arXiv subjects

Youngser Park

Publications and source records attributed to Youngser Park.

At least 19 recordsLinked to original sources

arXiv2026

Vertex misalignment and changepoint localization in network time series

Inference for time series of networks often relies on accurate vertex correspondence between network realizations at different times. In practice, however, such vertex alignments can be misspecified or unknown. We study the impact of vertex alignment on changepoint localization for dynamic networks through two illustrative models, each with a similar changepoint, with the key distinction being whether changepoint information is contained in marginal or joint distributions of the time-varying latent positions. We compare localization techniques ranging from the simple network statistic of average degree to the modern procedure of Euclidean mirrors. In one model, vertex misalignment causes little error, and in the other, it impairs localization in ways that cannot be corrected through graph matching or optimal transport, which we show are closely related in this setting. Our results demonstrate that robust network inference necessitates reckoning with the subtle interplay of marginal and joint information in the observed network time series.

math.ST↗

arXiv2026

Recovering manifold structure in LLM responses through a joint Euclidean mirror

Understanding the behavior of black-box large language models and determining effective means of comparing their performance is a key task in modern machine learning. We consider how large language models respond to a specific query by analyzing how the distributions of responses vary over different values of tuning parameters. We frame this problem in a general mathematical setting, treating the mapping from model parameters to response distributions as a structured family of probability measures, endowed with a geometry via a dissimilarity measure. We show how dissimilarities between response distributions can be represented in low-dimensional Euclidean space through a joint Euclidean mirror surface encoding the underlying geometry, which permits both qualitative and quantitative analysis of large language models and provides insight into predicting response distributions for different values of tuning parameters. We propose an estimation procedure for the underlying joint Euclidean mirror based on observed samples from the response distributions, and we prove its asymptotic properties. Additionally, we propose a statistically consistent procedure to infer the value of an unknown model parameter based on samples from the corresponding response distribution and the estimated joint Euclidean mirror. In an experimental setting with large language models, we find that changes in different tuning parameter values correspond to distinct directions in the embedding space, making it possible to estimate the tuning parameters that were used to generate a given response.

stat.ME↗

arXiv2026

Data Kernel Perspective Space Performance Guarantees for Synthetic Data from Transformer Models

Scarcity of labeled training data remains the long pole in the tent for building performant language technology and generative AI models. Transformer models -- particularly LLMs -- are increasingly being used to mitigate the data scarcity problem via synthetic data generation. However, because the models are black boxes, the properties of the synthetic data are difficult to predict. In practice it is common for language technology engineers to 'fiddle' with the LLM temperature setting and hope that what comes out the other end improves the downstream model. Faced with this uncertainty, here we propose Data Kernel Perspective Space (DKPS) to provide the foundation for mathematical analysis yielding concrete statistical guarantees for the quality of the outputs of transformer models. We first show the mathematical derivation of DKPS and how it provides performance guarantees. Next we show how DKPS performance guarantees can elucidate performance of a downstream task, such as neural machine translation models or LLMs trained using Contrastive Preference Optimization (CPO). Limitations of the current work and future research are also discussed.

cs.CL↗

arXiv2025

Concentration bounds on response-based vector embeddings of black-box generative models

Generative models, such as large language models or text-to-image diffusion models, can generate relevant responses to user-given queries. Response-based vector embeddings of generative models facilitate statistical analysis and inference on a given collection of black-box generative models. The Data Kernel Perspective Space embedding is one particular method of obtaining response-based vector embeddings for a given set of generative models, already discussed in the literature. In this paper, under appropriate regularity conditions, we establish high probability concentration bounds on the sample vector embeddings for a given set of generative models, obtained through the method of Data Kernel Perspective Space embedding. Our results tell us the required number of sample responses needed in order to approximate the population-level vector embeddings with a desired level of accuracy. The algebraic tools used to establish our results can be used further for establishing concentration bounds on Classical Multidimensional Scaling embeddings in general, when the dissimilarities are observed with noise.

