This paper presents a simple way to exploit partially annotated NER data by forcing the model to predict O labels matching the ratio of expected entity ratio.

They define a margin loss to match this ratio:

\renewcommand{\O}{\mathcal{O}}
\newcommand{\Lu}{L_u^{m}}
\newcommand{\1}{\unicode{x1D7D9}}
\newcommand{\rhohat}{\hat{\rho}_\theta}
\newcommand{\E}{\mathbb{E}}
\newcommand{\D}{\mathcal{D}}
\begin{align}
L_u(\theta;\D^m,\rho,\gamma) &= \max \{0, |\rho - \rhohat | - \gamma \} \\
\rhohat &= \frac{\sum\limits_{\substack{(x_{1:n_k}^k, y^k_{\O_k})\\ \in \D^m}} \E_{p(y^k_{1:n_k}|x_{1:n_k}^k;\theta)}[\sum\limits_{i=1}^{n_k} \1\{y^k_i \neq \text{O}\}]}{\sum\limits_{(x_{1:n_k}^k, y^k_{\O_k}) \in \D^m} n_k}
\end{align}

where the inner expectation can be summed directly but the outer exception is batch wise.

## Comments

- Nice finding. Sometimes I’m just amazed to see these clever findings. Simple and elegant.

Rating

- 5: Transformative: This paper is likely to change our field. It should be considered for a best paper award.
- 4.5: Exciting: It changed my thinking on this topic. I would fight for it to be accepted.
- 4: Strong: I learned a lot from it. I would like to see it accepted.
- 3.5: Leaning positive: It can be accepted more or less in its current form. However, the work it describes is not particularly exciting and/or inspiring, so it will not be a big loss if people don’t see it in this conference.
- 3: Ambivalent: It has merits (e.g., it reports state-of-the-art results, the idea is nice), but there are key weaknesses (e.g., I didn’t learn much from it, evaluation is not convincing, it describes incremental work). I believe it can significantly benefit from another round of revision, but I won’t object to accepting it if my co-reviewers are willing to champion it.
- 2.5: Leaning negative: I am leaning towards rejection, but I can be persuaded if my co-reviewers think otherwise.
- 2: Mediocre: I would rather not see it in the conference.
- 1.5: Weak: I am pretty confident that it should be rejected.
- 1: Poor: I would fight to have it rejected.

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