE (Synthetic Minority Over-sampling Technique)</strong> doesn't just duplicate data (like
	Random Over-Sampling). It creates novel synthetic examples by interpolating between existing minority
	instances.</p>
	<p>For a minority class point $x_i$, SMOTE finds its $k$-nearest minority neighbors. It picks one neighbor
	$x_{zi}$ and generates a synthetic point $x_{new}$ along the line segment joining them:</p>
	<div
	style="background: rgba(0,0,0,0.2); padding: 15px; border-radius: 8px; text-align: center; margin: 15px 0; font-size: 1.1em; color: #e4e6eb;">
	$$ x_{new} = x_i + \lambda \times (x_{zi} - x_i) $$
	</div>
	<p style="margin-bottom: 0;">Where $\lambda$ is a random number between 0 and 1. This creates a denser, more
	generalized decision region for the minority class.</p>
	</div>

	<div class="code-block" style="margin-top: 20px;">
	<div class="code-header">
	<span>imbalanced.py - Imblearn Resampling</span>
	<button class="copy-btn" onclick="copyCode(this)">Copy</button>
	</div>
	<pre><code>from imblearn.over_sampling import SMOTE
	from imblearn.under_sampling import RandomUnderSampler
	from imblearn.pipeline import Pipeline

	# 1. SMOTE (Over-sampling the minority class)
	smote = SMOTE(sampling_strategy='auto', k_neighbors=5, random_state=42)
	X_smote, y_smote = smote.fit_resample(X, y)

	# 2. Random Under-Sampling (Reducing the majority class)
	rus = RandomUnderSampler(sampling_strategy='auto', random_state=42)
	X_rus, y_rus = rus.fit_resample(X, y)

	# 3. Best Practice Pipeline: Under-sample majority THEN SMOTE minority
	# Prevents creating too many synthetic points if the imbalance is extreme
	resample_pipe = Pipeline([
	('rus', RandomUnderSampler(sampling_strategy=0.1)), # Reduce majority until minority is 10%
	('smote', SMOTE(sampling_strategy=0.5)) # SMOTE minority until it's 50%
	])
	X_resampled, y_resampled = resample_pipe.fit_resample(X, y)</code></pre>
	</div>
	</section>

	<!-- ========================== 8. EDA ================================ -->
	<section id="eda" class="topic-section">
	<h2>Exploratory Data Analysis (EDA)</h2>
	<p><strong>Exploratory Data Analysis (EDA)</strong> is a critical step in the machine learning pipeline that
	comes BEFORE feature engineering. EDA helps you understand your data, discover patterns, identify anomalies,
	detect outliers, test hypotheses, and check assumptions through summary statistics and graphical
	representations.</p>

	<div class="info-card">
	<strong>Key Questions EDA Answers:</strong>
	<ul>
	<li>How many columns are numerical vs. categorical?</li>
	<li>What does the data distribution look like?</li>
	<li>Are there missing values?</li>
	<li>Are there outliers?</li>
	<li>Is the data imbalanced (for classification problems)?</li>
	<li>What are the correlations between features?</li>
	<li>Are there any trends or patterns?</li>
	</ul>
	</div>

	<div class="info-card">
	<strong>Real-World Example:</strong> Imagine you're analyzing customer data for a bank to predict loan
	defaults. EDA helps you understand:
	<ul>
	<li>Age distribution of customers (histogram)</li>
	<li>Income levels (box plot for outliers)</li>
	<li>Correlation between income and loan amount (scatter plot)</li>
	<li>Missing values in employment history</li>
	<li>Class imbalance (5% defaults vs 95% non-defaults)</li>
	</ul>
	</div>

	<h3>Two Main Types of EDA</h3>

	<h4>1. Descriptive Statistics</h4>
	<p><strong>Purpose:</strong> Summarize and visualize what the data looks like</p>

	<div class="info-card">
	<strong>A. Central Tendency:</strong><br>
	• <strong>Mean (Average):</strong> μ = Σxᵢ / n<br>
	Example: Average income = $50,000 (Sensitive to outliers)<br>
	• <strong>Median:</strong> Middle value when sorted<br>
	Example: Median income = $45,000 (Robust to outliers)<br>
	• <strong>Mode:</strong> Most frequent value<br>
	Example: Most common age = 35 years<br><br>

	<strong>B. Variability (Spread):</strong><br>
	• <strong>Variance:</strong> σ² = Σ(xᵢ - μ)² / n (Measures how spread out data is)<br>
	• <strong>Standard Deviation:</strong> σ = √variance<br>
	68% of data within 1σ, 95% within 2σ, 99.7% within 3σ (for normal distribution)<br>
	• <strong>Interquartile Range (IQR):</strong> Q3 - Q1<br>
	Middle 50% of data, robust to outliers<br><br>

