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1
+ {
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+ "cells": [
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+ {
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+ "cell_type": "markdown",
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+ "id": "title-cell",
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+ "metadata": {},
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+ "source": [
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+ "# Sprint 5 Report – Resampling and Ensemble Techniques\n",
9
+ "**Course:** Data Intensive Systems (4DV652) \n",
10
+ "**Lab:** Lab Lecture 5 \n",
11
+ "**Deadline:** 2026-02-25 \n",
12
+ "\n",
13
+ "---\n",
14
+ "\n",
15
+ "## Overview\n",
16
+ "\n",
17
+ "This sprint focused on applying **heterogeneous ensemble methods** and **stacking** to challenge the current regression and classification champions established in Sprint 4. The team worked across two parallel tracks:\n",
18
+ "\n",
19
+ "- **Regression Ensemble** – Predict `AimoScore` (continuous target) using diverse base models with bootstrap sampling and aggregation strategies.\n",
20
+ "- **Classification Ensemble** – Predict `WeakestLink` (14-class target) using voting classifiers, bagging, and stacking.\n",
21
+ "\n",
22
+ "A custom `CorrelationFilter` transformer was also implemented as a reusable sklearn-compatible preprocessing component shared across both tracks.\n",
23
+ "\n",
24
+ "---"
25
+ ]
26
+ },
27
+ {
28
+ "cell_type": "markdown",
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+ "id": "ml-process-cell",
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+ "metadata": {},
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+ "source": [
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+ "## 1. ML Process Iteration\n",
33
+ "\n",
34
+ "### 1.1 Problem Framing Recap\n",
35
+ "\n",
36
+ "The dataset originates from movement quality assessments (NASM Overhead Squat Assessment). Two supervised learning tasks are defined:\n",
37
+ "\n",
38
+ "| Task | Target | Type | Sprint 4 Champion Score |\n",
39
+ "|------|--------|------|-------------------------|\n",
40
+ "| Regression | `AimoScore` (continuous) | Regression | RΒ² = 0.6356, RMSE = 0.1303 |\n",
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+ "| Classification | `WeakestLink` (14 classes) | Multiclass | Weighted F1 = 0.6110 |\n",
42
+ "\n",
43
+ "### 1.2 Sprint 5 Goals\n",
44
+ "\n",
45
+ "Per the lab assignment:\n",
46
+ "1. Define ensembles of independent models using bootstrap samples, different feature engineering, and diverse AI approaches.\n",
47
+ "2. Challenge the Sprint 4 champions using simple aggregation (averaging / majority vote) or stacking.\n",
48
+ "3. Deploy a new champion if the ensemble outperforms the previous one.\n",
49
+ "4. Validate improvement using the **corrected resampled t-test** (Nadeau & Bengio, 2003).\n",
50
+ "\n",
51
+ "---"
52
+ ]
53
+ },
54
+ {
55
+ "cell_type": "markdown",
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+ "id": "software-cell",
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+ "metadata": {},
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+ "source": [
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+ "## 2. Software Development: CorrelationFilter\n",
60
+ "\n",
61
+ "A custom `sklearn`-compatible transformer was implemented and used in both the regression and classification pipelines. It removes highly correlated features before model fitting, reducing redundancy while preserving sklearn `Pipeline` compatibility."
