Papers

This paper develops a nonparametric framework to identify and estimate distributional treatment effects under nonseparable endogeneity. We begin by revisiting the widely adopted rank similarity (RS) assumption and characterizing it by the relationship it imposes between observed and counterfactual potential outcome distributions. The characterization highlights the restrictiveness of RS, motivating a weaker identifying condition. Under this alternative, we construct identifying bounds on the distributional treatment effects of interest through a linear semi-infinite programming (SILP) formulation. Our identification strategy also clarifies how richer exogenous instrument variation, such as multi-valued or multiple instruments, can further tighten these bounds. Finally, exploiting the SILP's saddle-point structure and Karush-Kuhn-Tucker (KKT) conditions, we establish large-sample properties for the empirical SILP: consistency and asymptotic distribution results for the estimated bounds and associated solutions.

A variety of infinitely wide neural architectures (e.g., dense NNs, CNNs, and transformers) induce Gaussian process (GP) priors over their outputs. These relationships provide both an accurate characterization of the prior predictive distribution and enable the use of GP machinery to improve the uncertainty quantification of deep neural networks. In this work, we extend this connection to neural operators (NOs), a class of models designed to learn mappings between function spaces. Specifically, we show conditions for when arbitrary-depth NOs with Gaussian-distributed convolution kernels converge to function-valued GPs. Based on this result, we show how to compute the covariance functions of these NO-GPs for two NO parametrizations, including the popular Fourier neural operator (FNO). With this, we compute the posteriors of these GPs in regression scenarios, including PDE solution operators. This work is an important step towards uncovering the inductive biases of current FNO architectures and opens a path to incorporate novel inductive biases for use in kernel-based operator learning methods.

Causal mediation analysis in cluster-randomized trials (CRTs) is essential for explaining how cluster-level interventions affect individual outcomes, yet it is complicated by interference, post-treatment confounding, and hierarchical covariate adjustment. We develop a Bayesian nonparametric framework that simultaneously accommodates interference and a post-treatment confounder that precedes the mediator. Identification is achieved through a multivariate Gaussian copula that replaces cross-world independence with a single dependence parameter, yielding a built-in sensitivity analysis to residual post-treatment confounding. For estimation, we introduce a nested common atoms enriched Dirichlet process (CA-EDP) prior that integrates the Common Atoms Model (CAM) to share information across clusters while capturing between- and within-cluster heterogeneity, and an Enriched Dirichlet Process (EDP) structure delivering robust covariate adjustment without impacting the outcome model. We provide formal theoretical support for our prior by deriving the model's key distributional properties, including its partially exchangeable partition structure, and by establishing convergence guarantees for the practical truncation-based posterior inference strategy. We demonstrate the performance of the proposed methods in simulations and provide further illustration through a reanalysis of a completed CRT.

Uncertain knowledge graph embedding (UnKGE) methods learn vector representations that capture both structural and uncertainty information to predict scores of unseen triples. However, existing methods produce only point estimates, without quantifying predictive uncertainty-limiting their reliability in high-stakes applications where understanding confidence in predictions is crucial. To address this limitation, we propose UnKGCP, a framework that generates prediction intervals guaranteed to contain the true score with a user-specified level of confidence. The length of the intervals reflects the model's predictive uncertainty. UnKGCP builds on the conformal prediction framework but introduces a novel nonconformity measure tailored to UnKGE methods and an efficient procedure for interval construction. We provide theoretical guarantees for the intervals and empirically verify these guarantees. Extensive experiments on standard benchmarks across diverse UnKGE methods further demonstrate that the intervals are sharp and effectively capture predictive uncertainty.

Prediction is a central task of machine learning. Our goal is to solve large scale prediction problems using Generative Quantile Bayesian Prediction (GQBP).By directly learning predictive quantiles rather than densities we achieve a number of theoretical and practical advantages. We contrast our approach with state-of-the-art methods including conformal prediction, fiducial prediction and marginal likelihood. Our distinguishing feature of our method is the use of generative methods for predictive quantile maps. We illustrate our methodology for normal-normal learning and causal inference. Finally, we conclude with directions for future research.

