Papers

This paper evaluates the economic impact of Renewable Energy Communities (RECs) on the Italian wholesale power market. Combining a bottom-up engineering approach with a short-run economic impact assessment, the study begins by mapping existing and emerging RECs in Italy. We identify key characteristics of RECs, such as average installed capacity, institutional profiles of members, types of renewable systems used, and transmission across Italy's electricity market zones. This mapping yields representative REC configurations, which are employed within a bottom-up engineering model to generate energy injection and self-consumption profiles for different REC prosumer and producer categories (residential, public, small and medium enterprise, non-profit organization, and standalone installation), considering the different levels of solar irradiance in Italy based on latitude. These zonal results, aggregated on an hourly basis, inform the implementation of the synthetic counterfactual approach, which develops alternative scenarios (e.g., 5 GW target for REC-driven capacity set by Italian policy for 2027) to assess the impact of REC-driven injection and self-consumption on the Italian day-ahead power market. The findings suggest that REC deployment can increase equilibrium quantities during daylight in most of the time, while decreasing equilibrium quantities mostly during the cold months, as electrified heating drives greater self-consumption and offsets lower grid injections. Both positive and negative effects on equilibrium quantities suggest that REC deployment also has a potential to reduce wholesale electricity prices. Moreover, by reducing grid exchanges through higher self-consumption, REC proliferation can alleviate pressure on the distribution system.

The control variates method is a classical variance reduction technique for Monte Carlo estimators that exploits correlated auxiliary variables without introducing bias. In many applications, the quantity of interest can be expressed as a ratio of expectations. We propose a variance-reduced estimator for such ratios, which applies control variates to both the numerator and the denominator. The control variates coefficients are optimized jointly to minimize the approximated variance of the resulting estimator. This approach guarantees variance reduction and naturally extends to approximate control variates. Simulation studies show significant variance reduction, particularly when correlations between variables and control variates are strong. The practical value of the method is illustrated on multi-fidelity applications: estimating a proportion in an aircraft design use case and a conditional value-at-risk in an electromagnetic dataset.

Analysis and processing of data is a vital part of our modern society and requires vast amounts of computational resources. To reduce the computational burden, compressing and approximating data has become a central topic. We consider the approximation of labeled data samples, mathematically described as site-to-value maps between finite metric spaces. Within this setting, we identify the discrete modulus of continuity as an effective data-intrinsic quantity to measure regularity of site-to-value maps without imposing further structural assumptions. We investigate the consistency of the discrete modulus of continuity in the infinite data limit and propose an algorithm for its efficient computation. Building on these results, we present a sample based approximation theory for labeled data. For data subject to statistical uncertainty we consider multilevel approximation spaces and a variant of the multilevel Monte Carlo method to compute statistical quantities of interest. Our considerations connect approximation theory for labeled data in metric spaces to the covering problem for (random) balls on the one hand and the efficient evaluation of the discrete modulus of continuity to combinatorial optimization on the other hand. We provide extensive numerical studies to illustrate the feasibility of the approach and to validate our theoretical results.

Effective assessment of mobile network coverage and the precise identification of service weak spots are paramount for network operators striving to enhance user Quality of Experience (QoE). This paper presents a novel framework for mobile coverage and weak spot analysis utilising crowdsourced QoE data. The core of our methodology involves coverage analysis at the individual cell (antenna) level, subsequently aggregated to the site level, using empirical geolocation data. A key contribution of this research is the application of One-Class Support Vector Machine (OC-SVM) algorithm for calculating mobile network coverage. This approach models the decision hyperplane as the effective coverage contour, facilitating robust calculation of coverage areas for individual cells and entire sites. The same methodology is extended to analyse crowdsourced service loss reports, thereby identifying and quantifying geographically localised weak spots. Our findings demonstrate the efficacy of this novel framework in accurately mapping mobile coverage and, crucially, in highlighting granular areas of signal deficiency, particularly within complex urban environments.

Calibration of predicted probabilities is critical for reliable machine learning, yet it is poorly understood how standard training procedures yield well-calibrated models. This work provides the first theoretical proof that canonical $L_{2}$-regularized empirical risk minimization directly controls the smooth calibration error (smCE) without post-hoc correction or specialized calibration-promoting regularizer. We establish finite-sample generalization bounds for smCE based on optimization error, regularization strength, and the Rademacher complexity. We then instantiate this theory for models in reproducing kernel Hilbert spaces, deriving concrete guarantees for kernel ridge and logistic regression. Our experiments confirm these specific guarantees, demonstrating that $L_{2}$-regularized ERM can provide a well-calibrated model without boosting or post-hoc recalibration. The source code to reproduce all experiments is available at https://github.com/msfuji0211/erm_calibration.

