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stat.ML: explore 71 source-linked works published from 2023 to 2026, with original documents and citations.

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Includes records with this source-supplied label or an explicit phrase match in their metadata. Matches indicate a mention, not proof that a paper uses a method or tests a material. Source versions are consolidated by DOI.

Sources: arxiv. Collection updated 2026-09-14. Counts describe this index, not the complete source archives.

arXiv2026

Model Selection and Parameter Estimation of One-Dimensional Gaussian Mixture Models

In this paper, we study the problem of learning one-dimensional Gaussian mixture models (GMMs) with a specific focus on estimating both the model order and the mixing distribution from independent and identically distributed (i.i.d.) samples. This paper establishes the optimal sampling complexity for model order estimation in one-dimensional Gaussian mixture models. We prove a fundamental lower bound on the number of samples required to correctly identify the number of components with high probability, showing that this limit depends critically on the separation between component means and the total number of components. We then propose a Fourier-based approach to estimate both the model order and the mixing distribution. Our algorithm utilizes Fourier measurements constructed from the samples, and our analysis demonstrates that its sample complexity matches the established lower bound, thereby confirming its optimality. Numerical experiments further show that our method outperforms conventional techniques in terms of efficiency and accuracy.

stat.ML↗
arXiv2026

Stein's method for marginals on large graphical models

Many spatial models exhibit locality structures that effectively reduce their intrinsic dimensionality, enabling efficient approximation and sampling of high-dimensional distributions. However, existing approximation techniques primarily focus on joint distributions and do not provide precise accuracy control for low-dimensional marginals, which are of primary interest in many practical scenarios. By leveraging the locality structures, we establish a dimension independent uniform error bound for the marginals of approximate distributions. Inspired by the Stein's method, we introduce a novel $δ$-locality condition that quantifies the locality in distributions, and link it to the structural assumptions such as the sparse graphical models. The theoretical guarantee motivates the localization of existing sampling methods, as we illustrate through the localized likelihood-informed subspace method and localized score matching. We show that by leveraging the locality structure, these methods greatly reduce the sample complexity and computational cost via localized and parallel implementations.

stat.ML↗
arXiv2026

Latency-Response Theory Model: Evaluating Large Language Models via Response Accuracy and Chain-of-Thought Length

The proliferation of Large Language Models (LLMs) necessitates valid evaluation methods to provide guidance for both downstream applications and actionable future improvements. The Item Response Theory (IRT) model with Computerized Adaptive Testing has recently emerged as a promising framework for evaluating LLMs via their response accuracy. Beyond simple response accuracy, LLMs' chain of thought (CoT) lengths serve as a vital indicator of their reasoning ability. To leverage the CoT length information to assist LLM evaluation, we propose the \textbf{La}tency-\textbf{R}esponse \textbf{T}heory (LaRT) model, which jointly models both the response accuracy and CoT length by introducing a key correlation parameter between the latent ability and the latent speed. We derive an efficient stochastic approximation Expectation-Maximization algorithm for parameter estimation. We establish rigorous identifiability results for the latent ability and latent speed parameters to ensure the statistical validity of their estimation. Through both theoretical asymptotic analyses and simulation studies, we demonstrate LaRT's advantages over IRT in terms of superior estimation accuracy and shorter confidence intervals for latent trait estimation. To evaluate LaRT in real data, we collect responses from diverse LLMs on popular benchmark datasets. We find that LaRT yields different LLM rankings than IRT and outperforms IRT across multiple key evaluation metrics including predictive power, item efficiency, ranking validity, and LLM evaluation efficiency. Code and data are available at https://github.com/Toby-X/Latency-Response-Theory-Model

stat.ME↗
arXiv2026

Diffusion Models in Simulation-Based Inference: A Tutorial Review

Diffusion models have recently emerged as powerful learners for simulation-based inference (SBI), enabling fast and accurate estimation of latent parameters from simulated and real data. Their score-based formulation offers a flexible way to learn conditional or joint distributions over parameters and observations, thereby providing a versatile solution to various modeling problems. In this tutorial review, we synthesize recent developments on diffusion models for SBI, covering design choices for training, inference, and evaluation. We highlight opportunities created by various concepts such as guidance, score composition, flow matching, consistency models, and joint modeling. Furthermore, we discuss how efficiency and statistical accuracy are affected by noise schedules, parameterizations, and samplers. Finally, we illustrate these concepts with case studies across parameter dimensionalities, simulation budgets, and model types, and outline open questions for future research.

