Appearance
question:# PyTorch Autograd Coding Assessment Objective Demonstrate your understanding of PyTorch's autograd functionalities by implementing a custom backward function and utilizing higher-level API functions (Jacobians, Hessians). Problem Statement You are required to implement a PyTorch custom function that behaves like the `torch.exp` function but with a custom backward pass. Additionally, compute the Jacobian and Hessian matrices for a given loss function using PyTorch's higher-level API. Custom Function Implementation 1. Create a custom PyTorch function `ExpWithCustomGrad` that computes the exponential of a tensor. 2. Implement a custom backward pass for this function where the gradient is twice the standard gradient of `torch.exp`. Jacobian and Hessian Calculation 1. Given a simple neural network model and a scalar loss function, compute: - The Jacobian of the loss with respect to the model parameters. - The Hessian of the loss with respect to a specific parameter tensor in the model. # Implementation Details - Your custom function should inherit from `torch.autograd.Function` and override the `forward` and `backward` methods. - Use the custom function as the activation function in a simple neural network. - Define a scalar loss function (e.g., mean squared error). - Compute the gradients, Jacobians, and Hessians using the provided higher-level API functions from `torch.autograd.functional`. # Input and Output Formats - **Input**: A tensor `x` of shape (N, M) where N is the number of data points, and M is the number of features. - **Output**: Print the custom gradients, Jacobian, and Hessian matrices. # Constraints - Do not use any pre-existing functions for computing the Jacobian or Hessian other than those provided by `torch.autograd.functional`. # Performance Requirements - Your implementation should handle tensors of size up to (1000, 1000) efficiently. Example Suppose you have an input tensor `x` and a simple neural network with one linear layer followed by your custom activation function. If the loss is defined as the mean squared error between the model's output and some target tensor `y`, you should implement: 1. The custom forward and backward passes. 2. The calculation of the Jacobian and Hessian for this loss function. Code Template ```python import torch from torch.autograd import Function import torch.nn as nn import torch.autograd.functional as F class ExpWithCustomGrad(Function): @staticmethod def forward(ctx, input): ctx.save_for_backward(input) return input.exp() @staticmethod def backward(ctx, grad_output): # Implement custom backward pass input, = ctx.saved_tensors grad_input = 2 * grad_output * input.exp() # Custom gradient return grad_input # Simple neural network using custom activation function class SimpleModel(nn.Module): def __init__(self): super(SimpleModel, self).__init__() self.linear = nn.Linear(10, 5) def forward(self, x): x = self.linear(x) x = ExpWithCustomGrad.apply(x) return x # Create model, data, and target model = SimpleModel() x = torch.randn(100, 10, requires_grad=True) y = torch.randn(100, 5) # Define a loss function loss_func = nn.MSELoss() # Forward pass output = model(x) loss = loss_func(output, y) # Compute gradients using backward loss.backward() # Compute Jacobian def loss_fn(model_params): output = model(x) loss = loss_func(output, y) return loss params = list(model.parameters()) jacobian = F.jacobian(loss_fn, params) # Compute Hessian for the first parameter tensor hessian = F.hessian(loss_fn, params[0]) print("Jacobian:", jacobian) print("Hessian:", hessian) ``` Ensure your implementation adheres to these specifications and test it with different input sizes for robustness.
