Appearance
question:# Semi-Supervised Learning with Scikit-Learn In this assessment, you are required to demonstrate your understanding of semi-supervised learning techniques using the `sklearn.semi_supervised` module. Follow the instructions below and implement Python code to complete the task. Task 1. **Dataset Preparation**: - Use the `make_classification` function from `sklearn.datasets` to generate a synthetic dataset with 300 samples, 20 features, 2 informative features, and 2 classes. - Randomly label 30% of the samples and assign `-1` to the rest, indicating unlabeled data. 2. **Self-Training Classifier**: - Implement the `SelfTrainingClassifier` with a `DecisionTreeClassifier` as the base estimator. - Use a threshold of `0.8` and a maximum of `10` iterations (`max_iter=10`). - Fit the classifier on the generated dataset and evaluate its performance on the labeled data (use accuracy as the metric). 3. **Label Propagation**: - Implement both `LabelPropagation` and `LabelSpreading` using the RBF kernel. - Train these models on the same dataset and evaluate their performance using accuracy on the labeled data. 4. **Comparison and Analysis**: - Compare the performance of `SelfTrainingClassifier`, `LabelPropagation`, and `LabelSpreading`. - Print and plot the accuracy of each method. - Provide insights into which method performed better and why, based on the results. Input and Output Formats - **Input**: No specific input is required from the user. - **Output**: Print and plot the accuracy of each classifier. Provide a comparison and analysis in the form of comments or markdown text in the code. Constraints - Make sure you import necessary libraries and handle any exceptions that may arise. - The code should be optimized for readability and efficiency where possible. Example Solution Structure ```python import numpy as np import matplotlib.pyplot as plt from sklearn.datasets import make_classification from sklearn.tree import DecisionTreeClassifier from sklearn.semi_supervised import SelfTrainingClassifier, LabelPropagation, LabelSpreading from sklearn.metrics import accuracy_score # Step 1: Dataset Preparation def create_dataset(): # Your code here pass # Step 2: Self-Training Classifier def self_training_classifier(X, y): # Your code here pass # Step 3: Label Propagation def label_propagation_methods(X, y): # Your code here pass # Step 4: Comparison and Analysis def compare_methods(): # Your code here pass if __name__ == "__main__": compare_methods() ``` Complete the functions to achieve the tasks outlined. Good luck!
answer:import numpy as np import matplotlib.pyplot as plt from sklearn.datasets import make_classification from sklearn.tree import DecisionTreeClassifier from sklearn.semi_supervised import SelfTrainingClassifier, LabelPropagation, LabelSpreading from sklearn.metrics import accuracy_score # Step 1: Dataset Preparation def create_dataset(): X, y = make_classification(n_samples=300, n_features=20, n_informative=2, n_redundant=0, n_classes=2, random_state=42) rng = np.random.RandomState(42) random_unlabeled_points = rng.rand(len(y)) < 0.7 y[random_unlabeled_points] = -1 return X, y # Step 2: Self-Training Classifier def self_training_classifier(X, y): base_classifier = DecisionTreeClassifier() self_training_model = SelfTrainingClassifier(base_classifier, threshold=0.8, max_iter=10) self_training_model.fit(X, y) labeled_points_mask = y != -1 y_pred = self_training_model.predict(X[labeled_points_mask]) return accuracy_score(y[labeled_points_mask], y_pred) # Step 3: Label Propagation def label_propagation_methods(X, y): labeled_points_mask = y != -1 lp_model = LabelPropagation(kernel='rbf') lp_model.fit(X, y) lp_pred = lp_model.predict(X[labeled_points_mask]) lp_accuracy = accuracy_score(y[labeled_points_mask], lp_pred) ls_model = LabelSpreading(kernel='rbf') ls_model.fit(X, y) ls_pred = ls_model.predict(X[labeled_points_mask]) ls_accuracy = accuracy_score(y[labeled_points_mask], ls_pred) return lp_accuracy, ls_accuracy # Step 