stat.ML↗
arXiv2026

Model Selection and Parameter Estimation for Multidimensional Gaussian Mixture Models with a Common Covariance Matrix

We study model-order selection and component-mean estimation for multidimensional Gaussian mixture models with a known common covariance matrix. Using empirical characteristic-function measurements, we construct Fourier covariance matrices whose population counterparts have rank equal to the number of mixture components. We establish a minimax lower bound showing that distinguishing a separated $k$-component mixture from the class of $(k-1)$-component mixtures requires $Ω(Δ^{-(4k-4)})$ samples. We then develop an oracle spectral-thresholding estimator with a sufficient sample size of order $Δ^{-(8k-8)}$ for fixed $k$, together with a practical singular-value-ratio estimator. Given the model order, we estimate the component means by score-initialized gradient descent on a MUSIC-type projection objective. Under an explicit sample-size condition, a qualifying sample initialization lies in a certified attraction region with high probability, after which the iterates converge linearly. For fixed positive component separation, the resulting mean estimates achieve the parametric rate $\mathcal{O}_p(n^{-1/2})$. Numerical experiments demonstrate competitive accuracy and lower computational cost than expectation-maximization across a range of multidimensional settings.

stat.ML↗
arXiv2026

Mamba-Assisted Non-Markovian Closure for Reduced-Order Modeling

Reduced-order modeling of high-dimensional dynamical systems is often hindered by closure effects arising from unresolved variables, which can introduce non-Markovian dependence into the resolved dynamics. Motivated by the history-dependent memory term arising in the Mori--Zwanzig formalism, we recast non-Markovian closure modeling as a sequence modeling problem and propose the Mamba-Assisted Closure (MAC) framework. MAC employs a Mamba-based sequence model to predict the closure from the resolved trajectory and couples the learned closure with the reduced-order governing equations through a numerical integrator to advance the resolved variables in time. During training, the selective scan mechanism in Mamba enables efficient parallel sequence processing with linear scaling in sequence length, while autoregressive inference proceeds through recurrent state updates at essentially constant per-step cost. We evaluate MAC on four benchmark systems with complementary characteristics: the viscous Burgers' equation, the chaotic two-scale Lorenz '96 system, the 3-bus DeMarco--Zheng power-grid system, and the dispersive Korteweg--de Vries equation. Across these benchmarks, MAC consistently improves predictive accuracy and long-time rollout stability relative to the comparison models, demonstrating an effective and computationally scalable approach to non-Markovian closure modeling.

cs.LG↗
arXiv2026

Seq2Synth: Benchmarking Temporal Fidelity in Synthetic Sequential Tabular Data

Synthetic sequential tabular data are increasingly used for privacy-preserving data sharing and research, yet conventional tabular metrics often overlook temporal structure. Existing single-table and relational evaluation protocols largely collapse records into static distributions, leaving key temporal properties insufficiently evaluated. We introduce Seq2Synth, a unified benchmark for assessing these properties. Its taxonomy characterizes temporal and schema properties to determine applicable evaluations, covering timestamp, cross-sectional, longitudinal, and structural fidelity, alongside trajectory-aware utility and privacy. Across seven core datasets from a 13-dataset benchmark and eight generators, models with near-perfect static fidelity still violate basic temporal constraints, producing duplicate timestamps, irregular intervals, and incomplete observation grids. Moreover, static and temporal-aware rankings diverge substantially, showing that temporal fidelity must be evaluated directly rather than inferred from static or relational scores. Project page and online appendices are available at: https://seq2synth.github.io/.

cs.LG↗
arXiv2026

Fairness in multi-class multi-group classification problems via contextial coherent risk measures

We propose a new design of fair classifiers for multi-class classification problems in the presence of vector-valued sensitive attributes. In that scenario each sensitive attribute has multiple values and forms several groups relevant to the fairness consideration. Naturally those groups are overlapping and one should also analyze the interaction of factors. Additionally, the decision makers aided by the classification should not violate individual rights at the expense of satisfying fairness metrics at the group level. We propose an approach using the theory and methods of coherent measures of risk aiming at resolving the fairness challenges. Further, we propose a specialized numerical method for solving the resulting optimization problem. The method scales well with the increase of the number of observations. Additionally, we note that the obtained classifier is robust with respect to corrupted data or to situation when data is scarce. We demonstrate the advantages of the proposed framework in comparison to the support-vector machine framework and other methods handling fairness.