We consider tensor factorizations based on sparse measurements of the components of relatively high rank tensors. The measurements are designed in a way that the underlying graph of interactions is a random graph. The setup will be useful in cases where a substantial amount of data is missing, as in completion of relatively high rank matrices for recommendation systems heavily used in social network services. In order to obtain theoretical insights on the setup, we consider statistical inference of the tensor factorization in a high dimensional limit, which we call as dense limit, where the graphs are large and dense but not fully connected. We build message-passing algorithms and test them in a Bayes optimal teacher-student setting in some specific cases. We also develop a replica theory to examine the performance of statistical inference in the dense limit based on a cumulant expansion. The latter approach allows one to avoid blind usage of Gaussian ansatz which fails in some fully connected systems.

Synthetic data has been increasingly used to train frontier generative models. However, recent studies raise key concerns that iteratively retraining a generative model on its self-generated synthetic data may keep deteriorating model performance, a phenomenon often coined model collapse. In this paper, we investigate ways to modify the synthetic retraining process to avoid model collapse, and even possibly help reverse the trend from collapse to improvement. Our key finding is that by injecting information through an external synthetic data verifier, whether a human or a better model, synthetic retraining will not cause model collapse. Specifically, we situate our theoretical analysis in the fundamental linear regression setting, showing that verifier-guided retraining can yield near-term improvements, but ultimately drives the parameter estimate to the verifier's "knowledge center" in the long run. Our theory further predicts that, unless the verifier is perfectly reliable, these early gains will plateau and may even reverse. Indeed, our experiments across linear regression, Variational Autoencoders (VAEs) trained on MNIST, and fining-tuning SmolLM2-135M on the XSUM task confirm these theoretical insights.

Modern scientific and engineering design increasingly involves distributed optimization, where agents such as laboratories, simulations, or industrial partners pursue related goals under differing conditions. These agents often face heterogeneities in objectives, evaluation budgets, and accessible design variables, which complicates coordination and can lead to redundancy, poor resource use, and ineffective information sharing. Bayesian Optimization (BO) is a widely used decision-making framework for expensive black box functions, but its single-agent formulation assumes centralized control and full data sharing. Recent collaborative BO methods relax these assumptions, yet they often require uniform resources, fully shared input spaces, and fixed task alignment, conditions rarely satisfied in practice. To address these challenges, we introduce Adaptive Resource Aware Collaborative Bayesian Optimization (ARCO-BO), a framework that explicitly accounts for heterogeneity in multi-agent optimization. ARCO-BO combines three components: a similarity and optima-aware consensus mechanism for adaptive information sharing, a budget-aware asynchronous sampling strategy for resource coordination, and a partial input space sharing for heterogeneous design spaces. Experiments on synthetic and high-dimensional engineering problems show that ARCO-BO consistently outperforms independent BO and existing collaborative BO via consensus approach, achieving robust and efficient performance in complex multi-agent settings.

Biological machine learning is often bottlenecked by a lack of scaled data. One promising route to relieving data bottlenecks is through high throughput screens, which can experimentally test the activity of $10^6-10^{12}$ protein sequences in parallel. In this article, we introduce algorithms to optimize high throughput screens for data creation and model training. We focus on the large scale regime, where dataset sizes are limited by the cost of measurement and sequencing. We show that when active sequences are rare, we maximize information gain if we only collect positive examples of active sequences, i.e. $x$ with $y>0$. We can correct for the missing negative examples using a generative model of the library, producing a consistent and efficient estimate of the true $p(y | x)$. We demonstrate this approach in simulation and on a large scale screen of antibodies. Overall, co-design of experiments and inference lets us accelerate learning dramatically.

