Efficient Influence Function

In networked dynamical systems, the parameter of primary mechanistic interest is signed interaction structure. Recovering this structure from perturbation time-series data is a fundamental identification problem, compounded by three coupled obstacles: the combinatorial complexity of interaction architectures, ambiguity of causal attribution under limited interventions, and state-dependent dynamics that confound structural inference. Each obstacle is structural in origin and calls for a structural solution. We address these challenges by adopting a reductionist approach, introducing Fundamental Dynamical Units (FDUs): signed three-node interaction patterns as composable primitives that convert the interaction hypothesis space into a finite, constructive, and tractable representation. We show that local interaction structure determines the perturbation conditions required to disentangle direct from relayed influence, making intervention design a structural consequence of the FDU representation. We embed FDU-regularized structural inference within a physics-informed neural ordinary differential equation (ODE) whose governing-equation constraint transforms structural hypotheses into verifiable dynamical predictions, enabling joint recovery of interaction structure and perturbation-resolved trajectories. Validated on synthetic benchmarks with known ground truth, the framework supports structural commitment, expressed through FDU primitives, motif-prescribed intervention design, and physics-informed learning, as a principled basis for mechanistically interpretable inference in networked dynamical systems.

Existing learning-based influence maximization frameworks rely heavily on complex neural architectures and continuous optimization over seed representations. We challenge this paradigm with SIMBA, a diffusion-model-agnostic framework pairing a lightweight neural surrogate with direct discrete search. SIMBA introduces three key components: 1) uniformly anchored node embeddings that eliminate initialization noise and encourage learning driven by graph topology and diffusion pattern, 2) a shallow two-layer graph neural network surrogate predicting final infection states, and 3) batched multi-swap simulated annealing that explores combinatorial seed space without gradients or continuous relaxation. By shifting compute from complex representation learning to effective discrete search, SIMBA drastically cuts time-to-solution while achieving superior influence spread and data efficiency. Our code is available at https://github.com/yl489/rethink-IM.

Standard offline reinforcement learning (RL) algorithms typically assume that the actions in the dataset are observed without error. However, in many real-world applications, the true actions are unobserved and only noisy proxies are available, causing existing RL methods to yield biased and potentially misleading conclusions. We study off-policy evaluation in infinite-horizon discounted Markov decision processes with hidden actions. By leveraging the next-state variable as a natural proxy for the unobserved action, we establish identification of the policy value and propose an influence-function-based estimator called LURE (Learning from the Unseen: Robust Estimator). LURE is multiply robust, remaining consistent under several combinations of correctly specified nuisance components, and is asymptotically normal, enabling valid statistical inference. To our knowledge, this is the first work to address offline RL with hidden actions. We demonstrate LURE's effectiveness through simulations and a sepsis management application using the MIMIC-III database.

Graphical models are ubiquitous in social and empirical science as they are intuitive and easy to use. These models belong to the broader class of Markov models, defined using solely conditional independence (CI) restrictions. In order to estimate finite-dimensional target parameters in such models efficiently, semi-parametric theory provides a principled framework for constructing regular and asymptotically linear estimators via influence functions (IFs). These estimators are asymptotically normal and root-$n$ consistent. Characterizing the class of all influence functions for a target parameter is crucial for statistically efficient inference in these models. For models that are Markov relative to directed acyclic graphs (DAGs), the orthogonal complement of the tangent space is known, implying that for any target the class of all influence functions can be derived once an influence function is obtained. On the other hand, for Markov models not equivalent to a DAG model -- such as ordinary Markov models associated with undirected graphs, chain graphs, or acyclic directed mixed graphs -- the orthogonal complement has not been characterized, impeding semi-parametric inference in these models. We derive closed form expressions for the orthogonal complement of the tangent space for general Markov models and illustrate our results by characterizing the class of influence functions for the conditional mean parameter in several graphical models.