answer:import torch from torch.autograd import Function import torch.nn as nn import torch.autograd.functional as F class ExpWithCustomGrad(Function): @staticmethod def forward(ctx, input): ctx.save_for_backward(input) return input.exp() @staticmethod def backward(ctx, grad_output): # Retrieve saved tensor input, = ctx.saved_tensors # Custom gradient: twice the standard gradient of torch.exp grad_input = 2 * grad_output * input.exp() return grad_input # Simple neural network using custom activation function class SimpleModel(nn.Module): def __init__(self): super(SimpleModel, self).__init__() self.linear = nn.Linear(10, 5) def forward(self, x): x = self.linear(x) x = ExpWithCustomGrad.apply(x) return x # Function to compute loss def compute_loss(model, x, y): output = model(x) loss = nn.MSELoss()(output, y) return loss def main_example(): # Create model, data, and target model = SimpleModel() x = torch.randn(100, 10, requires_grad=True) y = torch.randn(100, 5) # Compute loss loss = compute_loss(model, x, y) # Backward pass loss.backward() # Obtain model parameters params = [p for p in model.parameters() if p.requires_grad] # Compute Jacobian and Hessian jacobian = [F.jacobian(lambda p: compute_loss(model, x, y), p) for p in params] hessian = [F.hessian(lambda p: compute_loss(model, x, y), p) for p in params] return loss, jacobian, hessian if __name__ == "__main__": loss, jacobian, hessian = main_example() print("Loss:", loss) print("Jacobian:", jacobian) print("Hessian:", hessian)
question:You are given a dataset representing sales data for a chain of stores. Each entry in the dataset includes the `store_id`, `item_id`, `date`, `units_sold`, and `total_sales`. Your task is to implement a function using pandas to assess and visualize various statistics based on the sales data. # Function Signature ```python import pandas as pd import matplotlib.pyplot as plt def analyze_sales(sales_df: pd.DataFrame) -> dict: Function to analyze sales data and provide insights. Parameters: sales_df (pd.DataFrame): A DataFrame containing sales data with columns ['store_id', 'item_id', 'date', 'units_sold', 'total_sales']. Returns: dict: A dictionary containing several analysis results: - 'total_units_sold_per_store': A DataFrame with total units sold per store. - 'total_sales_per_store': A DataFrame with total sales per store. - 'average_units_sold_per_item': A DataFrame with average units sold per item. - 'sales_summary': A DataFrame with mean, median, std, and total sales for each store. - 'total_sales_per_store_plot_path': A str indicating the path to the bar plot of total sales per store. ``` # Instructions 1. **Total Units Sold Per Store**: Compute the total number of units sold in each store. 2. **Total Sales Per Store**: Compute the total sales amount for each store. 3. **Average Units Sold Per Item**: Compute the average number of units sold per item across all stores. 4. **Sales Summary**: Provide a summary for each store consisting of the mean, median, standard deviation, and total of the `total_sales`. 5. **Visualization**: Create a bar plot showing the total sales for each store and save the plot to a file, returning the file path in the results dictionary. # Constraints - You can assume that the input DataFrame is valid and contains the specified columns. - Use appropriate pandas functions to group the data and perform the required computations. - The plot should be saved as `total_sales_per_store.png`. # Example Usage ```python # Sample DataFrame data = { 'store_id': [1, 1, 2, 2, 3, 3, 3], 'item_id': [101, 102, 101, 103, 102, 101, 104], 'date': ['2021-01-01', '2021-01-01', '2021-01-01', '2021-01-01', '2021-01-01', '2021-01-01', '2021-01-01'], 'units_sold': [10, 15, 13, 7, 10, 12, 5], 'total_sales': [100, 150, 130, 70, 100, 120, 50] } # Load data into DataFrame sales_df = pd.DataFrame(data) # Analyze sales results = analyze_sales(sales_df) # Access the results total_units_sold_per_store = results['total_units_sold_per_store'] total_sales_per_store = results['total_sales_per_store'] average_units_sold_per_item = results['average_units_sold_per_item'] sales_summary = results['sales_summary'] total_sales_per_store_plot_path = results['total_sales_per_store_plot_path'] print(total_units_sold_per_store) print(total_sales_per_store) print(average_units_sold_per_item) print(sales_summary) print(f"Plot saved at: {total_sales_per_store_plot_path}") ```
answer:import pandas as pd import matplotlib.pyplot as plt def analyze_sales(sales_df: pd.DataFrame) -> dict: Function to analyze sales data and provide insights. Parameters: sales_df (pd.DataFrame): A DataFrame containing sales data with columns ['store_id', 'item_id', 'date', 'units_sold', 'total_sales']. Returns: dict: A dictionary containing several analysis results: - 'total_units_sold_per_store': A DataFrame with total units sold per store. - 'total_sales_per_store': A DataFrame with total sales per store. - 'average_units_sold_per_item': A DataFrame with average units sold per item. - 'sales_summary': A DataFrame with mean, median, std, and total sales for each store. - 'total_sales_per_store_plot_path': A str indicating the path to the bar plot of total sales per store. # Total Units Sold Per Store total_units_sold_per_store = sales_df.groupby('store_id')['units_sold'].sum().reset_index() # Total Sales Per Store total_sales_per_store = sales_df.groupby('store_id')['total_sales'].sum().reset_index() # Average Units Sold Per Item average_units_sold_per_item = sales_df.groupby('item_id')['units_sold'].mean().reset_index() # Sales Summary sales_summary = sales_df.groupby('store_id')['total_sales'].agg(['mean', 'median', 'std', 'sum']).reset_index() # Visualization total_sales_per_store.plot(kind='bar', x='store_id', y='total_sales', legend=False) plt.xlabel('Store ID') plt.ylabel('Total Sales') plt.title('Total Sales per Store') plot_path = 'total_sales_per_store.png' plt.savefig(plot_path) plt.close() return { 'total_units_sold_per_store': total_units_sold_per_store, 'total_sales_per_store': total_sales_per_store, 'average_units_sold_per_item': average_units_sold_per_item, 'sales_summary': sales_summary, 'total_sales_per_store_plot_path': plot_path }