Deep learning models have proven enormously successful at using multiple layers of representation to learn relevant features of structured data. Encoding physical symmetries into these models can improve performance on difficult tasks, and recent work has motivated the principle of parameter symmetry breaking and restoration as a unifying mechanism underlying their hierarchical learning dynamics. We evaluate the role of parameter symmetry and network expressivity in the generalisation behaviour of neural networks when learning a real-space renormalisation group (RG) transformation, using the central limit theorem (CLT) as a test case map. We consider simple multilayer perceptrons (MLPs) and graph neural networks (GNNs), and vary weight symmetries and activation functions across architectures. Our results reveal a competition between symmetry constraints and expressivity, with overly complex or overconstrained models generalising poorly. We analytically demonstrate this poor generalisation behaviour for certain constrained MLP architectures by recasting the CLT as a cumulant recursion relation and making use of an established framework to propagate cumulants through MLPs. We also empirically validate an extension of this framework from MLPs to GNNs, elucidating the internal information processing performed by these more complex models. These findings offer new insight into the learning dynamics of symmetric networks and their limitations in modelling structured physical transformations.

Understanding the continuous evolution of populations from discrete temporal snapshots is a critical research challenge, particularly in fields like developmental biology and systems medicine where longitudinal tracking of individual entities is often impossible. Such trajectory inference is vital for unraveling the mechanisms of dynamic processes. While Schrödinger Bridge (SB) offer a potent framework, their traditional application to pairwise time points can be insufficient for systems defined by multiple intermediate snapshots. This paper introduces Multi-Marginal Schrödinger Bridge Matching (MSBM), a novel algorithm specifically designed for the multi-marginal SB problem. MSBM extends iterative Markovian fitting (IMF) to effectively handle multiple marginal constraints. This technique ensures robust enforcement of all intermediate marginals while preserving the continuity of the learned global dynamics across the entire trajectory. Empirical validations on synthetic data and real-world single-cell RNA sequencing datasets demonstrate the competitive or superior performance of MSBM in capturing complex trajectories and respecting intermediate distributions, all with notable computational efficiency.

Causal inference is only valid when its underlying assumptions are satisfied, one of the most central being the ignorability or unconfoundedness assumption. However, this hypothesis is often unrealistic in observational studies, as some confounding variables may remain unobserved. To address this limitation, sensitivity models for Inverse Probability Weighting (IPW) estimators, known as Marginal Sensitivity Models, have been introduced, allowing for a controlled relaxation of ignorability. A substantial body of literature has emerged around these models, aiming to derive sharp and robust bounds for both binary and continuous treatment effects. A key element of these approaches is the specification of a sensitivity parameter, referred to as the "confounding strength", which quantifies the extent of deviation from ignorability. Yet, determining an appropriate value for this parameter is challenging, and the final interpretation of sensitivity analyses can be unclear. We believe these difficulties represent major obstacles to the adoption of such methods in practice. Therefore, after introducing sensitivity analyses for IPW estimators, we review different strategies to estimate or lower bound the confounding strength, introduce a new method leveraging negative controls, provide a decision tree with guidelines to choose a suitable approach, and compare the methodologies in an in-depth simulation study.

This research proposes a systematic, large language model (LLM) approach for extracting product and service attributes, features, and associated sentiments from customer reviews. Grounded in marketing theory, the framework distinguishes perceptual attributes from actionable features, producing interpretable and managerially actionable insights. We apply the methodology to 20,000 Yelp reviews of Starbucks stores and evaluate eight prompt variants on a random subset of reviews. Model performance is assessed through agreement with human annotations and predictive validity for customer ratings. Results show high consistency between LLMs and human coders and strong predictive validity, confirming the reliability of the approach. Human coders required a median of six minutes per review, whereas the LLM processed each in two seconds, delivering comparable insights at a scale unattainable through manual coding. Managerially, the analysis identifies attributes and features that most strongly influence customer satisfaction and their associated sentiments, enabling firms to pinpoint "joy points," address "pain points," and design targeted interventions. We demonstrate how structured review data can power an actionable marketing dashboard that tracks sentiment over time and across stores, benchmarks performance, and highlights high-leverage features for improvement. Simulations indicate that enhancing sentiment for key service features could yield 1-2% average revenue gains per store.

