<ul><li>The popularity of Least Squares stems from its simplicity and its alignment with key statistical principles.</li><li>The Least Squares approach is favored for its mathematical clarity, providing closed-form solutions for optimization.</li><li>However, its reliability diminishes when data deviates from theoretical assumptions, like outliers in the distribution.</li><li>Least Squares is especially useful in Linear Regression, offering optimal coefficients estimation through OLS.</li><li>The conventional mean and median in statistics are directly linked to L2 and L1 losses, respectively.</li><li>Under the Gauss-Markov theorem, the OLS estimator is acclaimed as the Best Linear Unbiased Estimator.</li><li>OLS minimizes variance and maintains unbiasedness, outperforming other linear estimators.</li><li>Least Squares is also equivalent to Maximum Likelihood Estimation in normal error scenarios.</li><li>However, the reliance on normal errors makes Least Squares less effective in the presence of outliers.</li><li>To address this limitation, robust loss functions like Huber or Tukey are recommended for outlier resilience.</li></ul>

Least Squares: Where Convenience Meets Optimality

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