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Statistical Foundations for Learning on Graphs
(University of Waterloo, 2024-11-27) Baranwal, Aseem
Graph Neural Networks are one of the most popular architectures used to solve classification problems on data where entities have attribute information accompanied by relational information. Among them, Graph Convolutional Networks and Graph Attention Networks are two of the most popular GNN architectures.
In this thesis, I present a statistical framework for understanding node classification on feature-rich relational data. First, I use the framework to study the generalization error and the effects of existing neural network architectures, namely, graph convolutions and graph attention on the Contextual Stochastic Block Model in the regime where the average degree of a node is at least order log squared n in the number of nodes n.
Second, I propose a notion of asymptotic local optimality for node classification tasks and design a GNN architecture that is provably optimal in this notion, for the sparse regime, i.e., average degree O(1).
In the first part, I present a rigorous theoretical understanding of the effects of graph convolutions in neural networks through the node classification problem of a non-linearly separable Gaussian mixture model coupled with a stochastic block model.
First, I identify two quantities corresponding to the signal from the two sources of information: the graph, and the node features, followed by a result that shows that a single graph convolution expands the regime of the distance between the means where multi-layer networks can classify the data by a factor of up to one over square root of the expected degree of a node.
Second, I show that with a slightly stronger graph density, two graph convolutions improve this factor to up to 1/sqrt{n}, where n is the number of nodes in the graph.
This set of results provides both theoretical and empirical insights into the performance of graph convolutions placed in different combinations among the layers of a neural network, concluding that the performance is mutually similar for all combinations of the placement.
In the second part, the analysis of graph attention is provided, where the main result states that in a well-defined ``hard'' regime, every attention mechanism fails to distinguish the intra-class edges from the inter-class edges. In addition, if the signal in the node attributes is sufficiently weak, graph attention convolution cannot perfectly classify the nodes even if the intra-class edges are separable from the inter-class edges.
In the third part, I study the node classification problem on feature-decorated graphs in the sparse setting, i.e., when the expected degree of a node is O(1) in the number of nodes, in the fixed-dimensional asymptotic regime, i.e., the dimension of the feature data is fixed while the number of nodes is large. Such graphs are typically known to be locally tree-like. Here, I introduce a notion of Bayes optimality for node classification tasks, called asymptotic local Bayes optimality, and compute the optimal classifier according to this criterion for a fairly general statistical data model with arbitrary distributions of the node features and edge connectivity. The optimal classifier is implementable using a message-passing graph neural network architecture. This is followed by a result that precisely computes the generalization error of this optimal classifier, and compares its performance statistically against existing learning methods on a well-studied data model with naturally identifiable signal-to-noise ratios (SNRs). We find that the optimal message-passing architecture interpolates between a standard MLP in the regime of low graph signal and a typical graph convolutional layer in the regime of high graph signal. Furthermore, I provide a corresponding non-asymptotic result that demonstrates the practical potential of the asymptotically optimal classifier.
Culture Clash: When Deceptive Design Meets Diverse Player Expectations
(Association for Computing Machinery, 2024-10-14) Hadan, Hilda; Sgandurra, Sabrina; Zhang-Kennedy, Leah; Nacke, Lennart
Deceptive game designs that manipulate players are increasingly common in the gaming industry, but the impact on players is not well studied. While studies have revealed player frustration, there is a gap in understanding how cultural attributes affect the impact of deceptive design in games. This paper proposes a new research direction on the connection between the representation of culture in games and player response to deceptive designs. We believe that understanding the interplay between cultural attributes and deceptive design can inform the creation of games that are ethical and entertaining for players around the globe.
Computer-based Deceptive Game Design in Commercial Virtual Reality Games: A Preliminary Investigation
(Association for Computing Machinery, 2024-10-14) Hadan, Hilda; Zhang-Kennedy, Leah; Nacke, Lennart
As Virtual Reality (VR) games become more popular, it is crucial to understand how deceptive game design patterns manifest and impact player experiences in this emerging medium. Our study sheds light on the presence and effects of manipulative design techniques in commercial VR games compared to a traditional computer game. We conducted an autoethnography study and developed a VR Deceptive Game Design Assessment Guide based on a critical literature review. Using our guide, we compared how deceptive patterns in a popular computer game are different from two commercial VR titles. While VR’s technological constraints, such as battery life and limited temporal manipulation, VR’s unique sensory immersion amplified the impact of emotional and sensory deception. Current VR games showed similar but evolved forms of deceptive design compared to the computer game. We forecast more sophisticated player manipulation as VR technology advances. Our findings contribute to a better understanding of how deceptive game design persists and escalates in VR. We highlight the urgent need to develop ethical design guidelines for the rapidly advancing VR games industry.
Reconsidering the Trade-off between Speed and Accuracy: The Role of Perceived Goal Progress Velocity
(Springer Nature, 2024-11-12) Beck, James W.; Scholer, Abigail A.; Hughes, Jeffrey; Phan, Vincent
Previous research has found a consistent trade-off between speed and accuracy. Whereas completing work tasks quickly is generally associated with increased mistakes, slowing down allows individuals to work in a more careful and accurate manner. However, this previous work has not considered the implications that subjective speed perceptions have for accuracy. To this end, we draw on control theory accounts of goal progress velocity, which predict that feeling slow is associated with negative emotional experiences. We argue that slow perceived progress is frustrating, and that this frustration can hinder accuracy. We tested our hypotheses using an experiment in which participants (N = 92) completed a work simulation. Importantly, actual speed was held constant across conditions, and instead we manipulated participants’ subjective interpretations of their rate of progress. As expected, feeling slow was associated with increased frustration, which in turn was negatively associated with accuracy. The results of this study imply that, contrary to the typical finding of a trade-off between speed and accuracy, there are situations in which slowing down can actually hinder accuracy. Therefore, the current research adds important nuance to the literature on speed-accuracy trade-offs. Additionally, this research provides the most direct test of control theory predictions regarding velocity to date. We conclude with a discussion of the implications of these results for both theory and practice.
The wood frog (Rana sylvatica): An emerging comparative model for anuran immunity and host-ranavirus interactions
(Elsevier, 2023-10) Douglas, Alexander; Katzenback, Barbara
The wood frog (Rana sylvatica) is widely distributed across North America and is the only amphibian found north of the Arctic Circle due to its remarkable ability to tolerate whole-body freezing. Recent mass mortalities attributable to Ranavirus spp. (family Iridoviridae) in wild juvenile wood frogs, coupled with the apparent high susceptibility of wood frogs to experimental infection with frog virus 3 (FV3), the type species of the Ranavirus genus, or FV3-like isolates underscore the serious threat ranaviruses poses to wood frog populations. Despite the ecological relevance and unique life history of wood frogs, our understanding of the wood frog immune system and antiviral response to ranaviral infections is in its infancy. Here we aim to (1) synthesize the limited knowledge of wood frog immune defences, (2) review recent progress in establishing the wood frog as a study system for ranavirus infection, and (3) highlight the future use of wood frogs as a model anuran to provide insight into the evolution of anuran immune systems and antiviral responses.