Recent claims of strong performance by Large Language Models (LLMs) on causal discovery are undermined by a key flaw: many evaluations rely on benchmarks likely included in pretraining corpora. Thus, apparent success suggests that LLM-only methods, which ignore observational data, outperform classical statistical approaches. We challenge this narrative by asking: Do LLMs truly reason about causal structure, and how can we measure it without memorization concerns? Can they be trusted for real-world scientific discovery? We argue that realizing LLMs' potential for causal analysis requires two shifts: (P.1) developing robust evaluation protocols based on recent scientific studies to guard against dataset leakage, and (P.2) designing hybrid methods that combine LLM-derived knowledge with data-driven statistics. To address P.1, we encourage evaluating discovery methods on novel, real-world scientific studies. We outline a practical recipe for extracting causal graphs from recent publications released after an LLM's training cutoff, ensuring relevance and preventing memorization while capturing both established and novel relations. Compared to benchmarks like BNLearn, where LLMs achieve near-perfect accuracy, they perform far worse on our curated graphs, underscoring the need for statistical grounding. Supporting P.2, we show that using LLM predictions as priors for the classical PC algorithm significantly improves accuracy over both LLM-only and purely statistical methods. We call on the community to adopt science-grounded, leakage-resistant benchmarks and invest in hybrid causal discovery methods suited to real-world inquiry.

Some improved estimators of the location parameters of several exponential distributions with ordered restriction are derived and compared numerically using Monte Carlo simulations. Note that the two-parameter exponential distribution is very useful in different areas like survival analysis, reliability engineering and biomedical research, where products have a guaranteed failure-free operating time before failures begin to occur. In the present manuscript, we address the component-wise estimation of location parameters of $k~(\ge 2)$ exponential distributions under an asymmetric Linex loss function. The location parameter represents a minimum guaranteed period before failure. At first, we consider the estimation of the location parameters with ordered scale parameters. Next, we address the estimation of ordered location parameters. For this, we take three different cases into account as follows: $(i)$ scale parameters are known, $(ii)$ scale parameters are unknown but equal, $(iii)$ scale parameters are unknown and unequal. In these cases, we establish general inadmissibility results. Further, using the general result, the inadmissibility of the best affine equivariant estimator is proved. The improved estimators are written in explicit forms. Additionally, we show that the results for several important life-testing schemes namely $(i)$ Type-II censoring, $(ii)$ progressive type-II censoring and $(iii)$ record value data can be obtained using i.i.d sample.Finally, for each case, the Monte Carlo simulation technique is used to compare the performance of the proposed estimators based on their risk values. The numerical results reveal a significant improvement of the proposed estimators.

Modern datasets often contain high-dimensional features exhibiting complex dependencies. To effectively analyze such data, dimensionality reduction methods rely on estimating the dataset's intrinsic dimension (id) as a measure of its underlying complexity. However, estimating id is challenging due to its dependence on scale: at very fine scales, noise inflates id estimates, while at coarser scales, estimates stabilize to lower, scale-invariant values. This paper introduces a novel, scalable, and parallelizable method called eDCF, which is based on Connectivity Factor (CF), a local connectivity-based metric, to robustly estimate intrinsic dimension across varying scales. Our method consistently matches leading estimators, achieving comparable values of mean absolute error (MAE) on synthetic benchmarks with noisy samples. Moreover, our approach also attains higher exact intrinsic dimension match rates, reaching up to 25.0% compared to 16.7% for MLE and 12.5% for TWO-NN, particularly excelling under medium to high noise levels and large datasets. Further, we showcase our method's ability to accurately detect fractal geometries in decision boundaries, confirming its utility for analyzing realistic, structured data.

