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Assume that a classier has been trained already (no missing training data), but a prediction has been requested based on an observation that does not include every feature. How can we handle this missing feature?

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In evaluation (test) phase, when data point $x_n$ has $d$ missing features at indices $M=\{m_1,...,m_d\}$, corresponding terms $P(x_i|C_k),i \in M$ are simply removed from the classifier. That is, classifier $$C(x_n) = \underset{k \in \{1,..,K\}}{\mbox{argmax }}P(C_k)\prod_{i}P(x_i=x_{n,i}|C_k)$$ is replaced with $$C(x_n) = \underset{k \in \{1,..,K\}}{\mbox{argmax }}P(C_k)\prod_{\color{blue}{i:i \notin M}}P(x_i=x_{n,i}|C_k)$$

where $i$ iterates over features, $x_{n,i}$ denotes the $i$-th feature of data point $n$, and there is $K$ classes in total.

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You tend to avoid these situations while preprocessing your data. You impute the missing data. In production terms, frameworks like H2O handle quite elegantly. If you mean that there's a dimension mismatch, then H2O can still handle it.

H2O Missing values

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