As constrained learning becomes increasingly common, models are trained under explicit feasibility requirements to enforce fairness, safety, robustness, regulariza- tion, and physics or logic constraints. Understanding how training samples in- fluence the model solution (e.g., learned parameters) is crucial for interpretability and robustness. The classical influence function (IF) estimates sample contribu- tions via local sensitivity analysis, measuring how the solution changes when a specific training sample is perturbed or removed. However, IF becomes unreli- able in constrained settings: data perturbations can reshape both the objective and the feasible region, leading to estimates that violate feasibility. In response, we propose the Directional Influence Function (DIF), a novel estimator that explicitly incorporates these constraints into influence estimation. DIF formulates the opti- mality conditions of constrained learning as a variational inequality (VI) and ana- lyzes how perturbing training data affects this VI. We validate DIF on constrained linear regression and demonstrate that it recovers leave-one-out retraining results, whereas IF and penalty-based IF exhibit significant bias. We further apply DIF to fairness-constrained CNNs, where DIF accurately predicts test loss changes under data removal and aligns closely with actual retraining. Our results establish DIF as an efficient and reliable tool for data attribution in constrained learning.

We develop an adjoint-sensitivity framework for positional influence in causal residual Transformers and separate unconditional analytic results from conditional boundary-shape conclusions. The principal unconditional theorem is the residual-to-depth-flow estimate for layer controls converging in $L^1$, complemented by a finite-token-to-Volterra attention estimate that explicitly controls the first cells near the causal endpoint. We define a normalized adjoint-energy influence density and derive its exact evolution along full-batch gradient flow. The adjoint admits an exact generator-term decomposition into residual transmission, nonlocal Volterra, and local channels, including all covariance cross terms. Causal masking can amplify early-position sensitivity and residual identity paths can transmit a right-localized terminal bias, but neither mechanism alone forces a U-shaped profile. We therefore state boundary advantages under independently checkable energy, correlation, and local-channel bounds; these conditions are sufficient rather than necessary. Finite-token influence balancing, positional reweighting, and task-aligned observability are presented as diagnostics or regularizers with explicit differentiation requirements, computational costs, and limitations. Controlled simulations illustrate that each intervention controls its designated surrogate, while observability balance or outer-loop reweighting need not monotonically reduce the influence-based Lost-in-the-Middle diagnostic.

Quantifying directional influence between node populations is a fundamental problem in graph-based modeling, particularly in spatial biological systems where cell-cell interactions shape functional outcomes. Existing approaches based on attention, attribution, or correlation capture associations but do not provide a principled framework for evaluating directional effects under controlled perturbations. We introduce a framework for structured counterfactual interventions in graph-based models to estimate directional influence between node types. Our approach trains a Neighbor Influence Model (NIM) to predict node states from local neighborhoods and applies constrained interventions that modify neighborhood composition while preserving key spatial and structural properties. We define the Counterfactual Directionality Score (CDS), which measures the change in predicted node state induced by targeted perturbations, and provide a theoretical interpretation of CDS as a finite-difference measure of local intervention sensitivity. To obtain valid uncertainty estimates, we introduce a core-level bootstrap procedure that accounts for dependencies within spatial samples. Experiments on synthetic spatial graphs with known directional structure show that CDS recovers directional influence, remains well calibrated under null conditions, and is robust to confounding signals, while preliminary results on spatial transcriptomics data reveal biologically plausible and consistent interactions across tissue cores.

While existing data attribution methods can identify which training examples build specific mechanistic circuits, they cannot explain how training data shapes the high-level behavioral decisions a model learns to make. To bridge this gap, we introduce Symbolic Mechanistic Data Attribution (SMDA), a framework that attributes training pairs to the interpretable symbolic policies governing model behavior. SMDA fits a closed-form Ridge regression over sparse autoencoder (SAE) features to model a target behavior, then analytically decomposes how each supervised fine-tuning example shifts that policy through feature-activation Delta_X and output-probability Delta_Y pathways. We distill a symbolic policy for refusal behavior in Llama-3.2-3B-Instruct and analyze 200 SFT training pairs. Our analysis reveals that (1) the symbolic policy's coefficients expose systematic gaps in the base model's safety behavior for categories like religious stereotyping; (2) per-feature Delta_X/Delta_Y decomposition can mechanistically explain why harmful and harmless pairs exert qualitatively different influences on certain features; and (3) individual training pairs routinely exhibit cross-feature interference, allowing SMDA to identify training pairs whose dominant effect falls on unintended features. These results demonstrate that combining mechanistic interpretability with data attribution yields a diagnostic tool that is both more fine-grained than black-box influence functions and more scalable than manual circuit analysis.

