From 831a966afc45eb54e2c62a36387afa4ba2c301f8 Mon Sep 17 00:00:00 2001 From: Adarsh Chidirala <161786489+adarsh-chidirala@users.noreply.github.com> Date: Thu, 21 Nov 2024 20:30:49 -0600 Subject: [PATCH 01/23] Update README.md --- README.md | 138 +++++++++++++++++++++++++++++++++++++++++++++++------- 1 file changed, 120 insertions(+), 18 deletions(-) diff --git a/README.md b/README.md index f746e56..6b33f89 100644 --- a/README.md +++ b/README.md @@ -1,29 +1,131 @@ -# Project 2 +# Machine Learning +## Project 2 -Select one of the following two options: +# Group Members - Contribution -## Boosting Trees +* Venkata Naga Lakshmi Sai Snigdha Sri Jata - A20560684 - 33.33% +* Sharan Rama Prakash Shenoy - A20560684 - 33.33% +* Adarsh Chidirala - A20561069 - 33.33% -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. +# ################################################### +## Usage Instructions -Put your README below. Answer the following questions. +### Installation -* 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? +To get started with this project, first you need **Python 3.x**. Then follow these installation steps: -## Model Selection +#### 1. Clone the Repository to your local machine: -Implement generic k-fold cross-validation and bootstrapping model selection methods. +```bash +git clone https://github.com/adarsh-chidirala/Project2_Adarsh_Ch_Group.git +``` +#### 2. Steps to Run the Code on Mac -In your README, answer the following questions: +Follow these steps to set up and run the project: -* 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. +1. **Create a Virtual Environment**: + - Navigate to your project directory and create a virtual environment using: + ```bash + python3 -m venv myenv + ``` -See sections 7.10-7.11 of Elements of Statistical Learning and the lecture notes. Pay particular attention to Section 7.10.2. +2. **Activate the Virtual Environment**: + - Activate the created virtual environment by running: + ```bash + source myenv/bin/activate + ``` -As usual, above-and-beyond efforts will be considered for bonus points. +3. **Install Required Libraries**: + - Install the necessary Python libraries with the following command: + ```bash + pip install numpy pandas matplotlib scikit-learn + ``` + +4. **Run the Script**: + - Navigate to the directory containing your script and run it: + ```bash + python project2.py + ``` + +Make sure that the script `project2.py` and any required dataset files are correctly placed in your project directory. + +#### Steps to Run the Code on Windows + +Follow these instructions to set up and execute the project on a Windows system: + + +1. **Create a Virtual Environment**: + - Open Command Prompt and navigate to your project directory: + ```cmd + cd path\to\your\project\directory + ``` + - Create a virtual environment in your project directory by running: + ```cmd + python -m venv myenv + ``` + +2. **Activate the Virtual Environment**: + - Activate the virtual environment with the following command: + ```cmd + myenv\Scripts\activate + ``` + +3. **Install Required Libraries**: + - Install the necessary libraries by executing: + ```cmd + pip install numpy pandas matplotlib scikit-learn + ``` + +4. **Run the Script**: + - Make sure the script `project2.py` and any necessary dataset files are placed in your project directory. Run the script with: + ```cmd + python project2.py + ``` + +Ensure that all paths are correct