Retrieval-Augmented Generation (RAG) enhances Large Language Models by grounding their outputs in external documents. These systems, however, remain vulnerable to attacks on the retrieval corpus, such as prompt injection. RAG-based search systems (e.g., Google's Search AIOverview) present an interesting setting for studying and protecting against such threats, as defense algorithms can benefit from built-in reliability signals--like document ranking--and represent a non-LLM challenge for the adversary due to decades of work to thwart SEO. Motivated by, but not limited to, this scenario, this work introduces ReliabilityRAG, a framework for adversarial robustness that explicitly leverages reliability information of retrieved documents. Our first contribution adopts a graph-theoretic perspective to identify a "consistent majority" among retrieved documents to filter out malicious ones. We introduce a novel algorithm based on finding a Maximum Independent Set (MIS) on a document graph where edges encode contradiction. Our MIS variant explicitly prioritizes higher-reliability documents and provides provable robustness guarantees against bounded adversarial corruption under natural assumptions. Recognizing the computational cost of exact MIS for large retrieval sets, our second contribution is a scalable weighted sample and aggregate framework.

Identifying most influential sets (MIS) - size-$k$ subsets whose removal maximally changes a target estimand - is typically infeasible because it requires searching over $\binom{n}{k}$ subsets. For estimands with linear-fractional leave-set-out effects, we show that MIS selection reduces to a one-parameter sequence of top-$k$ problems. Dinkelbach's method yields an algorithm with $\mathcal{O}(n)$ cost per iteration and finite termination. For fixed residualized inputs, the algorithm returns a globally optimal set for the univariate ratio objective, including the oracle-residualized partial linear model. With estimated nuisance functions, uniform denominator and generated-score stability imply approximation to the first-order oracle orthogonal-score objective; exact set recovery follows under a separation condition. Simulations and applications show that the method recovers exact MIS that were previously computationally inaccessible.

Estimating the covariance of asset returns, i.e., the risk model, is a key component of financial portfolio construction and evaluation. Most risk modeling approaches produce a factor model that decomposes the asset variability into two components: the first attributed to a small number of factors that are common among the assets and the second attributed to the idiosyncratic behavior of each asset. Third-party providers typically provide risk models to investors, and while these models are typically of high quality, they may fail to capture important information, e.g., changing market regimes and transient factors. To overcome these limitations, we propose a systematic method based on maximum likelihood estimation to enhance an existing factor model by both refining the given model and adding new statistical factors. Our approach relies only on the observed sequence of realized returns and on the choice of two hyperparameters: the number of additional factors and the half-life parameter that determines the weights assigned to returns in the log-likelihood objective. Importantly, our methodology applies to the situation where asset returns may be missing, making it suitable for typical equity datasets. We demonstrate our approach on the Barra short-term US risk model, a high-quality risk model used in practice, for a universe of US high-capitalization equities. We show that the proposed extension captures structure in the returns that is missed by the original model.

Most existing approaches for dealing with noisy labels broadly fall into two categories: noise-modeling-based methods and memorization-effects-based methods.