Papers

Functional brain networks exhibit topological structures that reflect neural organization; however, statistical comparison of these networks is challenging for several reasons. This paper introduces a topologically invariant permutation test for detecting topological inequivalence. Under topological equivalence, topological features can be permuted separately between groups without distorting individual network structures. The test statistic uses $2$-Wasserstein distances on persistent diagrams, computed in closed form. To reduce variability in brain connectivities while preserving topology, heat kernel expansion on the Hodge Laplacian is applied with bandwidth $t$ controlling diffusion intensity. Theoretical results guarantee variance reduction through optimal Hilbert space projection. Simulations across diverse network topologies show superior performance compared to conventional two-sample tests and alternative metrics. Applied to resting-state fMRI data from the Multimodal Treatment of ADHD study, the method detects significant topological differences between cannabis users and non-users.

As of this writing, there are five years remaining for countries to reach their Sustainable Development Goals deadline of 2030 as agreed to by the member countries of the United Nations. Countries are, therefore, naturally interested in projections of progress toward these goals. A variety of statistical measures have been used to report on country-level progress toward the goals, but they have not utilized methodologies explicitly designed to obtain optimally predictive measures of rate of progress as the foundation for projecting trends. The focus of this paper is to provide Bayesian probabilistic projections of progress to SDG indicator 4.1.1, attaining minimum proficiency in reading and mathematics, with particular emphasis on competencies among lower secondary school children. Using data from the OECD PISA, as well as indicators drawn from the World Bank, the OECD, UNDP, and UNESCO, we employ a novel combination of Bayesian latent growth curve modeling Bayesian model averaging to obtain optimal estimates of the rate of progress in minimum proficiency percentages and then use those estimate to develop probabilistic projections into the future overall for all countries in the analysis. Four case study countries are also presented to show how the methods can be used for individual country projections.

The scalability of Generalized Linear Models (GLMs) for large-scale, high-dimensional data often forces a trade-off between computational feasibility and statistical accuracy, particularly for inference on pre-specified parameters. While subsampling methods mitigate computational costs, existing estimators are typically constrained by a suboptimal $r^{-1/2}$ convergence rate, where $r$ is the subsample size. This paper introduces a unified framework that systematically breaks this barrier, enabling efficient and precise inference regardless of the dimension of the target parameters. To overcome the accuracy loss and enhance computational efficiency, we propose three estimators tailored to different scenarios. For low-dimensional targets, we propose a de-variance subsampling (DVS) estimator that achieves a sharply improved convergence rate of $\max\{r^{-1}, n^{-1/2}\}$, permitting valid inference even with very small subsamples. As $r$ grows, a multi-step refinement of our estimator is proven to be asymptotically normal and semiparametric efficient when $r/\sqrt{n} \to \infty$, matching the performance of the full-sample estimator-a property confirmed by its Bahadur representation. Critically, we provide an improved principle to high-dimensional targets, developing a novel decorrelated score function that facilitates simultaneous inference for a diverging number of pre-specified parameters. Comprehensive numerical experiments demonstrate that our framework delivers a superior balance of computational efficiency and statistical accuracy across both low- and high-dimensional inferential tasks in large-scale GLM, thereby realizing the promise of unifiedly efficient inference for large-scale GLMs.

Anomaly Detection (AD) is evolving through algorithms capable of identifying outliers in complex datasets. The Isolation Forest (IF), a pivotal AD technique, exhibits adaptability limitations and biases. This paper introduces the Function-based Isolation Forest (FuBIF), a generalization of IF that enables the use of real-valued functions for dataset branching, significantly enhancing the flexibility of evaluation tree construction. Complementing this, the FuBIF Feature Importance (FuBIFFI) algorithm extends the interpretability in IF-based approaches by providing feature importance scores across possible FuBIF models. This paper details the operational framework of FuBIF, evaluates its performance against established methods, and explores its theoretical contributions. An open-source implementation is provided to encourage further research and ensure reproducibility.

Attention mechanism is a significant part of Transformer models. It helps extract features from embedded vectors by adding global information and its expressivity has been proved to be powerful. Nevertheless, the quadratic complexity restricts its practicability. Although several researches have provided attention mechanism in sparse form, they are lack of theoretical analysis about the expressivity of their mechanism while reducing complexity. In this paper, we put forward Random Batch Attention (RBA), a linear self-attention mechanism, which has theoretical support of the ability to maintain its expressivity. Random Batch Attention has several significant strengths as follows: (1) Random Batch Attention has linear time complexity. Other than this, it can be implemented in parallel on a new dimension, which contributes to much memory saving. (2) Random Batch Attention mechanism can improve most of the existing models by replacing their attention mechanisms, even many previously improved attention mechanisms. (3) Random Batch Attention mechanism has theoretical explanation in convergence, as it comes from Random Batch Methods on computation mathematics. Experiments on large graphs have proved advantages mentioned above. Also, the theoretical modeling of self-attention mechanism is a new tool for future research on attention-mechanism analysis.