question:**Objective:** Your task is to implement a class `Cell` that mimics the behavior of PyCellObject described in the documentation. The class should support the following operations: - Create a new cell object with an initial value. - Retrieve the current value of the cell. - Set a new value for the cell. # Class and Methods Description ```python class Cell: def __init__(self, initial_value: any): Initialize the cell with an initial value. :param initial_value: The initial value to store in the cell. # Your code here def get(self) -> any: Retrieve the value stored in the cell. :return: The current value in the cell. # Your code here def set(self, value: any): Set a new value in the cell. :param value: The new value to store in the cell. # Your code here ``` # Requirements 1. Implement the `Cell` class and its methods: - `__init__(self, initial_value: any)`: Initializes the cell with an initial value. - `get(self) -> any`: Returns the current value stored in the cell. - `set(self, value: any)`: Updates the cell with a new value. 2. Ensure the class handles different types of data (e.g., integers, strings, objects). 3. Enforce reference handling, i.e., the `set` method should replace the old reference with the new one. # Constraints - Do not use any cell-specific modules or libraries from Python C API. - The implementation should be in pure Python. # Example Usage ```python # Creating a cell with initial value 10 cell = Cell(10) # Getting the value print(cell.get()) # Output: 10 # Setting a new value cell.set(20) print(cell.get()) # Output: 20 # Setting a string value cell.set("Hello") print(cell.get()) # Output: Hello ``` # Additional Notes This question assesses your understanding of closures, reference management, and basic object-oriented programming concepts. Ensure your code follows best practices and is well-documented.
answer:class Cell: def __init__(self, initial_value: any): Initialize the cell with an initial value. :param initial_value: The initial value to store in the cell. self.value = initial_value def get(self) -> any: Retrieve the value stored in the cell. :return: The current value in the cell. return self.value def set(self, value: any): Set a new value in the cell. :param value: The new value to store in the cell. self.value = value
question:Objective Implement a function that plots both PDP and ICE plots based on a trained model, using the `sklearn` library. Problem Statement You are given a trained classification model, a dataset, and an index of features. Your task is to implement two functions: 1. `plot_partial_dependence` - to generate and display Partial Dependence Plots (PDP) for one or two specified features. 2. `plot_individual_conditional_expectation` - to generate and display Individual Conditional Expectation (ICE) plots for a specified feature. # Function Signature ```python def plot_partial_dependence(model, X, features): Plots Partial Dependence for specified features. Parameters: model: The trained model. X: The dataset (2D array-like structure). features: A list of feature indices or tuples (for two-way PDP). Returns: None # Your code here def plot_individual_conditional_expectation(model, X, feature): Plots Individual Conditional Expectation for the specified feature. Parameters: model: The trained model. X: The dataset (2D array-like structure). feature: The index of the feature for ICE plot. Returns: None # Your code here ``` # Example ```python from sklearn.datasets import make_classification from sklearn.ensemble import GradientBoostingClassifier from sklearn.inspection import PartialDependenceDisplay # Generating a sample dataset X, y = make_classification(n_samples=1000, n_features=10, random_state=42) # Training a model model = GradientBoostingClassifier().fit(X, y) # Plotting Partial Dependence for features 0 and (0, 1) plot_partial_dependence(model, X, [0, (0, 1)]) # Plotting Individual Conditional Expectation for feature 0 plot_individual_conditional_expectation(model, X, 0) ``` # Constraints - You should use `sklearn.inspection.PartialDependenceDisplay` for plotting. - The dataset `X` should be a 2D array-like structure. - Handle any necessary imports within your functions. # Notes - Ensure you provide a visually clear and interpretable plot. - PDP should provide insight into the average effect of the features. - ICE plots should visualize the effect for each sample separately.
answer:import matplotlib.pyplot as plt from sklearn.inspection import PartialDependenceDisplay def plot_partial_dependence(model, X, features): Plots Partial Dependence for specified features. Parameters: model: The trained model. X: The dataset (2D array-like structure). features: A list of feature indices or tuples (for two-way PDP). Returns: None display = PartialDependenceDisplay.from_estimator(model, X, features) display.figure_.suptitle('Partial Dependence Plots') plt.show() def plot_individual_conditional_expectation(model, X, feature): Plots Individual Conditional Expectation for the specified feature. Parameters: model: The trained model. X: The dataset (2D array-like structure). feature: The index of the feature for ICE plot. Returns: None display = PartialDependenceDisplay.from_estimator(model, X, [feature], kind='individual') display.figure_.suptitle('Individual Conditional Expectation Plots') plt.show()