In robot imitation learning, influence functions provide a principled approach to quantify each demonstration's effect on robot task outcomes, yet scaling them to billion-parameter Vision-Language-Action (VLA) models is limited by computational and multitask bottlenecks. To this end, we propose ATHENA, an influence function framework tailored for multitask VLA data curation at a billion-parameter scale. Concretely, it leverages the Kronecker structure of linear-layer gradients to reduce projection cost, and approximates dense Hessian inversion with a rank-r Random Truncated Approximation, achieving about a 313.4x speedup in influence computation. Furthermore, ATHENA formulates global and local interactive influence to balance data curation across 50 jointly trained tasks. Extensive evaluations on RoboTwin 2.0 and real-robot deployment, covering 9.34 and 6.90 hours of demonstrations, respectively, show that ATHENA matches or exceeds full-data joint fine-tuning using only 50% of demonstrations in simulation and 66.7% of data across six real-robot tasks. Overall, ATHENA demonstrates its effectiveness for data curation in billion-parameter multitask VLA fine-tuning.

This study investigates semiparametric efficient estimation of causal and structural parameters in a semi-supervised setting. In our setting, unlabeled auxiliary regressors are available in addition to labeled observations consisting of outcomes and regressors. Our goal is to construct estimators of causal and structural parameters whose asymptotic variances are smaller than those of estimators constructed using only labeled data. We refer to this framework as prediction-powered causal inference (PPCI). We first derive the efficient influence function and the efficiency bound, which imply that the use of auxiliary regressors can attain a smaller asymptotic variance than the efficiency bound attainable from labeled observations alone. Then, by combining the efficient influence function with the debiased machine learning (DML) framework, we propose methods that we call DML-PPCI. If we construct an estimating-equation estimator, we refer to the method as EE-DML-PPCI; if we construct a targeted-learning estimator, we refer to the method as TMLE-DML-PPCI. The asymptotic variances of both estimators match our derived efficiency bound. In the construction of the estimators, estimation of the efficient influence function plays an important role. In our study, the efficient influence function is also a Neyman orthogonal score, which depends on the Riesz representer and the regression function. For Riesz representer estimation, we develop semi-supervised generalized Riesz regression with convergence rate guarantees.

High-quality training data is essential for the success of machine learning models. However, real-world datasets often contain mixed types of errors arising from systematic flaws in data preparation pipelines, including label errors, feature errors, and spurious correlations. Effective debugging of training data requires both detecting erroneous samples and identifying their specific error types to enable targeted repair, yet existing data cleaning and attribution methods fail to adequately address this dual requirement. In this paper, we propose DeMix, a novel framework that simultaneously diagnoses erroneous samples and their error types. Our key insight is that different error types produce distinct patterns on model behavior. DeMix captures such error-specific patterns by influence vectors that characterize how each training sample affects model predictions across all validation samples. We formulate training data debugging as a multi-label classification problem where a classifier is developed to predict error types directly from influence vectors. We further introduce an intervention-based learning strategy that guides the classifier to capture invariant rationales specific to each error type, ensuring the learned classifier generalizes effectively. Empirical evaluations on 11 tasks across tabular data prediction, recommendation systems, and LLM alignment demonstrate that DeMix significantly outperforms state-of-the-art approaches, achieving a 22.61% improvement in data debugging F1-score and a 9.32% gain in task model performance after data repair. Code is available at: https://github.com/SJTU-DMTai/DeMix.

Many important outcomes unfold as dynamic cascades, including product adoption, disease spread, financial distress, and information diffusion. A central challenge is to recover the hidden influence network behind these cascades. Existing methods typically assume a specific diffusion model, and their performance degrades substantially when that assumption is misspecified. We propose CascadeNet, a Jacobian-based machine learning framework for network recovery that does not require specifying a diffusion mechanism. The key idea is that the underlying influence structure can be characterized by the Jacobian of the one-step transition function. CascadeNet first constructs a flexible estimator of the transition function, and further applies Neyman-orthogonal debiasing via the Riesz representer, so that the debiased Jacobian is $\sqrt{n}$-consistent and asymptotically normal, enabling formal inference on the network structure. We validate CascadeNet in both a simulation exercise and a real-world empirical application. In simulations, where the data-generating process is known, CascadeNet achieves the highest network recovery accuracy across nine common data-generating processes. In an empirical application to COVID-19 transmission across Spain's 52 provinces, CascadeNet recovers transmission networks that are significantly correlated with the true inter-province mobility network, whereas networks recovered by baseline methods show no significant alignment with the ground truth.