stat.ML↗
arXiv2026

Estimating Population-Risk Curves Along Nonconvex Gradient Flows from the Training Sample

We estimate the conditional population-risk curve of a realized smooth nonconvex gradient flow from the training sample. Flow approximate leave-one-out (Flow-ALO) propagates a deletion response and evaluates omitted observations at approximate deleted paths. The risk-curve error decomposes into response approximation, exact-LOO fluctuation, and deletion-to-full risk transfer. On each fixed finite horizon, bounded centered training-loss gradients, a one-sided Hessian lower bound, locally Lipschitz Hessians, and a strict tube-closure condition yield an explicit $(n-1)^{-2}$ bound for the deletion-response error. Bounded evaluation-loss gradients transfer the deletion-response bound to the score without requiring the Hessian to be invertible. Direct first-order jackknife cancellation and exact-LOO concentration control deletion-to-full risk transfer and fluctuation, respectively, completing recovery of the conditional population-risk curve. For bounded smooth two-layer mean-field networks training both layers, the score-error bound is uniform in width.

stat.ML↗
arXiv2026

Learning PDE Time-Stepping with Neural Cellular Automata

Classical numerical solvers for partial differential equations (PDEs) are computationally expensive to solve repeatedly across varying initial conditions, motivating the need for learned surrogates. In this paper, we propose a trainable Neural Cellular Automata (NCA) based surrogate model for learning long time PDE dynamics. Rather than mapping an entire initial field to a full trajectory in one shot, our proposed model learns a small, local, homogeneous update rule that is applied identically and repeatedly at every grid cell, mirroring the locality of differential operators. We benchmark this framework against three baselines: PDE - Net, a modified physics-informed neural network (PINN), and a Fourier Neural Operator (FNO), on five canonical PDEs (heat, advection, Burgers, Allen - Cahn, and Fisher - KPP), evaluated at temporal domain two times beyond the training temporal domain. The proposed model achieves the lowest long-horizon relative errors on the majority of the experiments.

cs.LG↗
arXiv2026

Simulation-Based Evaluation of Energy-Constrained Quantum-Classical Competition

This paper develops a simulation-based framework for evaluating the energy implications of quantum and classical computing firms competing in a market with limited energy resources. We model providers as differentiated Cournot competitors whose feasible service capacity is induced by technology-specific energy scaling laws: polylogarithmic for quantum algorithms that achieve an equivalent computational target and polynomial for classical emulation. For symmetric groups of quantum and classical firms, the equilibrium reduces to a tractable two-equation system that supports large scenario sweeps over market size, technology mix, and hardware coefficients. We characterize the capacity-constrained Nash equilibrium, prove the existence of a demand scale beyond which quantum service becomes more energy efficient, and report numerical experiments calibrated to trapped-ion and Rydberg platforms. The results identify when quantum energy advantage is only asymptotic and when it becomes operationally relevant.

quant-ph↗
arXiv2026

Optimal Estimation of Watermark Proportions in Hybrid AI-Human Texts

Text watermarks in large language models (LLMs) are an increasingly important tool for detecting synthetic text and distinguishing human-written content from LLM-generated text. While most existing studies focus on determining whether entire texts are watermarked, many real-world scenarios involve mixed-source texts, which blend human-written and watermarked content. In this paper, we address the problem of optimally estimating the watermark proportion in mixed-source texts. We cast this problem as estimating the proportion parameter in a mixture model based on \emph{pivotal statistics}. First, we show that this parameter is not even identifiable in certain watermarking schemes, let alone consistently estimable. In stark contrast, for watermarking methods that employ continuous pivotal statistics for detection, we demonstrate that the proportion parameter is identifiable under mild conditions. We propose efficient estimators for this class of methods, which include several popular unbiased watermarks as examples, and derive minimax lower bounds for any measurable estimator based on pivotal statistics, showing that our estimators achieve these lower bounds. Through evaluations on both synthetic data and mixed-source text generated by open-source models, we demonstrate that our proposed estimators consistently achieve high estimation accuracy.