We study the computational task of detecting and estimating correlated signals in a pair of spiked matrices $$ X=\tfrac{\lambda}{\sqrt{n}} xu^{\top}+W, \quad Y=\tfrac{\mu}{\sqrt{n}} yv^{\top}+Z $$ where the spikes $x,y$ have correlation $\rho$. Specifically, we consider two fundamental models: (1) Correlated spiked Wigner model with signal-to-noise ratio $\lambda,\mu$; (2) Correlated spiked $n*N$ Wishart (covariance) model with signal-to-noise ratio $\sqrt\lambda,\sqrt\mu$. We propose an efficient detection and estimation algorithm based on counting a specific family of edge-decorated cycles. The algorithm's performance is governed by the function $$ F(\lambda,\mu,\rho,\gamma)=\max\Big\{ \frac{ \lambda^2 }{ \gamma }, \frac{ \mu^2 }{ \gamma }, \frac{ \lambda^2 \rho^2 }{ \gamma-\lambda^2+\lambda^2 \rho^2 } + \frac{ \mu^2 \rho^2 }{ \gamma-\mu^2+\mu^2 \rho^2 } \Big\} \,. $$ We prove our algorithm succeeds for the correlated spiked Wigner model whenever $F(\lambda,\mu,\rho,1)>1$, and succeeds for the correlated spiked Wishart model whenever $F(\lambda,\mu,\rho,\tfrac{n}{N})>1$. Our result shows that an algorithm can leverage the correlation between the spikes to detect and estimate the signals even in regimes where efficiently recovering either $x$ from ${X}$ alone or $y$ from ${Y}$ alone is believed to be computationally infeasible. We complement our algorithmic results with evidence for a matching computational lower bound. In particular, we prove that when $F(\lambda,\mu,\rho,1)<1$ for the correlated spiked Wigner model and when $F(\lambda,\mu,\rho,\tfrac{n}{N})<1$ for the spiked Wishart model, all algorithms based on low-degree polynomials fails to distinguish $({X},{Y})$ with two independent noise matrices. This strongly suggests that $F=1$ is the precise computation threshold for our models.

We present a Riemannian framework for linear and quadratic discriminant classification on the tangent plane of the shape space of curves. The shape space is infinite dimensional and is constructed out of square root velocity functions of curves. We introduce the idea of mean and covariance of shape-valued random variables and samples from a tangent space to the pre-shape space (invariant to translation and scaling) and then extend it to the full shape space (rotational invariance). The shape observations from the population are approximated by coefficients of a Fourier basis of the tangent space. The algorithms for linear and quadratic discriminant analysis are then defined using reduced dimensional features obtained by projecting the original shape observations on to the truncated Fourier basis. We show classification results on synthetic data and shapes of cortical sulci, corpus callosum curves, as well as facial midline curve profiles from patients with fetal alcohol syndrome (FAS).

Validation plays a crucial role in the clustering process. Many different internal validity indexes exist for the purpose of determining the best clustering solution(s) from a given collection of candidates, e.g., as produced by different algorithms or different algorithm hyper-parameters. In this study, we present a comprehensive benchmark study of 26 internal validity indexes, which includes highly popular classic indexes as well as more recently developed ones. We adopted an enhanced revision of the methodology presented in Vendramin et al. (2010), developed here to address several shortcomings of this previous work. This overall new approach consists of three complementary custom-tailored evaluation sub-methodologies, each of which has been designed to assess specific aspects of an index's behaviour while preventing potential biases of the other sub-methodologies. Each sub-methodology features two complementary measures of performance, alongside mechanisms that allow for an in-depth investigation of more complex behaviours of the internal validity indexes under study. Additionally, a new collection of 16177 datasets has been produced, paired with eight widely-used clustering algorithms, for a wider applicability scope and representation of more diverse clustering scenarios.