Boosting methods often achieve excellent classification accuracy, but can experience notable performance degradation in the presence of label noise. Existing robust methods for boosting provide theoretical robustness guarantees for certain types of label noise, and can exhibit only moderate performance degradation. However, previous theoretical results do not account for realistic types of noise and finite training sizes, and existing robust methods can provide unsatisfactory accuracies, even without noise. This paper presents methods for robust minimax boosting (RMBoost) that minimize worst-case error probabilities and are robust to general types of label noise. In addition, we provide finite-sample performance guarantees for RMBoost with respect to the error obtained without noise and with respect to the best possible error (Bayes risk). The experimental results corroborate that RMBoost is not only resilient to label noise but can also provide strong classification accuracy.

We perform a non-asymptotic analysis of the contrastive divergence (CD) algorithm, a training method for unnormalized models. While prior work has established that (for exponential family distributions) the CD iterates asymptotically converge at an $O(n^{-1 / 3})$ rate to the true parameter of the data distribution, we show, under some regularity assumptions, that CD can achieve the parametric rate $O(n^{-1 / 2})$. Our analysis provides results for various data batching schemes, including the fully online and minibatch ones. We additionally show that CD can be near-optimal, in the sense that its asymptotic variance is close to the Cramér-Rao lower bound.

Dropout is common in clinical studies, with up to half of patients leaving early due to side effects or other reasons. When dropout is informative (i.e., dependent on survival time), it introduces censoring bias, because of which treatment effect estimates are also biased. In this paper, we propose an assumption-lean framework to assess the robustness of conditional average treatment effect (CATE) estimates in survival analysis when facing censoring bias. Unlike existing works that rely on strong assumptions, such as non-informative censoring, to obtain point estimation, we use partial identification to derive informative bounds on the CATE. Thereby, our framework helps to identify patient subgroups where treatment is effective despite informative censoring. We further propose a novel model-agnostic meta-learner, called SurvB-learner, to estimate the bounds that can be used in combination with arbitrary machine-learning models, and that has favorable theoretical properties such as double-robustness and quasi-oracle efficiency. We finally demonstrate the effectiveness of our meta-learner across various experiments using both simulated and real-world data.

We introduce a new analytical framework for modelling degree sequences in individual communities of real-world networks, e.g., citations to papers in different fields. Our work is inspired by a recent modification of the Price's model, which assumes that citations are gained partly accidentally, and to some extent preferentially. Our work addresses the need to represent the heterogeneity of various scientific domains, as standard homogeneous models fail to capture the distinct growth ratios and citing cultures of different fields. Extending the model to networks with a community structure allows us to devise the analytical formulae for, amongst others, citation counts in each cluster and their inequality as described by the Gini index. We also show that a citation count distribution in each community tends to a Pareto type II distribution. Thanks to the derived model parameter estimators, the new model can be fitted to real citation and similar networks.

A class of relative importance measures based on orthogonalization and reallocation, ORMs, has been found to effectively approximate the General Dominance index (GD). In particular, Johnson's Relative Weight (RW) has been deemed the most successful ORM in the literature. Nevertheless, the theoretical foundation of the ORMs remains unclear. To further understand the ORMs, we provide a generalized framework that breaks down the ORM into two functional steps: orthogonalization and reallocation. To assess the impact of each step on the performance of ORMs, we conduct extensive Monte Carlo simulations under various predictors' correlation structures and response variable distributions. Our findings reveal that Johnson's minimal transformation consistently outperforms other common orthogonalization methods. We also summarize the performance of reallocation methods under four scenarios of predictors' correlation structures in terms of the first principal component and the variance inflation factor (VIF). This analysis provides guidelines for selecting appropriate reallocation methods in different scenarios, illustrated with real-world dataset examples. Our research offers a deeper understanding of ORMs and provides valuable insights for practitioners seeking to accurately measure variable importance in various modeling contexts.