62
+ ]
63
+ },
64
+ {
65
+ "cell_type": "code",
66
+ "execution_count": null,
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+ "id": "correlation-filter-code",
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+ "metadata": {},
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+ "outputs": [],
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+ "source": [
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+ "from sklearn.base import BaseEstimator, TransformerMixin\n",
72
+ "import pandas as pd\n",
73
+ "import numpy as np\n",
74
+ "\n",
75
+ "class CorrelationFilter(BaseEstimator, TransformerMixin):\n",
76
+ " \"\"\"\n",
77
+ " Removes features that are highly correlated with another feature.\n",
78
+ " Threshold defaults to 0.99 (absolute Pearson correlation).\n",
79
+ " Sklearn-compatible: can be used in Pipeline objects.\n",
80
+ " \"\"\"\n",
81
+ " def __init__(self, threshold=0.99):\n",
82
+ " self.threshold = threshold\n",
83
+ " self.keep_cols_ = None\n",
84
+ "\n",
85
+ " def fit(self, X, y=None):\n",
86
+ " Xdf = pd.DataFrame(X) if not isinstance(X, pd.DataFrame) else X\n",
87
+ " # Compute absolute correlation matrix (upper triangle only)\n",
88
+ " corr = Xdf.corr(numeric_only=True).abs()\n",
89
+ " upper = corr.where(np.triu(np.ones(corr.shape), k=1).astype(bool))\n",
90
+ " to_drop = [col for col in upper.columns if any(upper[col] >= self.threshold)]\n",
91
+ " self.keep_cols_ = [c for c in Xdf.columns if c not in to_drop]\n",
92
+ " return self\n",
93
+ "\n",
94
+ " def transform(self, X):\n",
95
+ " Xdf = pd.DataFrame(X) if not isinstance(X, pd.DataFrame) else X\n",
96
+ " return Xdf[self.keep_cols_].copy()\n",
97
+ "\n",
98
+ "# Example usage\n",
99
+ "print(\"CorrelationFilter: removes columns with |corr| >= threshold.\")\n",
100
+ "print(\"Used in regression pipeline with threshold=0.95 for RandomForest.\")"
101
+ ]
102
+ },
103
+ {
104
+ "cell_type": "markdown",
105
+ "id": "regression-header",
106
+ "metadata": {},
107
+ "source": [
108
+ "---\n",
109
+ "## 3. Regression Ensemble (A5_Regression_Ensemble)\n",
110
+ "\n",
111
+ "### 3.1 Approach\n",
112
+ "\n",
113
+ "A heterogeneous ensemble was designed following the sprint lecture pattern:\n",
114
+ "\n",
115
+ "- **Bootstrap diversity**: Four different bootstrap-augmented training sets (`dataset2_train_augmented_1..4.csv`).\n",
116
+ "- **Model diversity**: Four distinct regressors (Lasso, Ridge, RandomForest, GradientBoosting), each trained on a different bootstrap sample.\n",
117
+ "- **Feature diversity**: Feature subsets were defined (full, angle-only, NASM-only, angle+NASM) to allow further differentiation.\n",
118
+ "- **Aggregation**: Two strategies β€” simple averaging and CV-RΒ²-weighted averaging.\n",
119
+ "\n",
120
+ "### 3.2 Ensemble Configuration\n",
121
+ "\n",
122
+ "| Model | Bootstrap Sample | Feature Set | Algorithm |\n",
123
+ "|-------|-----------------|-------------|----------|\n",
124
+ "| Lasso | 1 | Full | `LassoCV` (cv=5) |\n",
125
+ "| Ridge | 2 | Full | `RidgeCV` (cv=5) |\n",
126
+ "| RandomForest | 3 | Full | `RandomForestRegressor` (200 trees, depth=15) + CorrelationFilter(0.95) |\n",
127
+ "| GradientBoosting | 4 | Full | `GradientBoostingRegressor` (150 trees, depth=5, lr=0.1) |"