and relevant files are located in the specified directories. + + + +### Introduction +## Heart Arthemia Prediction Using Model Selection using + + + +### Usage of Model Selection + +## 1. Do your cross-validation and bootstrapping model selectors agree with a simpler model selector like AIC in simple cases (like linear regression)? + + +## 2. In what cases might the methods you've written fail or give incorrect or undesirable results? + + +## 3. What could you implement given more time to mitigate these cases or help users of your methods? + + +## 4. What parameters have you exposed to your users in order to use your model selectors. + + From 6a506ee8800d6a15c43c16d5107510580a3e0ee4 Mon Sep 17 00:00:00 2001 From: Adarsh Chidirala <161786489+adarsh-chidirala@users.noreply.github.com> Date: Thu, 21 Nov 2024 20:34:34 -0600 Subject: [PATCH 02/23] Update README.md --- README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/README.md b/README.md index 6b33f89..6d41bac 100644 --- a/README.md +++ b/README.md @@ -49,7 +49,7 @@ Follow these steps to set up and run the project: Make sure that the script `project2.py` and any required dataset files are correctly placed in your project directory. -#### Steps to Run the Code on Windows +#### 3. Steps to Run the Code on Windows Follow these instructions to set up and execute the project on a Windows system: From 3a98c1e5ca8065b86962fa5885639eb735af231a Mon Sep 17 00:00:00 2001 From: Adarsh Chidirala <161786489+adarsh-chidirala@users.noreply.github.com> Date: Thu, 21 Nov 2024 20:39:50 -0600 Subject: [PATCH 03/23] Update README.md --- README.md | 14 +++++++------- 1 file changed, 7 insertions(+), 7 deletions(-) diff --git a/README.md b/README.md index 6d41bac..291665f 100644 --- a/README.md +++ b/README.md @@ -86,23 +86,23 @@ Ensure that all paths are correct and relevant files are located in the specifie -### Introduction -## Heart Arthemia Prediction Using Model Selection using +## Introduction +### Heart Arthemia Prediction Using Model Selection using -### Usage of Model Selection +## Usage of Model Selection -## 1. Do your cross-validation and bootstrapping model selectors agree with a simpler model selector like AIC in simple cases (like linear regression)? +### 1. Do your cross-validation and bootstrapping model selectors agree with a simpler model selector like AIC in simple cases (like linear regression)? -## 2. In what cases might the methods you've written fail or give incorrect or undesirable results? +### 2. In what cases might the methods you've written fail or give incorrect or undesirable results? -## 3. What could you implement given more time to mitigate these cases or help users of your methods? +### 3. What could you implement given more time to mitigate these cases or help users of your methods? -## 4. What parameters have you exposed to your users in order to use your model selectors. +### 4. What parameters have you exposed to your users in order to use your model selectors. +- i. K-fold cross validation AIC score: + ![Patient Test Image](patient_ aic_k_fold.jpeg) +- ii. Bootstrap AIC score: + ![Patient Test Image](patient_ aic_bootstrap.jpeg) +- iii. K-fold cross validation AIC distribution: + ![Patient Test Image](patient_ aic_dis_k_fold.jpeg) +- iv. Bootstrap AIC distribution: + ![Patient Test Image](patient_ aic_dis_bootstrap.jpeg) +- v. Bootstrap AIC distribution: + ![Patient Test