We address the problem of survival regression modelling with multivariate responses and nonlinear covariate effects. Our model extends the proportional hazards model by introducing several weakly-parametric elements: the marginal baseline hazard functions are expressed as piecewise constants, association is modelled with copulas, and nonlinear covariate effects are handled by a single-index structure using a spline. The model permits a full likelihood approach to inference, making it possible to obtain individual-level survival or hazard function estimates. Performance of the new model is evaluated through simulation studies and application to the Busselton health study data. The results suggest that the proposed method can capture nonlinear covariate effects well, and that there is benefit to modeling the association between the correlated responses.

Covariate adjustment is a widely used technique in randomized clinical trials (RCTs) for improving the efficiency of treatment effect estimators. By adjusting for predictive baseline covariates, variance can be reduced, enhancing statistical precision and study power. Rosenblum and van der Laan [2010] use the framework of generalized linear models (GLMs) in a plug-in analysis to show efficiency gains using covariate adjustment for marginal effect estimation. Recently the use of prognostic scores as adjustment covariates has gained popularity. Schuler et al. [2022] introduce and validate the method for continuous endpoints using linear models. Building on this work Højbjerre-Frandsen et al. [2025] extends the method proposed by Schuler et al. [2022] to be used in combination with the GLM plug-in procedure [Rosenblum and van der Laan, 2010]. This method achieves semi-parametric efficiency under assumptions of additive treatment effects on the link scale. Additionally, Højbjerre-Frandsen et al. [2025] provide a formula for power approximation which is valid even under model misspecification, enabling realistic sample size estimation. This article introduces an R package, which implements the GLM plug-in method with or without PrOgnoSTic CovARiate aDjustment, postcard. The package has two core features: (1) estimating marginal effects and the variance hereof (with or without prognostic adjustment) and (2) approximating statistical power. Functionalities also include integration of the Discrete Super Learner for constructing prognostic scores and simulation capabilities for exploring the methods in practice. Through examples and simulations, we demonstrate postcard as a practical toolkit for statisticians.

Phylogenetic trees capture evolutionary relationships among species and reflect the forces that shaped them. While many studies rely on branch length information, the topology of phylogenetic trees (particularly their degree of imbalance) offers a robust framework for inferring evolutionary dynamics when timing data is uncertain. Classical metrics, such as the Colless and Sackin indices, quantify tree imbalance and have been extensively used to characterize phylogenies. Empirical phylogenies typically show intermediate imbalance, falling between perfectly balanced and highly skewed trees. This regime is marked by a power-law relationship between subtree sizes and their cumulative sizes, governed by a characteristic exponent. Although a recent niche-size model replicates this scaling, its mathematical origin and the exponent's value remain unclear. We present a generative model inspired by Kingman's coalescent that incorporates niche-like dynamics through preferential node coalescence. This process maps to Smoluchowski's coagulation kinetics and is described by a generalized Smoluchowski equation. Our model produces imbalanced trees with power-law exponents matching empirical and numerical observations, revealing the mathematical basis of observed scaling laws and offering new tools to interpret tree imbalance in evolutionary contexts.

Spatial generalized linear mixed-effects models are popularly used to analyze spatially indexed univariate responses. However, with modern technology, it is common to observe vector-valued mixed-type responses, e.g., a combination of binary, count, or continuous types, at each location. Methods for jointly modeling such mixed-type multivariate spatial responses are rare. Using multivariate Gaussian processes (GPs) in the latent layer, we present a class of Bayesian spatial methods applicable to any combination of exponential family responses. Since multivariate GP-based methods can suffer from computational bottlenecks when the number of spatial locations is high, we further employ a computationally efficient Vecchia approximation for fast posterior inference and prediction. Key theoretical properties of the proposed model, such as identifiability and the structure of the induced covariance, are established. Our approach employs a Markov chain Monte Carlo-based inference method that uses elliptical slice sampling within a blocked Metropolis-within-Gibbs sampling framework. We illustrate the efficacy of the proposed method through simulation studies and a real-data application on joint modeling of wildfire counts and burnt areas across the United States.

Statistical inference about the average effect in random-effects meta-analysis has been considered insufficient in the presence of substantial between-study heterogeneity. Predictive distributions are well-suited for quantifying heterogeneity since they are interpretable on the effect scale and provide clinically relevant information about future events. We construct predictive distributions accounting for uncertainty through confidence distributions from Edgington's $p$-value combination method and the generalized heterogeneity statistic. Simulation results suggest that 95% prediction intervals typically achieve nominal coverage when more than three studies are available and effectively reflect skewness of effect estimates in scenarios with 20 or less studies. Formulations that ignore uncertainty in heterogeneity estimation typically fail to achieve correct coverage, underscoring the need for this adjustment in random-effects meta-analysis.