4: Comparison and Analysis def compare_methods(): X, y = create_dataset() st_accuracy = self_training_classifier(X, y) lp_accuracy, ls_accuracy = label_propagation_methods(X, y) print(f"Self-Training Classifier Accuracy: {st_accuracy:.2f}") print(f"Label Propagation Accuracy: {lp_accuracy:.2f}") print(f"Label Spreading Accuracy: {ls_accuracy:.2f}") methods = ['Self-Training', 'Label Propagation', 'Label Spreading'] accuracies = [st_accuracy, lp_accuracy, ls_accuracy] plt.bar(methods, accuracies, color=['blue', 'green', 'red']) plt.ylabel('Accuracy') plt.title('Comparison of Semi-Supervised Learning Methods') plt.show() # Analysis print("nAnalysis:") if st_accuracy > lp_accuracy and st_accuracy > ls_accuracy: print("The Self-Training Classifier performed the best.") elif lp_accuracy > st_accuracy and lp_accuracy > ls_accuracy: print("The Label Propagation method performed the best.") elif ls_accuracy > st_accuracy and ls_accuracy > lp_accuracy: print("The Label Spreading method performed the best.") else: print("The methods showed comparable performance.") if __name__ == "__main__": compare_methods()
question:Objective Demonstrate your understanding of seaborn by setting themes and customizing plot appearances using seaborn and matplotlib. You are required to create a script that sets a specific theme, modifies certain plot elements, and generates different types of plots. Instructions: 1. Use the seaborn package to set a theme with the following specifications: - Style: "whitegrid" - Palette: "pastel" 2. Customize the theme further using matplotlib `rc` parameters to: - Remove the top and right spines from the plots. - Set the figure bg color to 'whitesmoke'. - Set the grid line color to 'lightgray'. 3. Generate a bar plot and a line plot using seaborn with the following data: - Bar plot data: - x values: `['A', 'B', 'C']` - y values: `[10, 20, 15]` - Line plot data: - x values: `range(10)` - y values: `[i ** 0.5 for i in range(10)]` 4. Ensure the plots are clearly labeled and titled: - Bar plot title: "Custom Themed Bar Plot" - Line plot title: "Custom Themed Line Plot" - x-axis label for bar plot: "Categories" - y-axis label for bar plot: "Values" - x-axis label for line plot: "X" - y-axis label for line plot: "Square Root of X" Expected Input There is no specific input required as the data for the plots is provided. Expected Output The output should be a Python script that: 1. Sets the specified seaborn theme. 2. Customizes the plot aesthetics with the given `rc` parameters. 3. Produces and displays a bar plot and a line plot with the provided data and labeling. Constraints and Performance - Use seaborn and matplotlib libraries. - The script should run efficiently and produce the plots without errors. Example Usage Here is an example of how the script might be structured: ```python import seaborn as sns import matplotlib.pyplot as plt # Setting the theme and custom parameters sns.set_theme(style="whitegrid", palette="pastel") custom_params = {"axes.spines.right": False, "axes.spines.top": False, "figure.facecolor": "whitesmoke", "grid.color": "lightgray"} sns.set(rc=custom_params) # Data for plots bar_x = ["A", "B", "C"] bar_y = [10, 20, 15] line_x = range(10) line_y = [i ** 0.5 for i in range(10)] # Creating the bar plot plt.figure() sns.barplot(x=bar_x, y=bar_y) plt.title("Custom Themed Bar Plot") plt.xlabel("Categories") plt.ylabel("Values") plt.show() # Creating the line plot plt.figure() sns.lineplot(x=line_x, y=line_y) plt.title("Custom Themed Line Plot") plt.xlabel("X") plt.ylabel("Square Root of X") plt.show() ```
answer:import seaborn as sns import matplotlib.pyplot as plt def create_plots(): # Setting the theme and custom parameters sns.set_theme(style="whitegrid", palette="pastel") custom_params = {"axes.spines.right": False, "axes.spines.top": False, "figure.facecolor": "whitesmoke", "grid.color": "lightgray"} sns.set(rc=custom_params) # Data for plots bar_x = ["A", "B", "C"] bar_y = [10, 20, 15] line_x = range(10) line_y = [i ** 0.5 for i in range(10)] # Creating the bar plot plt.figure() sns.barplot(x=bar_x, y=bar_y) plt.title("Custom Themed Bar Plot") plt.xlabel("Categories") plt.ylabel("Values") plt.show() # Creating the line plot plt.figure() sns.lineplot(x=line_x, y=line_y) plt.title("Custom Themed Line Plot") plt.xlabel("X") plt.ylabel("Square Root of X") plt.show()