Real-world multivariate time series anomalies are rare and often unlabeled. Additionally, prevailing methods rely on increasingly complex architectures tuned to benchmarks, detecting only fragments of anomalous segments and overstating performance. In this paper, we introduce OracleAD, a simple and interpretable unsupervised framework for multivariate time series anomaly detection. OracleAD encodes each variable's past sequence into a single causal embedding to jointly predict the present time point and reconstruct the input window, effectively modeling temporal dynamics. These embeddings then undergo a self-attention mechanism to project them into a shared latent space and capture spatial relationships. These relationships are not static, since they are modeled by a property that emerges from each variable's temporal dynamics. The projected embeddings are aligned to a Stable Latent Structure (SLS) representing normal-state relationships. Anomalies are identified using a dual scoring mechanism based on prediction error and deviation from the SLS, enabling fine-grained anomaly diagnosis at each time point and across individual variables. Since any noticeable SLS deviation originates from embeddings that violate the learned temporal causality of normal data, OracleAD directly pinpoints the root-cause variables at the embedding level. OracleAD achieves state-of-the-art results across multiple real-world datasets and evaluation protocols, while remaining interpretable through SLS.

Detecting symmetry from data is a fundamental problem in signal analysis, providing insight into underlying structure and constraints. When data emerge as trajectories of dynamical systems, symmetries encode structural properties of the dynamics that enable model reduction, principled comparison across conditions, and detection of regime changes. While recent optimal transport methods provide practical tools for data-driven symmetry detection in this setting, they rely on deterministic thresholds and lack uncertainty quantification, limiting robustness to noise and ability to resolve hierarchical symmetry structures. We present a Bayesian framework that formulates symmetry detection as probabilistic model selection over a lattice of candidate subgroups, using a Gibbs posterior constructed from Wasserstein distances between observed data and group-transformed copies. We establish three theoretical guarantees: $(i)$ a Bayesian Occam's razor favoring minimal symmetry consistent with data, $(ii)$ conjugation equivariance ensuring frame-independence, and $(iii)$ stability bounds under perturbations for robustness to noise. Posterior inference is performed via Metropolis-Hastings sampling and numerical experiments on equivariant dynamical systems and synthetic point clouds demonstrate accurate symmetry recovery under high noise and small sample sizes. An application to human gait dynamics reveals symmetry changes induced by mechanical constraints, demonstrating the framework's utility for statistical inference in biomechanical and dynamical systems.

Quantifying concordance between two random variables is crucial in applications. Traditional estimation techniques for commonly used concordance measures, such as Gini's gamma or Spearman's rho, often fail when data contain ties. This is particularly problematic for zero-inflated data, characterized by a combination of discrete mass in zero and a continuous component, which frequently appear in insurance, weather forecasting, and biomedical applications. This study provides a new formulation of Gini's gamma and Spearman's footrule, two rank-based concordance measures that incorporate absolute rank differences, tailored to zero-inflated continuous distributions. Along the way, we correct an expression of Spearman's rho for zero-inflated data previously presented in the literature. The best-possible upper and lower bounds for these measures in zero-inflated continuous settings are established, making the estimators useful and interpretable in practice. We pair our theoretical results with simulations and two real-life applications in insurance and weather forecasting, respectively. Our results illustrate the impact of zero inflation on dependence estimation, emphasizing the benefits of appropriately adjusted zero-inflated measures.

Sliced Wasserstein distances are widely used in practice as a computationally efficient alternative to Wasserstein distances in high dimensions. In this paper, motivated by theoretical foundations of this alternative, we prove quantitative estimates between the sliced $1$-Wasserstein distance and the $1$-Wasserstein distance. We construct a concrete example to demonstrate the exponents in the estimate is sharp. We also provide a general analysis for the case where slicing involves projections onto $k$-planes and not just lines.

This work introduces MAYA, a sequential imitation learning model based on multi-armed bandits, designed to reproduce and predict individual bees' decisions in contextualized foraging tasks. The model accounts for bees' limited memory through a temporal window $\tau$, whose optimal value is around 7 trials, with a slight dependence on weather conditions. Experimental results on real, simulated, and complementary (mice) datasets show that MAYA (particularly with the Wasserstein distance) outperforms imitation baselines and classical statistical models, while providing interpretability of individual learning strategies and enabling the inference of realistic trajectories for prospective ecological applications.