Traditional likelihood based methods for parameter estimation get highly affected when the given data is contaminated by outliers even in a small proportion. In this paper, we consider a robust parameter estimation method, namely the minimum logarithmic norm relative entropy (LNRE) estimation procedure, and study different (generalized) sufficiency principles associated with it. We introduce a new two-parameter power-law family of distributions (namely, $\mathcal{M}^{(\alpha,\beta)}$-family), which is shown to have a fixed number of sufficient statistics, independent of the sample size, with respect to the generalized likelihood function associated with the LNRE. Then, we obtain the generalized minimal sufficient statistic for this family and derive the generalized Rao-Blackwell theorem and the generalized Cramér-Rao lower bound for the minimum LNRE estimation. We also study the minimum LNRE estimators (MLNREEs) for the family of Student's distributions particularly in detail. Our general results reduces to the classical likelihood based results under the exponential family of distributions at specific choices of the tuning parameter $\alpha$ and $\beta$. Finally, we present simulation studies followed by a real data analysis, which highlight the practical utility of the MLNREEs for data contaminated by possible outliers. Along the way we also correct a mistake found in a recent paper on related theory of generalized likelihoods.

From the perspective of data reduction, the notions of minimal sufficient and complete statistics together play an important role in determining optimal statistics (estimators). The classical notion of sufficiency and completeness are not adequate in many robust estimations that are based on different divergences. Recently, the notion of generalized sufficiency based on a generalized likelihood function was introduced in the literature. It is important to note that the concept of sufficiency alone does not necessarily produce optimal statistics (estimators). Thus, in line with the generalized sufficiency, we introduce a generalized notion of completeness with respect to a generalized likelihood function. We then characterize the family of probability distributions that possesses completeness with respect to the generalized likelihood function associated with the density power divergence (DPD). Moreover, we show that the family of distributions associated with the logarithmic density power divergence (LDPD) is not complete. Further, we extend the Lehmann-Scheffé theorem and the Basu's theorem for the generalized likelihood estimation. Subsequently, we obtain the generalized uniformly minimum variance unbiased estimator (UMVUE) for the $\mathcal{B^{(\alpha)}}$-family. Further, we derive an formula of the asymptotic expected deficiency (AED) that is used to compare the performance between the minimum density power divergence estimator (MDPDE) and the generalized UMVUE for $\mathcal{B^{(\alpha)}}$-family. Finally, we provide an application of the developed results in stress-strength reliability model.

Principal component analysis (PCA) is a fundamental tool in multivariate statistics, yet its sensitivity to outliers and limitations in distributed environments restrict its effectiveness in modern large-scale applications. To address these challenges, we introduce the $\phi$-PCA framework which provides a unified formulation of robust and distributed PCA. The class of $\phi$-PCA methods retains the asymptotic efficiency of standard PCA, while aggregating multiple local estimates using a proper $\phi$ function enhances ordering-robustness, leading to more accurate eigensubspace estimation under contamination. Notably, the harmonic mean PCA (HM-PCA), corresponding to the choice $\phi(u)=u^{-1}$, achieves optimal ordering-robustness and is recommended for practical use. Theoretical results further show that robustness increases with the number of partitions, a phenomenon seldom explored in the literature on robust or distributed PCA. Altogether, the partition-aggregation principle underlying $\phi$-PCA offers a general strategy for developing robust and efficiency-preserving methodologies applicable to both robust and distributed data analysis.

I develop a nonparametric framework for identifying spatial boundaries of treatment effects without imposing parametric functional form restrictions. The method employs local linear regression with data-driven bandwidth selection to flexibly estimate spatial decay patterns and detect treatment effect boundaries. Monte Carlo simulations demonstrate that the nonparametric approach exhibits lower bias and correctly identifies the absence of boundaries when none exist, unlike parametric methods that may impose spurious spatial patterns. I apply this framework to bank branch openings during 2015–2020, matching 5,743 new branches to 5.9 million mortgage applications across 14,209 census tracts. The analysis reveals that branch proximity significantly affects loan application volume (8.5% decline per 10 miles) but not approval rates, consistent with branches stimulating demand through local presence while credit decisions remain centralized. Examining branch survival during the digital transformation era (2010–2023), I find a non-monotonic relationship with area income: high-income areas experience more closures despite conventional wisdom. This counterintuitive pattern reflects strategic consolidation of redundant branches in over-banked wealthy urban areas rather than discrimination against poor neighborhoods. Controlling for branch density, urbanization, and competition, the direct income effect diminishes substantially, with branch density emerging as the primary determinant of survival. These findings demonstrate the necessity of flexible nonparametric methods for detecting complex spatial patterns that parametric models would miss, and challenge simplistic narratives about banking deserts by revealing the organizational complexity underlying spatial consolidation decisions.

