Ranking of Large Language Model with Nonparametric Prompts

We consider the inference for the ranking of large language models (LLMs). Alignment arises as a big challenge to mitigate hallucinations in the use of LLMs. Ranking LLMs has been shown as a well-performing tool to improve alignment based on the best-of-$N$ policy. In this paper, we propose a new inferential framework for testing hypotheses and constructing confidence intervals of the ranking of language models. We consider the widely adopted Bradley-Terry-Luce (BTL) model, where each item is assigned a positive preference score that determines its pairwise comparisons' outcomes. We further extend it into the contextual setting, where the score of each model varies with the prompt. We show the convergence rate of our estimator. By extending the current Gaussian multiplier bootstrap theory to accommodate the supremum of not identically distributed empirical processes, we construct the confidence interval for ranking and propose a valid testing procedure. We also introduce the confidence diagram as a global ranking property. We conduct numerical experiments to assess the performance of our method.

Inference of Dependency Knowledge Graph for Electronic Health Records

The effective analysis of high-dimensional Electronic Health Record (EHR) data, with substantial potential for healthcare research, presents notable methodological challenges. Employing predictive modeling guided by a knowledge graph (KG), which enables efficient feature selection, can enhance both statistical efficiency and interpretability. While various methods have emerged for constructing KGs, existing techniques often lack statistical certainty concerning the presence of links between entities, especially in scenarios where the utilization of patient-level EHR data is limited due to privacy concerns. In this paper, we propose the first inferential framework for deriving a sparse KG with statistical guarantee based on the dynamic log-linear topic model proposed by \cite{arora2016latent}. Within this model, the KG embeddings are estimated by performing singular value decomposition on the empirical pointwise mutual information matrix, offering a scalable solution. We then establish entrywise asymptotic normality for the KG low-rank estimator, enabling the recovery of sparse graph edges with controlled type I error. Our work uniquely addresses the under-explored domain of statistical inference about non-linear statistics under the low-rank temporal dependent models, a critical gap in existing research. We validate our approach through extensive simulation studies and then apply the method to real-world EHR data in constructing clinical KGs and generating clinical feature embeddings.

Nonparametric Additive Value Functions: Interpretable Reinforcement Learning with an Application to Surgical Recovery

We propose a nonparametric additive model for estimating interpretable value functions in reinforcement learning. Learning effective adaptive clinical interventions that rely on digital phenotyping features is a major for concern medical practitioners. With respect to spine surgery, different post-operative recovery recommendations concerning patient mobilization can lead to significant variation in patient recovery. While reinforcement learning has achieved widespread success in domains such as games, recent methods heavily rely on black-box methods, such neural networks. Unfortunately, these methods hinder the ability of examining the contribution each feature makes in producing the final suggested decision. While such interpretations are easily provided in classical algorithms such as Least Squares Policy Iteration, basic linearity assumptions prevent learning higher-order flexible interactions between features. In this paper, we present a novel method that offers a flexible technique for estimating action-value functions without making explicit parametric assumptions regarding their additive functional form. This nonparametric estimation strategy relies on incorporating local kernel regression and basis expansion to obtain a sparse, additive representation of the action-value function. Under this approach, we are able to locally approximate the action-value function and retrieve the nonlinear, independent contribution of select features as well as joint feature pairs. We validate the proposed approach with a simulation study, and, in an application to spine disease, uncover recovery recommendations that are inline with related clinical knowledge.

Knowledge Graph Embedding with Electronic Health Records Data via Latent Graphical Block Model

Due to the increasing adoption of electronic health records (EHR), large scale EHRs have become another rich data source for translational clinical research. Despite its potential, deriving generalizable knowledge from EHR data remains challenging. First, EHR data are generated as part of clinical care with data elements too detailed and fragmented for research. Despite recent progress in mapping EHR data to common ontology with hierarchical structures, much development is still needed to enable automatic grouping of local EHR codes to meaningful clinical concepts at a large scale. Second, the total number of unique EHR features is large, imposing methodological challenges to derive reproducible knowledge graph, especially when interest lies in conditional dependency structure. Third, the detailed EHR data on a very large patient cohort imposes additional computational challenge to deriving a knowledge network. To overcome these challenges, we propose to infer the conditional dependency structure among EHR features via a latent graphical block model (LGBM). The LGBM has a two layer structure with the first providing semantic embedding vector (SEV) representation for the EHR features and the second overlaying a graphical block model on the latent SEVs. The block structures on the graphical model also allows us to cluster synonymous features in EHR. We propose to learn the LGBM efficiently, in both statistical and computational sense, based on the empirical point mutual information matrix. We establish the statistical rates of the proposed estimators and show the perfect recovery of the block structure. Numerical results from simulation studies and real EHR data analyses suggest that the proposed LGBM estimator performs well in finite sample.

