Higher Order Networks
We are interested in understanding how signals spread on a network. We ask questions like how does hate speech spread and how are echo chambers formed, how do alliances in games, politics, and other social systems change over time to devise an optimal strategy, how do causal relationships in diseases evolve, how can one effectively spread an idea through a network, can we identify biases in the system by studying the network structure, how does the geometry and topology of the network affect behavior?
A conventional network can only capture pairwise relationships, however many systems involve simultaneous interactions between 3 or more entities – e.g. simultaneous interactions between three (represented as a triangle) brain regions may indicate presence of a disease that isn’t captured by multiple pairwise interactions (represented as edges). We model this as a higher-order network and study the theory and behaviors of system that are modeled by higher order networks using dynamic network modeling, spectral analysis, inference, algebraic homology and topological data analysis on networks.
Selected publications:
Sarah Sotoudeh, Mason Porter*,Sanjukta Krishnagopal*, Studying patterns
of influence in Congress, and its role in bill-passing. (Submitted)
Malvina Bozhidarova, Jonathn Chang, Jim Liu, Chongyao Ma, Aishah Siddiqka,
Andrea Bertozzi, Jeffrey Brantingham, Junyuan Lee, Sanjukta Krishnagopal,
Hate Speech and Hate Crimes: A Data-driven Study of Evolving Social
Media Discourse around Marginalized Groups.
IEEE BigData 2023.
Sanjukta Krishnagopal, Rainer Von Coelln, Lisa Shulman and Michelle Girvan,
Predicting Subtypes in Evolving Diseases through Trajectory Clustering via
Bipartite Networks. Plos One.
Explainable AI for science
When using machine learning for scientific applications, we often expect the system we are learning to be described by underlying physical equations that approximate the system. For example, we know that many fluids can be described by the Navier-Stokes equation. On the one hand, the physical equations may not fully describe the data which often is affected by external factors. On the other hand, using machine learning to learn purely from data, may not generalize well to other regimes, where it may yield non-physically plausible predictions. Thus, by incorporating both data and some description of the underlying physical model or the underlying graphical structure, we hope to tempt the neural network into learning the true underlying dynamical system. We are interested in generalized methods, as well as applications to various physical systems include climate modeling. We do this through using tools from dynamical systems, graph neural networks, and physics informed neural networks.
Selected publications:
Sanjukta Krishnagopal, Luana Ruiz, Graph Neural Tangent Kernel: Convergence on large graphs. International Conference on Machine Learning (ICML) 2023
Sanjukta Krishnagopal, Yiannis Aloimonis and Michelle Girvan, Similarity
Learning and Generalization with Limited Data: A Reservoir Computing Approach.
Complexity.
Sanjukta Krishnagopal, Edward Ott, Michelle Girvan and Brian Hunt, Separation
of Chaotic Signals using Machine Learning.
Chaos: An Interdisciplinary Journal of Nonlinear Science 30.2 (2020)
Topological data analysis and topological ML
Topology or the study of holes can offer important insight into a system. For instance, in designing new chemicals or drugs and studying capture and binding, the structure and pores in atoms and molecules present important insight. Alternately, in studying the spread of forest fires, existence of holes or regions without trees can be harnessed to curtail the spread of a fire. Continuing, in studying the evolution of language, holes present new ways of understanding why some languages died and others didn’t. Characterizing regions of empty space (holes) in cosmological data can provide insight into possible candidates for new cosmological phenomenon. We use methods in topological data analysis such as persistent homology and develop new tools that study the role topological features in explaining systems. We are interested in studying how topology and geometry of datasets is captured in the neural network, and how one can design better ML architectures that can preserve geometric and topological properties in the latent representations that they learn.
Selected publications:
Sanjukta Krishnagopal, Ginestra Bianconi, Topology and dynamics of higherorder multiplex networks. Chaos, Solitons, and Fractals. arxiv 2308.14189
Sanjukta Krishnagopal, Jacob Bedrossian, Preserving data manifold structure
in latent space for exploration through network-geodesics .
IEEE Transactions on Neural Networks and Learning Systems (IJCNN)
Cognition and collective intelligence
We are interested in using biological and social human-behavior models to inform machine learning models, and inversely, testing mechanisms for how neurons in artificial neural networks collaborate in order to perform learning and decision-making in order to develop hypothesis for collective cognition and collective decision making in society. We use insight from network science, game theory, reinforcement learning, computational neuroscience, and machine learning.
Selected publications:
Sanjukta Krishnagopal, Success at high peaks: a multiscale approach combining
individual and expedition-wide factors .
Complex Networks and Their Applications X.
Eren Sezener, Agnieszka Grabska-Barwinska, Dimitar Kostadinov, Maxime
Beau, Sanjukta Krishnagopal, David Budden, Marcus Hutter, Joel Veness,
Matthew Botvinick, Claudia Clopath, Michael Hausser, Peter Latham, A
rapid and efficient learning rule for biological neural circuits. (Submitted)
Sanjukta Krishnagopal, Mason Porter, A neighborhood bounded-confidence model of opinion dynamics on dynamic networks. (Submitted)