Although using single-instance learning methods to solve multi-instance problems has achieved excellent performance in many tasks, the reasons for this success still lack a rigorous theoretical explanation. In particular, the potential relation between the number of causal factors (also called causal instances) in a bag and the model performance is not transparent. The goal of our study is to use the causal relationship between instances and bags to enhance the interpretability of multi-instance learning. First, we provide a lower bound on the number of instances required to determine causal factors in a real multi-instance learning task. Then, we provide a lower bound on the single-instance learning loss function when testing instances and training instances follow the same distribution and extend this conclusion to the situation where the distribution changes. Thus, theoretically, we demonstrate that the number of causal factors in the bag is an important parameter that affects the performance of the model when using single-instance learning methods to solve multi-instance learning problems. Finally, combining with a specific classification task, we experimentally validate our theoretical analysis.
The causal inference represented by counterfactual inference technology breathes new life into the current field of artificial intelligence. Although the fusion of causal inference and artificial intelligence has an excellent performance in many various applications, some theoretical justifications have not been well resolved. In this paper, we focus on two fundamental issues in causal inference: probabilistic evaluation of counterfactual queries and the assumptions used to evaluate causal effects. Both of these issues are closely related to counterfactual inference tasks. Among them, counterfactual queries focus on the outcome of the inference task, and the assumptions provide the preconditions for performing the inference task. Counterfactual queries are to consider the question of what kind of causality would arise if we artificially apply the conditions contrary to the facts. In general, to obtain a unique solution, the evaluation of counterfactual queries requires the assistance of a functional model. We analyze the limitations of the original functional model when evaluating a specific query and find that the model arrives at ambiguous conclusions when the unique probability solution is 0. In the task of estimating causal effects, the experiments are conducted under some strong assumptions, such as treatment-unit additivity. However, such assumptions are often insatiable in real-world tasks, and there is also a lack of scientific representation of the assumptions themselves. We propose a mild version of the treatment-unit additivity assumption coined as M-TUA based on the damped vibration equation in physics to alleviate this problem. M-TUA reduces the strength of the constraints in the original assumptions with reasonable formal expression.
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