Sampling from Constrained Gibbs Measures: with Applications to High-Dimensional Bayesian Inference

This paper considers a non-standard problem of generating samples from a low-temperature Gibbs distribution with \emph{constrained} support, when some of the coordinates of the mode lie on the boundary. These coordinates are referred to as the non-regular part of the model. We show that in a ``pre-asymptotic'' regime in which the limiting Laplace approximation is not yet valid, the low-temperature Gibbs distribution concentrates on a neighborhood of its mode. Within this region, the distribution is a bounded perturbation of a product measure: a strongly log-concave distribution in the regular part and a one-dimensional exponential-type distribution in each coordinate of the non-regular part. Leveraging this structure, we provide a non-asymptotic sampling guarantee by analyzing the spectral gap of Langevin dynamics. Key examples of low-temperature Gibbs distributions include Bayesian posteriors, and we demonstrate our results on three canonical examples: a high-dimensional logistic regression model, a Poisson linear model, and a Gaussian mixture model.

A Framework to Assess the Persuasion Risks Large Language Model Chatbots Pose to Democratic Societies

In recent years, significant concern has emerged regarding the potential threat that Large Language Models (LLMs) pose to democratic societies through their persuasive capabilities. We expand upon existing research by conducting two survey experiments and a real-world simulation exercise to determine whether it is more cost effective to persuade a large number of voters using LLM chatbots compared to standard political campaign practice, taking into account both the "receive" and "accept" steps in the persuasion process (Zaller 1992). These experiments improve upon previous work by assessing extended interactions between humans and LLMs (instead of using single-shot interactions) and by assessing both short- and long-run persuasive effects (rather than simply asking users to rate the persuasiveness of LLM-produced content). In two survey experiments (N = 10,417) across three distinct political domains, we find that while LLMs are about as persuasive as actual campaign ads once voters are exposed to them, political persuasion in the real-world depends on both exposure to a persuasive message and its impact conditional on exposure. Through simulations based on real-world parameters, we estimate that LLM-based persuasion costs between \$48-\$74 per persuaded voter compared to \$100 for traditional campaign methods, when accounting for the costs of exposure. However, it is currently much easier to scale traditional campaign persuasion methods than LLM-based persuasion. While LLMs do not currently appear to have substantially greater potential for large-scale political persuasion than existing non-LLM methods, this may change as LLM capabilities continue to improve and it becomes easier to scalably encourage exposure to persuasive LLMs.

An Analysis of COVID-19 Knowledge Graph Construction and Applications

The construction and application of knowledge graphs have seen a rapid increase across many disciplines in recent years. Additionally, the problem of uncovering relationships between developments in the COVID-19 pandemic and social media behavior is of great interest to researchers hoping to curb the spread of the disease. In this paper we present a knowledge graph constructed from COVID-19 related tweets in the Los Angeles area, supplemented with federal and state policy announcements and disease spread statistics. By incorporating dates, topics, and events as entities, we construct a knowledge graph that describes the connections between these useful information. We use natural language processing and change point analysis to extract tweet-topic, tweet-date, and event-date relations. Further analysis on the constructed knowledge graph provides insight into how tweets reflect public sentiments towards COVID-19 related topics and how changes in these sentiments correlate with real-world events.