128
+ ]
129
+ },
130
+ {
131
+ "cell_type": "code",
132
+ "execution_count": null,
133
+ "id": "regression-config-code",
134
+ "metadata": {},
135
+ "outputs": [],
136
+ "source": [
137
+ "# Ensemble configuration (from A5_Regression_Ensemble.ipynb)\n",
138
+ "ENSEMBLE_CONFIG = [\n",
139
+ " {\"name\": \"lasso\", \"bootstrap\": 1, \"features\": \"full\"},\n",
140
+ " {\"name\": \"ridge\", \"bootstrap\": 2, \"features\": \"full\"},\n",
141
+ " {\"name\": \"rf\", \"bootstrap\": 3, \"features\": \"full\"},\n",
142
+ " {\"name\": \"gb\", \"bootstrap\": 4, \"features\": \"full\"},\n",
143
+ "]\n",
144
+ "\n",
145
+ "# Feature subsets available (used for diversity)\n",
146
+ "FEATURE_SUBSETS = {\n",
147
+ " \"full\": \"all features\",\n",
148
+ " \"angle_only\": \"features with 'Angle' in name\",\n",
149
+ " \"nasm_only\": \"features with 'NASM' in name\",\n",
150
+ " \"angle_nasm\": \"angle + NASM features (excludes time)\",\n",
151
+ "}\n",
152
+ "\n",
153
+ "print(\"Ensemble configuration loaded.\")\n",
154
+ "print(f\"Number of base models: {len(ENSEMBLE_CONFIG)}\")"
155
+ ]
156
+ },
157
+ {
158
+ "cell_type": "markdown",
159
+ "id": "regression-results",
160
+ "metadata": {},
161
+ "source": [
162
+ "### 3.3 Base Model Results (Test Set)\n",
163
+ "\n",
164
+ "Each base model was trained on its assigned bootstrap sample and evaluated on the held-out test set. Cross-validation RΒ² scores were used to compute ensemble weights.\n",
165
+ "\n",
166
+ "| Model | Bootstrap | CV RΒ² | Test RΒ² | Test RMSE | Test MAE |\n",
167
+ "|-------|-----------|-------|---------|-----------|----------|\n",
168
+ "| Lasso | 1 | β€” | β€” | β€” | β€” |\n",
169
+ "| Ridge | 2 | β€” | β€” | β€” | β€” |\n",
170
+ "| RandomForest | 3 | β€” | β€” | β€” | β€” |\n",
171
+ "| GradientBoosting | 4 | β€” | β€” | β€” | β€” |\n",
172
+ "\n",
173
+ "> *Note: Exact numeric outputs are produced at runtime. The table above is populated when executing the notebook against the dataset.*\n",
174
+ "\n",
175
+ "### 3.4 Ensemble Aggregation Results\n",
176
+ "\n",
177
+ "| Method | RΒ² | RMSE | MAE | Corr |\n",
178
+ "|--------|----|------|-----|------|\n",
179
+ "| Simple Average | runtime | runtime | runtime | runtime |\n",
180
+ "| Weighted Average (CV RΒ²) | runtime | runtime | runtime | runtime |\n",
181
+ "| **A4 Champion (baseline)** | **0.6356** | **0.1303** | **0.0972** | **0.8089** |\n",
182
+ "\n",
183
+ "Weighted averaging assigns higher influence to models with better cross-validation RΒ² scores:\n",
184
+ "$$\\hat{y}_{\\text{ensemble}} = \\sum_{i=1}^{4} w_i \\hat{y}_i, \\quad w_i = \\frac{\\text{CV-R}^2_i}{\\sum_j \\text{CV-R}^2_j}$$"
185
+ ]
186
+ },
187
+ {
188
+ "cell_type": "markdown",
189
+ "id": "regression-ttest",
190
+ "metadata": {},
191
+ "source": [
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+ "### 3.5 Statistical Significance – Corrected Resampled t-test\n",
193
+ "\n",
194
+ "Standard paired t-tests overstate confidence when models are compared via cross-validation because training folds overlap. The **Nadeau & Bengio (2003) correction** accounts for this by inflating the variance:\n",
195
+ "\n",
196
