Improving Ranking Using Quantum Probability

Data management systems, like database, information extraction, information retrieval or learning systems, store, organize, index, retrieve and rank information units, such as tuples, objects, documents, items to match a pattern (e.g. classes and profiles) or meet a requirement (e.g., relevance, usefulness and utility). To this end, these systems rank information units by probability to decide whether an information unit matches a pattern or meets a requirement. Classical probability theory represents events as sets and probability as set measures. Thus, distributive and total probability laws are admitted. Quantum probability is a non-classical theory nor does admit distributive and total probability laws. Although ranking by probability is far from being perfect, it is optimal thanks to statistical decision theory and parameter tuning. The main question asked in the paper is whether further improvement over the optimality provided by probability may be obtained if the classical probability theory is replaced by quantum probability theory. Whereas classical probability (and detection theory) is based on sets such that the regions of acceptance / rejection are set-based detectors, quantum probability is based on subspace-based detectors. The paper shows that ranking information units by quantum probability differs from ranking them by classical probability provided the same data used for parameter estimation. As probability of detection (also known as recall or power) and probability of false alarm (also known as fallout or size) measure the quality of ranking, we point out and show that ranking by quantum probability yields higher probability of detection than ranking by classical probability provided a given probability of false alarm and the same parameter estimation data. As quantum probability provided more effective detectors than classical probability within other domains that data management, we conjencture that, the system that can implement subspace-based detectors shall be more effective than a system which implements a setbased detectors, the effectiveness being calculated as expected recall estimated over the probability of detection and expected fallout estimated over the probability of false alarm.