stat.ML↗
arXiv2026

Fitted Q-Evaluation without Bellman Completeness via Occupancy Weighting

Fitted \(Q\)-evaluation (FQE) is a standard regression-based method for off-policy evaluation, but under distribution shift, value-function realizability alone does not ensure convergence, and existing analyses often require Bellman completeness. We trace this instability to a geometric mismatch: standard FQE projects Bellman targets in the norm induced by the offline distribution, which need not preserve Bellman contraction. We therefore study \emph{occupancy-weighted FQE}, which changes only the regression weights. Weighting by a target-policy discounted occupancy ratio aligns the projection norm with the target-policy dynamics and restores contraction of the population projected Bellman operator. We derive finite-sample guarantees with estimated occupancy ratios and function-class misspecification, separating finite-iteration, statistical, approximation, and ratio-estimation errors. Exact occupancy weighting removes the need for Bellman completeness; with estimated weights, approximate completeness and value-function realizability reduce sensitivity to ratio-estimation error, with exact realizability yielding higher-order dependence. Combining occupancy-weighted FQE with fitted occupancy-ratio evaluation gives an end-to-end guarantee governed by the complexities and direct approximation errors of the value-function and occupancy-ratio classes. Under coverage, joint realizability of these two classes suffices for consistent estimation without Bellman or critic-side completeness. Controlled experiments illustrate the projection-norm mechanism and the finite-sample tradeoff between contraction and coverage.

stat.ML↗
arXiv2026

Soft Fitted Q-Iteration without Bellman Completeness: Occupancy Reweighting and Temperature Annealing

Fitted \(Q\)-iteration (FQI) is a standard regression-based method for optimal control in offline reinforcement learning, but its stability under function approximation often relies on Bellman completeness, which requires Bellman images of the fitted class to remain in the class. We study Kullback--Leibler (KL)-regularized, or soft, FQI relative to a fixed reference policy without this assumption. Our key insight is that soft control locally inherits the contraction of policy evaluation in a discounted-occupancy norm. At the soft-optimal fixed point, the linearization of the soft Bellman operator is exactly the Bellman operator for the soft-optimal policy, which contracts in its discounted-occupancy norm; projection in the same norm preserves this contraction. Standard soft FQI instead projects under the offline state-action distribution and need not preserve this property. Motivated by this observation, we propose \emph{occupancy-reweighted soft FQI}, which retains standard Bellman targets and least-squares updates while reweighting regressions by discounted-occupancy ratios induced by the current soft policy. Under \(Q\)-function realizability and local regularity, we establish local contraction and finite-sample convergence with estimated ratios, without Bellman completeness. We then use temperature annealing to convert the local result into global convergence from arbitrary initialization: sufficiently high temperature provides a globally contractive starting regime, while gradual cooling connects successive local contraction regions to any prescribed positive target temperature. Under an action-gap margin condition, switching at a fixed positive temperature to hard FQI with refreshed occupancy weights also yields population and finite-sample convergence to the unregularized optimum.

stat.ML↗
arXiv2026

The Geometric Mechanics of Contrastive Representation Learning: Alignment Potentials, Entropic Dispersion, and Cross-modal Divergence

While InfoNCE underlies modern contrastive learning, its geometric mechanisms remain under-characterized beyond the canonical alignment--uniformity decomposition. We develop a measure-theoretic framework in which representation measures evolve on a fixed embedding manifold. In the large-batch limit, we prove value and gradient consistency, linking the stochastic objective to explicit deterministic energy landscapes and revealing a geometric bifurcation between unimodal and symmetric multimodal regimes. In the unimodal case, the intrinsic energy is strictly convex and admits a unique Gibbs equilibrium, showing that entropy acts as a tie-breaker within the aligned basin. In the multimodal case, the intrinsic geometry becomes cross-coupled and contains a persistent negative symmetric divergence term: each modality's marginal reshapes the effective landscape of the other, allowing strong pairwise alignment to coexist with a persistent modality gap. Controlled synthetic experiments and analyses of pretrained CLIP representations support these predictions. Overall, our results shift the analytical lens from pointwise discrimination to population geometry, showing that pairwise alignment alone is insufficient to control cross-modal marginal structure.

cs.LG↗
arXiv2026

Universal Redundancies in Time Series Foundation Models

Time Series Foundation Models (TSFMs) leverage extensive pretraining to accurately predict unseen time series during inference, without the need for task-specific fine-tuning. Through large-scale evaluations on standard benchmarks, we find that leading transformer-based TSFMs exhibit redundant components in their intermediate layers. We introduce a set of tools for mechanistic interpretability of TSFMs, including ablations of specific components and direct logit attribution on the residual stream. Our findings are consistent across several leading TSFMs with diverse architectures, and across a diverse set of real-world and synthetic time-series datasets. We discover that all models in our study are robust to ablations of entire layers. Furthermore, we develop a theoretical framework framing transformers as kernel regressors, motivating a purely intrinsic strategy for ablating heads based on the stable rank of the per-head projection matrices. Using this approach, we uncover the specific heads responsible for degenerate phenomena widely observed in TSFMs, such as parroting of motifs from the context and seasonality bias. Our study sheds light on the universal properties of this emerging class of architectures for continuous-time sequence modeling.