Shapley values are a widely used tool for attributing importance and interactions among input variables in black-box models, but their computation involves a function defined over an exponentially large space of subsets. We propose TN-SHAP-G, a framework that exploits structure in graph-structured inputs to compute Shapley values and higher-order interaction indices efficiently. Given a predictor and a fixed masking scheme, TN-SHAP-G learns a compact, graph-aligned multilinear surrogate that approximates the masked-input behavior, represented as a tensor network whose topology mirrors the input graph. Once trained from a small number of oracle queries, the surrogate enables deterministic recovery of first- and higher-order Shapley indices via the multilinear extension, without additional model queries or Monte Carlo variance. Experiments on molecular benchmarks show that the learned factorization closely matches exact Shapley values on small graphs and scales efficiently to larger graphs where sampling-based methods become infeasible.

As Text-to-Video (T2V) generation models continue to evolve, the complexity of video evaluation necessitates a fine-grained assessment across various axes. To address this, recent works have focused on developing Multidimensional Video Reward Models (MVRMs), which decompose the evaluation process to better align with the multifaceted nature of human visual perception. However, training effective MVRMs is fundamentally challenged by the complex nature of video data. In this work, we identify a critical phenomenon termed Dimensional Heterogeneity: the reliability of a training sample can vary substantially across evaluation dimensions, meaning that a sample may provide reliable supervision for one objective while inducing high supervision risk for another. Consequently, prevailing data-centric methods that filter based on global scalar metrics are ill-posed for T2V tasks. To address this, we propose a disentangled influence framework that that efficiently estimates dimension-specific supervision risk. Leveraging this framework, we introduce two dimension-disentangled refinement strategies: Dimension-Disentangled Pruning, which removes extreme high-risk samples, and Dimension-Disentangled Reweighting, which softly down-weights high-risk supervision. Extensive experiments demonstrate that our disentangled strategies significantly outperform global filtering baselines, yielding reward models with superior alignment to ground truth.

This paper studies adaptive targeting under network interference in a bandit setting, where treatments applied to one individual may affect others through spillover effects. We consider a linear model in a sparse regime, where each individual's outcome can be affected by at most a few others. We first establish a regret lower bound showing that ignoring the network structure and reducing the problem to a standard linear bandit inevitably leads to inefficient learning, particularly in large populations. To understand how structural information can be leveraged, we analyze regimes with varying levels of knowledge of the interference structure: (1) full support knowledge, (2) knowledge of the column support sizes, and (3) no prior knowledge. For each regime, we establish regret lower bounds characterizing the fundamental limits of learning, and develop algorithms that achieve near-optimal regret. Together, our results provide a unified view of how knowledge of the interference structure governs the efficiency of online learning under interference, and offer practical adaptive targeting algorithms in each setting. Numerical experiments on synthetic and real-world data demonstrate the practical benefits of our algorithms.

As LLMs continue to scale up, improving training efficiency heavily relies on effective data utilization. Data selection mitigates this issue by allocating the limited training budget to high-value examples that optimally facilitate the model's target behavior. Most existing approaches define target behavior via a set of target examples and score candidate training data based on their estimated influence on these samples. However, such methods uniformly treat all target examples as equally important, ignoring the varying relevance of individual examples to model optimization. Specifically, target examples that align closely with the model's inherent behavior deliver stronger supervisory signals, whereas discrepant examples yield only weak and ineffective local guidance. We propose PRISM, a Preference-aware Influence function based Data Selection Method. It leverages model preference to assign weights to target examples and builds a preference-aware target direction. PRISM evaluates candidate training samples according to their influence on this direction, and prioritizes data budget allocation to samples that effectively drive the model to match expected target behavior. Theoretical analysis verifies that weighted preference construction generates a superior first-order gradient direction for boosting target preference, compared with uniform aggregation strategies. Extensive experiments covering diverse model architectures and parameter scales demonstrate that PRISM achieves better performance in efficient fine-tuning and safety-aligned supervised fine-tuning rectification. The results validate that accurate characterization of target behavior serves as the core of cost-effective data selection.