Image](patient_output.jpeg) From a4ca7e0cc0f4fdbd66b38aaf7eea033e7cf20612 Mon Sep 17 00:00:00 2001 From: Adarsh Chidirala <161786489+adarsh-chidirala@users.noreply.github.com> Date: Thu, 21 Nov 2024 23:14:22 -0600 Subject: [PATCH 05/23] Add files via upload --- customer_ aic_dis_bootstrap.png | Bin 0 -> 145094 bytes customer_ aic_distr_k_fold.png | Bin 0 -> 158072 bytes customer_ aic_k_fold.png | Bin 0 -> 213431 bytes customer_aic_bootstrap.png | Bin 0 -> 264673 bytes customer_dataset.csv | 101 +++++++++++++++ customer_output.png | Bin 0 -> 101556 bytes patient_ aic_bootstrap.png | Bin 0 -> 308791 bytes patient_ aic_dis_bootstrap.png | Bin 0 -> 156592 bytes patient_ aic_dis_k_fold.png | Bin 0 -> 147821 bytes patient_ aic_k_fold.png | Bin 0 -> 217911 bytes patient_data.csv | 101 +++++++++++++++ patient_output.png | Bin 0 -> 87589 bytes project2.py | 219 ++++++++++++++++++++++++++++++++ 13 files changed, 421 insertions(+) create mode 100644 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zkSa^@1W21cp~hocq9jQVCk$J;R^PMu9sQB&r`9(>G(1@6xx@VI`RRdmAbvcE#Dy2U zg(?5(Fo%$O+<*1~`HUKB&|$+lOVTPmj}iO=0rjpB1!(6L^+zAsZAq0T5f)u?s48b` z!paNC`*heV>E0#PQvqZFOGgLW!oLy<-mlQ7GbkmJ07-@_w=Q`&o-x~j)8Auz2CR^%Kj$>XYFzAYQ(86NRd@d~=oCGZ8{JeGYevJ56Bgz;Q{*)ksMe zHgCVAdq>X1Gs^mHV(bg;e%i`JPqWcKw&c(LO*aXN$$uzmf35Q@O=JH7R+IjUw)lp5 z#Ebla&Iv$7y&7PTA<(aT=EDCo=fcm14xVI_r(zZth!o`MI1tp9+T*&X& z>o2x38qm5f4m3AKi_#M$i#>j=Q$KME3t={sa9_3gHpQN6%Py_SH@3hL?gL;ah z0bK9(3y=@|@;Itbm*&*FUb^HR_d(yNyK+IuINMgV#4^uQ0Jk2?-aK{nDPSm7myfQg zse$s@j$M;VALF0whH?md$jEGfBJ?+t^+1-U*>@69bkc!p@ZmOfVM7dm_7haqQkfUaG`?-~zEwYs>gX z=MmnTb8iq&ZfB|NE0z!PNw)vGyMKFbL9or|`NiY3^QDFt@W7vn!X5b{xJkhO0q*c0 A2><{9 literal 0 HcmV?d00001 diff --git a/project2.py b/project2.py new file mode 100644 index 0000000..0585afd --- /dev/null +++ b/project2.py @@ -0,0 +1,219 @@ +import numpy as np +import pandas as pd +import matplotlib.pyplot as plt + +class Model_Selector: + def AIC_calculator(self, X, y, beta): + + #Calculating the AIC scores for the models + + length_y = len(y) + preds = X @ beta + residual = y - preds + rss = np.sum(residual**2) + square_of_sigma = rss / length_y + log_likelihood = -0.5 * length_y * (np.log(2 * np.pi * square_of_sigma) + 1) + + length_beta = len(beta) # Number of coefficients + aic_scores = 2 * length_beta - 2 * log_likelihood + return aic_scores + + def linear_regression_model(self, X, y): + + #Implement Linear regression model + + XTX = X.T @ X + XTy = X.T @ y + beta = np.linalg.solve(XTX, XTy) + return beta + + def ridge_regression_model(self, X, y, alpha=1.0): + #Implement Ridge Regression model. + + features_n = X.shape[1] + XTX = X.T @ X + alpha * np.eye(features_n) + XTy = X.T @ y + beta = np.linalg.solve(XTX, XTy) + return beta + + def lasso_regression_model(self, X, y, alpha=1.0, max_iter=1000, tol=1e-4): + #Implement Lasso Regression model + + n, m = X.shape + beta = np.zeros(m) + for _ in range(max_iter): + beta_value = beta.copy() + for j in range(m): + residual = y - X @ beta + beta[j] * X[:, j] + rho = X[:, j].T @ residual + if rho < -alpha: + beta[j] = (rho + alpha) / (X[:, j] @ X[:, j]) + elif rho > alpha: + beta[j] = (rho - alpha) / (X[:, j] @ X[:, j]) + else: + beta[j] = 0 + if np.linalg.norm(beta - beta_value, ord=1) < tol: + break + return beta + + def k_fold_cross_validation(self, X, y, model_fn, alpha=None, k=5): + n = len(y) + indices = np.arange(n) + np.random.shuffle(indices) + fold_size = n // k + aic_scores = [] + + for i in range(k): + test_indices = indices[i * fold_size:(i + 1) * fold_size] + train_indices = np.setdiff1d(indices, test_indices) + + X_train, X_test = X[train_indices], X[test_indices] + y_train, y_test = y[train_indices], y[test_indices] + + if alpha is not None: + beta = model_fn(X_train, y_train, alpha) + else: + beta = model_fn(X_train, y_train) + + aic_score = self.AIC_calculator(X_test, y_test, beta) + aic_scores.append(aic_score) + + return aic_scores + + def bootstrap_validation(self, X, y, model_fn, alpha=None, n_bootstraps=100): + n = len(y) + aic_scores = [] + + for _ in range(n_bootstraps): + bootstrap_indices = np.random.choice(n, size=n, replace=True) + X_bootstrap, y_bootstrap = X[bootstrap_indices], y[bootstrap_indices] + + if alpha is not None: + beta = model_fn(X_bootstrap, y_bootstrap, alpha) + else: + beta = model_fn(X_bootstrap, y_bootstrap) + + aic_score = self.AIC_calculator(X_bootstrap, y_bootstrap, beta) + aic_scores.append(aic_score) + + return aic_scores + +def summarize_results(aic_scores): + n = len(aic_scores) + mean_aic = sum(aic_scores) / n + variance = sum((x - mean_aic) ** 2 for x in aic_scores) / n + std_dev = variance ** 0.5 + return mean_aic, std_dev + +def plot_results(results): + """ + Plot the AIC results for k-Fold and Bootstrapping across models using horizontal bars. + """ + models = list(results.keys()) + mean_aic_kf = [results[model]["mean_aic_kf"] for model in models] + mean_aic_bootstrap = [results[model]["mean_aic_bootstrap"] for model in models] + kf_std_dev = [results[model]["kf_std_dev"] for model in models] + bootstrap_std_dev = [results[model]["bootstrap_std_dev"] for model in models] + + # k-Fold Horizontal Bar Plot with Error Bars + fig, ax = plt.subplots(figsize=(8, 6)) + ax.barh(models, mean_aic_kf, color='green', xerr=kf_std_dev, capsize=5) + ax.set_title('k-Fold Cross-Validation AIC') + ax.set_ylabel('Models') + ax.set_xlabel('AIC') + plt.show() + + # Bootstrap AIC Horizontal Bar Plot with Error Bars + fig, ax = plt.subplots(figsize=(8, 6)) + ax.barh(models, mean_aic_bootstrap, color='purple', xerr=bootstrap_std_dev, capsize=5) + ax.set_title('Bootstrap AIC') + ax.set_ylabel('Models') + ax.set_xlabel('AIC') + plt.show() + + # Boxplots for AIC Distribution + fig, ax = plt.subplots(figsize=(8, 6)) + ax.boxplot([results[model]["kf_scores"] for model in models], vert=True) + ax.set_title('k-Fold AIC Distribution') + ax.set_xticklabels(models) + ax.set_ylabel('AIC') + plt.show() + + fig, ax = plt.subplots(figsize=(8, 6)) + ax.boxplot([results[model]["bootstrap_scores"] for model in models], vert=True) + ax.set_title('Bootstrap AIC Distribution') + ax.set_xticklabels(models) + ax.set_ylabel('AIC') + plt.show() + +def generic_process(data, X_columns, y_column): + """ + Generic process to evaluate AIC for Linear, Ridge, and Lasso models on any dataset. + """ + # Split features and target + X = data[X_columns].values + y = data[y_column].values + + # Initialize Model_Selector + selector = Model_Selector() + + # Define models + models = { + 'linear': selector.linear_regression_model, + 'ridge': lambda X, y: selector.ridge_regression_model(X, y, alpha=1.0), + 'lasso': lambda X, y: selector.lasso_regression_model(X, y, alpha=1.0) + } + + results = {} + + for model_name, model_fn in models.items(): + print(f"Evaluating model: {model_name.capitalize()}") + + # Perform k-Fold Cross-Validation + aic_scores_kf = selector.k_fold_cross_validation(X, y, model_fn, k=5) + + # Perform Bootstrapping + aic_scores_bootstrap = selector.bootstrap_validation(X, y, model_fn, n_bootstraps=100) + + # Calculate mean and standard deviation + mean_aic_kf, std_aic_kf = summarize_results(aic_scores_kf) + mean_aic_bootstrap, std_aic_bootstrap = summarize_results(aic_scores_bootstrap) + + # Save the results + results[model_name] = { + "mean_aic_kf": mean_aic_kf, + "mean_aic_bootstrap": mean_aic_bootstrap, + "kf_std_dev": std_aic_kf, + "bootstrap_std_dev": std_aic_bootstrap, + "kf_scores": aic_scores_kf, + "bootstrap_scores": aic_scores_bootstrap + } + + # Find the best model + best_model = None + best_mean_aic = float('inf') + + for model_name, scores in results.items(): + avg_aic = (scores["mean_aic_kf"] + scores["mean_aic_bootstrap"]) / 2 + print(f"\n{model_name.capitalize()} - Mean AIC: k-Fold: {scores['mean_aic_kf']:.3f}, Bootstrapping: {scores['mean_aic_bootstrap']:.3f}") + + if avg_aic < best_mean_aic: + best_mean_aic = avg_aic + best_model = model_name + + print(f"\nBest Model: {best_model.capitalize()} with an average AIC of {best_mean_aic:.3f}") + + # Plot results + plot_results(results) + + +# Example Usage: +if __name__ == "__main__": + + data = pd.read_csv('patient_data.csv') + + feature_columns = ['RR_Interval','QRS_Duration','QT_Interval'] + target_column = 'Heart_Rate' + + # Run the process + generic_process(data, feature_columns, target_column) \ No newline at end of file From 190327c813120412fd448b6e9830bb92221cc52b Mon Sep 17 00:00:00 2001 From: Adarsh Chidirala <161786489+adarsh-chidirala@users.noreply.github.com> Date: Thu, 21 Nov 2024 23:16:32 -0600 Subject: [PATCH 06/23] Update README.md --- README.md | 1 - 1 file changed, 1 deletion(-) diff --git a/README.md b/README.md index da46670..69f989a 100644 --- a/README.md +++ b/README.md @@ -2,7 +2,6 @@ ## Project 2 # Group Members - Contribution - * Venkata Naga Lakshmi Sai Snigdha Sri Jata - A20560684 - 33.33% * Sharan Rama Prakash Shenoy - A20560684 - 33.33% * Adarsh Chidirala - A20561069 - 33.33% From 90dd7517df11f94aced06194d2b1223de55a8aab Mon Sep 17 00:00:00 2001 From: Adarsh Chidirala <161786489+adarsh-chidirala@users.noreply.github.com> Date: Thu, 21 Nov 2024 23:17:16 -0600 Subject: [PATCH 07/23] Update README.md --- README.md | 15 ++++++++------- 1 file changed, 8 insertions(+), 7 deletions(-) diff --git a/README.md b/README.md index 69f989a..a4bed15 100644 --- a/README.md +++ b/README.md @@ -169,21 +169,22 @@ Features (X_columns) and target (y_column): Columns to use from any dataset. - ii. Bootstrap AIC score: ![Customer Test Image](customer_aic_bootstrap.jpeg) - iii. K-fold cross validation AIC distribution: - ![Customer Test Image](customer_ aic_distr_k_fold.jpeg) + ![Customer Test Image](customer_aic_distr_k_fold.jpeg) - iv. Bootstrap AIC distribution: - ![Customer Test Image](customer_ aic_dis_bootstrap.jpeg) + ![Customer Test Image](customer_aic_dis_bootstrap.jpeg) - v. Bootstrap Output: ![Customer Test Image](customer_output.jpeg) ### 2. patient_data.csv: - Tests the model on a large dataset, and verifies if the predictions are reasonable. - i. K-fold cross validation AIC score: - ![Patient Test Image](patient_ aic_k_fold.jpeg) + ![Patient Test Image](patient_aic_k_fold.jpeg) - ii. Bootstrap AIC score: - ![Patient Test Image](patient_ aic_bootstrap.jpeg) + ![Patient Test Image](patient_aic_bootstrap.jpeg) - iii. K-fold