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Tian Bai

Publications and source records attributed to Tian Bai.

At least 19 recordsLinked to original sources
arXiv2026

Power-Optimal Risk Control via Standardized Margin Calibration

Machine learning can screen far more candidates than can be experimentally validated, creating a need for selection procedures that identify promising candidates while controlling risk before costly experimental validation. We propose Uncertainty-Normalized Empirical Calibration (UNEC), a p-value-free framework that ranks candidates by uncertainty-normalized predictive margins and directly calibrates a selection cutoff using held-out losses. UNEC supports flexible prediction models, general bounded losses, and diverse selection targets. We study marginal discovery risk (MDR) and selective discovery risk (SDR), with SDR reducing to the false discovery rate under binary loss. We establish finite-sample MDR control for an adjusted rule and asymptotic SDR control with explicit limiting risk and power. Under a location--scale model with a common one-sided binary target, we further show that UNEC asymptotically attains the oracle power benchmark among observation-wise selection rules. Simulations and molecular screening applications in solubility, toxicity, and lipophilicity demonstrate favorable risk--power trade-offs and substantial computational gains across binary and graded-loss settings.

stat.ME↗
arXiv2026

A uniform improvement to conformal risk control via a generalization of e-closure

We extend the recently introduced e-closure principle for multiple testing to general state and action spaces and to arbitrary, including continuously indexed, families of risks. A collection of e-values indexed by states and risks certifies a menu of actions, and every data-dependent selection from this menu controls each expected loss at its prescribed level. Conversely, every valid procedure is certified by its own normalized losses, which often leave part of the risk budget unused. We introduce a method called recertification, which spends this unused budget. Using known distributional structure, it enlarges the certifying e-values while preserving validity and selects a less conservative action from the enlarged menu. One particularly compelling application is to the popular framework of conformal risk control (CRC) with a known loss family. Here, recertification redistributes unused risk budget among the held-out points of each hypothetical augmented sample. The resulting controller is valid under every finite exchangeable law and less (usually strictly) conservative than CRC. For convex losses on an interval of actions, repeated recertification converges geometrically to an admissible controller. As a second example involving false discovery rate control with e-values, recertifying randomized e-BH yields a closed-form procedure that rejects a superset of randomized e-BH for every realization of the randomization and maximizes the expected number of rejections under the same constraints. Recertifying with the larger e-collection of closed e-BH gives a second closed-form procedure that rejects a superset of the first. Experiments on CIFAR-100 hierarchical classification and simulations demonstrate improved budget utilization and gains in informativeness and power over the corresponding baselines.

stat.ME↗
arXiv2026

Optimized Conformal Selection: Powerful Selective Inference After Data-Dependent Score Construction

We study data-driven score construction in conformal selection, which uses conformal p-values and multiple testing to select "interesting" instances with large unobserved labels from a pool of unlabeled data, while controlling the FDR in finite sample. While existing solutions require the score function to be constructed independent of the calibration and test data, it is desirable to select or construct powerful conformity score in a data-driven manner and to leverage all labeled data for score training when presented with many score choices and limited labeled data. We propose Optimized Conformal Selection (OptCS), a general framework that allows valid multiple testing after flexible data-driven score construction. We introduce general conditions under which OptCS constructs valid conformal p-values despite substantial data reuse and handles complex p-value dependencies to maintain finite-sample FDR control. We instantiate this general recipe to propose three FDR-controlling procedures, each optimizing the models differently: (i) selecting a powerful score function among multiple candidates, (ii) training the score with all labeled data without sample splitting, and (iii) combining full-sample training and model selection. We demonstrate the efficacy of our methods via simulation studies and real applications in drug discovery and large language models.