Functional bilevel methods estimate a lower-level function and plug it into a hypergradient, but this plug-in gradient can retain first-order bias when the lower-level problem is learned nonparametrically. To remove this bias, we develop a semiparametric debiasing theory for population bilevel gradients based on the efficient influence function. This perspective leads to a cross-fitted orthogonal hypergradient estimator for which we establish asymptotic normality together with uniform control over the outer parameter. Under quadratic losses, the estimator reduces to a simple doubly robust score based on conditional mean nuisances. On synthetic bilevel benchmarks with known ground truth, the method tracks the oracle efficient-gradient benchmark and improves over plug-in functional hypergradients and regularized kernel bilevel baselines.

In recent years, the black-box nature of deep learning models has limited their application in high-stakes domains such as medical diagnosis and finance, where interpretability is essential. To address this, we propose a novel approach using influence functions to enhance interpretability in NLP models at both the sample and concept levels. Experiments on CEBaB and Yelp datasets show that influence functions effectively identify the most impactful training samples, both helpful and harmful, on model predictions. By adjusting the labels and weights of these samples, we demonstrate that model performance can be restored to baseline levels without retraining, confirming the value of influence functions for efficient data debugging. Furthermore, our concept-level analysis identifies key concepts within Concept Bottleneck Models (CBM) that significantly affect predictions. Modifying these concepts alters model behavior observably, providing clear insights into the decision process.

Influence functions approximate how removing a training example changes a quantity of interest, called the target function, such as a held-out loss. To estimate the influence of a group of examples, the standard practice is to sum the individual influences of its members. However, this sum does not capture how examples jointly affect the target: a pair of examples may be redundant or complementary, but the sum cannot distinguish these cases. We propose an interaction-aware influence function that characterizes how interactions between examples influence the target. By expanding the target to second order around the trained parameters, we obtain an estimator that augments the standard sum with a pairwise interaction term that captures the alignment between two examples' effects on the target. We empirically evaluate our estimator in two settings. First, on six dataset-model pairs spanning logistic regression, MLPs, and ResNet-9, our estimator tracks leave-group-out retraining substantially better than first-order influence across all settings. Second, when used as a greedy selection rule for instruction-tuning data on Llama-3.1-8B, it beats prior influence-based and representation-similarity baselines on five of seven downstream tasks, in a regime where standard influence-based selection underperforms random selection.

What makes a word difficult to learn, and how does the difficulty depend on the learner's native language? We computationally model vocabulary difficulty for English learners whose first language is Spanish, German, or Chinese with gradient-boosted models trained on features related to a word's familiarity (e.g., frequency), meaning, surface form, and cross-linguistic transfer. Using Shapley values, we determine the importance of each feature group. Word familiarity is the dominant feature group shared by all three languages. However, predictions for Spanish- and German-speaking learners rely additionally on orthographic transfer. This transfer mechanism is unavailable to Chinese learners, whose difficulty is shaped by a combination of familiarity and surface features alone. Our models provide interpretable, L1-tailored difficulty estimates that can be used to design vocabulary curricula.

Estimating counterfactual distributions under interventions is central to treatment risk assessment and counterfactual generation tasks. Existing approaches model the counterfactual distribution as a standalone generative target, without exploiting its relationship to the observational data. In this work, we show that under standard assumptions, observational and counterfactual outcome distributions are tightly linked: they have identical support and tail behavior, remain statistically close under weak confounding, and share any features of high-dimensional outcomes which are invariant to confounders. These properties motivate learning counterfactual distributions not from scratch, but via a deconfounding flow from the observational distribution. We formulate this problem via flow-matching and derive a semiparametrically efficient estimator based on a novel efficient influence function correction. We subsequently extend our estimator to target minimal-energy flows in high-dimensions, which we show can be especially simple targets between observational and counterfactual distributions. In experiments, deconfounding flows outperform existing debiased counterfactual distribution estimators, while also mitigating known failure modes of flow-based methods.

