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| kb:estimation_methods [2022-02-15 19:33] – [Feature matching] jaeyoung | kb:estimation_methods [2024-04-30 04:03] (current) – external edit 127.0.0.1 | ||
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| Moments of distributions are commonly used as features for feature matching. The $k$-th moment of a random variable $X$ is $\mathbb{E}[X^k]$. | Moments of distributions are commonly used as features for feature matching. The $k$-th moment of a random variable $X$ is $\mathbb{E}[X^k]$. | ||
| + | To estimate the moment from empirical data $X_1, ... X_n$, replace expectation with the average: | ||
| + | $$ \hat{\mathbb{E}}[X^k] = \frac{1}{n} \sum_{i=1}^n X_i^k $$ | ||
| ===== Maximum likelihood estimator ===== | ===== Maximum likelihood estimator ===== | ||