stat.ME↗
arXiv2026

Polynomial Kernels for Interval Completion

An interval graph is the intersection graph of a family of intervals on the real line. \textsc{Interval Completion} asks whether a given graph can be transformed into an interval graph by adding at most $k$ edges. Although the problem is fixed-parameter tractable when parameterized by $k$, whether it admits a polynomial kernel has long been an open question. We resolve this question by giving the first polynomial kernel for \textsc{Interval Completion}. Our main contribution is a parameter-preserving polynomial-time reduction from \textsc{Interval Completion} to \textsc{Odd Cycle Transversal} (OCT). Combining this reduction with the known randomized and deterministic polynomial kernels for OCT and a polynomial-time reduction back to \textsc{Interval Completion}, we obtain a randomized kernel with $\widetilde O(k^{18})$ vertices and $\widetilde O(k^{36})$ edges, and a deterministic kernel with $O(k^{36})$ vertices and $O(k^{72})$ edges. Here, $\widetilde O$ suppresses polylogarithmic factors in $k$.

cs.DS↗
arXiv2026

Integrating knowledge from case reports: a medical ontology based multimodal information system with structured summary

Published medical case reports serve as a crucial medical information carrier, documenting discoveries in rare diseases, diagnostic methods, and innovative treatments. Despite the wealth of clinical knowledge in millions of case reports in the public medicine literature database (PubMed), accessing relevant information efficiently is hindered by the limitations of traditional keyword-based retrieval tools on unstructured and diverse case reports. To address the above issues, we introduce a comprehensive multimodal information system for case reports integrating structured clinical summaries of patients including medical images and biomedical named entities from 52949 open-access case reports published from 2000 to 2021. The multimodal essential information is organized in a well-structured medical ontology. Also, a powerful interface for searching and browsing case reports is designed to assist junior clinicians in retrieving cases effectively and improving the identification and diagnosis of rare diseases.

cs.AI↗
arXiv2026

Scaling Representation Diversity: Modulated Attention and Reconstructive Regularization for Visual Grounding

Referring Expression Comprehension (REC) is commonly studied under dataset-specific fine-tuning, resulting in specialist models with limited cross-dataset generalization. In this work, we revisit REC from the perspective of unified open-vocabulary grounding and identify representation degeneration as a key obstacle to scaling a single generalist model. To preserve representation diversity, we propose a holistic data-model co-design framework. Architecturally, we introduce the Modulated Attention-Contrastive Head (mACH) for efficient token-level vision-language alignment and a text-conditioned JEPA auxiliary stream that provides complementary gradient support to preserve alignment-active representations without inference overhead. On the data side, we introduce Objects365-Caption, enriching Objects365 with context-aware referring expressions for large-scale language supervision. We further provide a theoretical analysis showing that complementary gradient subspaces preserve alignment capacity and thereby scale representation diversity. Extensive experiments demonstrate that our single-checkpoint framework achieves highly competitive performance on standard REC benchmarks while exhibiting strong generalization across heterogeneous grounding datasets without benchmark-specific adaptation.

cs.CV↗
arXiv2026

Feedback Set Problems on Bounded-Degree (Planar) Graphs

The feedback set problems are about removing the minimum number of vertices or edges from a graph to break all its cycles. Much effort has gone into understanding their complexity on planar graphs as well as on graphs of bounded degree. We obtain a complete complexity classification for these problems on bounded-degree digraphs, including the planar case. In particular, we show that both problems are $\NP$-complete on digraphs of maximum degree three, while on planar digraphs the feedback vertex set problem is polynomial-time solvable when each vertex has either indegree at most one or outdegree at most one, and $\NP$-complete otherwise. We also give tight degree bounds for the connected feedback vertex set problem on undirected graphs, both planar and non-planar. We close the paper with a historical account of results for feedback vertex set on undirected graphs of bounded degree.

