From 575ecbcd864654731a60d89c0682b369c9976428 Mon Sep 17 00:00:00 2001 From: Amruta Pawar Date: Thu, 21 Nov 2024 22:14:06 -0600 Subject: [PATCH 1/7] Files uploaded --- model.py | 201 ++++++++ tests/WineQT.csv | 1144 ++++++++++++++++++++++++++++++++++++++++++ tests/heart.csv | 1026 +++++++++++++++++++++++++++++++++++++ tests/small_test.csv | 51 ++ 4 files changed, 2422 insertions(+) create mode 100644 model.py create mode 100644 tests/WineQT.csv create mode 100644 tests/heart.csv create mode 100644 tests/small_test.csv diff --git a/model.py b/model.py new file mode 100644 index 0000000..8ed18d4 --- /dev/null +++ b/model.py @@ -0,0 +1,201 @@ +import csv +import random +import math +import matplotlib.pyplot as plt + +def load_csv(file_path, target_column): + """ + Load a CSV file and split into features (X) and target (y). + + Parameters: + file_path: Path to the CSV file. + target_column: Name of the target column. + + Returns: + X: List of feature rows (2D list). + y: List of target values (1D list). + """ + with open(file_path, 'r') as file: + reader = csv.DictReader(file) + data = list(reader) + + X = [] + y = [] + for row in data: + y.append(float(row[target_column])) + X.append([float(value) for key, value in row.items() if key != target_column]) + + return X, y + +def mean_squared_error(y_true, y_pred): + return sum((yt - yp) ** 2 for yt, yp in zip(y_true, y_pred)) / len(y_true) + +def r_squared(y_true, y_pred): + mean_y = sum(y_true) / len(y_true) + ss_total = sum((yt - mean_y) ** 2 for yt in y_true) + ss_residual = sum((yt - yp) ** 2 for yt, yp in zip(y_true, y_pred)) + return 1 - (ss_residual / ss_total) + +def split_data(X, y, indices): + X_split = [X[i] for i in indices] + y_split = [y[i] for i in indices] + return X_split, y_split + +def k_fold_cv(model, X, y, k=5, metric='mse', random_seed=None): + if random_seed is not None: + random.seed(random_seed) + + indices = list(range(len(X))) + random.shuffle(indices) + fold_size = len(X) // k + scores = [] + + for i in range(k): + test_indices = indices[i * fold_size:(i + 1) * fold_size] + train_indices = indices[:i * fold_size] + indices[(i + 1) * fold_size:] + + X_train, y_train = split_data(X, y, train_indices) + X_test, y_test = split_data(X, y, test_indices) + + model.fit(X_train, y_train) + y_pred = model.predict(X_test) + + if metric == 'mse': + scores.append(mean_squared_error(y_test, y_pred)) + elif metric == 'r2': + scores.append(r_squared(y_test, y_pred)) + else: + raise ValueError(f"Unsupported metric: {metric}") + + return sum(scores) / len(scores) + +def bootstrap(model, X, y, num_samples=100, metric='mse', random_seed=None): + if random_seed is not None: + random.seed(random_seed) + + scores = [] + n = len(X) + + for _ in range(num_samples): + bootstrap_indices = [random.randint(0, n - 1) for _ in range(n)] + oob_indices = list(set(range(n)) - set(bootstrap_indices)) + + X_sample, y_sample = split_data(X, y, bootstrap_indices) + X_oob, y_oob = split_data(X, y, oob_indices) + + if not oob_indices: + continue + + model.fit(X_sample, y_sample) + y_pred = model.predict(X_oob) + + if metric == 'mse': + scores.append(mean_squared_error(y_oob, y_pred)) + elif metric == 'r2': + scores.append(r_squared(y_oob, y_pred)) + else: + raise ValueError(f"Unsupported metric: {metric}") + + return sum(scores) / len(scores) + +def calculate_aic(model, X, y): + model.fit(X, y) + y_pred = model.predict(X) + resid = [yt - yp for yt, yp in zip(y, y_pred)] + n = len(y) + p = len(X[0]) + rss = sum(r ** 2 for r in