stat.ML↗

arXiv2025

Graph Neural Networks Powered by Encoder Embedding for Improved Node Learning

Graph neural networks (GNNs) have emerged as a powerful framework for a wide range of node-level graph learning tasks. However, their performance typically depends on random or minimally informed initial feature representations, where poor initialization can lead to slower convergence and increased training instability. In this paper, we address this limitation by leveraging a statistically grounded one-hot graph encoder embedding (GEE) as a high-quality, structure-aware initialization for node features. Integrating GEE into standard GNNs yields the GEE-powered GNN (GG) framework. Across extensive simulations and real-world benchmarks, GG provides consistent and substantial performance gains in both unsupervised and supervised settings. For node classification, we further introduce GG-C, which concatenates the outputs of GG and GEE and outperforms competing methods, achieving roughly 10-50% accuracy improvements across most datasets. These results demonstrate the importance of principled, structure-aware initialization for improving the efficiency, stability, and overall performance of graph neural network architecture, enabling models to better exploit graph topology from the outset.

cs.LG↗

arXiv2025

Multi-rank Subspace Change-point Detection with Application in Monitoring Robotic Swarms

We study real-time detection of low-rank changes in the covariance structure of high-dimensional streaming data, motivated by robotic swarm monitoring. Building on the spiked covariance model, we propose the Multi-rank Subspace-CUSUM (MRS-C) procedure, which extends classical CUSUM by tracking projection energy onto an estimated signal subspace. We analyze the immediate-change expected detection delay (EDD), deriving closed-form choices of the window size and drift parameter that minimize the leading-order asymptotic EDD approximation. We further establish an oracle-relative asymptotic efficiency result, with an explicit efficiency constant that depends on heterogeneity in spike strengths. When the signal rank is unknown, we propose a practical parallel procedure. Simulations and robotic swarm-behavior data illustrate robustness and effectiveness.

stat.ME↗

arXiv2025

Principal Graph Encoder Embedding and Principal Community Detection

In this paper, we introduce the concept of principal communities and propose a principal graph encoder embedding method that concurrently detects these communities and achieves vertex embedding. Given a graph adjacency matrix with vertex labels, the method computes a sample community score for each community, ranking them to measure community importance and estimate a set of principal communities. The method then produces a vertex embedding by retaining only the dimensions corresponding to these principal communities. Theoretically, we define the population version of the encoder embedding and the community score based on a random Bernoulli graph distribution. We prove that the population principal graph encoder embedding preserves the conditional density of the vertex labels and that the population community score successfully distinguishes the principal communities. We conduct a variety of simulations to demonstrate the finite-sample accuracy in detecting ground-truth principal communities, as well as the advantages in embedding visualization and subsequent vertex classification. The method is further applied to a set of real-world graphs, showcasing its numerical advantages, including robustness to label noise and computational scalability.

cs.SI↗

arXiv2024

Statistical inference on black-box generative models in the data kernel perspective space

Generative models are capable of producing human-expert level content across a variety of topics and domains. As the impact of generative models grows, it is necessary to develop statistical methods to understand collections of available models. These methods are particularly important in settings where the user may not have access to information related to a model's pre-training data, weights, or other relevant model-level covariates. In this paper we extend recent results on representations of black-box generative models to model-level statistical inference tasks. We demonstrate that the model-level representations are effective for multiple inference tasks.

cs.LG↗

arXiv2024

Graph Encoder Ensemble for Simultaneous Vertex Embedding and Community Detection

In this paper, we introduce a novel and computationally efficient method for vertex embedding, community detection, and community size determination. Our approach leverages a normalized one-hot graph encoder and a rank-based cluster size measure. Through extensive simulations, we demonstrate the excellent numerical performance of our proposed graph encoder ensemble algorithm.