cs.CC↗
arXiv2026

Clustering Permutations under the Ulam Metric: A Parameterized Complexity Study

Rank aggregation seeks a representative permutation for a collection of rankings and plays a central role in areas such as social choice, information retrieval, and computational biology. Two fundamental aggregation tasks are the center and median problems, which minimize the maximum and the total distance to the input permutations, respectively. While these problems are well understood under Kendall's tau and related distances, their parameterized complexity under the Ulam metric, an edit-distance-based metric on permutations, has remained largely unexplored. In this work, we initiate a systematic study of the parameterized complexity of rank aggregation under the Ulam metric. We consider both the center and median problems, as well as their generalizations to the $k$-center and $k$-median clustering settings, parameterized by the number of centers $k$ and the distance budget $d$ (corresponding to the maximum distance for center variants and the total distance for median variants). Both problems are known to be NP-hard already for $k=1$. We show that the Ulam $k$-center problem remains NP-hard when $d=1$, but is fixed-parameter tractable when parameterized by $k + d$. Our algorithm is based on a novel local-search framework tailored to the non-local nature of Ulam distances. We complement this by proving that no polynomial kernel exists for the $k+d$ parameterization unless NP $\subseteq$ coNP/poly. For the Ulam $k$-median problem parameterized by the total distance $d$, we establish W[1]-hardness and provide an XP algorithm. We also provide a polynomial kernel for the parameter $k + d$, which in turn yields a fixed-parameter tractable algorithm.

cs.DS↗
arXiv2026

P$^2$HCT: Plug-and-Play Hierarchical C2F Transformer for Multi-Scale Feature Fusion

Feature fusion plays a pivotal role in achieving high performance in vision models, yet existing attention-based fusion techniques often suffer from substantial computational overhead and implementation complexity, particularly in resource-constrained settings. To address these limitations, we introduce the Plug-and-Play Hierarchical C2F Transformer (P$^2$HCT), a lightweight module that combines coarse-to-fine token selection with shared attention parameters to preserve spatial details while reducing inference cost. P$^2$HCT is trainable using coarse attention alone and can be seamlessly activated at inference to enhance accuracy without retraining. Integrated into real-time detectors such as YOLOv11-N/S/M, P$^2$HCT achieves mAP gains of 0.9\%, 0.5\%, and 0.4\% on MS COCO with minimal latency increase. Similarly, embedding P$^2$HCT into ResNet-18/50/101 backbones improves ImageNet top-1 accuracy by 6.5\%, 1.7\%, and 1.0\%, respectively. These results underscore P$^2$HCT's effectiveness as a hardware-friendly and general-purpose enhancement for both detection and classification tasks.

cs.CV↗
arXiv2026

Conformal Selective Prediction with General Risk Control

In deploying artificial intelligence (AI) models, selective prediction offers the option to abstain from making a prediction when uncertain about model quality. To fulfill its promise, it is crucial to enforce strict and precise error control over cases where the model is trusted. We propose Selective Conformal Risk control with E-values (SCoRE), a new framework for deriving such decisions for any trained model and any user-defined, bounded and continuously-valued risk. SCoRE offers two types of guarantees on the risk among ``positive'' cases in which the system opts to trust the model. Built upon conformal inference and hypothesis testing ideas, SCoRE first constructs a class of (generalized) e-values, which are non-negative random variables whose product with the unknown risk has expectation no greater than one. Such a property is ensured by data exchangeability without requiring any modeling assumptions. Passing these e-values on to hypothesis testing procedures, we yield the binary trust decisions with finite-sample error control. SCoRE avoids the need of uniform concentration, and can be readily extended to settings with distribution shifts. We evaluate the proposed methods with simulations and demonstrate their efficacy through applications to error management in drug discovery, health risk prediction, and large language models.

stat.ME↗
arXiv2026

Optimal Stopping with a Predicted Prior

There are two major models of value uncertainty in the optimal stopping literature: the secretary model, which assumes no prior knowledge, and the prophet inequality model, which assumes full information about value distributions. In practice, decision makers often rely on machine-learned priors that may be erroneous. Motivated by this gap, we formulate the model of optimal stopping with a predicted prior to design algorithms that are both consistent, exploiting the prediction when accurate, and robust, retaining worst-case guarantees when it is not. Existing secretary and prophet inequality algorithms are either pessimistic in consistency or not robust to misprediction. A randomized combination only interpolates their guarantees linearly. We show that a family of bi-criteria algorithms achieves improved consistency-robustness trade-offs, both for maximizing the expected accepted value and for maximizing the probability of accepting the maximum value. We further prove that for the latter objective, no algorithm can simultaneously match the best prophet inequality algorithm in consistency, and the best secretary algorithm in robustness.

