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From Atoms to Possible Worlds: Probabilistic Inference in the Discrete-Continuous Domain

Boek - Dissertatie

Life is uncertain, full of ambiguities. Paradoxically, only embracing stochasticity, not fighting randomness, lets us cut through the surrounding fog of noise and find meaning. Similarly, machines will only make sense of the world accepting its probabilistic nature. This dissertation studies probabilistic artificial intelligence, a broad field of research. We will investigate probabilistic AI at three distinct conceptual levels, or three levels of abstraction. Throughout all three levels of abstraction, special focus is given to problems that incorporate discrete and continuous random variables alike - a challenge only embraced by very few. We start our study with logic atoms (Boolean variables) from which we build probabilistic logic formulas. A variable instantiation, which satisfies a probabilistic logic formula with probability greater than zero, is also called a possible world. In the last two chapters of the thesis these possible worlds will model the real-world observed through a 3D-camera. 1. Microscopic Level: The microscopic level studies the marriage of logic and probability theory. We formalize their combination by starting out from logic atoms, in the context of weighted model integration, from which we then construct entire probabilistic models. We introduce a range of state-of-the-art probabilistic inference algorithms. The presented algorithms are based on knowledge compilation and arithmetic circuits, and use either symbolic integration for exact inference or Monte Carlo integration for approximate inference. The algorithms show that probabilistic inference techniques from the purely discrete or the purely continuous domain can be adapted to perform probabilistic inference in the discrete-continuous domain. 2. Macroscopic Level: While the microscopic level constitutes a principled approach to expressing probabilistic models, the level of abstraction is rather ill-suited for human users. We introduce DC-ProbLog, a probabilistic logic programming language that allows users to operate at a high-level of abstraction. We show that we can perform inference by mapping back to weighted model integration (the microscopic level). 3. Cognitive Level: At the cognitive level we build a perceptual anchoring system. Perceptual anchoring solves the problem of creating and maintaining, in time and space, the correspondence between symbols and objects in the real-world. Our system constructs a probabilistic model of the surrounding world (perceived through a 3D-camera) and has the capability of probabilistically reasoning about objects that are present. The key contribution is the design of a framework that combines perceptual anchoring and probabilistic programming (macroscopic level). The probabilistic reasoning capacity is useful in situations where objects are not directly observed but occluded by other objects. Occluded objects can then be anchored through probabilistic reasoning.
Jaar van publicatie:2020
Toegankelijkheid:Open