+ "$$\\text{Var}_{\\text{corrected}} = \\left(\\frac{1}{k} + \\frac{n_{\\text{test}}}{n_{\\text{train}}}\\right) \\cdot \\hat{\\sigma}^2_{\\Delta}$$\n",
197
+ "\n",
198
+ "For this dataset, $n_{\\text{test}}/n_{\\text{train}} \\approx 0.25$, meaning variance is inflated by ~25%, making it harder to claim statistically significant improvement.\n",
199
+ "\n",
200
+ "Hypotheses tested (Ξ± = 0.05):\n",
201
+ "- Hβ‚€: Ensemble MSE = Champion MSE \n",
202
+ "- H₁: Ensemble MSE β‰  Champion MSE (two-tailed)\n",
203
+ "\n",
204
+ "| Comparison | t-stat | p-value | Significant? |\n",
205
+ "|------------|--------|---------|-------------|\n",
206
+ "| Simple Avg vs Champion | runtime | runtime | runtime |\n",
207
+ "| Weighted Avg vs Champion | runtime | runtime | runtime |"
208
+ ]
209
+ },
210
+ {
211
+ "cell_type": "code",
212
+ "execution_count": null,
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+ "id": "regression-ttest-code",
214
+ "metadata": {},
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+ "outputs": [],
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+ "source": [
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+ "# Corrected resampled t-test implementation (Nadeau & Bengio, 2003)\n",
218
+ "import numpy as np\n",
219
+ "from scipy import stats\n",
220
+ "\n",
221
+ "def corrected_resampled_ttest(errors_1, errors_2, n_train, n_test):\n",
222
+ " \"\"\"\n",
223
+ " Corrected resampled t-test for comparing two models.\n",
224
+ " Accounts for variance inflation due to overlapping cross-validation folds.\n",
225
+ " \n",
226
+ " Args:\n",
227
+ " errors_1, errors_2: arrays of per-sample squared errors for model 1 and 2\n",
228
+ " n_train: number of training samples\n",
229
+ " n_test: number of test samples\n",
230
+ " Returns:\n",
231
+ " t_stat, p_value, mean_diff\n",
232
+ " \"\"\"\n",
233
+ " diff = errors_1 - errors_2\n",
234
+ " mean_diff = np.mean(diff)\n",
235
+ " var_diff = np.var(diff, ddof=1)\n",
236
+ "\n",
237
+ " # Correction factor: accounts for n_test/n_train overlap\n",
238
+ " correction = (1 / len(diff)) + (n_test / n_train)\n",
239
+ " corrected_var = correction * var_diff\n",
240
+ "\n",
241
+ " t_stat = mean_diff / np.sqrt(corrected_var)\n",
242
+ " p_value = 2 * stats.t.sf(np.abs(t_stat), df=len(diff) - 1)\n",
243
+ " return t_stat, p_value, mean_diff\n",
244
+ "\n",
245
+ "print(\"Corrected resampled t-test function defined.\")\n",
246
+ "print(\"Positive mean_diff => champion has higher MSE (ensemble is better).\")"
247
+ ]
248
+ },
249
+ {
250
+ "cell_type": "markdown",
251
+ "id": "regression-champion",
252
+ "metadata": {},
253
+ "source": [
254
+ "### 3.6 Champion Decision (Regression)\n",
255
+ "\n",
256
+ "The best-performing ensemble method (Simple Average or Weighted Average) is compared against the A4 champion. If the ensemble exceeds RΒ² = 0.6356, the model is saved as `aimoscores_ensemble_A5.pkl`.\n",
257
+ "\n",
258
+ "The best ensemble selection logic:\n",
259
+ "- Best aggregation method: `weighted` if weighted RΒ² > average RΒ², else `average`\n",
260
+ "- Saved only if it outperforms the A4 champion\n",
261
+ "\n",
262
+ "---"
263
+ ]
264
+ },
265
+ {
266
+ "cell_type": "markdown",
267
+ "id": "classification-header",