cs.DS↗
arXiv2026

Contracting with a Mechanism Designer

This paper explores the economic interactions within modern crowdsourcing markets. In these markets, employers issue requests for tasks, platforms facilitate the recruitment of crowd workers, and workers complete tasks for monetary rewards. Recognizing that these roles serve distinct functions within the ecosystem, we introduce a three-party model that distinguishes among the principal (the requester), the intermediary (the platform), and the pool of agents (the workers). The principal, unable to directly engage with agents, relies on the intermediary to recruit and incentivize them. This interaction unfolds in two stages: first, the principal designs a profit-sharing contract with the intermediary; second, the intermediary implements a mechanism to select an agent to complete the delegated task. We analyze the proposed model as an extensive-form Stackelberg game. Our contributions are threefold. First, we fully characterize the subgame perfect equilibrium of our model. In particular, the principal's contract design problem can be represented as virtual value pricing, a novel auction-theoretic formulation. We identify the optimality of linear contracts, even when the task has multiple outcomes and agents' cost distributions are asymmetric. Second, to quantify the principal's utility loss from delegation and information asymmetry, we introduce the price of double marginalization (PoDM) and the classical price of anarchy (PoA). We derive tight or nearly tight bounds on both ratios under regular and monotone hazard rate distributions. Finally, we extend our analysis to two natural variants of the base model: (i) the intermediary is restricted to anonymous pricing mechanisms, and (ii) the principal lacks precise information about the market size.

cs.GT↗
arXiv2026

ExpAlign: Expectation-Guided Vision-Language Alignment for Open-Vocabulary Grounding

Open-vocabulary grounding requires accurate vision-language alignment under weak supervision, yet existing methods either rely on global sentence embeddings that lack fine-grained expressiveness or introduce token-level alignment with explicit supervision or heavy cross-attention designs. We propose ExpAlign, a theoretically grounded vision-language alignment framework built on a principled multiple instance learning formulation. ExpAlign introduces an Expectation Alignment Head that performs attention-based soft MIL pooling over token-region similarities, enabling implicit token and instance selection without additional annotations. To further stabilize alignment learning, we develop an energy-based multi-scale consistency regularization scheme, including a Top-K multi-positive contrastive objective and a Geometry-Aware Consistency Objective derived from a Lagrangian-constrained free-energy minimization. Extensive experiments show that ExpAlign consistently improves open-vocabulary detection and zero-shot instance segmentation, particularly on long-tail categories. Most notably, it achieves 36.2 AP$_r$ on the LVIS minival split, outperforming other state-of-the-art methods at comparable model scale, while remaining lightweight and inference-efficient.

cs.CV↗
arXiv2026

On the Leaky Private Information Retrieval with Side Information

This paper investigates the problem of Leaky Private Information Retrieval with Side Information (L-PIR-SI), providing a fundamental characterization of the trade-off among leaky privacy, side information, and download cost. We propose a unified probabilistic framework to design L-PIR-SI schemes under $\varepsilon$-differential privacy variants of both $W$-privacy and $(W, S)$-privacy. Explicit upper bounds on the download cost are derived, which strictly generalize existing results: our bounds recover the capacity of perfect PIR-SI as $\varepsilon \to 0$, and reduce to the known $\varepsilon$-leaky PIR rate in the absence of side information. Furthermore, we conduct a refined analysis of the privacy--utility trade-off at the scaling-law level, demonstrating that the leakage ratio exponent scales as $\mathcal{O}(\log \frac{K}{M + 1})$ under leaky $W$-privacy, and as $\mathcal{O}(\log K)$ under leaky $(W, S)$-privacy in the minimal non-trivial setting $M = 1$, where $K$ and $M$ denote the number of messages and the side information size, respectively.