Lattice field theories are fundamental testbeds for computational physics; yet, sampling their Boltzmann distributions remains challenging due to multimodality and long-range correlations. While normalizing flows offer a promising alternative, their application to large lattices is often constrained by prohibitive memory requirements and the challenge of maintaining sufficient model expressivity. We propose sparse triangular transport maps that explicitly exploit the conditional independence structure of the lattice graph under periodic boundary conditions using monotone rectified neural networks (MRNN). We introduce a comprehensive framework for triangular transport maps that navigates the fundamental trade-off between exact sparsity (respecting marginal conditional independence in the target distribution) and approximate sparsity (computational tractability without fill-ins). Restricting each triangular map component to a local past enables site-wise parallel evaluation and linear time complexity in lattice size $N$, while preserving the expressive, invertible structure. Using $\phi^4$ in two dimensions as a controlled setting, we analyze how node labelings (orderings) affect the sparsity and performance of triangular maps. We compare against Hybrid Monte Carlo (HMC) and established flow approaches (RealNVP).

Machine unlearning seeks to efficiently remove the influence of selected data while preserving generalization. Significant progress has been made in low dimensions $(p \ll n)$, but high dimensions pose serious theoretical challenges as standard optimization assumptions of $\Omega(1)$ strong convexity and $O(1)$ smoothness of the per-example loss $f$ rarely hold simultaneously in proportional regimes $(p\sim n)$. In this work, we introduce $\varepsilon$-Gaussian certifiability, a canonical and robust notion well-suited to high-dimensional regimes, that optimally captures a broad class of noise adding mechanisms. Then we theoretically analyze the performance of a widely used unlearning algorithm based on one step of the Newton method in the high-dimensional setting described above. Our analysis shows that a single Newton step, followed by a well-calibrated Gaussian noise, is sufficient to achieve both privacy and accuracy in this setting. This result stands in sharp contrast to the only prior work that analyzes machine unlearning in high dimensions \citet{zou2025certified}, which relaxes some of the standard optimization assumptions for high-dimensional applicability, but operates under the notion of $\varepsilon$-certifiability. That work concludes %that a single Newton step is insufficient even for removing a single data point, and that at least two steps are required to ensure both privacy and accuracy. Our result leads us to conclude that the discrepancy in the number of steps arises because of the sub optimality of the notion of $\varepsilon$-certifiability and its incompatibility with noise adding mechanisms, which $\varepsilon$-Gaussian certifiability is able to overcome optimally.

Out-of-Distribution (OOD) detection is a cornerstone for the safe deployment of AI systems in the open world. However, existing methods treat OOD detection as a binary classification problem, a cognitive flattening that fails to distinguish between semantically close (Near-OOD) and distant (Far-OOD) unknown risks. This limitation poses a significant safety bottleneck in applications requiring fine-grained risk stratification. To address this, we propose a paradigm shift from a conventional probabilistic view to a principled information-theoretic framework. We formalize the core task as quantifying the Semantic Surprise of a new sample and introduce a novel ternary classification challenge: In-Distribution (ID) vs. Near-OOD vs. Far-OOD. The theoretical foundation of our work is the concept of Low-Entropy Semantic Manifolds, which are explicitly structured to reflect the data's intrinsic semantic hierarchy. To construct these manifolds, we design a Hierarchical Prototypical Network. We then introduce the Semantic Surprise Vector (SSV), a universal probe that decomposes a sample's total surprise into three complementary and interpretable dimensions: conformity, novelty, and ambiguity. To evaluate performance on this new task, we propose the Normalized Semantic Risk (nSR), a cost-sensitive metric. Experiments demonstrate that our framework not only establishes a new state-of-the-art (sota) on the challenging ternary task, but its robust representations also achieve top results on conventional binary benchmarks, reducing the False Positive Rate by over 60% on datasets like LSUN.

