# MIPART: A Partial Decision Tree-Based Method for Multiple-Instance Classification
## 1 Introduction  
_Multi-instance learning_ (MIL) [1] represents a distinctive approach within machine learning, designed to handle tasks where labels are assigned not to individual instances but to collections of instances, known as _hags_. In this framework, a bag is labeled positive if at least one of its instances belongs to the target class; otherwise, it is labeled negative. This paradigm proves particularly advantageous in real-world applications involving grouped data or ambiguous labels. For example, in drug discovery, a chemical compound or bag may only be classified as active if at least one of its molecular conformations or instances produces a desired biological effect. Similarly, in image classification, an entire image or bag may be labeled as containing a specific object even if only a single region or instance depicts that object. By associating labels with bags, MIL captures these nuanced relationships, making it an essential tool for fields that require robust the handling of complex data structures and incomplete instance-level labeling [2]. Despite its advantages, multi-instance learning presents unique challenges, particularly in accurately classifying bags based on their instances. Since only the bag-level label is known, the learning algorithm must infer complex relationships among instances within a bag, making the training process more intricate. In many cases, instances within a positive bag exhibit considerable variability, with only a subset actually contributing to the bag's label. This intra-bag diversity, especially when mixed with negative instances, requires models to distinguish which instances drive the bag's classification. Additionally, the computational demands of analyzing all instances within each bag further complicate MIL applications. Addressing these challenges calls for innovative approaches that can handle intra-bag diversity, maintain computational efficiency, and ensure accurate classification across diverse application domains [3, 4]. Various methods have been developed to tackle the complexities of multi-instance learning, each bringing distinct advantages and limitations. Techniques such as citation k-nearest neighbors (Citation-KNN) [5], multi-instance boosting (MIBoost) [6], multi-instance expectation-maximization diverse density (MIEMDD) [7], multi-instance logistic regression (MILR) [8], multi-instance support vector machine (MISVM) [9], and multi-instance tree inference (MITI) [10], represent a range of approaches that attempt to improve accuracy by leveraging instance relationships within bags or adapting traditional learning algorithms to the multi-instance context. Although these approaches have made significant advancements, they often fall short in scenarios involving high intra-bag diversity or computational constraints. Certain approaches, may perform well on specific types of data but struggle with datasets characterized by high intra-bag variability or limited labeled instances. Consequently, there remains a need for a more flexible, accurate method that addresses these limitations over diverse multi-instance datasets. One promising avenue for enhancing multi-instance learning lies in utilizing of the partial decision tree (PART) algorithm [11], which has established itself as an influential approach within the realm of classification, particularly noted for its efficiency and interpretability. PART generates rules from a training dataset by employing a decision tree to identify relevant instances and create human-readable rules for classification. Unlike traditional decision tree methods that can become overly complex, PART focuses on generating a limited number of rules, enhancing both the clarity of the model and the speed of classification. This method effectively captures the relationships among instances while maintaining a balance between accuracy and computational efficiency.