arXiv subjects

Eric Bridgeford

Publications and source records attributed to Eric Bridgeford.

10 recordsLinked to original sources

arXiv2025

Detecting Perspective Shifts in Multi-agent Systems

Generative models augmented with external tools and update mechanisms (or \textit{agents}) have demonstrated capabilities beyond intelligent prompting of base models. As agent use proliferates, dynamic multi-agent systems have naturally emerged. Recent work has investigated the theoretical and empirical properties of low-dimensional representations of agents based on query responses at a single time point. This paper introduces the Temporal Data Kernel Perspective Space (TDKPS), which jointly embeds agents across time, and proposes several novel hypothesis tests for detecting behavioral change at the agent- and group-level in black-box multi-agent systems. We characterize the empirical properties of our proposed tests, including their sensitivity to key hyperparameters, in simulations motivated by a multi-agent system of evolving digital personas. Finally, we demonstrate via natural experiment that our proposed tests detect changes that correlate sensitively, specifically, and significantly with a real exogenous event. As far as we are aware, TDKPS is the first principled framework for monitoring behavioral dynamics in black-box multi-agent systems -- a critical capability as generative agent deployment continues to scale.

cs.AI↗

arXiv2022

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↗

arXiv2021

The Phantom Alignment Strength Conjecture: Practical use of graph matching alignment strength to indicate a meaningful graph match

The alignment strength of a graph matching is a quantity that gives the practitioner a measure of the correlation of the two graphs, and it can also give the practitioner a sense for whether the graph matching algorithm found the true matching. Unfortunately, when a graph matching algorithm fails to find the truth because of weak signal, there may be "phantom alignment strength" from meaningless matchings that, by random noise, have fewer disagreements than average (sometimes substantially fewer); this alignment strength may give the misleading appearance of significance. A practitioner needs to know what level of alignment strength may be phantom alignment strength and what level indicates that the graph matching algorithm obtained the true matching and is a meaningful measure of the graph correlation. The {\it Phantom Alignment Strength Conjecture} introduced here provides a principled and practical means to approach this issue. We provide empirical evidence for the conjecture, and explore its consequences.

math.OC↗

arXiv2020

Multiscale Comparative Connectomics

The connectome, a map of the structural and/or functional connections in the brain, provides a complex representation of the neurobiological phenotypes on which it supervenes. This information-rich data modality has the potential to transform our understanding of the relationship between patterns in brain connectivity and neurological processes, disorders, and diseases. However, existing computational techniques used to analyze connectomes are oftentimes insufficient for interrogating multi-subject connectomics datasets: many current methods are either solely designed to analyze single connectomes or leverage heuristic graph statistics that are unable to capture the complete topology of multiscale connections between brain regions. To enable more rigorous connectomics analysis, we introduce a set of robust and interpretable effect size measures motivated by recent theoretical advances in random graph models. These measures facilitate simultaneous analysis of multiple connectomes across different scales of network topology, enabling the robust and reproducible discovery of hierarchical brain structures that vary in relation to phenotypic profiles. In addition to explaining the theoretical foundations and guarantees of our algorithms, we demonstrate their superiority over current state-of-the-art connectomics methods through extensive simulation studies and real-data experiments. Using a set of high-resolution connectomes obtained from genetically distinct mouse strains (including the BTBR mouse -- a standard model of autism -- and three behavioral wild-types), we illustrate how our methods successfully uncover latent information in multi-subject connectomics data and yield valuable insights into the connective correlates of neurological phenotypes that other methods do not capture. The data and code necessary to reproduce our analyses are available at https://github.com/neurodata/MCC.

q-bio.NC↗

arXiv2020

Statistical Analysis of Data Repeatability Measures

The advent of modern data collection and processing techniques has seen the size, scale, and complexity of data grow exponentially. A seminal step in leveraging these rich datasets for downstream inference is understanding the characteristics of the data which are repeatable -- the aspects of the data that are able to be identified under a duplicated analysis. Conflictingly, the utility of traditional repeatability measures, such as the intraclass correlation coefficient, under these settings is limited. In recent work, novel data repeatability measures have been introduced in the context where a set of subjects are measured twice or more, including: fingerprinting, rank sums, and generalizations of the intraclass correlation coefficient. However, the relationships between, and the best practices among these measures remains largely unknown. In this manuscript, we formalize a novel repeatability measure, discriminability. We show that it is deterministically linked with the correlation coefficient under univariate random effect models, and has desired property of optimal accuracy for inferential tasks using multivariate measurements. Additionally, we overview and systematically compare repeatability statistics using both theoretical results and simulations. We show that the rank sum statistic is deterministically linked to a consistent estimator of discriminability. The power of permutation tests derived from these measures are compared numerically under Gaussian and non-Gaussian settings, with and without simulated batch effects. Motivated by both theoretical and empirical results, we provide methodological recommendations for each benchmark setting to serve as a resource for future analyses. We believe these recommendations will play an important role towards improving repeatability in fields such as functional magnetic resonance imaging, genomics, pharmacology, and more.

stat.AP↗

arXiv2020

Vertex nomination: The canonical sampling and the extended spectral nomination schemes

