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DTSTAMP:20251205T094831
DTSTART;TZID=America/Detroit:20251211T100000
DTEND;TZID=America/Detroit:20251211T120000
SUMMARY:Lecture / Discussion:Statistical Modeling for Structured Network and Functional Data
DESCRIPTION:The rapid growth of complex modern datasets involves structured dependencies. These structures introduce new challenges for statistical learning and require statistical frameworks which can capture higher-order interactions\, relational patterns\, and temporal dynamics.  Motivated by these challenges\, this dissertation consists of three parts for modeling structured network and functional data. \n\nThe first chapter focuses on modeling higher-order interactions in complex networks. Most statistical models for networks focus on pairwise interactions between nodes. However\, many real-world networks involve higher-order interactions among multiple nodes\, such as co-authors collaborating on a paper. Hypergraphs provide a natural representation for these networks\, with each hyperedge representing a set of nodes. The majority of existing hypergraph models assume uniform hyperedges (i.e.\, edges of the same size) or rely on diversity among nodes. In this work\, we propose a new hypergraph model based on non-symmetric determinantal point processes. The proposed model naturally accommodates non-uniform hyperedges\, has tractable probability mass functions\, and accounts for both node similarity and diversity in hyperedges. For model estimation\, we maximize the likelihood function under constraints using a computationally efficient projected adaptive gradient descent algorithm. We establish the consistency and asymptotic normality of the estimator.\n\nThe second chapter presents a probabilistic model for community detection in signed networks. Community detection\, discovering the underlying communities within a network from observed connections\, is a fundamental problem in network analysis\, yet it remains underexplored for signed networks. In signed networks\, both edge connection patterns and edge signs are informative\, and structural balance theory (e.g.\, triangles aligned with ``the enemy of my enemy is my friend'' and ``the friend of my friend is my friend'' are more prevalent) provides a global higher-order principle that guides community formation.  We propose a Balanced Stochastic Block Model (BSBM)\, which incorporates balance theory into the network generating process such that balanced triangles are more likely to occur. We develop a fast profile pseudo-likelihood estimation algorithm with provable convergence and establish that our estimator achieves strong consistency under weaker signal conditions than methods for the binary SBM that rely solely on edge connectivity. \n\nThe third chapter develops a generative modeling framework for functional data\, where each sample is observed over a continuum of time or space. Classical functional data analysis mainly relies on low-rank representations such as functional principal component analysis (FPCA) or spline bases\, and focuses on developing discriminative models such as regression and classification. They do not characterize the probability distribution of functional observations. To directly learn the distribution of functional data\, we propose a generative model defined on a separable Hilbert space. The generator is formulated as a latent neural ordinary differential equation (ODE) which captures temporal dynamics for functional data\,  combined with a decoder incorporating Fourier features and learned time embeddings for flexible function representation.  The target distribution is estimated via a generalized energy-score loss\, which is well-defined for arbitrary measures on separable Hilbert spaces without requiring the existence of Radon–Nikodym derivatives. Furthermore\, we establish the error bounds comparing the learned and true functional distributions.
UID:142410-21890806@events.umich.edu
URL:https://events.umich.edu/event/142410
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Dissertation
LOCATION:West Hall - 438
CONTACT:
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DTSTAMP:20251125T121517
DTSTART;TZID=America/Detroit:20251211T110000
DTEND;TZID=America/Detroit:20251211T190000
SUMMARY:Auditions:Path Forward
DESCRIPTION:Exhibition Dates: December 3-13Opening Reception: Friday\, December 5\, 6-8 p.m.\nPath Forward\, the 2025 Stamps BA Senior Studio Exhibition\, weaves meditations on nature\, the inner and outer workings of our human bodies from the functional to the phenomenal\, the paces of daily lives whether reading or rushing\, in friendship or in family and exploring memories of real and imagined pasts as they intersect with the here and now. Featuring work in experimental video\, fashion\, painting\, illustration and sculpture\, Path Forward postulates stepping stones for near and possible futures.\nThe Bachelor of Arts (BA) Senior Studio (ARTDES 401) is offered for Stamps BA students in their final year of study. The BA Senior Studio Exhibition offers these students the opportunity to build on the particular characteristics of the BA degree\, and focus on creating and exhibiting a culminating\, self-directed project. Students work independently or collaboratively to define a project plan with goals\, benchmarks\, and a timeline. \nThe BA Senior Studio Exhibition is a new tradition for Stamps. These students and instructors have worked collaboratively to produce a fully self-directed show from start to finish\, emphasizing the skills and practices associated with producing professional exhibitions\, in addition to their studio work. \nFaculty\nNick Tobier\, ProfessorMichaela Nichelle\, GSI\nBA Student Artists &amp\; Designers\nJulia BonannoLina HashimotoMargherita HillAnna HowellRiley HuhtaLaura JhiradUrvi JoshiAmanda KubitzGreta LeishearStella MooreEmma OstermeyerJaime SalmonsonMeredith SouleAna SwansonSam Weinfield
UID:137211-21879966@events.umich.edu
URL:https://events.umich.edu/event/137211
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Art
LOCATION:Off Campus Location
CONTACT:
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