cs.SI↗

arXiv2024

Multiple Network Embedding for Anomaly Detection in Time Series of Graphs

This paper considers the graph signal processing problem of anomaly detection in time series of graphs. We examine two related, complementary inference tasks: the detection of anomalous graphs within a time series, and the detection of temporally anomalous vertices. We approach these tasks via the adaptation of statistically principled methods for joint graph inference, specifically \emph{multiple adjacency spectral embedding} (MASE). We demonstrate that our method is effective for our inference tasks. Moreover, we assess the performance of our method in terms of the underlying nature of detectable anomalies. We further provide the theoretical justification for our method and insight into its use. Applied to the Enron communication graph, a large-scale commercial search engine time series of graphs, and a larval Drosophila connectome data, our approaches demonstrate their applicability and identify the anomalous vertices beyond just large degree change.

stat.ME↗

arXiv2024

Tracking the perspectives of interacting language models

Large language models (LLMs) are capable of producing high quality information at unprecedented rates. As these models continue to entrench themselves in society, the content they produce will become increasingly pervasive in databases that are, in turn, incorporated into the pre-training data, fine-tuning data, retrieval data, etc. of other language models. In this paper we formalize the idea of a communication network of LLMs and introduce a method for representing the perspective of individual models within a collection of LLMs. Given these tools we systematically study information diffusion in the communication network of LLMs in various simulated settings.

cs.AI↗

arXiv2024

Euclidean mirrors and dynamics in network time series

Analyzing changes in network evolution is central to statistical network inference, as underscored by recent challenges of predicting and distinguishing pandemic-induced transformations in organizational and communication networks. We consider a joint network model in which each node has an associated time-varying low-dimensional latent vector of feature data, and connection probabilities are functions of these vectors. Under mild assumptions, the time-varying evolution of the latent vectors exhibits low-dimensional manifold structure under a suitable notion of distance. This distance can be approximated by a measure of separation between the observed networks themselves, and there exist Euclidean representations for underlying network structure, as characterized by this distance, at any given time. These Euclidean representations, called Euclidean mirrors, permit the visualization of network evolution and transform network inference questions such as change-point and anomaly detection into a classical setting. We illustrate our methodology with real and synthetic data, and identify change points corresponding to massive shifts in pandemic policies in a communication network of a large organization.

stat.ME↗

arXiv2024

Euclidean mirrors and first-order changepoints in network time series

We describe a model for a network time series whose evolution is governed by an underlying stochastic process, known as the latent position process, in which network evolution can be represented in Euclidean space by a curve, called the Euclidean mirror. We define the notion of a first-order changepoint for a time series of networks, and construct a family of latent position process networks with underlying first-order changepoints. We prove that a spectral estimate of the associated Euclidean mirror localizes these changepoints, even when the graph distribution evolves continuously, but at a rate that changes. Simulated and real data examples on organoid networks show that this localization captures empirically significant shifts in network evolution.

stat.ME↗

arXiv2024

Consistent response prediction for multilayer networks on unknown manifolds

Our paper deals with a collection of networks on a common set of nodes, where some of the networks are associated with responses. Assuming that the networks correspond to points on a one-dimensional manifold in a higher dimensional ambient space, we propose an algorithm to consistently predict the response at an unlabeled network. Our model involves a specific multiple random network model, namely the common subspace independent edge model, where the networks share a common invariant subspace, and the heterogeneity amongst the networks is captured by a set of low dimensional matrices. Our algorithm estimates these low dimensional matrices that capture the heterogeneity of the networks, learns the underlying manifold by isomap, and consistently predicts the response at an unlabeled network. We provide theoretical justifications for the use of our algorithm, validated by numerical simulations. Finally, we demonstrate the use of our algorithm on larval Drosophila connectome data.

