Explaining Categorical Feature Interactions Using Graph Covariance and LLMs

Modern datasets often consist of numerous samples with abundant features and associated timestamps. Analyzing such datasets to uncover underlying events typically requires complex statistical methods and substantial domain expertise. A notable example, and the primary data focus of this paper, is the global synthetic dataset from the Counter Trafficking Data Collaborative (CTDC) -- a global hub of human trafficking data containing over 200,000 anonymized records spanning from 2002 to 2022, with numerous categorical features for each record. In this paper, we propose a fast and scalable method for analyzing and extracting significant categorical feature interactions, and querying large language models (LLMs) to generate data-driven insights that explain these interactions. Our approach begins with a binarization step for categorical features using one-hot encoding, followed by the computation of graph covariance at each time. This graph covariance quantifies temporal changes in dependence structures within categorical data and is established as a consistent dependence measure under the Bernoulli distribution. We use this measure to identify significant feature pairs, such as those with the most frequent trends over time or those exhibiting sudden spikes in dependence at specific moments. These extracted feature pairs, along with their timestamps, are subsequently passed to an LLM tasked with generating potential explanations of the underlying events driving these dependence changes. The effectiveness of our method is demonstrated through extensive simulations, and its application to the CTDC dataset reveals meaningful feature pairs and potential data stories underlying the observed feature interactions.

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.

Investigating social alignment via mirroring in a system of interacting language models

Alignment is a social phenomenon wherein individuals share a common goal or perspective. Mirroring, or mimicking the behaviors and opinions of another individual, is one mechanism by which individuals can become aligned. Large scale investigations of the effect of mirroring on alignment have been limited due to the scalability of traditional experimental designs in sociology. In this paper, we introduce a simple computational framework that enables studying the effect of mirroring behavior on alignment in multi-agent systems. We simulate systems of interacting large language models in this framework and characterize overall system behavior and alignment with quantitative measures of agent dynamics. We find that system behavior is strongly influenced by the range of communication of each agent and that these effects are exacerbated by increased rates of mirroring. We discuss the observed simulated system behavior in the context of known human social dynamics.

Embedding-based statistical inference on generative models

The recent cohort of publicly available generative models can produce human expert level content across a variety of topics and domains. Given a model in this cohort as a base model, methods such as parameter efficient fine-tuning, in-context learning, and constrained decoding have further increased generative capabilities and improved both computational and data efficiency. Entire collections of derivative models have emerged as a byproduct of these methods and each of these models has a set of associated covariates such as a score on a benchmark, an indicator for if the model has (or had) access to sensitive information, etc. that may or may not be available to the user. For some model-level covariates, it is possible to use "similar" models to predict an unknown covariate. In this paper we extend recent results related to embedding-based representations of generative models -- the data kernel perspective space -- to classical statistical inference settings. We demonstrate that using the perspective space as the basis of a notion of "similar" is effective for multiple model-level inference tasks.

Optimizing the Induced Correlation in Omnibus Joint Graph Embeddings

Theoretical and empirical evidence suggests that joint graph embedding algorithms induce correlation across the networks in the embedding space. In the Omnibus joint graph embedding framework, previous results explicitly delineated the dual effects of the algorithm-induced and model-inherent correlations on the correlation across the embedded networks. Accounting for and mitigating the algorithm-induced correlation is key to subsequent inference, as sub-optimal Omnibus matrix constructions have been demonstrated to lead to loss in inference fidelity. This work presents the first efforts to automate the Omnibus construction in order to address two key questions in this joint embedding framework: the correlation-to-OMNI problem and the flat correlation problem. In the flat correlation problem, we seek to understand the minimum algorithm-induced flat correlation (i.e., the same across all graph pairs) produced by a generalized Omnibus embedding. Working in a subspace of the fully general Omnibus matrices, we prove both a lower bound for this flat correlation and that the classical Omnibus construction induces the maximal flat correlation. In the correlation-to-OMNI problem, we present an algorithm -- named corr2Omni -- that, from a given matrix of estimated pairwise graph correlations, estimates the matrix of generalized Omnibus weights that induces optimal correlation in the embedding space. Moreover, in both simulated and real data settings, we demonstrate the increased effectiveness of our corr2Omni algorithm versus the classical Omnibus construction.

Consistent estimation of generative model representations in the data kernel perspective space

Generative models, such as large language models and text-to-image diffusion models, produce relevant information when presented a query. Different models may produce different information when presented the same query. As the landscape of generative models evolves, it is important to develop techniques to study and analyze differences in model behaviour. In this paper we present novel theoretical results for embedding-based representations of generative models in the context of a set of queries. We establish sufficient conditions for the consistent estimation of the model embeddings in situations where the query set and the number of models grow.

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.

MedFuzz: Exploring the Robustness of Large Language Models in Medical Question Answering

Large language models (LLM) have achieved impressive performance on medical question-answering benchmarks. However, high benchmark accuracy does not imply that the performance generalizes to real-world clinical settings. Medical question-answering benchmarks rely on assumptions consistent with quantifying LLM performance but that may not hold in the open world of the clinic. Yet LLMs learn broad knowledge that can help the LLM generalize to practical conditions regardless of unrealistic assumptions in celebrated benchmarks. We seek to quantify how well LLM medical question-answering benchmark performance generalizes when benchmark assumptions are violated. Specifically, we present an adversarial method that we call MedFuzz (for medical fuzzing). MedFuzz attempts to modify benchmark questions in ways aimed at confounding the LLM. We demonstrate the approach by targeting strong assumptions about patient characteristics presented in the MedQA benchmark. Successful "attacks" modify a benchmark item in ways that would be unlikely to fool a medical expert but nonetheless "trick" the LLM into changing from a correct to an incorrect answer. Further, we present a permutation test technique that can ensure a successful attack is statistically significant. We show how to use performance on a "MedFuzzed" benchmark, as well as individual successful attacks. The methods show promise at providing insights into the ability of an LLM to operate robustly in more realistic settings.

Refined Graph Encoder Embedding via Self-Training and Latent Community Recovery

This paper introduces a refined graph encoder embedding method, enhancing the original graph encoder embedding using linear transformation, self-training, and hidden community recovery within observed communities. We provide the theoretical rationale for the refinement procedure, demonstrating how and why our proposed method can effectively identify useful hidden communities via stochastic block models, and how the refinement method leads to improved vertex embedding and better decision boundaries for subsequent vertex classification. The efficacy of our approach is validated through a collection of simulated and real-world graph data.

Continuous Multidimensional Scaling

Multidimensional scaling (MDS) is the act of embedding proximity information about a set of $n$ objects in $d$-dimensional Euclidean space. As originally conceived by the psychometric community, MDS was concerned with embedding a fixed set of proximities associated with a fixed set of objects. Modern concerns, e.g., that arise in developing asymptotic theories for statistical inference on random graphs, more typically involve studying the limiting behavior of a sequence of proximities associated with an increasing set of objects. Standard results from the theory of point-to-set maps imply that, if $n$ is fixed and a sequence of proximities converges, then the limit of the embedded structures is the embedded structure of the limiting proximities. But what if $n$ increases? It then becomes necessary to reformulate MDS so that the entire sequence of embedding problems can be viewed as a sequence of optimization problems in a fixed space. We present such a reformulation and derive some consequences.