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In robust regression, replacing the likelihood function from Gaussian to a t-distribution is equivalent to reducing the weight of outliers, because the log-likelihood of the t-distribution penalizes extreme values more slowly.
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8/31/2026
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UnverifiedStudent's t-distribution is a heavy-tailed distribution whose tails decay more slowly than the Gaussian distribution, making it more robust to outliers.78% similarUnverifiedBayesian decision theory selects the action a* that minimizes expected loss, i.e., a* = argmin_a E[L(θ, a)|x], where the expectation is taken with respect to the posterior distribution p(θ|x).66% similarUnverifiedThe Cauchy distribution is a special case of the t-distribution with degrees of freedom ν=1; its mean and variance both do not exist, the sample mean does not converge, and the CLT fails here.66% similarUnverifiedAssuming the data follows a Gaussian distribution, maximizing the likelihood is equivalent to minimizing the mean squared error.66% similarUnverifiedAssuming the data follows a Bernoulli or multinomial distribution, maximizing the likelihood is equivalent to minimizing the cross-entropy loss function.65% similar
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