cross validation AIC distribution: - ![Patient Test Image](patient_ aic_dis_k_fold.jpeg) + ![Patient Test Image](patient_aic_dis_k_fold.jpeg) - iv. Bootstrap AIC distribution: - ![Patient Test Image](patient_ aic_dis_bootstrap.jpeg) -- v. Bootstrap AIC distribution: + ![Patient Test Image](patient_aic_dis_bootstrap.jpeg) +- v. Bootstrap Output: ![Patient Test Image](patient_output.jpeg) + From f579c442544499342c81c04cb35e5297a15b7e4f Mon Sep 17 00:00:00 2001 From: Adarsh Chidirala <161786489+adarsh-chidirala@users.noreply.github.com> Date: Thu, 21 Nov 2024 23:18:12 -0600 Subject: [PATCH 08/23] Update README.md --- README.md | 21 +++++++++++---------- 1 file changed, 11 insertions(+), 10 deletions(-) diff --git a/README.md b/README.md index a4bed15..b536873 100644 --- a/README.md +++ b/README.md @@ -165,26 +165,27 @@ Features (X_columns) and target (y_column): Columns to use from any dataset. ### 1. customer_dataset.csv: - Tests the model on a small dataset, and verifies if the predictions are reasonable. - i. K-fold cross validation AIC score: - ![Customer Test Image](customer_aic_k_fold.jpeg) + ![Customer Test Image](customer_aic_k_fold.png) - ii. Bootstrap AIC score: - ![Customer Test Image](customer_aic_bootstrap.jpeg) + ![Customer Test Image](customer_aic_bootstrap.png) - iii. K-fold cross validation AIC distribution: - ![Customer Test Image](customer_aic_distr_k_fold.jpeg) + ![Customer Test Image](customer_aic_distr_k_fold.png) - iv. Bootstrap AIC distribution: - ![Customer Test Image](customer_aic_dis_bootstrap.jpeg) + ![Customer Test Image](customer_aic_dis_bootstrap.png) - v. Bootstrap Output: - ![Customer Test Image](customer_output.jpeg) + ![Customer Test Image](customer_output.png) ### 2. patient_data.csv: - Tests the model on a large dataset, and verifies if the predictions are reasonable. - i. K-fold cross validation AIC score: - ![Patient Test Image](patient_aic_k_fold.jpeg) + ![Patient Test Image](patient_aic_k_fold.png) - ii. Bootstrap AIC score: - ![Patient Test Image](patient_aic_bootstrap.jpeg) + ![Patient Test Image](patient_aic_bootstrap.png) - iii. K-fold cross validation AIC distribution: - ![Patient Test Image](patient_aic_dis_k_fold.jpeg) + ![Patient Test Image](patient_aic_dis_k_fold.png) - iv. Bootstrap AIC distribution: - ![Patient Test Image](patient_aic_dis_bootstrap.jpeg) + ![Patient Test Image](patient_aic_dis_bootstrap.png) - v. Bootstrap Output: - ![Patient Test Image](patient_output.jpeg) + ![Patient Test Image](patient_output.png) + From 50924bda817ec66f8e47fbccdea34de214a3cd73 Mon Sep 17 00:00:00 2001 From: Adarsh Chidirala <161786489+adarsh-chidirala@users.noreply.github.com> Date: Thu, 21 Nov 2024 23:21:08 -0600 Subject: [PATCH 09/23] Update README.md --- README.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/README.md b/README.md index b536873..2575b55 100644 --- a/README.md +++ b/README.md @@ -169,7 +169,7 @@ Features (X_columns) and target (y_column): Columns to use from any dataset. - ii. Bootstrap AIC score: ![Customer Test Image](customer_aic_bootstrap.png) - iii. K-fold cross validation AIC distribution: - ![Customer Test Image](customer_aic_distr_k_fold.png) + ![Customer Test Image](customer_aic_dis_bootstrap.png) - iv. Bootstrap AIC distribution: ![Customer Test Image](customer_aic_dis_bootstrap.png) - v. Bootstrap Output: @@ -178,7 +178,7 @@ Features (X_columns) and target (y_column): Columns to use from any dataset. ### 2. patient_data.csv: - Tests the model on a large dataset, and verifies if the predictions are reasonable. - i. K-fold cross validation AIC score: - ![Patient Test Image](patient_aic_k_fold.png) + ![Patient Test Image](patient_ aic_k_fold.png) - ii. Bootstrap AIC score: ![Patient Test Image](patient_aic_bootstrap.png) - iii. 