Marketing Mix Modeling (MMM) estimates the impact of marketing activities on business outcomes such as sales or revenue. Traditional MMM approaches rely on linear regression or Bayesian hierarchical models that assume channel independence and struggle to capture temporal dynamics and non-linear saturation. DeepCausalMMM addresses these limitations by combining deep learning, causal inference, and marketing science. It uses Gated Recurrent Units (GRUs) to learn temporal patterns (adstock, lag) while learning statistical dependencies between channels through Directed Acyclic Graph (DAG) structure with upper triangular constraints. It implements Hill equation saturation curves for diminishing returns and budget optimization. Key features: (1) data-driven hyperparameters learned from data with defaults, (2) linear mean scaling of the dependent variable, (3) configurable attribution priors with dynamic loss scaling, (4) multi-region modeling with shared and region-specific parameters, (5) robust methods including Huber loss, (6) response curve analysis.

Finding "true" clusters in a data set is a challenging problem. Clustering solutions obtained using different models and algorithms do not necessarily provide compact and well-separated clusters or the optimal number of clusters. Cluster validity indices are commonly applied to identify such clusters. Nevertheless, these indices are typically relative, and they are used to compare clustering algorithms or choose the parameters of a clustering algorithm. Moreover, the success of these indices depends on the underlying data structure. This paper introduces novel absolute cluster indices to determine both the compactness and separability of clusters. We define a compactness function for each cluster and a set of neighboring points for cluster pairs. This function is utilized to determine the compactness of each cluster and the whole cluster distribution. The set of neighboring points is used to define the margin between clusters and the overall distribution margin. The proposed compactness and separability indices are applied to identify the true number of clusters. Using a number of synthetic and real-world data sets, we demonstrate the performance of these new indices and compare them with other widely-used cluster validity indices.

Reverse Kullback-Leibler (KL) divergence-based regularization with respect to a fixed reference policy is widely used in modern reinforcement learning to preserve the desired traits of the reference policy and sometimes to promote exploration (using uniform reference policy, known as entropy regularization). Beyond serving as a mere anchor, the reference policy can also be interpreted as encoding prior knowledge about good actions in the environment. In the context of alignment, recent game-theoretic approaches have leveraged KL regularization with pretrained language models as reference policies, achieving notable empirical success in self-play methods. Despite these advances, the theoretical benefits of KL regularization in game-theoretic settings remain poorly understood. In this work, we develop and analyze algorithms that provably achieve improved sample efficiency under KL regularization. We study both two-player zero-sum matrix games and Markov games: for matrix games, we propose OMG, an algorithm based on best response sampling with optimistic bonuses, and extend this idea to Markov games through the algorithm SOMG, which also uses best response sampling and a novel concept of superoptimistic bonuses. Both algorithms achieve a logarithmic regret in $T$ that scales inversely with the KL regularization strength $\beta$ in addition to the traditional $\widetilde{\mathcal{O}}(\sqrt{T})$ regret without the $\beta^{-1}$ dependence.

Time integration of stiff systems is a primary source of computational cost in combustion, hypersonics, and other reactive transport systems. This stiffness can introduce time scales significantly smaller than those associated with other physical processes, requiring extremely small time steps in explicit schemes or computationally intensive implicit methods. Consequently, strategies to alleviate challenges posed by stiffness are important. While neural operators (DeepONets) can act as surrogates for stiff kinetics, a reliable operator learning strategy is required to appropriately account for differences in error between output variables and samples. Here, we develop AMORE, Adaptive Multi-Output Operator Network, a framework comprising an operator capable of predicting multiple outputs and adaptive loss functions ensuring reliable operator learning. The operator predicts all thermochemical states from given initial conditions. We propose two adaptive loss functions within the framework, considering each state variable's and sample's error to penalize the loss function. We designed the trunk to automatically satisfy Partition of Unity. To enforce unity mass-fraction constraint exactly, we propose an invertible analytical map that transforms the $n$-dimensional species mass-fraction vector into an ($n-1$)-dimensional space. We extend the proposed adaptive loss functions to trunk and branch training in two-step training of DeepONet with multiple outputs. We implemented another unity mass fraction constraint exactly using a softmax function on the predicted mass fraction. We demonstrate efficacy and applicability of our models through two examples: syngas (12 states), GRI-Mech 3.0 (24 active states out of 54). The proposed DeepONet will be a backbone for future CFD studies to accelerate turbulent combustion simulations. AMORE is a general framework, and here, we also demonstrate it for FNO.