stat.ME↗

arXiv2024

Random line graphs and edge-attributed network inference

We extend the latent position random graph model to the line graph of a random graph, which is formed by creating a vertex for each edge in the original random graph, and connecting each pair of edges incident to a common vertex in the original graph. We prove concentration inequalities for the spectrum of a line graph, as well as limiting distribution results for the largest eigenvalue and the empirical spectral distribution in certain settings. For the stochastic blockmodel, we establish that although naive spectral decompositions can fail to extract necessary signal for edge clustering, there exist signal-preserving singular subspaces of the line graph that can be recovered through a carefully-chosen projection. Moreover, we can consistently estimate edge latent positions in a random line graph, even though such graphs are of a random size, typically have high rank, and possess no spectral gap. Our results demonstrate that the line graph of a stochastic block model exhibits underlying block structure, and in simulations, we synthesize and test our methods against several commonly-used techniques, including tensor decompositions, for cluster recovery and edge covariate inference. By naturally incorporating information encoded in both vertices and edges, the random line graph improves network inference.

cs.SI↗

arXiv2023

Discovering Communication Pattern Shifts in Large-Scale Labeled Networks using Encoder Embedding and Vertex Dynamics

Analyzing large-scale time-series network data, such as social media and email communications, poses a significant challenge in understanding social dynamics, detecting anomalies, and predicting trends. In particular, the scalability of graph analysis is a critical hurdle impeding progress in large-scale downstream inference. To address this challenge, we introduce a temporal encoder embedding method. This approach leverages ground-truth or estimated vertex labels, enabling an efficient embedding of large-scale graph data and the processing of billions of edges within minutes. Furthermore, this embedding unveils a temporal dynamic statistic capable of detecting communication pattern shifts across all levels, ranging from individual vertices to vertex communities and the overall graph structure. We provide theoretical support to confirm its soundness under random graph models, and demonstrate its numerical advantages in capturing evolving communities and identifying outliers. Finally, we showcase the practical application of our approach by analyzing an anonymized time-series communication network from a large organization spanning 2019-2020, enabling us to assess the impact of Covid-19 on workplace communication patterns.

cs.SI↗

arXiv2023

Dynamic Silos: Increased Modularity in Intra-organizational Communication Networks during the Covid-19 Pandemic

Workplace communications around the world were drastically altered by Covid-19, related work-from-home orders, and the rise of remote work. To understand these shifts, we analyzed aggregated, anonymized metadata from over 360 billion emails within 4,361 organizations worldwide. By comparing month-to-month and year-over-year metrics, we examined changes in network community structures over 24 months before and after Covid-19. We also examined shifts across multiple communication media (email, instant messages, video calls, and calendaring software) within a single global organization, and compared them to communications shifts that were driven by changes in formal organizational structure. We found that, in 2020, organizations around the world became more siloed than in 2019, evidenced by increased modularity. This shift was concurrent with decreased stability within silos. Collectively, our analyses indicate that following the onset of Covid-19, employees began to shift more dynamically between subcommunities (teams, workgroups or functional areas). At the same time, once in a subcommunity, they limited their communication to other members of that community. We term these network changes dynamic silos. We provide initial insights into the meaning and implications of dynamic silos for the future of work.

stat.ML↗

arXiv2023

Discovering a change point and piecewise linear structure in a time series of organoid networks via the iso-mirror

Recent advancements have been made in the development of cell-based in-vitro neuronal networks, or organoids. In order to better understand the network structure of these organoids, a super-selective algorithm has been proposed for inferring the effective connectivity networks from multi-electrode array data. In this paper, we apply a novel statistical method called spectral mirror estimation to the time series of inferred effective connectivity organoid networks. This method produces a one-dimensional iso-mirror representation of the dynamics of the time series of the networks which exhibits a piecewise linear structure. A classical change point algorithm is then applied to this representation, which successfully detects a change point coinciding with the neuroscientifically significant time inhibitory neurons start appearing and the percentage of astrocytes increases dramatically. This finding demonstrates the potential utility of applying the iso-mirror dynamic structure discovery method to inferred effective connectivity time series of organoid networks.

stat.AP↗