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面试手撕笔记ML/DL

news 2025/1/6 16:05:17

数据集

数据集的批处理迭代器

Deep-ML | Batch Iterator for Dataset

实现一个批量可迭代函数，该函数在numpy数组X和可选numpy数组y中进行采样。该函数应该生成指定大小的批量。如果提供了y，则该函数应生成（X, y）对的批次；否则，它应该只产生X批次。

Example:

Input:

X = np.array([[1, 2], [3, 4], [5, 6], [7, 8], [9, 10]])y = np.array([1, 2, 3, 4, 5])batch_size = 2batch_iterator(X, y, batch_size)

Output:

[[[[1, 2], [3, 4]], [1, 2]],[[[5, 6], [7, 8]], [3, 4]],[[[9, 10]], [5]]]

import numpy as npdef batch_iterator(X, y=None, batch_size=64):n_samples = X.shape[0]batches = []for i in range(0, n_samples, batch_size):begin, end = i, min(i + batch_size, n_samples)if y is not None:batches.append([X[begin:end], y[begin:end]])else:batches.append(X[begin:end])return batches

激活函数

sigmoid


import math
def sigmoid(z: float) -> float:result = 1 / (1 + math.exp(-z))return round(result, 4)

relu

Deep-ML | Implement ReLU Activation Function

leaky relu

Deep-ML | Leaky ReLU Activation Function

def leaky_relu(z: float, alpha: float = 0.01) -> float|int:return z if z > 0 else alpha * z

softmax

Deep-ML | Softmax Activation Function Implementation

import mathdef softmax(scores: list[float]) -> list[float]:exp_scores = [math.exp(score) for score in scores]sum_exp_scores = sum(exp_scores)probabilities = [round(score / sum_exp_scores, 4) for score in exp_scores]return probabilities

梯度下降

使用梯度下降的线性回归（MSE）


import numpy as np
def linear_regression_gradient_descent(X: np.ndarray, y: np.ndarray, alpha: float, iterations: int) -> np.ndarray:m, n = X.shapetheta = np.zeros((n, 1))for _ in range(iterations):predictions = X @ thetaerrors = predictions - y.reshape(-1, 1)updates = X.T @ errors / mtheta -= alpha * updatesreturn np.round(theta.flatten(), 4)

MSE 损失的多种梯度下降

import numpy as npdef gradient_descent(X, y, weights, learning_rate, n_iterations, batch_size=1, method='batch'):m = len(y)for _ in range(n_iterations):if method == 'batch':# Calculate the gradient using all data pointspredictions = X.dot(weights)errors = predictions - ygradient = 2 * X.T.dot(errors) / mweights = weights - learning_rate * gradientelif method == 'stochastic':# Update weights for each data point individuallyfor i in range(m):prediction = X[i].dot(weights)error = prediction - y[i]gradient = 2 * X[i].T.dot(error)weights = weights - learning_rate * gradientelif method == 'mini_batch':# Update weights using sequential batches of data points without shufflingfor i in range(0, m, batch_size):X_batch = X[i:i+batch_size]y_batch = y[i:i+batch_size]predictions = X_batch.dot(weights)errors = predictions - y_batchgradient = 2 * X_batch.T.dot(errors) / batch_sizeweights = weights - learning_rate * gradientreturn weights