23 lines
569 B
Markdown
23 lines
569 B
Markdown
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# Gaussian Classifier
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- With $T$ labelled data
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$$q_t(i)=
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\begin{cases}
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1 & \text{if class } i \\
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0 & \text{otherwise}
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\end{cases}$$
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- Indicator function
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- Mean parameter
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$$\hat m_i=\frac{\sum_tq_t(i)o_t}{\sum_tq_t(i)}$$
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- Variance parameter
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$$\hat v_i=\frac{\sum_tq_t(i)(o_t-\hat m_i)^2}{\sum_tq_t(i)}$$
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- Distribution weight
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- Class prior
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- $P(N_i)$
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$$\hat c_i=\frac 1 T \sum_tq_t(i)$$
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$$\hat \mu_i=\frac{\sum_{t=1}^Tq_t(i)o_t}{\sum_{t=1}^Tq_t(i)}$$
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$$\hat\sum_i=\frac{\sum_{t=1}^Tq_t(i)(o_t-\mu_i)(o_t-\mu_i)^T}{\sum_{t=1}^Tq_t(i)}$$
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- For K-dimensional
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