	<strong>C. Correlation & Associations:</strong><br>
	• <strong>Pearson Correlation:</strong> r = Cov(X,Y) / (σₓ × σᵧ)<br>
	Range: -1 to +1<br>
	r = +1: Perfect positive correlation<br>
	r = 0: No linear correlation<br>
	r = -1: Perfect negative correlation<br>
	• <strong>Thresholds:</strong> \|r\| > 0.7: Strong, \|r\| = 0.5-0.7: Moderate, \|r\| < 0.3: Weak
	</div>

	<h4>2. Inferential Statistics</h4>
	<p><strong>Purpose:</strong> Make inferences or generalizations about the population from the sample</p>
	<p><strong>Key Question:</strong> Can we claim this effect exists in the larger population, or is it just by
	chance?</p>

	<div class="info-card">
	<strong>A. Hypothesis Testing:</strong><br>
	• <strong>Null Hypothesis (H₀):</strong> No effect exists (e.g., "Mean of Group A = Mean of Group B")<br>
	• <strong>Alternative Hypothesis (H₁):</strong> Effect exists (e.g., "Mean of Group A ≠ Mean of Group B")<br>
	• <strong>P-value:</strong> Probability of observing data if H₀ is true<br>
	p < 0.05: Reject H₀ (effect is statistically significant)<br>
	p > 0.05: Fail to reject H₀ (not enough evidence)<br><br>

	<strong>Example:</strong><br>
	• H₀: "There is no difference between positive and negative movie review lengths"<br>
	• H₁: "Negative reviews are longer than positive reviews"<br>
	• After t-test: p = 0.003 (< 0.05)<br>
	• Conclusion: Reject H₀ → Negative reviews ARE significantly longer<br><br>

	<strong>B. Confidence Intervals:</strong><br>
	• Range where true population parameter likely lies<br>
	• 95% CI: We're 95% confident the true value is within this range<br>
	• Example: "Average customer age is 35 ± 2 years (95% CI: [33, 37])"<br><br>

	<strong>C. Effect Size:</strong><br>
	• Cohen's d = (mean₁ - mean₂) / pooled_std<br>
	• Small effect: d = 0.2, Medium: d = 0.5, Large: d = 0.8
	</div>

	<h3>Algorithm Steps for EDA</h3>
	<div class="info-card">
	<strong>1. Load and Inspect Data:</strong> df.head(), df.info(), df.describe()<br>
	<strong>2. Handle Missing Values:</strong> Identify (df.isnull().sum()), Visualize, Decide<br>
	<strong>3. Analyze Distributions:</strong> Histograms, count plots, box plots<br>
	<strong>4. Check for Imbalance:</strong> Count target classes, plot distribution<br>
	<strong>5. Correlation Analysis:</strong> Correlation matrix, heatmap, identify multicollinearity<br>
	<strong>6. Statistical Testing:</strong> Compare groups (t-test, ANOVA), test assumptions, calculate effect
	sizes
	</div>

	<h3>Interactive EDA Dashboard</h3>
	<div class="form-group">
	<label for="edaFeature" class="form-label">Select Feature:</label>
	<select id="edaFeature" class="form-control w-100">
	<option value="age">Age</option>
	<option value="income">Income</option>
	<option value="credit">Credit Score</option>
	</select>
	</div>

	<div class="form-group">
	<label for="confidenceLevel" class="form-label">Confidence Level: <span
	id="confidenceValue">95</span>%</label>
	<input type="range" id="confidenceLevel" min="90" max="99" step="1" value="95" class="form-control" />
	</div>

	<div class="form-group">
	<button id="btn-histogram" class="btn btn--primary">Show Histogram</button>
	<button id="btn-boxplot" class="btn btn--primary">Show Box Plot</button>
	<button id="btn-correlation" class="btn btn--primary">Show Correlation</button>
	</div>

	<div class="canvas-wrapper">
	<canvas id="canvas-eda" width="800" height="500"></canvas>
	</div>

	<div class="callout callout--insight">💡 EDA typically takes 30-40% of total project time. Good EDA reveals
	which features to engineer.</div>
	<div class="callout callout--mistake">⚠️ Common Mistakes: Skipping EDA, not checking outliers before scaling,
	ignoring missing value patterns, overlooking class imbalance, ignoring multicollinearity.</div>
	<div class="callout callout--tip">✅ Best Practices: ALWAYS start with EDA, visualize EVERY feature, check
	correlations with target, document insights, use both descriptive and inferential statistics.</div>

