@phdthesis{Quinzan2023,
  author    = {Quinzan, Francesco},
  title     = {Combinatorial problems and scalability in artificial intelligence},
  doi       = {10.25932/publishup-61111},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-611114},
  school      = {Universit{\"a}t Potsdam},
  pages     = {xi, 141},
  year      = {2023},
  abstract  = {Modern datasets often exhibit diverse, feature-rich, unstructured data, and they are massive in size. This is the case of social networks, human genome, and e-commerce databases. As Artificial Intelligence (AI) systems are increasingly used to detect pattern in data and predict future outcome, there are growing concerns on their ability to process large amounts of data. Motivated by these concerns, we study the problem of designing AI systems that are scalable to very large and heterogeneous data-sets. Many AI systems require to solve combinatorial optimization problems in their course of action. These optimization problems are typically NP-hard, and they may exhibit additional side constraints. However, the underlying objective functions often exhibit additional properties. These properties can be exploited to design suitable optimization algorithms. One of these properties is the well-studied notion of submodularity, which captures diminishing returns. Submodularity is often found in real-world applications. Furthermore, many relevant applications exhibit generalizations of this property. In this thesis, we propose new scalable optimization algorithms for combinatorial problems with diminishing returns. Specifically, we focus on three problems, the Maximum Entropy Sampling problem, Video Summarization, and Feature Selection. For each problem, we propose new algorithms that work at scale. These algorithms are based on a variety of techniques, such as forward step-wise selection and adaptive sampling. Our proposed algorithms yield strong approximation guarantees, and the perform well experimentally. We first study the Maximum Entropy Sampling problem. This problem consists of selecting a subset of random variables from a larger set, that maximize the entropy. By using diminishing return properties, we develop a simple forward step-wise selection optimization algorithm for this problem. Then, we study the problem of selecting a subset of frames, that represent a given video. Again, this problem corresponds to a submodular maximization problem. We provide a new adaptive sampling algorithm for this problem, suitable to handle the complex side constraints imposed by the application. We conclude by studying Feature Selection. In this case, the underlying objective functions generalize the notion of submodularity. We provide a new adaptive sequencing algorithm for this problem, based on the Orthogonal Matching Pursuit paradigm. Overall, we study practically relevant combinatorial problems, and we propose new algorithms to solve them. We demonstrate that these algorithms are suitable to handle massive datasets. However, our analysis is not problem-specific, and our results can be applied to other domains, if diminishing return properties hold. We hope that the flexibility of our framework inspires further research into scalability in AI.},
  language  = {en}
}