resid) + return n * math.log(rss / n) + 2 * p + +def plot_results(y_true, y_pred): + """ + Plot observed vs. predicted values and residuals. + + Parameters: + y_true: List of true target values. + y_pred: List of predicted target values. + """ + # Observed vs. Predicted + plt.figure(figsize=(12, 6)) + plt.subplot(1, 2, 1) + plt.scatter(y_true, y_pred, alpha=0.7, edgecolors='k') + plt.plot([min(y_true), max(y_true)], [min(y_true), max(y_true)], 'r--', label="Ideal Fit") + plt.title("Observed vs Predicted") + plt.xlabel("Observed Values") + plt.ylabel("Predicted Values") + plt.legend() + plt.grid(True) + + # Residuals + residuals = [yt - yp for yt, yp in zip(y_true, y_pred)] + plt.subplot(1, 2, 2) + plt.scatter(y_pred, residuals, alpha=0.7, edgecolors='k') + plt.axhline(y=0, color='r', linestyle='--', label="Zero Residual Line") + plt.title("Residuals") + plt.xlabel("Predicted Values") + plt.ylabel("Residuals") + plt.legend() + plt.grid(True) + + # Show plots + plt.tight_layout() + plt.show() + +class LinearRegression: + def __init__(self): + self.coef_ = [] + self.intercept_ = 0 + + def fit(self, X, y): + n = len(X) + p = len(X[0]) + X_flat = [x + [1] for x in X] + XtX = [[sum(X_flat[i][k] * X_flat[i][j] for i in range(n)) for j in range(p + 1)] for k in range(p + 1)] + Xty = [sum(X_flat[i][j] * y[i] for i in range(n)) for j in range(p + 1)] + self.coef_, self.intercept_ = self.solve_linear_system(XtX, Xty) + + def predict(self, X): + return [sum(c * x for c, x in zip(self.coef_, xi)) + self.intercept_ for xi in X] + + def solve_linear_system(self, A, b): + n = len(A) + for i in range(n): + for j in range(i + 1, n): + factor = A[j][i] / A[i][i] + for k in range(i, n): + A[j][k] -= factor * A[i][k] + b[j] -= factor * b[i] + x = [0] * n + for i in range(n - 1, -1, -1): + x[i] = (b[i] - sum(A[i][j] * x[j] for j in range(i + 1, n))) / A[i][i] + return x[:-1], x[-1] + +if __name__ == "__main__": + # Example CSV Usage + file_path = "mlp\small_test.csv" # Replace with your CSV file path + target_column = "target" # Replace with your target column name + + # Load data from CSV + X, y = load_csv("mlp\small_test.csv", "y") + + # Create a Linear Regression model + model = LinearRegression() + + # K-Fold Cross-Validation + kfold_score = k_fold_cv(model, X, y, k=5, metric='mse', random_seed=42) + print(f"K-Fold Cross-Validation MSE: {kfold_score:.4f}") + + # Bootstrapping + bootstrap_score = bootstrap(model, X, y, num_samples=100, metric='mse', random_seed=42) + print(f"Bootstrapping MSE: {bootstrap_score:.4f}") + + # AIC + aic_score = calculate_aic(model, X, y) + print(f"AIC: {aic_score:.4f}") + + # Fit the model and get predictions + model.fit(X, y) + y_pred = model.predict(X) + + # Plot results + plot_results(y, y_pred) diff --git a/tests/WineQT.csv b/tests/WineQT.csv new file mode 100644 index 0000000..215185e --- /dev/null +++ b/tests/WineQT.csv @@ -0,0 +1,1144 @@ +fixed acidity,volatile acidity,citric acid,residual sugar,chlorides,free sulfur dioxide,total sulfur dioxide,density,pH,sulphates,alcohol,quality,Id +7.4,0.7,0.0,1.9,0.076,11.0,34.0,0.9978,3.51,0.56,9.4,5,0 +7.8,0.88,0.0,2.6,0.098,25.0,67.0,0.9968,3.2,0.68,9.8,5,1 +7.8,0.76,0.04,2.3,0.092,15.0,54.0,0.997,3.26,0.65,9.8,5,2 +11.2,0.28,0.56,1.9,0.075,17.0,60.0,0.998,3.16,0.58,9.8,6,3 +7.4,0.7,0.0,1.9,0.076,11.0,34.0,0.9978,3.51,0.56,9.4,5,4 +7.4,0.66,0.0,1.8,0.075,13.0,40.0,0.9978,3.51,0.56,9.4,5,5 +7.9,0.6,0.06,1.6,0.069,15.0,59.0,0.9964,3.3,0.46,9.4,5,6 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+-5.130765599150095,8.959898235120185,1.1701541118251235,22.753375944830324 +9.607901921761815,-9.108821424255002,5.524296399378377,-41.93781490943017 +-2.9201254899877434,5.134928295361929,-9.896226148902585,43.58829658171542 +6.956501039100711,0.8359369151964895,-6.1636372998431295,16.225403196517274 +7.725179239543149,-4.913104095867496,-1.110476120153832,-9.936035489824537 +-6.142683379729563,1.4244393989902058,1.8529074318076262,5.554396424524908 +-2.0474061706133977,-1.2170618863263076,8.899325908803291,-23.596187786238964 +9.359523403637155,3.4124788823300065,-1.4222946765509725,2.4507844709064064 +-8.642800876507275,-9.508822574677566,2.9901775243378577,-16.775543378589024 +-2.470992582133973,5.1672327675732195,-8.753045094764744,40.855147394263106 +-7.756097982925145,5.227601844332813,-3.179199348468109,30.739018818654756 +5.393783291304004,-1.5186710515725927,-7.469139234639499,17.503383657767756 +-7.644671911438172,1.8115363641056241,-6.167155079348694,33.57677356652164 +6.557442460132911,-4.44188855380612,-6.368621306151785,7.435670420087931 +0.21009363927752744,-2.719754693698011,1.0885820356480096,-6.289562485886653 +-8.571672299069252,8.890348599509473,5.468260371802332,15.412904086362603 +7.872454219630789,-3.9905860234116357,0.9068940749874717,-16.017543419998542 From c4b604775d8efa0ca36e9343ebb25f89854eb85f Mon Sep 17 00:00:00 2001 From: Amruta Pawar Date: Thu, 21 Nov 2024 22:39:18 -0600 Subject: [PATCH 2/7] Update README.md --- README.md | 70 +++++++++++++++++++++++++++++++++++++++++-------------- 1 file changed, 52 insertions(+), 18 deletions(-) diff --git a/README.md b/README.md index f746e56..4e076cb 100644 --- a/README.md +++ b/README.md @@ -1,29 +1,63 @@ -# Project 2 +## Amruta Sanjay Pawar- A20570864 +## Raghav Shah- A20570886 +## Shreedhruthi Boinpally- A20572883 +# Linear Regression with Evaluation Metrics -Select one of the following two options: +This project demonstrates the implementation of a custom linear regression model in Python and evaluates its performance using K-Fold Cross-Validation, Bootstrapping, and Akaike Information Criterion (AIC). The project uses a dataset named `heart.csv` for testing and validation. -## Boosting Trees +## Objective +To test and evaluate the performance of a custom linear regression model on the any dataset using the following metrics: +1. K-Fold Cross-Validation Mean Squared Error (MSE) +2. Bootstrapping Mean Squared Error (MSE) +3. Akaike Information Criterion (AIC) -Implement the gradient-boosting tree algorithm (with the usual fit-predict interface) as described in Sections 10.9-10.10 of Elements of Statistical Learning (2nd Edition). Answer the questions below as you did for Project 1. +### Do your cross-validation and bootstrapping model selectors agree with a simpler model selector like AIC in simple cases (like linear regression)? +Yes, in our testing with the `heart.csv` dataset using linear regression, the model selectors produced consistent results: +- **K-Fold Cross-Validation MSE**: 0.1241 +- **Bootstrapping MSE**: 0.1254 +- **AIC**: -2137.2136 -Put your README below. Answer the following questions. +These results indicate that cross-validation, bootstrapping, and AIC agree when evaluating the model’s fit to the data for simple cases. -* What does the model you have implemented do and when should it be used? -* How did you test your model to determine if it is working reasonably correctly? -* What parameters have you exposed to users of your implementation in order to tune performance? (Also perhaps