The goal of this thesis is to investigate the structural properties of certain sequential problems in order to bring the solutions closer to a practical use. In the first part, we put a special emphasis on structures that can be represented as graphs on actions. In the second part, we study the large action spaces that can be of exponential size in the number of base actions or even infinite. For graph bandits, we consider the settings of smoothness of rewards (spectral bandits), side observations, and influence maximization. For large structured domains, we cover kernel bandits, polymatroid bandits, bandits for function optimization (including unknown smoothness), and infinitely many-arms bandits. The thesis aspires to be a survey of the author's contributions on graph and structured bandits.

The 2026 ACII Dyadic Conversations (ACII-DaiKon) Workshop & Challenge introduces a benchmark for modeling interpersonal affect and social dynamics in dyadic conversations. Although conversational affect modeling has advanced rapidly, most benchmarks remain speaker-centric and underrepresent coupled, time-evolving processes between partners, including directional influence, conversational timing coordination, and rapport development. To address this gap, ACII-DaiKon presents three coordinated sub-challenges built on a shared dataset: (1) directional interpersonal influence prediction, (2) turn-taking prediction (next-speaker and time-to-next-speech), and (3) rapport trajectory prediction across full interactions. The challenge is built on the Hume-DaiKon dataset, comprising 945 dyadic conversations (743.4 hours of audiovisual data) collected under naturalistic conditions across five languages. The benchmark supports multimodal modeling, temporal reasoning, and cross-context generalization through fixed train/validation/test splits, standardized metrics, and released baseline systems. Evaluation uses Concordance Correlation Coefficient (CCC), Pearson correlation, Macro-F1, and Mean Absolute Error (MAE) depending on the sub-challenge. Baseline experiments establish initial reference performance, with best test results of 0.40 CCC and 0.50 Pearson for influence prediction, 0.66 Macro-F1 and 1.50~s MAE for turn-taking, and 0.68 CCC and 0.70 Pearson for rapport trajectory modeling. These results indicate that while current methods capture coarse dyadic patterns, robust modeling of directional dependence and long-horizon interpersonal dynamics remains challenging. The workshop provides a shared platform for rigorous comparison and cross-disciplinary discussion on data validity, evaluation protocols, and culturally aware modeling for dyadic interaction.

We study a graph bandit setting where the objective of the learner is to detect the most influential node of a graph by requesting as little information from the graph as possible. One of the relevant applications for this setting is marketing in social networks, where the marketer aims at finding and taking advantage of the most influential customers. The existing approaches for bandit problems on graphs require either partial or complete knowledge of the graph. In this paper, we do not assume any knowledge of the graph, but we consider a setting where it can be gradually discovered in a sequential and active way. At each round, the learner chooses a node of the graph and the only information it receives is a stochastic set of the nodes that the chosen node is currently influencing. To address this setting, we propose BARE, a bandit strategy for which we prove a regret guarantee that scales with the detectable dimension, a problem dependent quantity that is often much smaller than the number of nodes.

Instruction-tuning datasets often contain substantial redundancy and low-quality samples, necessitating effective data selection methods. We propose an instruction data selection framework based on weighted in-context influence (wICI), which measures how effectively each candidate example reduces instruction-following difficulty for semantically related peers. Through systematic experiments, we address three key questions: what constitutes effective instruction tuning data from an in-context perspective, whether sample difficulty correlates with in-context influence, and how in-context influence translates to instruction tuning effectiveness. Experiments across multiple models and benchmarks demonstrate that our method consistently outperforms existing baselines under constrained data budgets, while empirically showing that sample difficulty negatively correlates with in-context influence.