	<div class="info-card" style="margin-top: 20px; border-left-color: #9900ff;">
	<h3 style="margin-top: 0; color: #9900ff;">🧠 Under the Hood: Skewness & Kurtosis</h3>
	<p>Beyond mean and variance, we examine the geometric shape of our distributions using the 3rd and 4th
	statistical moments.</p>
	<p><strong>Skewness ($s$)</strong> measures asymmetry. Positive means right-tailed, negative means
	left-tailed:</p>
	<div
	style="background: rgba(0,0,0,0.2); padding: 15px; border-radius: 8px; text-align: center; margin: 15px 0; font-size: 1.1em; color: #e4e6eb;">
	$$ s = \frac{\frac{1}{n} \sum_{i=1}^{n} (x_i - \bar{x})^3}{\sigma^3} $$
	</div>
	<p><strong>Kurtosis ($k$)</strong> measures "tailedness" (presence of outliers). A normal distribution has a
	kurtosis of 3. High kurtosis means heavy tails:</p>
	<div
	style="background: rgba(0,0,0,0.2); padding: 15px; border-radius: 8px; text-align: center; margin: 15px 0; font-size: 1.1em; color: #e4e6eb;">
	$$ k = \frac{\frac{1}{n} \sum_{i=1}^{n} (x_i - \bar{x})^4}{\sigma^4} $$
	</div>
	</div>

	<div class="code-block" style="margin-top: 20px;">
	<div class="code-header">
	<span>eda.py - Automated & Visual EDA</span>
	<button class="copy-btn" onclick="copyCode(this)">Copy</button>
	</div>
	<pre><code>import pandas as pd
	import seaborn as sns
	import matplotlib.pyplot as plt

	# 1. Deep Descriptive Stats (includes skewness)
	display(df.describe().T)
	print("Skewness:\n", df.skew())
	print("\nMissing Values:\n", df.isnull().sum())

	# 2. Visual Distributions (Pairplot)
	# Plots histograms on the diagonal and scatter plots for every relationship
	sns.pairplot(df, hue='target_class', diag_kind='kde', corner=True)
	plt.show()

	# 3. Correlation Heatmap
	plt.figure(figsize=(10, 8))
	corr_matrix = df.corr(method='spearman') # Spearman is robust to non-linear relationships
	sns.heatmap(corr_matrix, annot=True, cmap='coolwarm', vmin=-1, vmax=1)
	plt.title("Spearman Correlation Heatmap")
	plt.show()</code></pre>
	</div>

	<h3>Use Cases and Applications</h3>
	<ul>
	<li><strong>Healthcare:</strong> Analyzing patient data before building disease prediction models</li>
	<li><strong>Finance:</strong> Understanding customer demographics before credit scoring</li>
	<li><strong>E-commerce:</strong> Analyzing purchase patterns before recommendation systems</li>
	<li><strong>Marketing:</strong> Understanding customer segments before targeted campaigns</li>
	<li><strong>Time Series:</strong> Checking for seasonality and trends in sales data</li>
	</ul>

	<h3>Summary & Key Takeaways</h3>
	<p>Exploratory Data Analysis is the foundation of any successful machine learning project. It combines
	<strong>descriptive statistics</strong> (mean, median, variance, correlation) with <strong>inferential
	statistics</strong> (hypothesis testing, confidence intervals) to understand data deeply.
	</p>
	<p><strong>Descriptive EDA</strong> answers: "What is happening in the dataset?"<br>
	<strong>Inferential EDA</strong> answers: "Can we claim this effect exists in the larger population?"
	</p>
	<p>Remember: <strong>Data → EDA → Feature Engineering → ML → Deployment</strong></p>
	</section>

	<!-- =================== 9. FEATURE TRANSFORMATION ==================== -->
	<section id="feature-transformation" class="topic-section">
	<h2>Feature Transformation</h2>
	<p>Feature transformation creates new representations of data to capture non-linear patterns. Techniques like
	polynomial features, binning, and mathematical transformations unlock hidden relationships.</p>

	<div class="info-card">
	<strong>Real Example:</strong> Predicting house prices with polynomial features (adding x² terms) improves
	model fit for non-linear relationships between square footage and price.
	</div>

	<h3>Mathematical Foundations</h3>
	<div class="info-card">
	<strong>Polynomial Features:</strong> Transform (x₁, x₂) → (1, x₁, x₂, x₁², x₁x₂, x₂²)<br>
	• Degree 2 example: For features (x, y) → (1, x, y, x², xy, y²)<br>
	• 2 features with degree=2 creates 6 features total<br><br>
	<strong>Binning:</strong> Convert continuous → categorical<br>
	• Equal-width: Divide range into equal intervals<br>
	• Quantile: Each bin has equal number of samples<br>
	• Example: Age (0-100) → [0-18], [19-35], [36-60], [61+]<br><br>
	<strong>Mathematical Transformations:</strong><br>
	• Square Root: √x (reduces right skew)<br>
	• Log Transform: log(1 + x)<br>
	• Box-Cox: λ = 0: log(x), λ ≠ 0: (x^λ - 1)/λ
	</div>