cs.LG↗
arXiv2026

Accelerate Vector Diffusion Maps by Landmarks

We propose a landmark-constrained algorithm, LA-VDM (Landmark Accelerated Vector Diffusion Maps), to accelerate the Vector Diffusion Maps (VDM) framework built upon the Graph Connection Laplacian (GCL), which captures pairwise connection relationships within complex datasets. LA-VDM introduces a novel two-stage normalization that effectively address nonuniform sampling densities in both the data and the landmark sets. Under a manifold model with the frame bundle structure, we show that we can accurately recover the parallel transport with landmark-constrained diffusion from a point cloud, and hence asymptotically LA-VDM converges to the connection Laplacian. The performance and accuracy of LA-VDM are demonstrated through experiments on simulated datasets and an application to nonlocal image denoising.

stat.ML↗
arXiv2026

Sub-Gaussian Concentration and Entropic Normality of the Maximum Likelihood Estimator

It is well known that, under standard regularity conditions, the maximum likelihood estimator (MLE) satisfies a central limit theorem and converges in distribution to a Gaussian random variable as the sample size grows. This paper strengthens this classical result by developing several stronger forms of asymptotic normality for the normalized MLE. With additional assumptions on the score, we first establish sub-Gaussian tail bounds and convergence of all moments for the normalized estimation error. We then prove an entropic central limit theorem for a smoothed version of the estimator, showing convergence in relative entropy to the limiting Gaussian law. When the Fisher information of the normalized estimate is bounded, or its density has bounded first derivative, we further show that the smoothing can be removed, yielding entropic normality of the MLE itself. The proofs develop auxiliary tools that may be of independent interest, including exponential consistency bounds, high-moment estimates, and entropy-control arguments for the estimator.

cs.IT↗
Compare source metadata on this page
WorkPublishedSource identifierSource
Model Selection and Parameter Estimation of One-Dimensional Gaussian Mixture Models2026-08-312404.12613arxiv
Stein's method for marginals on large graphical models2026-08-312410.11771arxiv
Latency-Response Theory Model: Evaluating Large Language Models via Response Accuracy and Chain-of-Thought Length2026-08-312512.07019arxiv
Diffusion Models in Simulation-Based Inference: A Tutorial Review2026-08-312512.20685arxiv
Model Selection and Parameter Estimation for Multidimensional Gaussian Mixture Models with a Common Covariance Matrix2026-08-312603.19657arxiv
Mamba-Assisted Non-Markovian Closure for Reduced-Order Modeling2026-08-312606.05371arxiv
Seq2Synth: Benchmarking Temporal Fidelity in Synthetic Sequential Tabular Data2026-08-312607.15606arxiv
Fairness in multi-class multi-group classification problems via contextial coherent risk measures2026-08-312608.30223arxiv
Estimating Population-Risk Curves Along Nonconvex Gradient Flows from the Training Sample2026-08-312608.30261arxiv
Learning PDE Time-Stepping with Neural Cellular Automata2026-08-312608.30328arxiv
Simulation-Based Evaluation of Energy-Constrained Quantum-Classical Competition2026-08-302308.08025arxiv
Optimal Estimation of Watermark Proportions in Hybrid AI-Human Texts2026-08-302506.22343arxiv
Fitted Q-Evaluation without Bellman Completeness via Occupancy Weighting2026-08-302512.23805arxiv
Soft Fitted Q-Iteration without Bellman Completeness: Occupancy Reweighting and Temperature Annealing2026-08-302512.23927arxiv
The Geometric Mechanics of Contrastive Representation Learning: Alignment Potentials, Entropic Dispersion, and Cross-modal Divergence2026-08-302601.19597arxiv
Universal Redundancies in Time Series Foundation Models2026-08-302602.01605arxiv
Accelerate Vector Diffusion Maps by Landmarks2026-08-302603.21247arxiv
Sub-Gaussian Concentration and Entropic Normality of the Maximum Likelihood Estimator2026-08-302605.07107arxiv

These are bibliographic comparisons, not experimental rankings. Follow the original document for methods and conditions.