Suppose that one particular block in a stochastic block model is of interest, but block labels are only observed for a few of the vertices in the network. Utilizing a graph realized from the model and the observed block labels, the vertex nomination task is to order the vertices with unobserved block labels into a ranked nomination list with the goal of having an abundance of interesting vertices near the top of the list. There are vertex nomination schemes in the literature, including the optimally precise canonical nomination scheme~$\mathcal{L}^C$ and the consistent spectral partitioning nomination scheme~$\mathcal{L}^P$. While the canonical nomination scheme $\mathcal{L}^C$ is provably optimally precise, it is computationally intractable, being impractical to implement even on modestly sized graphs. With this in mind, an approximation of the canonical scheme---denoted the {\it canonical sampling nomination scheme} $\mathcal{L}^{CS}$---is introduced; $\mathcal{L}^{CS}$ relies on a scalable, Markov chain Monte Carlo-based approximation of $\mathcal{L}^{C}$, and converges to $\mathcal{L}^{C}$ as the amount of sampling goes to infinity. The spectral partitioning nomination scheme is also extended to the {\it extended spectral partitioning nomination scheme}, $\mathcal{L}^{EP}$, which introduces a novel semisupervised clustering framework to improve upon the precision of $\mathcal{L}^P$. Real-data and simulation experiments are employed to illustrate the precision of these vertex nomination schemes, as well as their empirical computational complexity. Keywords: vertex nomination, Markov chain Monte Carlo, spectral partitioning, Mclust MSC[2010]: 60J22, 65C40, 62H30, 62H25

stat.ML↗

arXiv2019

On a 'Two Truths' Phenomenon in Spectral Graph Clustering

Clustering is concerned with coherently grouping observations without any explicit concept of true groupings. Spectral graph clustering - clustering the vertices of a graph based on their spectral embedding - is commonly approached via K-means (or, more generally, Gaussian mixture model) clustering composed with either Laplacian or Adjacency spectral embedding (LSE or ASE). Recent theoretical results provide new understanding of the problem and solutions, and lead us to a 'Two Truths' LSE vs. ASE spectral graph clustering phenomenon convincingly illustrated here via a diffusion MRI connectome data set: the different embedding methods yield different clustering results, with LSE capturing left hemisphere/right hemisphere affinity structure and ASE capturing gray matter/white matter core-periphery structure.

stat.ML↗

arXiv2018

A Community-Developed Open-Source Computational Ecosystem for Big Neuro Data

Big imaging data is becoming more prominent in brain sciences across spatiotemporal scales and phylogenies. We have developed a computational ecosystem that enables storage, visualization, and analysis of these data in the cloud, thusfar spanning 20+ publications and 100+ terabytes including nanoscale ultrastructure, microscale synaptogenetic diversity, and mesoscale whole brain connectivity, making NeuroData the largest and most diverse open repository of brain data.

q-bio.NC↗

arXiv2017

Supervised Dimensionality Reduction for Big Data

To solve key biomedical problems, experimentalists now routinely measure millions or billions of features (dimensions) per sample, with the hope that data science techniques will be able to build accurate data-driven inferences. Because sample sizes are typically orders of magnitude smaller than the dimensionality of these data, valid inferences require finding a low-dimensional representation that preserves the discriminating information (e.g., whether the individual suffers from a particular disease). There is a lack of interpretable supervised dimensionality reduction methods that scale to millions of dimensions with strong statistical theoretical guarantees.We introduce an approach, XOX, to extending principal components analysis by incorporating class-conditional moment estimates into the low-dimensional projection. The simplest ver-sion, "Linear Optimal Low-rank" projection (LOL), incorporates the class-conditional means. We prove, and substantiate with both synthetic and real data benchmarks, that LOL and its generalizations in the XOX framework lead to improved data representations for subsequent classification, while maintaining computational efficiency and scalability. Using multiple brain imaging datasets consisting of >150 million features, and several genomics datasets with>500,000 features, LOL outperforms other scalable linear dimensionality reduction techniques in terms of accuracy, while only requiring a few minutes on a standard desktop computer.

stat.ML↗

arXiv2016

Discovering and Deciphering Relationships Across Disparate Data Modalities

Understanding the relationships between different properties of data, such as whether a connectome or genome has information about disease status, is becoming increasingly important in modern biological datasets. While existing approaches can test whether two properties are related, they often require unfeasibly large sample sizes in real data scenarios, and do not provide any insight into how or why the procedure reached its decision. Our approach, "Multiscale Graph Correlation" (MGC), is a dependence test that juxtaposes previously disparate data science techniques, including k-nearest neighbors, kernel methods (such as support vector machines), and multiscale analysis (such as wavelets). Other methods typically require double or triple the number samples to achieve the same statistical power as MGC in a benchmark suite including high-dimensional and nonlinear relationships - spanning polynomial (linear, quadratic, cubic), trigonometric (sinusoidal, circular, ellipsoidal, spiral), geometric (square, diamond, W-shape), and other functions, with dimensionality ranging from 1 to 1000. Moreover, MGC uniquely provides a simple and elegant characterization of the potentially complex latent geometry underlying the relationship, providing insight while maintaining computational efficiency. In several real data applications, including brain imaging and cancer genetics, MGC is the only method that can both detect the presence of a dependency and provide specific guidance for the next experiment and/or analysis to conduct.

stat.ML↗