	<div class="form-group">
	<button id="btn-polynomial" class="btn btn--primary">Add Polynomial Features</button>
	<button id="btn-binning" class="btn btn--primary">Apply Binning</button>
	<button id="btn-log" class="btn btn--primary">Log Transform</button>
	</div>

	<div class="canvas-wrapper">
	<canvas id="canvas-transformation" width="700" height="350"></canvas>
	</div>

	<div class="callout callout--insight">💡 Polynomial features capture curve fitting, but degree=3 on 10 features
	creates 286 features!</div>
	<div class="callout callout--mistake">⚠️ Always scale features after polynomial transformation to prevent
	magnitude issues.</div>
	<div class="callout callout--tip">✅ Start with degree=2 and visualize distributions before/after transformation.
	</div>

	<div class="info-card" style="margin-top: 20px; border-left-color: #9900ff;">
	<h3 style="margin-top: 0; color: #9900ff;">🧠 Under the Hood: Power Transforms</h3>
	<p>When log transformations $\ln(1+x)$ aren't enough to fix severe skewness, we use parametric Power
	Transformations like <strong>Box-Cox</strong> (requires $x > 0$) or <strong>Yeo-Johnson</strong> (supports
	negative values). They automatically find the optimal $\lambda$ parameter using Maximum Likelihood
	Estimation.</p>
	<p><strong>Box-Cox Transformation Formula:</strong></p>
	<div
	style="background: rgba(0,0,0,0.2); padding: 15px; border-radius: 8px; text-align: center; margin: 15px 0; font-size: 1.1em; color: #e4e6eb;">
	$$ x^{(\lambda)} = \begin{cases} \frac{x^\lambda - 1}{\lambda} & \text{if } \lambda \neq 0 \\ \ln(x) &
	\text{if } \lambda = 0 \end{cases} $$
	</div>
	<p style="margin-bottom: 0;">These transforms stretch and compress the variable to map it as closely to a
	Gaussian (Normal) distribution as mathematically possible.</p>
	</div>

	<div class="code-block" style="margin-top: 20px;">
	<div class="code-header">
	<span>transformation.py - Power Transforms & Binning</span>
	<button class="copy-btn" onclick="copyCode(this)">Copy</button>
	</div>
	<pre><code>import numpy as np
	from sklearn.preprocessing import PowerTransformer, KBinsDiscretizer

	# 1. Power Transformation (Yeo-Johnson)
	# Attempts to map skewed feature to a Gaussian distribution
	pt = PowerTransformer(method='yeo-johnson', standardize=True)
	df['income_gaussian'] = pt.fit_transform(df[['income']])

	# 2. Log Transformation (np.log1p handles zeros safely by doing log(1+x))
	df['revenue_log'] = np.log1p(df['revenue'])

	# 3. Discretization / Binning
	# Converts continuous age into 5 categorical bins (quantiles ensures equal frequency per bin)
	binner = KBinsDiscretizer(n_bins=5, encode='ordinal', strategy='quantile')
	df['age_group'] = binner.fit_transform(df[['age']])</code></pre>
	</div>

	<h3>Use Cases</h3>
	<ul>
	<li>Polynomial features for non-linear house price prediction</li>
	<li>Binning age into groups for marketing segmentation</li>
	<li>Log transformation for right-skewed income data</li>
	</ul>
	</section>

	<!-- =================== 10. FEATURE CREATION ========================= -->
	<section id="feature-creation" class="topic-section">
	<h2>Feature Creation</h2>
	<p>Creating new features from existing ones based on domain knowledge. Interaction terms, ratios, and
	domain-specific calculations enhance model performance.</p>

	<div class="info-card">
	<strong>Real Example:</strong> E-commerce revenue = price × quantity. Profit margin = (selling_price -
	cost_price) / cost_price. These derived features often have stronger predictive power than raw features.
	</div>

	<h3>Mathematical Foundations</h3>
	<div class="info-card">
	<strong>Interaction Terms:</strong> feature₁ × feature₂<br>
	• Example: advertising_budget × seasonality → total_impact<br>
	• Why: Captures how one feature's effect depends on another<br><br>
	<strong>Ratio Features:</strong> feature₁ / feature₂<br>
	• Example: price/sqft, income/age<br><br>
	<strong>Domain-Specific Features:</strong><br>
	• BMI = weight(kg) / height²(m²)<br>
	• Speed = distance / time<br>
	• Profit margin = (revenue - cost) / cost<br><br>
	<strong>Time-Based Features:</strong><br>
	• Extract: year, month, day, weekday, hour<br>
	• Create: is_weekend, is_holiday, season
	</div>

