arXiv subjects

Karissa Huang

Publications and source records attributed to Karissa Huang.

4 recordsLinked to original sources

arXiv2026

Detecting weighted hidden cliques

We study a generalization of the classical hidden clique problem to graphs with real-valued edge weights. Formally, we define a hypothesis testing problem. Under the null hypothesis, edges of a complete graph on $n$ vertices are associated with independent and identically distributed edge weights from a distribution $P$. Under the alternate hypothesis, $k$ vertices are chosen at random and the edge weights between them are drawn from a distribution $Q$, while the remaining are sampled from $P$. The goal is to decide, upon observing the edge weights, which of the two hypotheses they were generated from. We investigate the problem under two different scenarios: (1) when $P$ and $Q$ are completely known, and (2) when there is only partial information of $P$ and $Q$. In the first scenario, we obtain statistical limits on $k$ when the two hypotheses are distinguishable, and when they are not. Additionally, in each of the scenarios, we provide bounds on the minimal risk of the hypothesis testing problem when $Q$ is not absolutely continuous with respect to $P$. We also provide computationally efficient spectral tests that can distinguish the two hypotheses as long as $k=Ω(\sqrt{n})$ in both the scenarios.

math.ST↗

arXiv2026

Auditing the Auditors: Does Community-based Moderation Get It Right?

Online social platforms increasingly rely on crowd-sourced systems to label misleading content at scale, but these systems must both aggregate users' evaluations and decide whose evaluations to trust. To address the latter, many platforms audit users by rewarding agreement with the final aggregate outcome, a design we term consensus-based auditing. We analyze the consequences of this design in X's Community Notes, which in September 2022 adopted consensus-based auditing that ties users' eligibility for participation to agreement with the eventual platform outcome. We find evidence of strategic conformity: minority contributors' evaluations drift toward the majority and their participation share falls on controversial topics, where independent signals matter most. We formalize this mechanism in a behavioral model in which contributors trade off private beliefs against anticipated penalties for disagreement. Motivated by these findings, we propose a two-stage auditing and aggregation algorithm that weights contributors by the stability of their past residuals rather than by agreement with the majority. The method first accounts for differences across content and contributors, and then measures how predictable each contributor's evaluations are relative to the latent-factor model. Contributors whose evaluations are consistently informative receive greater influence in aggregation, even when they disagree with the prevailing consensus. In the Community Notes data, this approach improves out-of-sample predictive performance while avoiding penalization of disagreement.

cs.SI↗

arXiv2026

Travel Bans vs. Other Disease Mitigation Measures: A Mathematical Analysis

As the world grows increasingly connected, infectious disease transmission and outbreaks have become a pressing global concern for public health officials and policymakers. While policy interventions to contain and prevent the spread of disease have been proposed and implemented, there has been little rigorous quantitative analysis of the effectiveness of such interventions. In this paper, we study the susceptible-infected-recovered (SIR) infection process on a dynamic network model that models two communities with travel between them with the infection starting in one of them. In particular, we consider two Erdős--Rényi graphs where edges are dynamically changing based on node travel between the graphs. We characterize the time evolution of the outbreaks in both communities and pin down the time for when the infection first reaches the second community. Finally, we analyze two types of interventions--travel bans and intra-community interventions in the second community--and prove that travel bans are not effective, while the second type are effective even without travel bans, provided they sufficiently reduce the effective reproduction number. We complement our analytic results by numerical simulations on large networks with realistic degree distributions and disease recovery times, showing that these results are robust, and hold for settings that model actual contact networks and disease spread more closely.

math.PR↗

arXiv2024

A Law of Large Numbers for SIR on the Stochastic Block Model: A Proof via Herd Immunity

In this paper, we study the dynamics of the susceptible-infected-recovered (SIR) model on a network with community structure, namely the stochastic block model (SBM). As usual, the SIR model is a stochastic model for an epidemic where infected vertices infect susceptible neighbors at some rate $η$ and recover at rate $γ$, and the SBM is a random graph model where vertices are partitioned into a finite number of communities. The connection probability between two vertices depends on their community affiliation, here scaled so that the average degrees have a finite limit as the network grows. We prove laws of large numbers (LLN) for the epidemic's trajectory to a system of ordinary differential equations over any time horizon (finite or infinite), including in particular a LLN for the final size of the infection. Our proofs rely on two main ingredients: (i) a new coupling of the SIR epidemic and the randomness of the SBM, revealing a vector-valued random variable that drives the epidemic (related to what is usually called the ``force of the infection'' via a linear transformation), and (ii) a novel technique for analyzing the limiting behavior of the infinite time horizon for the infection, using the fact that once the infection passes the herd immunity threshold it dies out quickly and has a negligible impact on the overall size of the infection.

math.PR↗