268
+ "metadata": {},
269
+ "source": [
270
+ "## 4. Classification Ensemble (A5_Classification_Ensemble)\n",
271
+ "\n",
272
+ "### 4.1 Problem Setup\n",
273
+ "\n",
274
+ "- **Target**: `WeakestLink` β€” the movement category with the highest deviation score across 14 NASM categories.\n",
275
+ "- **Features**: Merged movement features from `aimoscores.csv` + weakest link labels from `scores_and_weaklink.csv`.\n",
276
+ "- **Class imbalance**: Addressed using `class_weight='balanced'` and `class_weight='balanced_subsample'`.\n",
277
+ "- **A4 Champion baseline**: Random Forest with weighted F1 = **0.6110**.\n",
278
+ "\n",
279
+ "### 4.2 Data Preparation"
280
+ ]
281
+ },
282
+ {
283
+ "cell_type": "code",
284
+ "execution_count": null,
285
+ "id": "classification-setup",
286
+ "metadata": {},
287
+ "outputs": [],
288
+ "source": [
289
+ "# Classification setup (from A5_Classification_Ensemble.ipynb)\n",
290
+ "RANDOM_STATE = 42\n",
291
+ "N_SPLITS = 5\n",
292
+ "CHAMPION_F1 = 0.6110 # Sprint 4 benchmark\n",
293
+ "\n",
294
+ "# 14 WeakestLink categories\n",
295
+ "weaklink_categories = [\n",
296
+ " 'ExcessiveForwardLean', 'ForwardHead', 'LeftArmFallForward',\n",
297
+ " 'LeftAsymmetricalWeightShift', 'LeftHeelRises', 'LeftKneeMovesInward',\n",
298
+ " 'LeftKneeMovesOutward', 'LeftShoulderElevation', 'RightArmFallForward',\n",
299
+ " 'RightAsymmetricalWeightShift', 'RightHeelRises', 'RightKneeMovesInward',\n",
300
+ " 'RightKneeMovesOutward', 'RightShoulderElevation',\n",
301
+ "]\n",
302
+ "\n",
303
+ "# WeakestLink = the category with the highest deviation score\n",
304
+ "# weaklink_scores_df['WeakestLink'] = weaklink_scores_df[weaklink_categories].idxmax(axis=1)\n",
305
+ "\n",
306
+ "print(f\"Number of classes: {len(weaklink_categories)}\")\n",
307
+ "print(f\"Sprint 4 champion F1: {CHAMPION_F1}\")"
308
+ ]
309
+ },
310
+ {
311
+ "cell_type": "markdown",
312
+ "id": "classification-ensembles",
313
+ "metadata": {},
314
+ "source": [
315
+ "### 4.3 Ensemble Strategies\n",
316
+ "\n",
317
+ "Four ensemble strategies were designed and evaluated using **5-fold stratified cross-validation**:\n",
318
+ "\n",
319
+ "#### Ensemble 1 – Hard Voting\n",
320
+ "Each base classifier casts a vote; the class with the most votes wins. Base classifiers: Random Forest, Logistic Regression, XGBoost, LightGBM, KNN (k=7), LDA.\n",
321
+ "\n",
322
+ "#### Ensemble 2 – Soft Voting \n",
323
+ "Same base classifiers, but predictions are combined via averaged class probabilities. Generally more accurate than hard voting when calibrated probability estimates are available.\n",
324
+ "\n",
325
+ "#### Ensemble 3 – Bootstrap Bagging on LDA \n",
326
+ "`BaggingClassifier` wrapping `LinearDiscriminantAnalysis` (50 estimators, 80% sample size, 90% feature subset). Demonstrates how bagging can stabilise a weak linear model.\n",
327
+ "\n",
328
+ "#### Ensemble 4 – Stacking (LR meta-learner) \n",
329
+ "Base classifiers: Random Forest, Logistic Regression, KNN, LDA. Meta-learner: `LogisticRegression` trained on out-of-fold predictions (5-fold CV). The meta-learner learns *how to combine* base model outputs, replacing simple voting with a learned aggregation function."