provide some basic usage examples.) -* Are there specific inputs that your implementation has trouble with? Given more time, could you work around these or is it fundamental? +--- -## Model Selection +### In what cases might the methods you've written fail or give incorrect or undesirable results? +1. **Small datasets**: Bootstrapping may produce biased results due to repeated sampling from limited data. +2. **Imbalanced data**: K-Fold Cross-Validation may fail if folds are not stratified. +3. **High-dimensional data**: AIC may over-penalize complex models, leading to biased selection. +4. **Outliers**: All methods may give undesirable results if outliers dominate the dataset. -Implement generic k-fold cross-validation and bootstrapping model selection methods. +--- -In your README, answer the following questions: +### What could you implement given more time to mitigate these cases or help users of your methods? +- Implement **Stratified K-Folds** for handling imbalanced datasets. +- Incorporate **robust regression techniques** to handle outliers effectively. +- Use **Bayesian Information Criterion (BIC)** alongside AIC for high-dimensional datasets. +- Add automated **dataset analysis and warnings** for users regarding dataset size, balance, or presence of outliers. -* Do your cross-validation and bootstrapping model selectors agree with a simpler model selector like AIC in simple cases (like linear regression)? -* In what cases might the methods you've written fail or give incorrect or undesirable results? -* What could you implement given more time to mitigate these cases or help users of your methods? -* What parameters have you exposed to your users in order to use your model selectors. +--- -See sections 7.10-7.11 of Elements of Statistical Learning and the lecture notes. Pay particular attention to Section 7.10.2. +### What parameters have you exposed to your users in order to use your model selectors? +- **K-Fold Cross-Validation**: + - `k`: Number of folds. + - `metric`: Metric to evaluate (e.g., MSE or R²). + - `random_seed`: Seed for reproducibility. + +- **Bootstrapping**: + - `num_samples`: Number of bootstrap samples. + - `metric`: Metric to evaluate (e.g., MSE or R²). + - `random_seed`: Seed for reproducibility. + +- **AIC**: + - Requires no additional parameters and uses the full dataset. + +These parameters allow users to adapt the methods to their specific datasets and modeling requirements. + + +## How to Run +1. Clone this repository +2. Install required Python libraries (`matplotlib` for plotting) from cmd. +3. Replace with your CSV file path in model.py +4. Replace with your target column name in model.py +5. Then run model.py file -As usual, above-and-beyond efforts will be considered for bonus points. From f08f85b84af5afbd4956d308193c1b4a32014c54 Mon Sep 17 00:00:00 2001 From: Amruta Pawar Date: Thu, 21 Nov 2024 22:41:13 -0600 Subject: [PATCH 3/7] Update model.py --- model.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/model.py b/model.py index 8ed18d4..d721bca 100644 --- a/model.py +++ b/model.py @@ -176,7 +176,7 @@ def solve_linear_system(self, A, b): target_column = "target" # Replace with your target column name # Load data from CSV - X, y = load_csv("mlp\small_test.csv", "y") + X, y = load_csv("file_path", "target_column") # Create a Linear Regression model model = LinearRegression() From fe96cfaec040178e80d0e42af42d04dc1ec5c739 Mon Sep 17 00:00:00 2001 From: Amruta Pawar Date: Thu, 21 Nov 2024 22:42:51 -0600 Subject: [PATCH 