This paper introduces a novel spatial scalar-on-function quantile regression model that extends classical scalar-on-function models to account for spatial dependence and heterogeneous conditional distributions. The proposed model incorporates spatial autocorrelation through a spatially lagged response and characterizes the entire conditional distribution of a scalar outcome given a functional predictor. To address the endogeneity induced by the spatial lag term, we develop two robust estimation procedures based on instrumental variable strategies. $\sqrt{n}$-consistency and asymptotic normality of the proposed estimators are established under mild regularity conditions. We demonstrate through extensive Monte Carlo simulations that the proposed estimators outperform existing mean-based and robust alternatives, particularly in settings with strong spatial dependence and outlier contamination. We apply our method to high-resolution environmental data from the Lombardy region in Italy, using daily ozone trajectories to predict daily mean particulate matter with a diameter of less than 2.5 micrometers concentrations. The empirical results confirm the superiority of our approach in predictive accuracy, robustness, and interpretability across various quantile levels. Our method has been implemented in the ssofqrm R package.

We develop here a semiparametric Gaussian mixture model (SGMM) for unsupervised learning with valuable spatial information taken into consideration. Specifically, we assume for each instance a random location. Then, conditional on this random location, we assume for the feature vector a standard Gaussian mixture model (GMM). The proposed SGMM allows the mixing probability to be nonparametrically related to the spatial location. Compared with a classical GMM, SGMM is considerably more flexible and allows the instances from the same class to be spatially clustered. To estimate the SGMM, novel EM algorithms are developed and rigorous asymptotic theories are established. Extensive numerical simulations are conducted to demonstrate our finite sample performance. For a real application, we apply our SGMM method to the CAMELYON16 dataset of whole-slide images (WSIs) for breast cancer detection. The SGMM method demonstrates outstanding clustering performance.

While significant progress has been made in heterogeneous treatment effect (HTE) estimation, the evaluation of HTE estimators remains underdeveloped. In this article, we propose a robust evaluation framework based on relative error, which quantifies performance differences between two HTE estimators. We first derive the key theoretical conditions on the nuisance parameters that are necessary to achieve a robust estimator of relative error. Building on these conditions, we introduce novel loss functions and design a neural network architecture to estimate nuisance parameters and obtain robust estimation of relative error, thereby achieving reliable evaluation of HTE estimators. We provide the large sample properties of the proposed relative error estimator. Furthermore, beyond evaluation, we propose a new learning algorithm for HTE that leverages both the previously HTE estimators and the nuisance parameters learned through our neural network architecture. Extensive experiments demonstrate that our evaluation framework supports reliable comparisons across HTE estimators, and the proposed learning algorithm for HTE exhibits desirable performance.

Conformal Prediction (CP) is a powerful statistical machine learning tool to construct uncertainty sets with coverage guarantees, which has fueled its extensive adoption in generating prediction regions for decision-making tasks, e.g., Trajectory Optimization (TO) in uncertain environments. However, existing methods predominantly employ a sequential scheme, where decisions rely unidirectionally on the prediction regions, and consequently the information from decision-making fails to be fed back to instruct CP. In this paper, we propose a novel Feedback-Based CP (Fb-CP) framework for shrinking-horizon TO with a joint risk constraint over the entire mission time. Specifically, a CP-based posterior risk calculation method is developed by fully leveraging the realized trajectories to adjust the posterior allowable risk, which is then allocated to future times to update prediction regions. In this way, the information in the realized trajectories is continuously fed back to the CP, enabling attractive feedback-based adjustments of the prediction regions and a provable online improvement in trajectory performance. Furthermore, we theoretically prove that such adjustments consistently maintain the coverage guarantees of the prediction regions, thereby ensuring provable safety. Additionally, we develop a decision-focused iterative risk allocation algorithm with theoretical convergence analysis for allocating the posterior allowable risk which closely aligns with Fb-CP. Furthermore, we extend the proposed method to handle distribution shift. The effectiveness and superiority of the proposed method are demonstrated through benchmark experiments.