question:# Question: Isotonic Regression with Custom Interpolation You are given a dataset consisting of 1-dimensional feature values `X` and corresponding target values `y`. Your task is to implement a function that performs isotonic regression on the data and then uses the fitted model to predict values for a new set of feature values. You should also implement custom interpolation for predicting new data points that fall between the original feature values. Function Signature ```python def isotonic_regression_with_interpolation(X_train: List[float], y_train: List[float], X_test: List[float], increasing: Union[bool, str] = "auto") -> List[float]: pass ``` Input - `X_train`: A list of floats representing the training feature values. - `y_train`: A list of floats representing the training target values. - `X_test`: A list of floats representing the test feature values. - `increasing`: A boolean or string ('auto') indicating whether the fitted values should be non-decreasing (True) or non-increasing (False). If set to 'auto', the direction is chosen based on Spearman's rank correlation coefficient. Output A list of floats representing the predicted values for each feature in `X_test`. Constraints - The lengths of `X_train` and `y_train` will be equal. - The elements of `X_train` and `X_test` are arbitrary real numbers. - The size of `X_train` and `y_train` will not exceed 10,000. Performance Requirements - The function should run efficiently with respect to both time and space complexity. - Scikit-learn's `IsotonicRegression` should be used for fitting the model. # Example ```python X_train = [1, 2, 3, 4, 5] y_train = [5, 6, 7, 8, 9] X_test = [1.5, 2.5, 3.5] # Assuming 'increasing' defaults to 'auto' print(isotonic_regression_with_interpolation(X_train, y_train, X_test)) # Output: [5.5, 6.5, 7.5] (exact values may vary) ``` # Explanation In this example, the training data [5, 6, 7, 8, 9] is fitted to a non-decreasing function of the training features [1, 2, 3, 4, 5]. The predicted values for test features [1.5, 2.5, 3.5] are interpolated as [5.5, 6.5, 7.5], assuming we fit a linear piecewise function. # Note Ensure your implementation uses scikit-learn's `IsotonicRegression` class for fitting the data.
answer:from typing import List, Union from sklearn.isotonic import IsotonicRegression import numpy as np from scipy.stats import spearmanr def isotonic_regression_with_interpolation(X_train: List[float], y_train: List[float], X_test: List[float], increasing: Union[bool, str] = "auto") -> List[float]: # Convert the train arrays to numpy arrays for easier manipulation X_train = np.array(X_train) y_train = np.array(y_train) # Determine the 'increasing' parameter if set to 'auto' if increasing == 'auto': corr, _ = spearmanr(X_train, y_train) increasing = corr >= 0 # Fit the isotonic regression model iso_reg = IsotonicRegression(increasing=increasing) y_train_ = iso_reg.fit_transform(X_train, y_train) # Perform interpolation for the test points def interpolate(x): # If x is exactly one of the training points, return the corresponding isotonic y if x in X_train: return y_train_[X_train.tolist().index(x)] # Find the interval [x_i, x_{i+1}] that contains x idx = np.searchsorted(X_train, x, side='right') - 1 if idx == -1: return y_train_[0] # If x is less than any x_i, return the smallest y_i if idx == len(X_train) - 1: return y_train_[-1] # If x is greater than any x_i, return the largest y_i x1, x2 = X_train[idx], X_train[idx + 1] y1, y2 = y_train_[idx], y_train_[idx + 1] # Linear interpolation return y1 + (y2 - y1) * (x - x1) / (x2 - x1) y_test_pred = [interpolate(x) for x in X_test] return y_test_pred