Max-linear Bayesian networks are recursive max-linear structural equation models represented by an edge weighted directed acyclic graph (DAG). The identifiability and estimation of max-linear Bayesian networks is an intricate issue as Gissibl, Klüppelberg, and Lauritzen have shown. As such, a max-linear Bayesian network is generally unidentifiable and standard likelihood theory cannot be applied. We can associate tropical polyhedra to max-linear Bayesian networks. Using this, we investigate the minimum-ratio estimator proposed by Gissibl, Klüppelberg, and Lauritzen and give insight on the structure of minimal best-case samples for parameter recovery which we describe in terms of set covers of certain triangulations. We also combine previous work on estimating max-linear models from Tran, Buck, and Klüppelberg to apply our geometric approach to the structural inference of max-linear models. This is tested extensively on simulated data and on real world data set, the NHANES report for 2015–2016 and the upper Danube network data.

The analysis of randomized trials is often complicated by the occurrence of intercurrent events and missing values. Even though there are different strategies to address missing values it is still common to require missing values imputation. In the present article we explore the estimation of treatment effects in RCTs from a causal inference perspective under different missing data mechanisms with a particular emphasis on missings not at random (MNAR). By modelling the missingness process with directed acylcic graphs and patient-specific potential response variables, we present a new approach to obtain an unbiased estimation of treatment effects without needing to impute missing values. Additionally, we provide a formal that the average conditional log-odds ratio is a robust measure even under MNAR missing values if adjusted by sufficient confounders.

Identifying periods associated with emotional stress in older patients with mood disorders and chronic pain is important in mental health research. Existing approaches often rely on conventional change point detection methods, require explicit modeling of relationships between variables, and return discrete change point estimates. These limitations are problematic when distributional shifts are complex, dependencies are difficult to specify, or changes occur asynchronously across series. We propose a hotspot detection framework, where hotspots are temporal regions in which statistical features of passive sensing variables and stress indicators change at the same or nearby times. We extend the moving-sum scheme to detect changes within and across series, and construct hotspots using distance-based test statistics and confidence intervals. The method does not require a specific functional relationship between series and summarizes changes as intervals rather than isolated time points. Simulation studies show that the proposed Joint- and Bi-MOSUM procedures generally achieve higher power and better control of false detections when multiple types of changes coexist. The two hotspot rules also provide complementary summaries. We further illustrate the method using ALACRITY Phase I data, where the proposed approach identifies complex distributional changes in stress levels that occur in temporal proximity to changes in passive sensing measures.

Synthesizing information from multiple data sources is crucial for constructing accurate individualized treatment rules (ITRs). However, privacy concerns often present significant barriers to the integrative analysis of such multi-source data. Classical meta-learning, which averages local estimates to derive the final ITR, is frequently suboptimal due to biases in these local estimates. To address these challenges, we propose a convolution-smoothed weighted support vector machine for learning the optimal ITR. The accompanying loss function is both convex and smooth, which allows us to develop an efficient multi-round distributed learning procedure for ITRs. Such distributed learning ensures optimal statistical performance with a fixed number of communication rounds, thereby minimizing coordination costs across data centers while preserving data privacy. Our method avoids pooling subject-level raw data and instead requires only sharing summary statistics. Additionally, we develop an efficient coordinate gradient descent algorithm, which guarantees at least linear convergence for the resulting optimization problem. Extensive simulations and an application to sepsis treatment across multiple intensive care units validate the effectiveness of the proposed method.

Backtesting risk measures is a central task in financial regulation. While standard backtests evaluate whether a forecasting model is statistically consistent with observed losses, regulatory practice often requires assessing the performance of an internal model relative to benchmark models. We develop a non-parametric sequential framework for comparative backtests of general elicitable risk measures using e-values and e-processes. The proposed methods provide anytime-valid inference and remain robust under dependence and model misspecification. In particular, we propose a modified three-zone approach based on weak dominance, which yields more informative conclusions in comparative backtesting. As a technical building block, we also construct general standard e-backtests for identifiable risk measures and characterize the associated e-values and e-processes. The resulting procedures apply to a broad class of commonly used risk measures, including the mean, variance, Value-at-Risk, Expected Shortfall, and expectiles. Simulation studies and empirical analyses illustrate the effectiveness of the proposed approach.

Link prediction is a fundamental problem in network science, aiming to infer potential or missing links based on observed network structures. With the increasing adoption of parameterized models, the rigor of evaluation protocols has become critically important. However, a previously common practice of using the test set during hyperparameter tuning has led to human-induced information leakage, thereby inflating the reported model performance. To address this issue, this study introduces a novel evaluation metric, Loss Ratio, which quantitatively measures the extent of performance overestimation. We conduct large-scale experiments on 60 real-world networks across six domains. The results demonstrate that the information leakage leads to an average overestimation of about 3.6%, with the bias reaching over 15% for specific algorithms. Meanwhile, heuristic and random-walk-based methods exhibit greater robustness and stability. The analysis uncovers a pervasive information leakage issue in link prediction evaluation and underscores the necessity of adopting standardized data splitting strategies to enable fair and reproducible benchmarking of link prediction models.