Large language models (LLMs) are highly sensitive to prompts, but most automatic prompt optimization (APO) methods assume access to ground-truth references (e.g., labeled validation data) that are costly to obtain. We propose the Prompt Duel Optimizer (PDO), a sample-efficient framework for label-free prompt optimization based on pairwise preference feedback from an LLM judge. PDO casts prompt selection as a dueling-bandit problem and combines (i) Double Thompson Sampling to prioritize informative comparisons under a fixed judge budget, with (ii) top-performer guided mutation to expand the candidate pool while pruning weak prompts. Experiments on BIG-bench Hard (BBH) and MS MARCO show that PDO consistently identifies stronger prompts than label-free baselines, while offering favorable quality–cost trade-offs under constrained comparison budgets.

Incomplete multi-view data, where certain views are entirely missing for some samples, poses significant challenges for traditional multi-view clustering methods. Existing deep incomplete multi-view clustering approaches often rely on static fusion strategies or two-stage pipelines, leading to suboptimal fusion results and error propagation issues. To address these limitations, this paper proposes a novel incomplete multi-view clustering framework based on Hierarchical Semantic Alignment and Cooperative Completion (HSACC). HSACC achieves robust cross-view fusion through a dual-level semantic space design. In the low-level semantic space, consistency alignment is ensured by maximizing mutual information across views. In the high-level semantic space, adaptive view weights are dynamically assigned based on the distributional affinity between individual views and an initial fused representation, followed by weighted fusion to generate a unified global representation. Additionally, HSACC implicitly recovers missing views by projecting aligned latent representations into high-dimensional semantic spaces and jointly optimizes reconstruction and clustering objectives, enabling cooperative learning of completion and clustering. Experimental results demonstrate that HSACC significantly outperforms state-of-the-art methods on five benchmark datasets. Ablation studies validate the effectiveness of the hierarchical alignment and dynamic weighting mechanisms, while parameter analysis confirms the model's robustness to hyperparameter variations. The code is available at https://github.com/XiaojianDing/2025-NeurIPS-HSACC.

This paper presents a conformal prediction method for classification in highly imbalanced and open-set settings, where there are many possible classes and not all may be represented in the data. Existing approaches require a finite, known label space and typically involve random sample splitting, which works well when there is a sufficient number of observations from each class. Consequently, they have two limitations: (i) they fail to provide adequate coverage when encountering new labels at test time, and (ii) they may become overly conservative when predicting previously seen labels. To obtain valid prediction sets in the presence of unseen labels, we compute and integrate into our predictions a new family of conformal p-values that can test whether a new data point belongs to a previously unseen class. We study these p-values theoretically, establishing their optimality, and uncover an intriguing connection with the classical Good–Turing estimator for the probability of observing a new species. To make more efficient use of imbalanced data, we also develop a selective sample splitting algorithm that partitions training and calibration data based on label frequency, leading to more informative predictions. Despite breaking exchangeability, this allows maintaining finite-sample guarantees through suitable re-weighting. With both simulated and real data, we demonstrate our method leads to prediction sets with valid coverage even in challenging open-set scenarios with infinite numbers of possible labels, and produces more informative predictions under extreme class imbalance.

In the era of big data, integrating multi-source functional data to extract a subspace that captures the shared subspace across sources has attracted considerable attention. In practice, data collection procedures often follow source-specific protocols. Directly averaging sample covariance operators across sources implicitly assumes homogeneity, which may bias the recovery of both shared and source-specific variation patterns. To address this issue, we propose a projection-based data integration method that explicitly separates the shared and source-specific subspaces. The method first estimates source-specific projection operators via smoothing to accommodate the nonparametric nature of functional data. The shared subspace is then isolated by examining the eigenvalues of the averaged projection operator across all sources. If a source-specific subspace is of interest, we re-project the associated source-specific covariance estimator onto the subspace orthogonal to the estimated shared subspace, and estimate the source-specific subspace from the resulting projection. We further establish the asymptotic properties of both the shared and source-specific subspace estimators. Extensive simulation studies demonstrate the effectiveness of the proposed method across a wide range of settings. Finally, we illustrate its practical utility with an example of air pollutant data.