arXiv subjects

Carey E. Priebe

Publications and source records attributed to Carey E. Priebe.

At least 55 records · Page 3Linked to original sources

arXiv2024

Occam Factor for Random Graphs: Erdös-Rényi, Independent Edge, and Rank-1 Stochastic Blockmodel

We investigate the evidence/flexibility (i.e., "Occam") paradigm and demonstrate the theoretical and empirical consistency of Bayesian evidence for the task of determining an appropriate generative model for network data. This model selection framework involves determining a collection of candidate models, equipping each of these models' parameters with prior distributions derived via the encompassing priors method, and computing or approximating each models' evidence. We demonstrate how such a criterion may be used to select the most suitable model among the Erdös-Rényi (ER) model, independent edge (IE) model, and rank-1 stochastic blockmodel (SBM). The Erdös-Rényi may be considered as being linearly nested within IE, a fact which permits exponential family results. The rank-1 SBM is not so ideal, so we propose a numerical method to approximate its evidence. We apply this paradigm to brain connectome data. Future work necessitates deriving and equipping additional candidate random graph models with appropriate priors so they may be included in the paradigm.

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

Approximately optimal domain adaptation with Fisher's Linear Discriminant

We propose a class of models based on Fisher's Linear Discriminant (FLD) in the context of domain adaptation. The class is the convex combination of two hypotheses: i) an average hypothesis representing previously seen source tasks and ii) a hypothesis trained on a new target task. For a particular generative setting we derive the optimal convex combination of the two models under 0-1 loss, propose a computable approximation, and study the effect of various parameter settings on the relative risks between the optimal hypothesis, hypothesis i), and hypothesis ii). We demonstrate the effectiveness of the proposed optimal classifier in the context of EEG- and ECG-based classification settings and argue that the optimal classifier can be computed without access to direct information from any of the individual source tasks. We conclude by discussing further applications, limitations, and possible future directions.

eess.SP↗

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↗

arXiv2024

Comparing Foundation Models using Data Kernels

Recent advances in self-supervised learning and neural network scaling have enabled the creation of large models, known as foundation models, which can be easily adapted to a wide range of downstream tasks. The current paradigm for comparing foundation models involves evaluating them with aggregate metrics on various benchmark datasets. This method of model comparison is heavily dependent on the chosen evaluation metric, which makes it unsuitable for situations where the ideal metric is either not obvious or unavailable. In this work, we present a methodology for directly comparing the embedding space geometry of foundation models, which facilitates model comparison without the need for an explicit evaluation metric. Our methodology is grounded in random graph theory and enables valid hypothesis testing of embedding similarity on a per-datum basis. Further, we demonstrate how our methodology can be extended to facilitate population level model comparison. In particular, we show how our framework can induce a manifold of models equipped with a distance function that correlates strongly with several downstream metrics. We remark on the utility of this population level model comparison as a first step towards a taxonomic science of foundation models.

cs.LG↗

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

Correcting a Nonparametric Two-sample Graph Hypothesis Test for Graphs with Different Numbers of Vertices with Applications to Connectomics

Random graphs are statistical models that have many applications, ranging from neuroscience to social network analysis. Of particular interest in some applications is the problem of testing two random graphs for equality of generating distributions. Tang et al. (2017) propose a test for this setting. This test consists of embedding the graph into a low-dimensional space via the adjacency spectral embedding (ASE) and subsequently using a kernel two-sample test based on the maximum mean discrepancy. However, if the two graphs being compared have an unequal number of vertices, the test of Tang et al. (2017) may not be valid. We demonstrate the intuition behind this invalidity and propose a correction that makes any subsequent kernel- or distance-based test valid. Our method relies on sampling based on the asymptotic distribution for the ASE. We call these altered embeddings the corrected adjacency spectral embeddings (CASE). We also show that CASE remedies the exchangeability problem of the original test and demonstrate the validity and consistency of the test that uses CASE via a simulation study. Lastly, we apply our proposed test to the problem of determining equivalence of generating distributions in human connectomes extracted from diffusion magnetic resonance imaging (dMRI) at different scales.

stat.ME↗

arXiv2023

A Statistical Turing Test for Generative Models

The emergence of human-like abilities of AI systems for content generation in domains such as text, audio, and vision has prompted the development of classifiers to determine whether content originated from a human or a machine. Implicit in these efforts is an assumption that the generation properties of a human are different from that of the machine. In this work, we provide a framework in the language of statistical pattern recognition that quantifies the difference between the distributions of human and machine-generated content conditioned on an evaluation context. We describe current methods in the context of the framework and demonstrate how to use the framework to evaluate the progression of generative models towards human-like capabilities, among many axes of analysis.

cs.AI↗

arXiv2023

Why do networks have inhibitory/negative connections?

Why do brains have inhibitory connections? Why do deep networks have negative weights? We propose an answer from the perspective of representation capacity. We believe representing functions is the primary role of both (i) the brain in natural intelligence, and (ii) deep networks in artificial intelligence. Our answer to why there are inhibitory/negative weights is: to learn more functions. We prove that, in the absence of negative weights, neural networks with non-decreasing activation functions are not universal approximators. While this may be an intuitive result to some, to the best of our knowledge, there is no formal theory, in either machine learning or neuroscience, that demonstrates why negative weights are crucial in the context of representation capacity. Further, we provide insights on the geometric properties of the representation space that non-negative deep networks cannot represent. We expect these insights will yield a deeper understanding of more sophisticated inductive priors imposed on the distribution of weights that lead to more efficient biological and machine learning.