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customer_aic_distr_k_fold.png | Bin 0 -> 158072 bytes customer_aic_k_fold.png | Bin 0 -> 213431 bytes customer_output.png | Bin 0 -> 101556 bytes patient_aic_bootstrap.png | Bin 0 -> 308791 bytes patient_aic_dis_bootstrap.png | Bin 0 -> 156592 bytes patient_aic_dis_k_fold.png | Bin 0 -> 147821 bytes patient_aic_k_fold.png | Bin 0 -> 217911 bytes patient_output.png | Bin 0 -> 87589 bytes 10 files changed, 0 insertions(+), 0 deletions(-) create mode 100644 customer_aic_bootstrap.png create mode 100644 customer_aic_dis_bootstrap.png create mode 100644 customer_aic_distr_k_fold.png create mode 100644 customer_aic_k_fold.png create mode 100644 customer_output.png create mode 100644 patient_aic_bootstrap.png create mode 100644 patient_aic_dis_bootstrap.png create mode 100644 patient_aic_dis_k_fold.png create mode 100644 patient_aic_k_fold.png create mode 100644 patient_output.png diff --git a/customer_aic_bootstrap.png b/customer_aic_bootstrap.png new file mode 100644 index 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zkSa^@1W21cp~hocq9jQVCk$J;R^PMu9sQB&r`9(>G(1@6xx@VI`RRdmAbvcE#Dy2U zg(?5(Fo%$O+<*1~`HUKB&|$+lOVTPmj}iO=0rjpB1!(6L^+zAsZAq0T5f)u?s48b` z!paNC`*heV>E0#PQvqZFOGgLW!oLy<-mlQ7GbkmJ07-@_w=Q`&o-x~j)8Auz2CR^%Kj$>XYFzAYQ(86NRd@d~=oCGZ8{JeGYevJ56Bgz;Q{*)ksMe zHgCVAdq>X1Gs^mHV(bg;e%i`JPqWcKw&c(LO*aXN$$uzmf35Q@O=JH7R+IjUw)lp5 z#Ebla&Iv$7y&7PTA<(aT=EDCo=fcm14xVI_r(zZth!o`MI1tp9+T*&X& z>o2x38qm5f4m3AKi_#M$i#>j=Q$KME3t={sa9_3gHpQN6%Py_SH@3hL?gL;ah z0bK9(3y=@|@;Itbm*&*FUb^HR_d(yNyK+IuINMgV#4^uQ0Jk2?-aK{nDPSm7myfQg zse$s@j$M;VALF0whH?md$jEGfBJ?+t^+1-U*>@69bkc!p@ZmOfVM7dm_7haqQkfUaG`?-~zEwYs>gX z=MmnTb8iq&ZfB|NE0z!PNw)vGyMKFbL9or|`NiY3^QDFt@W7vn!X5b{xJkhO0q*c0 A2><{9 literal 0 HcmV?d00001 From 4868a46a74ac8c4ce872eb4592fd645c6fc1bedf Mon Sep 17 00:00:00 2001 From: Adarsh Chidirala <161786489+adarsh-chidirala@users.noreply.github.com> Date: Thu, 21 Nov 2024 23:26:40 -0600 Subject: [PATCH 21/23] Update README.md --- README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/README.md b/README.md index 2575b55..11b25ac 100644 --- a/README.md +++ b/README.md @@ -178,7 +178,7 @@ Features (X_columns) and target (y_column): Columns to use from any dataset. ### 2. patient_data.csv: - Tests the model on a large dataset, and verifies if the predictions are reasonable. - i. K-fold cross validation AIC score: - ![Patient Test Image](patient_ aic_k_fold.png) + ![Patient Test Image](patient_aic_k_fold.png) - ii. Bootstrap AIC score: ![Patient Test Image](patient_aic_bootstrap.png) - iii. K-fold cross validation AIC distribution: From a4130f8bef27e055e03068941b9334912f095819 Mon Sep 17 00:00:00 2001 From: Adarsh Chidirala <161786489+adarsh-chidirala@users.noreply.github.com> Date: Thu, 21 Nov 2024 23:27:45 -0600 Subject: [PATCH 22/23] Update README.md --- README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/README.md b/README.md index 11b25ac..b536873 100644 --- a/README.md +++ b/README.md @@ -169,7 +169,7 @@ Features (X_columns) and target (y_column): Columns to