330
+ ]
331
+ },
332
+ {
333
+ "cell_type": "code",
334
+ "execution_count": null,
335
+ "id": "classification-ensembles-code",
336
+ "metadata": {},
337
+ "outputs": [],
338
+ "source": [
339
+ "# Ensemble model definitions (from A5_Classification_Ensemble.ipynb)\n",
340
+ "from sklearn.ensemble import (\n",
341
+ " RandomForestClassifier, VotingClassifier, BaggingClassifier, StackingClassifier\n",
342
+ ")\n",
343
+ "from sklearn.linear_model import LogisticRegression\n",
344
+ "from sklearn.discriminant_analysis import LinearDiscriminantAnalysis\n",
345
+ "from sklearn.neighbors import KNeighborsClassifier\n",
346
+ "# import xgboost as xgb\n",
347
+ "# import lightgbm as lgb\n",
348
+ "\n",
349
+ "# ---- Ensemble 4: Stacking ----\n",
350
+ "stacking = StackingClassifier(\n",
351
+ " estimators=[\n",
352
+ " ('rf', RandomForestClassifier(n_estimators=100, max_depth=15,\n",
353
+ " min_samples_split=5, min_samples_leaf=2,\n",
354
+ " class_weight='balanced_subsample',\n",
355
+ " random_state=RANDOM_STATE, n_jobs=-1)),\n",
356
+ " ('lr', LogisticRegression(max_iter=1000, class_weight='balanced',\n",
357
+ " random_state=RANDOM_STATE)),\n",
358
+ " ('knn', KNeighborsClassifier(n_neighbors=7)),\n",
359
+ " ('lda', LinearDiscriminantAnalysis()),\n",
360
+ " ],\n",
361
+ " final_estimator=LogisticRegression(\n",
362
+ " C=1.0, max_iter=1000, class_weight='balanced', random_state=RANDOM_STATE\n",
363
+ " ),\n",
364
+ " cv=5,\n",
365
+ " passthrough=False,\n",
366
+ " n_jobs=-1,\n",
367
+ ")\n",
368
+ "\n",
369
+ "print(\"Stacking classifier defined with LR meta-learner.\")"
370
+ ]
371
+ },
372
+ {
373
+ "cell_type": "markdown",
374
+ "id": "classification-results",
375
+ "metadata": {},
376
+ "source": [
377
+ "### 4.4 Cross-Validation Results\n",
378
+ "\n",
379
+ "All models were evaluated with 5-fold **StratifiedKFold** cross-validation on the training set, using weighted F1-score as the primary metric.\n",
380
+ "\n",
381
+ "| Model | CV F1 (mean) | CV F1 (std) | CV Accuracy | CV Precision | CV Recall |\n",
382
+ "|-------|-------------|------------|------------|-------------|----------|\n",
383
+ "| A4 Champion – Random Forest | ~0.6110 | β€” | β€” | β€” | β€” |\n",
384
+ "| Hard Voting | runtime | runtime | runtime | runtime | runtime |\n",
385
+ "| Soft Voting | runtime | runtime | runtime | runtime | runtime |\n",
386
+ "| Bootstrap Bagging (LDA) | runtime | runtime | runtime | runtime | runtime |\n",
387
+ "| Stacking (LR meta) | runtime | runtime | runtime | runtime | runtime |\n",
388
+ "\n",
389
+ "> *The bar chart below (produced at runtime) visually compares all approaches, with the red dashed line marking the Sprint 4 champion.*\n",
390
+ "\n",
391
+ "### 4.5 Statistical Significance Tests\n",
392
+ "\n",
393
+ "The corrected resampled t-test was applied for each ensemble vs the A4 champion (same implementation as the regression track).\n",
394
+ "\n",
395
+ "| Ensemble | t-stat | p-value | Better than Champion? |\n",
396
+ "|----------|--------|---------|----------------------|\n",
397
+ "| Hard Voting | runtime | runtime | runtime |\n",
398
+ "| Soft Voting | runtime | runtime | runtime |\n",
399
+ "| Bootstrap Bagging (LDA) | runtime | runtime | runtime |\n",
400
+ "| Stacking (LR meta) | runtime | runtime | runtime |\n",
401
+ "\n",
402
+ "### 4.6 Final Test Set Results\n",
403
+ "\n",
404
+ "All models were retrained on the full training set and evaluated on the held-out 20% test split.\n",
405
+ "\n",
406
+ "| Model | Test F1 | Test Accuracy | Test Precision | Test Recall |\n",
407
+ "|-------|---------|--------------|---------------|------------|\n",
408
+ "| Best Ensemble (champion) | runtime | runtime | runtime | runtime |\n",
409
+ "| A4 Champion – Random Forest | ~0.6110 | β€” | β€” | β€” |\n",
410
+ "\n",
411
+ "### 4.7 Champion Decision (Classification)\n",
412
+ "\n",
413
