This is a classic proof in mathematical statistics. That is, whether the variance of the sum of two random variables equals the sum of their variances.
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Gradient descent is an iterative method used in most modern models to help find optimal parameters. However, in today’s era of big data, the massive amount of data results in significant time costs for gradient descent. One key goal is to compute parameters quickly without sacrificing accuracy.
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Why do we need sampling? What are the benefits for data analysis? When building models, we sometimes find that the amount of data required for training is too large, which prolongs the training time. The purpose of sampling is to select a representative finite sample from a large population and perform statistical analysis on it, thereby inferring the characteristics or properties of the overall population.
From this, we can see that a sample is a subset of the population. Sampling methods refer to how we reasonably select a subset of the population as a sample. Since the sample size is smaller than the population, we hope that the sample statistics calculated from the selected sample approximate the population statistics, minimizing the bias introduced by sampling.
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Logistic regression is a type of binary classification model derived from linear regression. Unlike linear regression, which fits a regression line that passes through the data points by minimizing the sum of squared distances, known as the least squares method. The goal of logistic regression is to find a decision boundary that clearly separates the data into two distinct classes.