	<div class="form-group">
	<button id="btn-interaction" class="btn btn--primary">Create Interaction</button>
	<button id="btn-ratio" class="btn btn--primary">Create Ratio</button>
	<button id="btn-bmi" class="btn btn--primary">Calculate BMI</button>
	</div>

	<div class="canvas-wrapper">
	<canvas id="canvas-creation" width="700" height="350"></canvas>
	</div>

	<div class="callout callout--insight">💡 Interaction terms are especially powerful in linear models - neural
	networks learn them automatically.</div>
	<div class="callout callout--mistake">⚠️ Creating features without domain knowledge leads to meaningless
	combinations.</div>
	<div class="callout callout--tip">✅ Always check correlation between new and existing features to avoid
	redundancy.</div>

	<div class="info-card" style="margin-top: 20px; border-left-color: #9900ff;">
	<h3 style="margin-top: 0; color: #9900ff;">🧠 Under the Hood: Polynomial Combinations</h3>
	<p>Scikit-Learn's `PolynomialFeatures` generates a new feature matrix consisting of all polynomial
	combinations of the features with degree less than or equal to the specified degree.</p>
	<p>For two features $X = [x_1, x_2]$ and a degree of 2, the expanded polynomial vector is:</p>
	<div
	style="background: rgba(0,0,0,0.2); padding: 15px; border-radius: 8px; text-align: center; margin: 15px 0; font-size: 1.1em; color: #e4e6eb;">
	$$ [1,\; x_1,\; x_2,\; x_1^2,\; x_1 \cdot x_2,\; x_2^2] $$
	</div>
	<p style="margin-bottom: 0;">Notice the $x_1 \cdot x_2$ term. This is an <strong>interaction term</strong>,
	which lets a linear model learn conditional relationships (e.g., "if $x_1$ is high, the effect of $x_2$
	changes").</p>
	</div>

	<div class="code-block" style="margin-top: 20px;">
	<div class="code-header">
	<span>creation.py - Automated Polynomial Features</span>
	<button class="copy-btn" onclick="copyCode(this)">Copy</button>
	</div>
	<pre><code>from sklearn.preprocessing import PolynomialFeatures
	import pandas as pd

	# Assume df has two features: 'length' and 'width'
	X = df[['length', 'width']]

	# Create polynomial and interaction features up to degree 2
	# include_bias=False prevents adding a column of 1s (intercept)
	poly = PolynomialFeatures(degree=2, include_bias=False)
	X_poly = poly.fit_transform(X)

	# Get the names of the new features (e.g., 'length^2', 'length width')
	feature_names = poly.get_feature_names_out(['length', 'width'])
	df_poly = pd.DataFrame(X_poly, columns=feature_names)

	print(df_poly.head())</code></pre>
	</div>

	<h3>Use Cases</h3>
	<ul>
	<li>BMI from height and weight in healthcare prediction</li>
	<li>Click-through rate = clicks / impressions in digital marketing</li>
	<li>Revenue = price × quantity in retail analytics</li>
	</ul>
	</section>

	<!-- ================ 11. DIMENSIONALITY REDUCTION ==================== -->
	<section id="dimensionality-reduction" class="topic-section">
	<h2>Dimensionality Reduction</h2>
	<p>Reducing the number of features while preserving information. PCA (Principal Component Analysis) projects
	high-dimensional data onto lower dimensions by finding directions of maximum variance.</p>

	<div class="info-card">
	<strong>Real Example:</strong> Image compression and genome analysis with thousands of genes benefit from PCA.
	First 2-3 principal components often capture 80%+ of variance.
	</div>

	<h3>PCA Mathematical Foundations</h3>
	<div class="info-card">
	<strong>Algorithm Steps:</strong><br>
	1. Standardize data: $X_{scaled} = \frac{X - \mu}{\sigma}$<br>
	2. Compute covariance matrix: $\Sigma = \frac{1}{n-1} X^T X$<br>
	3. Calculate eigenvalues $\lambda$ and eigenvectors $v$<br>
	4. Sort eigenvectors by eigenvalues (descending)<br>
	5. Select top $k$ eigenvectors (principal components)<br>
	6. Transform: $X_{new} = X \times v_k$<br><br>
	<strong>Explained Variance:</strong> $\frac{\lambda_i}{\sum \lambda_j}$<br>
	<strong>Cumulative Variance:</strong> Shows total information preserved<br><br>
	<strong>Why PCA Works:</strong><br>
	• Removes correlated features<br>
	• Captures maximum variance in fewer dimensions<br>
	• Components are orthogonal (no correlation)
	</div>