LATTE: Label-efficient Incident Phenotyping from Longitudinal Electronic Health Records

Electronic health record (EHR) data are increasingly used to support real-world evidence (RWE) studies. Yet its ability to generate reliable RWE is limited by the lack of readily available precise information on the timing of clinical events such as the onset time of heart failure. We propose a LAbel-efficienT incidenT phEnotyping (LATTE) algorithm to accurately annotate the timing of clinical events from longitudinal EHR data. By leveraging the pre-trained semantic embedding vectors from large-scale EHR data as prior knowledge, LATTE selects predictive EHR features in a concept re-weighting module by mining their relationship to the target event and compresses their information into longitudinal visit embeddings through a visit attention learning network. LATTE employs a recurrent neural network to capture the sequential dependency between the target event and visit embeddings before/after it. To improve label efficiency, LATTE constructs highly informative longitudinal silver-standard labels from large-scale unlabeled patients to perform unsupervised pre-training and semi-supervised joint training. Finally, LATTE enhances cross-site portability via contrastive representation learning. LATTE is evaluated on three analyses: the onset of type-2 diabetes, heart failure, and the onset and relapses of multiple sclerosis. We use various evaluation metrics present in the literature including the $ABC_{gain}$, the proportion of reduction in the area between the observed event indicator and the predicted cumulative incidences in reference to the prediction per incident prevalence. LATTE consistently achieves substantial improvement over benchmark methods such as SAMGEP and RETAIN in all settings.

Combinatorial Inference on the Optimal Assortment in Multinomial Logit Models

Assortment optimization has received active explorations in the past few decades due to its practical importance. Despite the extensive literature dealing with optimization algorithms and latent score estimation, uncertainty quantification for the optimal assortment still needs to be explored and is of great practical significance. Instead of estimating and recovering the complete optimal offer set, decision-makers may only be interested in testing whether a given property holds true for the optimal assortment, such as whether they should include several products of interest in the optimal set, or how many categories of products the optimal set should include. This paper proposes a novel inferential framework for testing such properties. We consider the widely adopted multinomial logit (MNL) model, where we assume that each customer will purchase an item within the offered products with a probability proportional to the underlying preference score associated with the product. We reduce inferring a general optimal assortment property to quantifying the uncertainty associated with the sign change point detection of the marginal revenue gaps. We show the asymptotic normality of the marginal revenue gap estimator, and construct a maximum statistic via the gap estimators to detect the sign change point. By approximating the distribution of the maximum statistic with multiplier bootstrap techniques, we propose a valid testing procedure. We also conduct numerical experiments to assess the performance of our method.

Federated Offline Reinforcement Learning

Evidence-based or data-driven dynamic treatment regimes are essential for personalized medicine, which can benefit from offline reinforcement learning (RL). Although massive healthcare data are available across medical institutions, they are prohibited from sharing due to privacy constraints. Besides, heterogeneity exists in different sites. As a result, federated offline RL algorithms are necessary and promising to deal with the problems. In this paper, we propose a multi-site Markov decision process model which allows both homogeneous and heterogeneous effects across sites. The proposed model makes the analysis of the site-level features possible. We design the first federated policy optimization algorithm for offline RL with sample complexity. The proposed algorithm is communication-efficient and privacy-preserving, which requires only a single round of communication interaction by exchanging summary statistics. We give a theoretical guarantee for the proposed algorithm without the assumption of sufficient action coverage, where the suboptimality for the learned policies is comparable to the rate as if data is not distributed. Extensive simulations demonstrate the effectiveness of the proposed algorithm. The method is applied to a sepsis data set in multiple sites to illustrate its use in clinical settings.

Lagrangian Inference for Ranking Problems

We propose a novel combinatorial inference framework to conduct general uncertainty quantification in ranking problems. We consider the widely adopted Bradley-Terry-Luce (BTL) model, where each item is assigned a positive preference score that determines the Bernoulli distributions of pairwise comparisons' outcomes. Our proposed method aims to infer general ranking properties of the BTL model. The general ranking properties include the "local" properties such as if an item is preferred over another and the "global" properties such as if an item is among the top $K$-ranked items. We further generalize our inferential framework to multiple testing problems where we control the false discovery rate (FDR), and apply the method to infer the top-$K$ ranked items. We also derive the information-theoretic lower bound to justify the minimax optimality of the proposed method. We conduct extensive numerical studies using both synthetic and real datasets to back up our theory.

BELT: Blockwise Missing Embedding Learning Transfomer

Matrix completion has attracted a lot of attention in many fields including statistics, applied mathematics and electrical engineering. Most of works focus on the independent sampling models under which the individual observed entries are sampled independently. Motivated by applications in the integration of multiple (point-wise mutual information) PMI matrices, we propose the model {\bf B}lockwise missing {\bf E}mbedding {\bf L}earning {\bf T}ransformer (BELT) to treat row-wise/column-wise missingness. Specifically, our proposed method aims at efficient matrix recovery when every pair of matrices from multiple sources has an overlap. We provide theoretical justification for the proposed BELT method. Simulation studies show that the method performs well in finite sample under a variety of configurations. The method is applied to integrate several PMI matrices built by EHR data and Chinese medical text data, which enables us to construct a comprehensive embedding set for CUI and Chinese with high quality.

Heteroskedastic and Imbalanced Deep Learning with Adaptive Regularization

Real-world large-scale datasets are heteroskedastic and imbalanced -- labels have varying levels of uncertainty and label distributions are long-tailed. Heteroskedasticity and imbalance challenge deep learning algorithms due to the difficulty of distinguishing among mislabeled, ambiguous, and rare examples. Addressing heteroskedasticity and imbalance simultaneously is under-explored. We propose a data-dependent regularization technique for heteroskedastic datasets that regularizes different regions of the input space differently. Inspired by the theoretical derivation of the optimal regularization strength in a one-dimensional nonparametric classification setting, our approach adaptively regularizes the data points in higher-uncertainty, lower-density regions more heavily. We test our method on several benchmark tasks, including a real-world heteroskedastic and imbalanced dataset, WebVision. Our experiments corroborate our theory and demonstrate a significant improvement over other methods in noise-robust deep learning.