Evidence derived primarily from physical models has identified saltwater disposal as the dominant causal factor that contributes to induced seismicity. To complement physical models, statistical/machine learning (ML) models are designed to measure associations from observational data, either with parametric regression models or more flexible ML models. However, it is often difficult to interpret the statistical significance of a parameter or the predicative power of a model as evidence of causation. We adapt a causal inference framework with the potential outcomes perspective to explicitly define what we meant by causal effect and declare necessary identification conditions to recover unbiased causal effect estimates. In particular, we illustrate the threat of time-varying confounding in observational longitudinal geoscience data through simulations and adapt established statistical methods for longitudinal analysis from the causal interference literature to estimate the effect of wastewater disposal on earthquakes in the Fort-Worth Basin of North Central Texas from 2013 to 2016.

In this work, we propose a sparse transformer architecture that incorporates prior information about the underlying data distribution directly into the transformer structure of the neural network. The design of the model is motivated by a special optimal transport problem, namely the regularized Wasserstein proximal operator, which admits a closed-form solution and turns out to be a special representation of transformer architectures. Compared with classical flow-based models, the proposed approach improves the convexity properties of the optimization problem and promotes sparsity in the generated samples. Through both theoretical analysis and numerical experiments, including applications in generative modeling and Bayesian inverse problems, we demonstrate that the sparse transformer achieves higher accuracy and faster convergence to the target distribution than classical neural ODE-based methods.

We propose STANE (Shared and Time-specific Adaptive Network Embedding), a new joint embedding framework for dynamic networks that captures both stable global structures and localized temporal variations. To further improve the model's adaptability to transient changes, we introduce Sparse STANE, which models time-specific changes as sparse perturbations, thereby improving interpretability. Unlike existing methods that either overlook cross-time similarities or enforce overly smooth evolution, Sparse STANE integrates temporal clustering with sparse deviation modeling to strike a flexible balance between persistence and change. We also provide non-asymptotic error guarantees of embeddings and show that our estimator can reliably identify changed node pairs when deviations are sparse. On synthetic and real-world political conflict networks, STANE and its extensions improve temporal clustering accuracy and structural recovery, outperforming state-of-the-art baselines. These results highlight the potential of STANE in applications such as international relations modeling, where both persistent and transient connections matter. Our findings underscore the power of structured dynamic embeddings for revealing interpretable patterns in network evolution.

Deep learning has led researchers to rethink the relationship between memorization and generalization. In many settings, memorization does not hurt generalization due to implicit regularization and may help by memorizing long-tailed examples. In this paper, we consider the synergy between memorization and simple composition – the ability to make correct prediction on a combination of long-tailed features. Theoretically, we show that for a linear setting, memorization together with composition can help the model make correct predictions on rare test examples that require a combination of long-tailed features, even if such combinations were never observed in the training data. Experiments on neural network architecture on simple data show that the theoretical insight extends beyond the linear setting, and we further observe that the composition capability of the model depends on its architecture.

Federated learning of causal estimands offers a powerful strategy to improve estimation efficiency by leveraging data from multiple study sites while preserving privacy. Existing literature has primarily focused on the average treatment effect using single data source, whereas our work addresses a broader class of causal measures across multiple sources. We derive and compare semiparametrically efficient estimators under two transportability assumptions, which impose different restrictions on the data likelihood and illustrate the efficiency-robustness tradeoff. This estimator also permits the incorporation of flexible machine learning algorithms for nuisance functions while maintaining parametric convergence rates and nominal coverage. To further handle scenarios where some source sites violate transportability, we propose a Post-Federated Weighting Selection (PFWS) framework, which is a two-step procedure that adaptively identifies compatible sites and achieves the semiparametric efficiency bound asymptotically. This framework mitigates the efficiency loss of weighting methods and the instability and computational burden of direct site selection in finite samples. Through extensive simulations and real-data analysis, we demonstrate that our PFWS framework achieves superior variance efficiency compared with the target-only analyses across diverse transportability scenarios.