	<div class="form-group">
	<label for="slider-components" class="form-label">Number of Components: <span id="pcaValue">2</span></label>
	<input type="range" id="slider-components" min="1" max="3" step="1" value="2" class="form-control" />
	</div>

	<button id="btn-pca-apply" class="btn btn--primary">Apply PCA</button>

	<div class="canvas-wrapper">
	<canvas id="canvas-pca" width="700" height="400"></canvas>
	</div>

	<div class="callout callout--insight">💡 PCA is unsupervised - it doesn't use the target variable. First PC
	always captures most variance.</div>
	<div class="callout callout--mistake">⚠️ Not standardizing before PCA is a critical error - features with large
	scales will dominate.</div>
	<div class="callout callout--tip">✅ Aim for 95% cumulative explained variance when choosing number of
	components.</div>

	<div class="info-card" style="margin-top: 20px; border-left-color: #9900ff;">
	<h3 style="margin-top: 0; color: #9900ff;">🧠 Under the Hood: PCA Math</h3>
	<p>PCA finds the directions (Principal Components) that maximize the variance of the data. Mathematically, it
	works by computing the covariance matrix of the standardized dataset $X$:</p>
	<div
	style="background: rgba(0,0,0,0.2); padding: 15px; border-radius: 8px; text-align: center; margin: 15px 0; font-size: 1.1em; color: #e4e6eb;">
	$$ \Sigma = \frac{1}{n-1} X^T X $$
	</div>
	<p>Then, we solve for the eigenvectors $V$ and eigenvalues $\lambda$ solving $\Sigma V = \lambda V$.</p>
	<ul style="margin-top: 10px; margin-bottom: 0;">
	<li><strong>Eigenvectors</strong> ($v_i$) are the axes of the new feature space (the directions).</li>
	<li><strong>Eigenvalues</strong> ($\lambda_i$) represent the magnitude of variance captured by each vector.
	</li>
	</ul>
	</div>

	<div class="code-block" style="margin-top: 20px;">
	<div class="code-header">
	<span>pca.py - Principal Component Analysis</span>
	<button class="copy-btn" onclick="copyCode(this)">Copy</button>
	</div>
	<pre><code>from sklearn.decomposition import PCA
	from sklearn.preprocessing import StandardScaler
	import matplotlib.pyplot as plt
	import numpy as np

	# 1. ALWAYS scale data before PCA
	scaler = StandardScaler()
	X_scaled = scaler.fit_transform(X)

	# 2. Fit PCA without specifying components to see all variance
	pca_full = PCA()
	pca_full.fit(X_scaled)

	# 3. Plot Cumulative Explained Variance
	cumulative_variance = np.cumsum(pca_full.explained_variance_ratio_)
	plt.plot(cumulative_variance, marker='o')
	plt.axhline(y=0.95, color='r', linestyle='--') # 95% threshold
	plt.xlabel('Number of Components')
	plt.ylabel('Cumulative Explained Variance')
	plt.show()

	# 4. Apply PCA retaining 95% variance
	# Float between 0 and 1 selects components covering that % of variance
	pca = PCA(n_components=0.95)
	X_pca = pca.fit_transform(X_scaled)
	print(f"Reduced from {X.shape[1]} to {X_pca.shape[1]} features.")</code></pre>
	</div>

	<h3>Use Cases</h3>
	<ul>
	<li>Image compression (reduce pixel dimensions)</li>
	<li>Genomics (thousands of genes → few principal components)</li>
	<li>Visualization (project high-D data to 2D for plotting)</li>
	<li>Speed up training (fewer features = faster models)</li>
	</ul>

	<h3>Common Mistakes</h3>
	<ul>
	<li>⚠️ Applying PCA before train-test split (data leakage)</li>
	<li>⚠️ Using PCA with categorical features (PCA is for numerical data)</li>
	<li>⚠️ Losing interpretability (PCs are linear combinations)</li>
	</ul>
	</section>

	<!-- ================== 12. TEXT DATA (NLP BASICS) ==================== -->
	<section id="text-data" class="topic-section">
	<h2>Text Data (NLP Basics)</h2>
	<p>Real-world tabular data often contains unstructured text (e.g., reviews, titles). Algorithms require numbers,
	so we must vectorize this text into numerical representations.</p>

	<div class="info-card">
	<strong>Real Example:</strong> Converting thousands of Amazon product reviews into numeric features allows a
	classification model to predict positive vs. negative sentiment.
	</div>

