classification_ssl.md

Classification - Semi-Supervised learning (SSL)¹

Evens Salies, v1: 01/2025

In ML, the concept of SSL is used in situations where, for some $i$'s, $Y_i$ is not observed. In econometrics, such a situation occurs e.g. when $Y_i$ is missing at random (MAR). But also, when there is sample selection. Imagine two situations:

(1) $Y_i$ is sales, $X_i$ tells whether firm $i$ has transformed R&D into some marketed product, $D_i$ is a dummy that takes the value 1 if $i$ has received some subsidy. This is only possible for firms that have completed their R&D program, regardless whether they were subsidised or not.

(2) In Tran and Salies' (2023) paper, $Y_i$ is publication speed during the Covid-19 pandemic and $D_i$ is a dummy that takes the value 1 if research team $i$ cites open-access papers (0 if it cites subscription-access papers). The problem is that many teams do not cite any paper at all.

We want to evaluate $D_i\rightarrow Y_i$, given $X_i$.

$$(Y_i, D_i, X_i). \\[12pt]$$

ML is more situable for problems like (2). As stated in Géron (2022, p. 14), "you will often have plenty of unlabeled instances [$Y_i$ not observed], and few labeled instances."

Split the set of $n$ firms $I$ into two subsets $I_U$ and $I_L$ where indices "U" and "L" stand for "unlabelled" and "labeled". Without loss of generality, $I=I_U+I_L$, so $I_U\cap I_L=\emptyset$. We have $(Y_i, D_i, X_i)\ \forall i\in I_L$ and $(?, D_i, X_i)\ \forall i\in I_U$.

Data

Tan Tran, Evens Salies. How important is open-source science for invention speed. 2023. hal-04239561

Bibliography

Footnotes

1. Géron, A., 2022. Hands-on machine learning with Scikit-Learn, Keras, and TensorFlow, O'Reilly, 834 p. ↩