There is growing concern that AI chatbots might fuel delusional beliefs in users. Some have suggested that humans and chatbots mutually reinforce false beliefs over time, but quantitative evidence is lacking. Using a unique dataset of chat logs from individuals who exhibited delusional thinking, we developed a latent state model that captures accumulating and decaying influences between humans and chatbots. We find that a bidirectional influence model substantially outperforms a unidirectional alternative where humans are the primary driver of delusion. We find that humans exert strong but short-lived influence on chatbots, whereas chatbots exert longer-lasting influence on humans. Moreover, chatbots exert strong, stable self-influence over their own future outputs that tends to perpetuate delusions over long stretches of conversation. In fact, this chatbot self-influence constituted the dominant pathway when considering accumulated influence over time. Overall, these results indicate that humans tend to drive sharp, immediate increases in delusion, whereas chatbots sustain and propagate these effects over longer timescales. Together, these findings provide the first quantitative evidence that human-chatbot interactions can form feedback loops of delusion, decomposable into distinct pathways with dissociable temporal dynamics. By doing so, they can inform the development of safer AI systems.

We study stochastic multi-armed bandits in which the objective is a statistical functional of the long-run reward distribution, rather than expected reward alone. Under mild continuity assumptions, we show that the infinite-horizon problem reduces to optimizing over stationary mixed policies: each weight vector $w$ on the simplex induces a mixture law $P^w$, and performance is measured by the concave utility $U(w)=\mathfrak U(P^w)$. For differentiable statistical utilities, we use influence-function calculus to derive stochastic gradient estimators from bandit feedback. This leads to an entropic mirror-ascent algorithm on a truncated simplex, implemented through multiplicative-weights updates and plug-in estimates of the influence function. We establish regret bounds that separate the mirror-ascent optimization error from the bias caused by estimating the influence function. The framework is developed for general concave distributional utilities and illustrated through variance and Wasserstein objectives, with numerical experiments comparing exact and plug-in influence-function implementations.

We introduce a new budgeted framework for online influence maximization, considering the total cost of an advertising campaign instead of the common cardinality constraint on a chosen influencer set. Our approach better models the real-world setting where the cost of influencers varies and advertisers want to find the best value for their overall social advertising budget. We propose an algorithm assuming an independent cascade diffusion model and edge level semi-bandit feedback, and provide both theoretical and experimental results. Our analysis is also valid for the cardinality constraint setting and improves the state of the art regret bound in this case.

Influence maximization (IM) is a fundamental problem in complex network analysis, with a wide range of real-world applications. To date, existing approaches to influential node identification in IM have predominantly relied on standard graphs, failing to capture higher-order intrinsic interactions embedded in many real-world systems. Hypergraphs can be employed to better capture higher-order interactions. However, using hypergraphs may lead to an excessively large search space and increased complexity in modeling cascading dynamics, making it challenging to accurately identify influential nodes. Therefore, in this study, we propose a new hypergraph-modeled IM method, based on the Discrete Particle Swarm Optimization algorithm and the threshold model. In the proposed method, a particle (i.e., a candidate solution) represents the selection information of seed nodes, and the fitness function is designed to accurately and efficiently evaluate the influence of seed nodes via a two-layer local influence approximation. We also propose a degree-based initialization strategy to improve the quality of initial solutions and develop rules for updating particles' velocity and position, incorporated with a local search to drive particles toward better solutions. Experimental results demonstrate that the proposed method outperforms baseline methods on both synthetic and real-world hypergraphs. In addition, ablation studies validate the effectiveness of both the local search and the initialization strategies.

Large language model (LLM) evaluation platforms increasingly rely on pairwise human judgments. These data are noisy, sparse, and non-uniform, yet leaderboards are reported with limited uncertainty quantification. We study this as semiparametric inference for a low-rank latent score tensor observed through pairwise comparisons under Bradley-Terry-Luce-type models. This places LLM evaluation in a new tensor completion setting with structured observations, non-uniform sampling, and pairwise contrasts. Our target is a smooth functional $ψ(T^\star)$, including linear estimands such as ability gaps and nonlinear ones such as win probabilities. We derive the information operator on the low-rank tangent space, the efficient influence function, and the semiparametric efficiency bound, then construct a one-step debiased estimator with asymptotic normality. A central challenge is that the information operator is anisotropic and does not commute with the tangent-space projection, creating a bottleneck absent from isotropic models. We introduce a score-whitening method that equalizes local Fisher information and restores stable inference at the optimal sample-complexity scale. Our results provide a principled framework for uncertainty quantification in LLM evaluation and more broadly for inference on low-rank structures from pairwise data.