+ "The top-ranked ensemble by CV F1 is selected as the new champion and saved to `models/ensemble_classification_champion.pkl`. The artifact includes the model, scaler, feature columns, CV metrics, test metrics, and improvement percentage vs Sprint 4."
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+ ]
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+ },
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+ {
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+ "cell_type": "markdown",
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+ "id": "summary-cell",
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+ "metadata": {},
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+ "source": [
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+ "---\n",
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+ "## 5. Sprint Summary\n",
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+ "\n",
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+ "### 5.1 What Was Done\n",
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+ "\n",
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+ "| Component | Owner Track | Description |\n",
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+ "|-----------|------------|-------------|\n",
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+ "| `CorrelationFilter.py` | Shared | Custom sklearn transformer removing highly correlated features |\n",
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+ "| Regression Ensemble | Regression track | 4 base models (Lasso, Ridge, RF, GB) Γ— 4 bootstrap samples, simple + weighted averaging |\n",
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+ "| Classification Ensemble | Classification track | Hard Voting, Soft Voting, Bagging (LDA), Stacking (LR meta) |\n",
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+ "| Statistical Testing | Both tracks | Corrected resampled t-test (Nadeau & Bengio 2003) |\n",
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+ "| Champion Deployment | Both tracks | Pickle artifacts saved if ensemble outperforms A4 champion |\n",
433
+ "\n",
434
+ "### 5.2 Key Design Decisions\n",
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+ "\n",
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+ "**Regression:** Bootstrap-based diversity was the primary source of independence between base models. Weighted averaging was used as the aggregation method with weights derived from CV-RΒ² scores, giving better-performing models proportionally more influence.\n",
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+ "\n",
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+ "**Classification:** A broader range of diversity strategies was explored β€” algorithm diversity (RF, LR, XGB, LGB, KNN, LDA), voting schemes (hard vs soft), and a stacking approach where a meta-learner replaces manual aggregation. Class imbalance was consistently addressed with `class_weight='balanced'`.\n",
439
+ "\n",
440
+ "**Statistical rigor:** The Nadeau-Bengio correction was applied in both tracks rather than a naive t-test, accounting for the overlap between cross-validation folds (correction factor β‰ˆ 1.25 for this dataset).\n",
441
+ "\n",
442
+ "### 5.3 Limitations and Next Steps\n",
443
+ "\n",
444
+ "- Feature subset diversity (angle-only, NASM-only) was defined but ultimately the final configuration used full features for all base models in the regression track. Future iterations could test whether feature-diverse ensembles further reduce error.\n",
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+ "- The classification stacking approach used `passthrough=False`, meaning the meta-learner only sees predicted class probabilities, not the original features. Including raw features (`passthrough=True`) could be explored.\n",
446
+ "- More ensemble members (e.g., 8–10 base models) could be evaluated to assess the accuracy-variance tradeoff more thoroughly."
447
+ ]
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+ },
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