cs.LG↗

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

Quantifying Network Similarity using Graph Cumulants

How might one test the hypothesis that networks were sampled from the same distribution? Here, we compare two statistical tests that use subgraph counts to address this question. The first uses the empirical subgraph densities themselves as estimates of those of the underlying distribution. The second test uses a new approach that converts these subgraph densities into estimates of the \textit{graph cumulants} of the distribution (without any increase in computational complexity). We demonstrate -- via theory, simulation, and application to real data -- the superior statistical power of using graph cumulants. In summary, when analyzing data using subgraph/motif densities, we suggest using the corresponding graph cumulants instead.

stat.ME↗

arXiv2023

Prospective Learning: Principled Extrapolation to the Future

Learning is a process which can update decision rules, based on past experience, such that future performance improves. Traditionally, machine learning is often evaluated under the assumption that the future will be identical to the past in distribution or change adversarially. But these assumptions can be either too optimistic or pessimistic for many problems in the real world. Real world scenarios evolve over multiple spatiotemporal scales with partially predictable dynamics. Here we reformulate the learning problem to one that centers around this idea of dynamic futures that are partially learnable. We conjecture that certain sequences of tasks are not retrospectively learnable (in which the data distribution is fixed), but are prospectively learnable (in which distributions may be dynamic), suggesting that prospective learning is more difficult in kind than retrospective learning. We argue that prospective learning more accurately characterizes many real world problems that (1) currently stymie existing artificial intelligence solutions and/or (2) lack adequate explanations for how natural intelligences solve them. Thus, studying prospective learning will lead to deeper insights and solutions to currently vexing challenges in both natural and artificial intelligences.

cs.LG↗

arXiv2023

The Value of Out-of-Distribution Data

We expect the generalization error to improve with more samples from a similar task, and to deteriorate with more samples from an out-of-distribution (OOD) task. In this work, we show a counter-intuitive phenomenon: the generalization error of a task can be a non-monotonic function of the number of OOD samples. As the number of OOD samples increases, the generalization error on the target task improves before deteriorating beyond a threshold. In other words, there is value in training on small amounts of OOD data. We use Fisher's Linear Discriminant on synthetic datasets and deep networks on computer vision benchmarks such as MNIST, CIFAR-10, CINIC-10, PACS and DomainNet to demonstrate and analyze this phenomenon. In the idealistic setting where we know which samples are OOD, we show that these non-monotonic trends can be exploited using an appropriately weighted objective of the target and OOD empirical risk. While its practical utility is limited, this does suggest that if we can detect OOD samples, then there may be ways to benefit from them. When we do not know which samples are OOD, we show how a number of go-to strategies such as data-augmentation, hyper-parameter optimization, and pre-training are not enough to ensure that the target generalization error does not deteriorate with the number of OOD samples in the dataset.

cs.LG↗

arXiv2023

Vertex Nomination in Richly Attributed Networks

Vertex nomination is a lightly-supervised network information retrieval task in which vertices of interest in one graph are used to query a second graph to discover vertices of interest in the second graph. Similar to other information retrieval tasks, the output of a vertex nomination scheme is a ranked list of the vertices in the second graph, with the heretofore unknown vertices of interest ideally concentrating at the top of the list. Vertex nomination schemes provide a useful suite of tools for efficiently mining complex networks for pertinent information. In this paper, we explore, both theoretically and practically, the dual roles of content (i.e., edge and vertex attributes) and context (i.e., network topology) in vertex nomination. We provide necessary and sufficient conditions under which vertex nomination schemes that leverage both content and context outperform schemes that leverage only content or context separately. While the joint utility of both content and context has been demonstrated empirically in the literature, the framework presented in this paper provides a novel theoretical basis for understanding the potential complementary roles of network features and topology.

cs.IR↗

arXiv2023

Independence testing for inhomogeneous random graphs

Testing for independence between graphs is a problem that arises naturally in social network analysis and neuroscience. In this paper, we address independence testing for inhomogeneous Erdős-Rényi random graphs on the same vertex set. We first formulate a notion of pairwise correlations between the edges of these graphs and derive a necessary condition for their detectability. We next show that the problem can exhibit a statistical vs. computational tradeoff, i.e., there are regimes for which the correlations are statistically detectable but may require algorithms whose running time is exponential in n, the number of vertices. Finally, we consider a special case of correlation testing when the graphs are sampled from a latent space model (graphon) and propose an asymptotically valid and consistent test procedure that also runs in time polynomial in n.

stat.ME↗

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↗

arXiv2022

Subgraph nomination: Query by Example Subgraph Retrieval in Networks

This paper introduces the subgraph nomination inference task, in which example subgraphs of interest are used to query a network for similarly interesting subgraphs. This type of problem appears time and again in real world problems connected to, for example, user recommendation systems and structural retrieval tasks in social and biological/connectomic networks. We formally define the subgraph nomination framework with an emphasis on the notion of a user-in-the-loop in the subgraph nomination pipeline. In this setting, a user can provide additional post-nomination light supervision that can be incorporated into the retrieval task. After introducing and formalizing the retrieval task, we examine the nuanced effect that user-supervision can have on performance, both analytically and across real and simulated data examples.

cs.LG↗

arXiv2022

Dynamic Network Sampling for Community Detection

We propose a dynamic network sampling scheme to optimize block recovery for stochastic blockmodel (SBM) in the case where it is prohibitively expensive to observe the entire graph. Theoretically, we provide justification of our proposed Chernoff-optimal dynamic sampling scheme via the Chernoff information. Practically, we evaluate the performance, in terms of block recovery, of our method on several real datasets from different domains. Both theoretically and practically results suggest that our method can identify vertices that have the most impact on block structure so that one can only check whether there are edges between them to save significant resources but still recover the block structure.

cs.SI↗