4/7] Update README.md --- README.md | 7 ++++--- 1 file changed, 4 insertions(+), 3 deletions(-) diff --git a/README.md b/README.md index 4e076cb..149a0be 100644 --- a/README.md +++ b/README.md @@ -1,3 +1,4 @@ +## Team members: ## Amruta Sanjay Pawar- A20570864 ## Raghav Shah- A20570886 ## Shreedhruthi Boinpally- A20572883 @@ -57,7 +58,7 @@ These parameters allow users to adapt the methods to their specific datasets and ## How to Run 1. Clone this repository 2. Install required Python libraries (`matplotlib` for plotting) from cmd. -3. Replace with your CSV file path in model.py -4. Replace with your target column name in model.py -5. Then run model.py file +3. Replace file_path: Path to the CSV file in model.py +4. Replace target_column: Name of the target column in model.py +6. Then run model.py file From fbac278c8911f21e85381afa823bc8a6ce4251d7 Mon Sep 17 00:00:00 2001 From: Amruta Pawar Date: Thu, 21 Nov 2024 22:43:53 -0600 Subject: [PATCH 5/7] Update README.md --- README.md | 4 +++- 1 file changed, 3 insertions(+), 1 deletion(-) diff --git a/README.md b/README.md index 149a0be..155e811 100644 --- a/README.md +++ b/README.md @@ -1,8 +1,10 @@ + ## Team members: ## Amruta Sanjay Pawar- A20570864 ## Raghav Shah- A20570886 ## Shreedhruthi Boinpally- A20572883 -# Linear Regression with Evaluation Metrics + +# Model Selection This project demonstrates the implementation of a custom linear regression model in Python and evaluates its performance using K-Fold Cross-Validation, Bootstrapping, and Akaike Information Criterion (AIC). The project uses a dataset named `heart.csv` for testing and validation. From 5e99d221e2ba87f85f89550ab9e2a1c643415237 Mon Sep 17 00:00:00 2001 From: Amruta Pawar Date: Thu, 21 Nov 2024 22:50:16 -0600 Subject: [PATCH 6/7] Update README.md --- README.md | 5 +++-- 1 file changed, 3 insertions(+), 2 deletions(-) diff --git a/README.md b/README.md index 155e811..cd095cd 100644 --- a/README.md +++ b/README.md @@ -60,7 +60,8 @@ These parameters allow users to adapt the methods to their specific datasets and ## How to Run 1. Clone this repository 2. Install required Python libraries (`matplotlib` for plotting) from cmd. -3. Replace file_path: Path to the CSV file in model.py -4. Replace target_column: Name of the target column in model.py +3. If you want test with some other dataset then replace the following values : + Replace file_path: Path to the CSV file + Replace target_column: Name of the target column (For eample in heart.csv it is target) 6. Then run model.py file From ca909866d9b69c4bc74f86378e54ac2d4878fe03 Mon Sep 17 00:00:00 2001 From: Amruta Pawar Date: Thu, 21 Nov 2024 22:50:51 -0600 Subject: [PATCH 7/7] Update README.md --- README.md | 4 +--- 1 file changed, 1 insertion(+), 3 deletions(-) diff --git a/README.md b/README.md index cd095cd..79c6049 100644 --- a/README.md +++ b/README.md @@ -60,8 +60,6 @@ These parameters allow users to adapt the methods to their specific datasets and ## How to Run 1. Clone this repository 2. Install required Python libraries (`matplotlib` for plotting) from cmd. -3. If you want test with some other dataset then replace the following values : - Replace file_path: Path to the CSV file - Replace target_column: Name of the target column (For eample in heart.csv it is target) +3. If you want test with some other dataset then replace the following values : Replace file_path: Path to the CSV file, Replace target_column: Name of the target column (For eample in heart.csv it is target) 6. Then run model.py file