	<h3>Mathematical Foundations</h3>
	<div class="info-card">
	<strong>Bag of Words (BoW):</strong> Represents text by counting the frequency of each word, ignoring grammar
	and order.<br><br>
	<strong>TF-IDF (Term Frequency - Inverse Document Frequency):</strong><br>
	Penalizes frequent, uninformative words (like "the", "and") while boosting rare, meaningful words.<br><br>
	<div
	style="background: rgba(0,0,0,0.2); padding: 15px; border-radius: 8px; text-align: center; margin: 15px 0; font-size: 1.1em; color: #e4e6eb;">
	$$ \text{TF-IDF}(t, d, D) = \text{TF}(t, d) \times \text{IDF}(t, D) $$
	</div>
	• $\text{TF}$: (count of term $t$ in document $d$) / (total terms in $d$)<br>
	• $\text{IDF}$: $\log \left( \frac{\text{Total Documents } N}{\text{Documents containing term } t} \right)$
	</div>

	<div class="code-block" style="margin-top: 20px;">
	<div class="code-header">
	<span>text_features.py - Scikit-Learn Vectorizers</span>
	<button class="copy-btn" onclick="copyCode(this)">Copy</button>
	</div>
	<pre><code>from sklearn.feature_extraction.text import CountVectorizer, TfidfVectorizer
	import pandas as pd

	# Sample text column
	corpus = [
	"Machine learning is amazing",
	"Deep learning is the future of learning",
	"Data science and artificial intelligence"
	]

	# 1. Bag of Words (CountVectorizer)
	# Creates a column for every unique word in the corpus
	vectorizer = CountVectorizer(stop_words='english')
	X_bow = vectorizer.fit_transform(corpus)

	# 2. TF-IDF (TfidfVectorizer)
	# Converts words to continuous weights between 0 and 1
	tfidf = TfidfVectorizer(stop_words='english', max_features=100)
	X_tfidf = tfidf.fit_transform(corpus)

	# Quick way to view features as a DataFrame
	tfidf_df = pd.DataFrame(X_tfidf.toarray(), columns=tfidf.get_feature_names_out())
	print(tfidf_df.head())</code></pre>
	</div>

	<h3>Meta-Features</h3>
	<p>Before throwing text into a vectorizer, you can extract powerful <strong>meta-features</strong> using pure
	Python or Pandas:</p>
	<ul>
	<li><strong>Word count:</strong> <code>df['text'].apply(lambda x: len(str(x).split()))</code></li>
	<li><strong>Character count:</strong> <code>df['text'].apply(lambda x: len(str(x)))</code></li>
	<li><strong>Count of punctuation/capitals:</strong> (Often strongly correlated with SPAM or fake reviews).
	</li>
	</ul>
	</section>

	<!-- ================= 13. TIME-SERIES ENGINEERING ==================== -->
	<section id="time-series" class="topic-section">
	<h2>Time-Series Feature Engineering</h2>
	<p>Time-series data assumes that past values influence future values. We cannot simply shuffle rows; order
	matters. We must engineer features that capture chronological patterns.</p>

	<h3>Mathematical Foundations</h3>
	<div class="info-card">
	<strong>Lag Features:</strong> Shifting the target variable back by $t$ steps. "What was yesterday's
	sales?"<br>
	$X_{lag\_1} = Y_{t-1}$<br><br>
	<strong>Rolling Windows:</strong> Computing statistics over a moving window of past data. Smoothes out
	short-term fluctuations to reveal trends.<br>
	• Simple Moving Average (SMA) for window $w$:
	<div
	style="background: rgba(0,0,0,0.2); padding: 15px; border-radius: 8px; text-align: center; margin: 15px 0; font-size: 1.1em; color: #e4e6eb;">
	$$ SMA_t = \frac{1}{w} \sum_{i=1}^{w} Y_{t-i} $$
	</div>
	<strong>Expanding Windows:</strong> Computes statistics from the very beginning of the dataset up to the
	current point $t$ (e.g., cumulative sum or cumulative max).
	</div>

	<div class="code-block" style="margin-top: 20px;">
	<div class="code-header">
	<span>time_series.py - Lags and Rolling Windows</span>
	<button class="copy-btn" onclick="copyCode(this)">Copy</button>
	</div>
	<pre><code>import pandas as pd

	# Assuming 'df' is sorted chronologically and indexed by Date
	# 1. Lag Features (Looking back in time)
	# What was the value 1 day ago? 7 days ago?
	df['sales_lag_1'] = df['sales'].shift(1)
	df['sales_lag_7'] = df['sales'].shift(7)

	# 2. Rolling Window Features
	# The average and standard deviation over the last 7 days
	df['sales_rolling_mean_7d'] = df['sales'].rolling(window=7).mean()
	df['sales_rolling_std_7d'] = df['sales'].rolling(window=7).std()