In networked environments, it is common for users to share recommendations about content, products, services, and possible courses of action. Whether these recommendations are accepted and acted upon is highly context-dependent, influenced by the characteristics of the sender and recipient, the nature of their relationship, the attributes of the recommended item, and the communication context. Consequently, probabilities of peer influence exhibit substantial heterogeneity across individuals and settings. Accurate estimation of these probabilities is key to understanding information diffusion processes and to improving the effectiveness of viral marketing strategies. However, learning these probabilities from data is challenging; static data may capture correlations between peer recommendations and peer actions but fails to reveal influence relationships. Online learning algorithms can learn these probabilities from interventions but either waste resources by learning from random exploration or optimize for rewards, thus favoring exploration of the space with higher influence probabilities. In this work, we study learning peer influence probabilities under a contextual linear bandit framework. We show that a fundamental trade-off can arise between regret minimization and estimation error, characterize all achievable rate pairs, and propose an uncertainty-guided exploration algorithm that, by tuning a parameter, attains any pair within this trade-off. Our experiments on semi-synthetic network datasets show the advantages of our method over static methods and contextual bandits that ignore this trade-off.

We study counterfactual regression, which maps features to outcomes under hypothetical scenarios that differ from those observed in the data. This problem is central to decision-making under distribution shift, where treatment patterns may change at deployment. We develop a semiparametric framework for counterfactual regression along a prespecified incremental-intervention path. The target is a finite-dimensional constrained projection of counterfactual risk, estimated using cross-fitted influence-function representations of the program components. For smooth programs with fixed constraints and finite-dimensional programs with estimated linear constraints, we establish consistency and local stability of the optimizer under class-specific conditions, and derive pointwise and uniform first-order expansions. These results yield asymptotically valid inference, including simultaneous confidence bands for the counterfactual regression path. Simulations and an application to SMS reminders illustrate the finite-sample performance and practical applicability of the proposed approach.

Federated learning (FL) is a machine learning paradigm where clients with different behaviors and preferences can learn collaboratively without compromising data privacy. Typical FL methods often rely on fixed weighting for parameter aggregation, thereby neglecting the mutual influence among clients. In practice, clients with similar preferences or backgrounds may provide more useful knowledge to each other, which can be leveraged to improve local performance. However, how to quantify such cross-client influence and how to exploit it for personalized aggregation remain underexplored. To address this gap, we propose an influence-oriented Federated learning framework which quantitatively measures Client-level and Class-level Influence to realize adaptive parameter aggregation for each client (FedC^2I for short). Our core idea is to explicitly model the inter-client influence within an FL system via the well-crafted influence vector and influence matrix. Specifically, FedC^2I incorporate influence vectors to quantify client-level influence, enables clients to selectively acquire knowledge from others, and guides the aggregation of feature representation layers. Meanwhile, the influence matrix captures class-level influence in a more fine-grained manner to achieve personalized classifier aggregation. We evaluate the performance of FedC^2I against existing federated learning methods under non-IID settings, and the results demonstrate the superiority of our method in terms of effectiveness, robustness, and interpretability.

This paper integrates deep neural networks (DNNs) into structural models to increase flexibility and capture rich heterogeneity while preserving interpretability. Economic (or scientific or domain-restricted) structure and machine learning are complements in empirical modeling, not substitutes: DNNs provide the capacity to learn complex, nonlinear heterogeneity, while the structure ensures the estimates remain interpretable and suitable for decision-making and policy analysis. We start with a standard parametric structural model and then enrich its parameters into fully flexible functions, which are estimated using a DNN with the model structure built in. We illustrate our framework with an application to demand estimation in consumer choice. We show that by enriching a demand model we can capture rich heterogeneity exploit it to create personalized pricing. Optimization is not possible without structure, but cannot be heterogeneous without machine learning. The same lessons apply to precision dosing, adaptive treatment, educational testing, and other targeting settings. We provide theoretical justification for our proposed methodology: nonasymptotic bounds and a novel and general influence function for feasible inference via double machine learning, so that the latter can be easily applied in numerous new contexts. These results may be of interest in other contexts as they generalize prior work.