\section{Conclusion} \label{sec:conclusion}
In conclusion, our study is the first to demonstrate the impossibility of boosting weak classifiers to a strong classifier in the LLP and MIL settings. For LLP our work rules out boosting using weak classifiers of any accuracy $ < 1$, while for MIL the possibility of boosting weak classifiers with accuracy $< 2/3$ is eliminated. Complementing these findings in the LLP context, we propose an algorithm that converts a weak classifier for composite bags into a strong classifier for an input collection of original bags. The algorithm constructs unions of constantly many original bags to achieve error amplification. A more efficient sampling based version of the same provides high probability guarantees, which we also experimentally validate on three real and two synthetic datasets.
Future work includes ruling out boosting for MIL using weak classifiers with accuracy in $[2/3, 1)$. A related question remains on how to effectively obtain a strong classifier in the MIL setting on using weak classifiers on composite bags.