Heavy-Tailed Distribution
A probability distribution whose tail decays more slowly than an exponential decay, with the tail following a power law. Extreme values occur with a probability far higher than under a Gaussian distribution.
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Heavy-tailed distributions refer to distributions whose tail probabilities decay slower than exponential speed, such as the Pareto distribution, Student's t distribution, and log-normal distribution; higher-order moments of such distributions may not exist or may diverge, leading to infinite variance.
Real-world data such as financial returns, earthquake magnitudes, and network traffic often exhibit heavy-tailed characteristics.
Standard Gaussian diffusion models have inherent limitations in capturing heavy-tailed distributions.
A heavy-tailed distribution means that the tail of the probability distribution decays much more slowly than that of a normal distribution, meaning that the probability of extreme values occurring is far higher than intuition suggests.
Student's t-distribution is a heavy-tailed distribution whose tails decay more slowly than the Gaussian distribution, making it more robust to outliers.
The robustness of a distribution essentially depends on how its tail behavior is modeled, and replacing the Gaussian distribution with a heavy-tailed distribution can improve a model's stability against outliers.
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Heavy-tailed distributions refer to distributions whose tail probabilities decay slower than exponential speed, such as the Pareto distribution, Student's t distribution, and log-normal distribution; higher-order moments of such distributions may not exist or may diverge, leading to infinite variance.
50%UnverifiedReal-world data such as financial returns, earthquake magnitudes, and network traffic often exhibit heavy-tailed characteristics.
50%UnverifiedStandard Gaussian diffusion models have inherent limitations in capturing heavy-tailed distributions.
50%UnverifiedA heavy-tailed distribution means that the tail of the probability distribution decays much more slowly than that of a normal distribution, meaning that the probability of extreme values occurring is far higher than intuition suggests.
50%UnverifiedStudent's t-distribution is a heavy-tailed distribution whose tails decay more slowly than the Gaussian distribution, making it more robust to outliers.
50%UnverifiedThe robustness of a distribution essentially depends on how its tail behavior is modeled, and replacing the Gaussian distribution with a heavy-tailed distribution can improve a model's stability against outliers.
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