Efficient PAC Learnability of Dynamical Systems Over Multilayer Networks

Networked dynamical systems are widely used as formal models of real-world cascading phenomena, such as the spread of diseases and information. Prior research has addressed the problem of learning the behavior of an unknown dynamical system when the underlying network has a single layer. In this work, we study the learnability of dynamical systems over multilayer networks, which are more realistic and challenging. First, we present an efficient PAC learning algorithm with provable guarantees to show that the learner only requires a small number of training examples to infer an unknown system. We further provide a tight analysis of the Natarajan dimension which measures the model complexity. Asymptotically, our bound on the Nararajan dimension is tight for almost all multilayer graphs. The techniques and insights from our work provide the theoretical foundations for future investigations of learning problems for multilayer dynamical systems.

IrrNet: Advancing Irrigation Mapping with Incremental Patch Size Training on Remote Sensing Imagery

Irrigation mapping plays a crucial role in effective water management, essential for preserving both water quality and quantity, and is key to mitigating the global issue of water scarcity. The complexity of agricultural fields, adorned with diverse irrigation practices, especially when multiple systems coexist in close quarters, poses a unique challenge. This complexity is further compounded by the nature of Landsat's remote sensing data, where each pixel is rich with densely packed information, complicating the task of accurate irrigation mapping. In this study, we introduce an innovative approach that employs a progressive training method, which strategically increases patch sizes throughout the training process, utilizing datasets from Landsat 5 and 7, labeled with the WRLU dataset for precise labeling. This initial focus allows the model to capture detailed features, progressively shifting to broader, more general features as the patch size enlarges. Remarkably, our method enhances the performance of existing state-of-the-art models by approximately 20%. Furthermore, our analysis delves into the significance of incorporating various spectral bands into the model, assessing their impact on performance. The findings reveal that additional bands are instrumental in enabling the model to discern finer details more effectively. This work sets a new standard for leveraging remote sensing imagery in irrigation mapping.

Learning the Topology and Behavior of Discrete Dynamical Systems

Discrete dynamical systems are commonly used to model the spread of contagions on real-world networks. Under the PAC framework, existing research has studied the problem of learning the behavior of a system, assuming that the underlying network is known. In this work, we focus on a more challenging setting: to learn both the behavior and the underlying topology of a black-box system. We show that, in general, this learning problem is computationally intractable. On the positive side, we present efficient learning methods under the PAC model when the underlying graph of the dynamical system belongs to some classes. Further, we examine a relaxed setting where the topology of an unknown system is partially observed. For this case, we develop an efficient PAC learner to infer the system and establish the sample complexity. Lastly, we present a formal analysis of the expressive power of the hypothesis class of dynamical systems where both the topology and behavior are unknown, using the well-known formalism of the Natarajan dimension. Our results provide a theoretical foundation for learning both the behavior and topology of discrete dynamical systems.

Resource Sharing Through Multi-Round Matchings

Applications such as employees sharing office spaces over a workweek can be modeled as problems where agents are matched to resources over multiple rounds. Agents' requirements limit the set of compatible resources and the rounds in which they want to be matched. Viewing such an application as a multi-round matching problem on a bipartite compatibility graph between agents and resources, we show that a solution (i.e., a set of matchings, with one matching per round) can be found efficiently if one exists. To cope with situations where a solution does not exist, we consider two extensions. In the first extension, a benefit function is defined for each agent and the objective is to find a multi-round matching to maximize the total benefit. For a general class of benefit functions satisfying certain properties (including diminishing returns), we show that this multi-round matching problem is efficiently solvable. This class includes utilitarian and Rawlsian welfare functions. For another benefit function, we show that the maximization problem is NP-hard. In the second extension, the objective is to generate advice to each agent (i.e., a subset of requirements to be relaxed) subject to a budget constraint so that the agent can be matched. We show that this budget-constrained advice generation problem is NP-hard. For this problem, we develop an integer linear programming formulation as well as a heuristic based on local search. We experimentally evaluate our algorithms on synthetic networks and apply them to two real-world situations: shared office spaces and matching courses to classrooms.

Resource Allocation to Agents with Restrictions: Maximizing Likelihood with Minimum Compromise

Many scenarios where agents with restrictions compete for resources can be cast as maximum matching problems on bipartite graphs. Our focus is on resource allocation problems where agents may have restrictions that make them incompatible with some resources. We assume that a Principle chooses a maximum matching randomly so that each agent is matched to a resource with some probability. Agents would like to improve their chances of being matched by modifying their restrictions within certain limits. The Principle's goal is to advise an unsatisfied agent to relax its restrictions so that the total cost of relaxation is within a budget (chosen by the agent) and the increase in the probability of being assigned a resource is maximized. We establish hardness results for some variants of this budget-constrained maximization problem and present algorithmic results for other variants. We experimentally evaluate our methods on synthetic datasets as well as on two novel real-world datasets: a vacation activities dataset and a classrooms dataset.