non-monochromatic bag
Learnability of Linear Thresholds from Label Proportions
If all the bags are non-monochromatic (i.e., bags of size two with
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Supplementary Appendix for: Algorithms and Hardness for Learning Linear Thresholds from Label Proportions
Further, we have the following. Therefore, let us consider 0 p 1 / 2 . Differentiating w.r.t we obtain, @ ( p,) @ = (6 p 4) + 2(1 p), and, @ Observing that (1 / 3, 2 / 3) = 4 / 9 completes the analysis. Our hardness result is via a reduction from the Smooth-Label-Cover problem defined below. Theorem 4.1 directly follows from the following theorem.
Algorithms and Hardness for Learning Linear Thresholds from Label Proportions
LLP learnability of L TFs i.e, given a collection of bags and their label proportions consistent with an
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Learnability of Linear Thresholds from Label Proportions
If all the bags are non-monochromatic (i.e., bags of size two with
Country:
- North America > United States > Massachusetts > Middlesex County > Cambridge (0.04)
- Asia > India (0.04)
Technology:
- Information Technology > Artificial Intelligence > Machine Learning > Statistical Learning (0.70)
- Information Technology > Artificial Intelligence > Machine Learning > Learning Graphical Models > Directed Networks > Bayesian Learning (0.67)
- Information Technology > Artificial Intelligence > Machine Learning > Neural Networks (0.46)
Country:
- Europe > United Kingdom > England > Cambridgeshire > Cambridge (0.04)
- Asia > India (0.04)
Technology:
- Information Technology > Artificial Intelligence > Representation & Reasoning (0.68)
- Information Technology > Artificial Intelligence > Machine Learning > Learning Graphical Models > Directed Networks > Bayesian Learning (0.67)
- Information Technology > Artificial Intelligence > Machine Learning > Statistical Learning (0.47)
- Information Technology > Artificial Intelligence > Machine Learning > Neural Networks (0.46)