cs.IT↗
arXiv2026

Multi-Stage Patient Role-Playing Framework for Realistic Clinical Interactions

The simulation of realistic clinical interactions plays a pivotal role in advancing clinical Large Language Models (LLMs) and supporting medical diagnostic education. Existing approaches and benchmarks rely on generic or LLM-generated dialogue data, which limits the authenticity and diversity of doctor-patient interactions. In this work, we propose the first Chinese patient simulation dataset (Ch-PatientSim), constructed from realistic clinical interaction scenarios to comprehensively evaluate the performance of models in emulating patient behavior. Patients are simulated based on a five-dimensional persona structure. To address issues of the persona class imbalance, a portion of the dataset is augmented using few-shot generation, followed by manual verification. We evaluate various state-of-the-art LLMs and find that most produce overly formal responses that lack individual personality. To address this limitation, we propose a training-free Multi-Stage Patient Role-Playing (MSPRP) framework, which decomposes interactions into three stages to ensure both personalization and realism in model responses. Experimental results demonstrate that our approach significantly improves model performance across multiple dimensions of patient simulation.

cs.CL↗
arXiv2026

VERHallu: Evaluating and Mitigating Event Relation Hallucination in Video Large Language Models

Video Large Language Models (VideoLLMs) exhibit various types of hallucinations. Existing research has primarily focused on hallucinations involving the presence of events, objects, and scenes in videos, while largely neglecting event relation hallucination. In this paper, we introduce a novel benchmark for evaluating the Video Event Relation Hallucination, named VERHallu. This benchmark focuses on causal, temporal, and subevent relations between events, encompassing three types of tasks: relation classification, question answering, and counterfactual question answering, for a comprehensive evaluation of event relation hallucination. Additionally, it features counterintuitive video scenarios that deviate from typical pretraining distributions, with each sample accompanied by human-annotated candidates covering both vision-language and pure language biases. Our analysis reveals that current state-of-the-art VideoLLMs struggle with dense-event relation reasoning, often relying on prior knowledge due to insufficient use of frame-level cues. Although these models demonstrate strong grounding capabilities for key events, they often overlook the surrounding subevents, leading to an incomplete and inaccurate understanding of event relations. To tackle this, we propose a Key-Frame Propagating (KFP) strategy, which reallocates frame-level attention within intermediate layers to enhance multi-event understanding. Experiments show it effectively mitigates the event relation hallucination without affecting inference speed.

cs.CV↗
arXiv2025

Adaptive Grid Designs for Classifying Monotonic Binary Deterministic Computer Simulations

This research is motivated by the need for effective classification in ice-breaking dynamic simulations, aimed at determining the conditions under which an underwater vehicle will break through the ice. This simulation is extremely time-consuming and yields deterministic, binary, and monotonic outcomes. Detecting the critical edge between the negative-outcome and positive-outcome regions with minimal simulation runs necessitates an efficient experimental design for selecting input values. In this paper, we derive lower bounds on the number of functional evaluations needed to ensure a certain level of classification accuracy for arbitrary static and adaptive designs. We also propose a new class of adaptive designs called adaptive grid designs, which are sequences of grids with increasing resolution such that lower resolution grids are proper subsets of higher resolution grids. By prioritizing simulation runs at lower resolution points and skipping redundant runs, adaptive grid designs require the same order of magnitude of runs as the best possible adaptive design, which is an order of magnitude fewer than the best possible static design. Numerical results across test functions, the road crash simulation and the ice-breaking simulation validate the superiority of adaptive grid designs.

stat.ME↗
arXiv2025

A Cooperative Statistical Approach for Abnormal Node Detection with Adversary Resistance

Distinguishing abnormal nodes from those with normal packet loss in clusters helps reduce the loss of clustered network resources. The detection performance of existing detection schemes is limited by the techniques to quantify node behaviors, and most schemes cannot avoid being misled by the falsified information. This paper presents a novel probabilistic abnormal node detection scheme CSD -- Cooperative Statistical Detection -- for accurate and efficient detection in the existence of falsified detection data in clustered networks. Specifically, employing the likelihood ratio test (LRT) based detection method to measure node forwarding behaviors, we propose a modified Z-score based falsification-resistant mechanism to filter out falsifications. We show that both the false alarm and missed detection probabilities can decrease exponentially if and only if the transmissions from the nodes falsifying the data are less than half of the total. Furthermore, the optimal threshold of the modified Z-score method is derived, which guarantees perfect detection of our CSD under any falsification strategy in the proposed detection model. Evaluation results validate the effectiveness, robustness, and superiority of our scheme compared to the state-of-the-art.

eess.SY↗