use from any dataset. - ii. Bootstrap AIC score: ![Customer Test Image](customer_aic_bootstrap.png) - iii. K-fold cross validation AIC distribution: - ![Customer Test Image](customer_aic_dis_bootstrap.png) + ![Customer Test Image](customer_aic_distr_k_fold.png) - iv. Bootstrap AIC distribution: ![Customer Test Image](customer_aic_dis_bootstrap.png) - v. Bootstrap Output: From d6ccca8bffeda15289329894d08253e791d60f59 Mon Sep 17 00:00:00 2001 From: Adarsh Chidirala <161786489+adarsh-chidirala@users.noreply.github.com> Date: Thu, 21 Nov 2024 23:52:24 -0600 Subject: [PATCH 23/23] README.md --- README.md | 9 ++++----- 1 file changed, 4 insertions(+), 5 deletions(-) diff --git a/README.md b/README.md index b536873..4848459 100644 --- a/README.md +++ b/README.md @@ -125,17 +125,16 @@ To determine whether cross-validation and bootstrapping model selectors agree wi ### 2. In what cases might the methods you've written fail or give incorrect or undesirable results? Failures or undesirable results may occur under these conditions: -**Small Datasets:** Cross-validation and bootstrapping can give unreliable AIC scores when the dataset is too small. -**Non-balance Data:** Models trained on non-balance datasets might make biased predictions which affects the AIC calculations. +**Small Datasets:** k-fold Cross-validation and bootstrapping can give unreliable AIC scores when the dataset is too small. +**Non-balance Data:** Models training on the non-balance datasets, might make biased predictions which affects the AIC calculations. **Connected Predictions:** Strong connections between predictions can lead to wrong estimates, affecting AIC evaluations. **Wrong Model Assumptions:** AIC relies on specific model assumptions (e.g., linear regression assumes Gaussian errors). If these assumptions are wrong, AIC might not show the true model fit. -**Overfitting with Bootstrapping:** Repeated sampling with replacement might make bootstrapped datasets favor complex models too much, leading to high AIC values. +**Overfitting with Bootstrapping:** Repeated sampling with replacement might make bootstrapped datasets favor complex models too much, leading to high AIC values. ### 3. What could you implement given more time to mitigate these cases or help users of your methods? -1. Use Ridge and Lasso penalties during cross-validation: Regularization adds a penalty to the model's complexity to reduce overfitting. Ridge regression adds an L2 penalty (squared magnitude_value of coefficients), while Lasso regression adds an L1 penalty (absolute value of coefficients). +1. Use Ridge and Lasso penalties during cross-validation: Regularization adds a penalty to the model's complexity to reduce overfitting. Ridge regression adds an L2 penalty , while Lasso regression adds an L1 penalty. Use RidgeCV and LassoCV from scikit-learn: These classes perform cross-validation to find the better regularization parameter (alpha) for Ridge and Lasso regression. -Handle Imbalanced Data: 2. Use categorized sampling for k-fold cross-validation: Categorized k-fold ensures that each fold has the equal proportion of class labels as the original dataset, which shows imbalanced datasets. Implement balanced bootstrapping: Bootstrapping involves sampling with a stategy of replacement. Balanced bootstrapping ensures that each class is represented equally in each sample.

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