question:Objective: Demonstrate your understanding of fundamental and advanced concepts using the `statistics` module in Python. Description: You must implement a function `analyze_data_statistics(data)` that takes a list of floating-point numbers as input and calculates: 1. Arithmetic mean 2. Geometric mean (if the data does not contain negative values or zeros) 3. Harmonic mean (if the data does not contain negative values) 4. Median 5. Population variance 6. Sample variance 7. Population standard deviation 8. Sample standard deviation 9. Quantiles (quartiles, deciles, and percentiles) 10. Pearson's correlation coefficient between the input data and a second list of equal length consisting of uniformly distributed random numbers between min and max of the input data. You also need to handle edge cases appropriately (e.g., empty data, negative or zero values where not allowed). Input: - `data`: A list of floating-point numbers [x1, x2, ..., xn] Output: Return a dictionary with the following keys: - `mean` - `geometric_mean` - `harmonic_mean` - `median` - `population_variance` - `sample_variance` - `population_standard_deviation` - `sample_standard_deviation` - `quantiles` (including keys: `quartiles`, `deciles`, and `percentiles`) - `correlation_with_uniform_dist` Constraints: - The input data will always have at least two elements. Example: ```python def analyze_data_statistics(data): # Your code here data = [2.5, 3.6, 4.8, 1.9, 3.3, 2.7, 3.1] result = analyze_data_statistics(data) print(result) ``` Expected output: ```python { 'mean': 3.1285714285714286, 'geometric_mean': 3.04615093433451, 'harmonic_mean': 3.009264756249907, 'median': 3.1, 'population_variance': 0.8044897959183676, 'sample_variance': 0.9382380952380953, 'population_standard_deviation': 0.8969331293961479, 'sample_standard_deviation': 0.9686162280458832, 'quantiles': { 'quartiles': [2.5, 3.1, 3.6], 'deciles': [1.9, 2.31, 2.7, 3.03, 3.1, 3.157142857142857, 3.424, 3.6, 4.02], 'percentiles': [...] }, 'correlation_with_uniform_dist': -0.1489825 } ``` Note: - You may assume the input data contains sufficient elements to calculate all the requested statistics. - For `quantiles`, the output should show the required cut points as sub-values.
answer:import statistics import numpy as np def analyze_data_statistics(data): Given a list of floating-point numbers, calculates various statistical metrics. :param data: list of float :return: dict containing mean, geometric_mean, harmonic_mean, median, population_variance, sample_variance, population_standard_deviation, sample_standard_deviation, quantiles, correlation_with_uniform_dist if not data: raise ValueError("The input data must contain at least two elements.") result = {} # Arithmetic mean result['mean'] = statistics.mean(data) # Geometric mean if all(x > 0 for x in data): result['geometric_mean'] = statistics.geometric_mean(data) else: result['geometric_mean'] = None # Harmonic mean if all(x > 0 for x in data): result['harmonic_mean'] = statistics.harmonic_mean(data) else: result['harmonic_mean'] = None # Median result['median'] = statistics.median(data) # Population variance result['population_variance'] = statistics.pvariance(data) # Sample variance result['sample_variance'] = statistics.variance(data) # Population standard deviation result['population_standard_deviation'] = statistics.pstdev(data) # Sample standard deviation result['sample_standard_deviation'] = statistics.stdev(data) # Quantiles quartiles = [np.percentile(data, q) for q in [25, 50, 75]] deciles = [np.percentile(data, q) for q in range(10, 100, 10)] percentiles = [np.percentile(data, q) for q in range(1, 101)] result['quantiles'] = { 'quartiles': quartiles, 'deciles': deciles, 'percentiles': percentiles } # Pearson's correlation coefficient with a random uniform distribution min_val, max_val = min(data), max(data) uniform_data = np.random.uniform(min_val, max_val, len(data)) result['correlation_with_uniform_dist'] = np.corrcoef(data, uniform_data)[0, 1] return result