	# 3. Expanding Window Features
	# Year-to-date maximum sales
	df['sales_expanding_max'] = df['sales'].expanding().max()

	# Drop NaNs generated by shifting/rolling
	df.dropna(inplace=True)</code></pre>
	</div>
	</section>

	<!-- ===================== 14. TARGET LEAKAGE ========================= -->
	<section id="target-leakage" class="topic-section">
	<h2>Target Leakage (Data Leakage)</h2>
	<p>Data Leakage occurs when information from outside the training dataset is used to create the model. This
	guarantees amazing performance during training/validation, but total failure in the real world.</p>

	<div class="callout callout--mistake">⚠️ The most common cause of leakage is performing feature engineering
	(Scaling, Imputing, TF-IDF) on the ENTIRE dataset <strong>before</strong> calling train_test_split.</div>

	<div class="info-card" style="margin-top: 20px; border-left-color: #ff3366;">
	<h3 style="margin-top: 0; color: #ff3366;">🧠 Under the Hood: The Contamination Problem</h3>
	<p>Imagine using <code>StandardScaler</code> on your entire dataset. The scaler calculates the global $\mu$
	(mean) and $\sigma$ (standard deviation) to scale the data.</p>
	<p>If you split the data <em>after</em> scaling, your Training Data has been transformed using the mean of the
	Test Data. The Test Data is supposed to be completely unseen, but you just "leaked" its summary statistics
	into the training process.</p>
	</div>

	<div class="code-block" style="margin-top: 20px;">
	<div class="code-header">
	<span>leakage.py - The Golden Rule of Fit vs Transform</span>
	<button class="copy-btn" onclick="copyCode(this)">Copy</button>
	</div>
	<pre><code>from sklearn.model_selection import train_test_split
	from sklearn.preprocessing import StandardScaler

	# ❌ BAD PRACTICE (Creates Leakage)
	scaler_bad = StandardScaler()
	X_scaled_bad = scaler_bad.fit_transform(X) # Entire dataset sees the scaler
	X_train_bad, X_test_bad = train_test_split(X_scaled_bad)

	# ✅ GOOD PRACTICE (No Leakage)
	X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2)

	scaler = StandardScaler()
	# Fit ONLY on the training data to learn parameters (mean, std)
	X_train_scaled = scaler.fit_transform(X_train)

	# Transform test data using the parameters learned from the training data
	X_test_scaled = scaler.transform(X_test)</code></pre>
	</div>
	<div class="callout callout--tip">✅ The easiest way to mathematically prevent leakage in production is to
	package all your feature engineering steps inside a <strong>Scikit-Learn Pipeline</strong>.</div>
	</section>

	<!-- ================ 15. AUTOMATED FEATURE ENGINEERING =============== -->
	<section id="automated-fe" class="topic-section">
	<h2>Automated Feature Engineering</h2>
	<p>In complex, multi-table relational databases, manually creating features is incredibly tedious. Automated
	Feature Engineering relies on algorithms to automatically synthesize hundreds of new features from relational
	datasets.</p>

	<h3>Deep Feature Synthesis (DFS)</h3>
	<p>DFS stacks mathematical primitives (like computing sums, counts, averages, and time-since-last-event) across
	entity relationships (e.g., Customers $\xrightarrow{\text{1 to M}}$ Orders $\xrightarrow{\text{1 to M}}$
	Order_Items).</p>

	<div class="info-card">
	<strong>Real Example:</strong> From a raw database of e-commerce transactions, DFS can automatically generate
	complex features like: <em>"The average value of a customer's orders over the last 30 days"</em> or <em>"The
	standard deviation of time between a user's logins."</em>
	</div>

	<div class="code-block" style="margin-top: 20px;">
	<div class="code-header">
	<span>autofe.py - Featuretools Library</span>
	<button class="copy-btn" onclick="copyCode(this)">Copy</button>
	</div>
	<pre><code>import featuretools as ft

	# Assume we have three Pandas DataFrames: clients, loans, and payments
	# Step 1: Create an EntitySet (a representation of your database)
	es = ft.EntitySet(id="banking")

	# Step 2: Add dataframes to the EntitySet with primary keys
	es = es.add_dataframe(dataframe_name="clients", dataframe=clients_df, index="client_id")
	es = es.add_dataframe(dataframe_name="loans", dataframe=loans_df, index="loan_id")

	# Step 3: Define relational joins (Foreign Keys)
	es = es.add_relationship("clients", "client_id", "loans", "client_id")

	# Step 4: Run Deep Feature Synthesis!
	# Automatically generates agg features for clients based on their loans history
	feature_matrix, feature_defs = ft.dfs(
	entityset=es,
	target_dataframe_name="clients",
	agg_primitives=["mean", "sum", "mode", "std"],
	trans_primitives=["month", "hour"],
	max_depth=2 # Stacks primitives up to 2 layers deep
	)

	print(f"Automatically generated {len(feature_defs)} features!")</code></pre>
	</div>
	</section>
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