An appropriate distance metric is crucial for categorical data clustering, as the distance between categorical data cannot be directly calculated. However, the distances between attribute values usually vary in different clusters induced by their different distributions, which has not been taken into account, thus leading to unreasonable distance measurement. Therefore, we propose a cluster-customized distance metric for categorical data clustering, which can competitively update distances based on different distributions of attributes in each cluster. In addition, we extend the proposed distance metric to the mixed data that contains both numerical and categorical attributes. Experiments demonstrate the efficacy of the proposed method, i.e., achieving an average ranking of around first in fourteen datasets. The source code is available at https://anonymous.4open.science/r/CADM-47D8

Agentic language models compose multi step reasoning chains, yet intermediate steps can be corrupted by inconsistent context, retrieval errors, or adversarial inputs, which makes post hoc evaluation too late because errors propagate before detection. We introduce a diagnostic that requires no additional training and uses only the forward pass to emit a binary accept or reject signal during agent execution. The method analyzes token graphs induced by attention and computes two spectral statistics in early layers, namely the high frequency energy ratio and spectral entropy. We formalize these signals, establish invariances, and provide finite sample estimators with uncertainty quantification. Under a two regime mixture assumption with a monotone likelihood ratio property, we show that a single threshold on the high frequency energy ratio is optimal in the Bayes sense for detecting context inconsistency. Empirically, the high frequency energy ratio exhibits robust bimodality during context verification across multiple model families, which enables gating decisions with overhead below one millisecond on our hardware and configurations. We demonstrate integration into retrieval augmented agent pipelines and discuss deployment as an inline safety monitor. The approach detects contamination while the model is still processing the text, before errors commit to the reasoning chain.

We introduce a method for evaluating interventional queries and Average Treatment Effects (ATEs) in the presence of generalized incomplete contingency tables (GICTs), contingency tables containing a full row of random (sampling) zeros, rendering some conditional probabilities undefined. Rather than discarding such entries or imputing missing values, we model the unknown probabilities as free parameters and derive symbolic expressions for the queries that incorporate them. By extremizing these expressions over all values consistent with basic probability constraints and the support of all variables, we obtain sharp bounds for the query of interest under weak assumptions of small missing frequencies. These bounds provide a formal quantification of the uncertainty induced by the generalized incompleteness of the contingency table and ensure that the true value of the query will always lie within them. The framework applies independently of the missingness mechanism and offers a conservative yet rigorous approach to causal inference under random data gaps.

Bayesian posterior distributions naturally represent parameter uncertainty informed by data. However, when the parameter space is complex, as in many nonparametric settings where it is infinite-dimensional or combinatorially large, standard summaries such as posterior means, credible intervals, or simple notions of multimodality are often unavailable, hindering interpretable posterior uncertainty quantification. We introduce Conformalized Bayesian Inference (CBI), a broadly applicable and computationally efficient framework for posterior inference on nonstandard parameter spaces. CBI yields a point estimate, a credible region with assumption-free posterior coverage guarantees, and a principled analysis of posterior multimodality, requiring only Monte Carlo samples from the posterior and a notion of discrepancy between parameters. The method builds a pseudo-density score for each parameter value, yielding a MAP-like point estimate and a credible region derived from conformal prediction principles. The key conceptual step underlying this construction is the reinterpretation of posterior inference as prediction on the parameter space. A final density-based clustering step identifies representative posterior modes. We investigate a number of theoretical and methodological properties of CBI and demonstrate its practicality, scalability, and versatility in simulated and real data clustering applications with random partition models. An accompanying Python library, cbi_partitions, is available at github.com/nbariletto/cbi_partitions_repo.

The Kolmogorov–Smirnov (KS) test is a widely used statistical test that assesses the conformity of a sample to a specified distribution. Its efficacy, however, diminishes with serially dependent data and when parameters within the hypothesized distribution are unknown. For independent data, parametric and nonparametric bootstrap procedures are available to adjust for estimated parameters. For serially dependent stationary data, parametric bootstrap has been developed with a working serial dependence structure. A counterpart for the nonparametric bootstrap approach, which needs a bias correction, has not been studied. Addressing this gap, our study introduces a bias correction method employing a nonparametric block bootstrap, which approximates the distribution of the KS statistic in assessing the goodness-of-fit of the marginal distribution of a stationary series, accounting for unspecified serial dependence and unspecified parameters. We assess its effectiveness through simulations, scrutinizing both its size and power. The practicality of our method is further illustrated with an examination of stock returns from the S&P 500 index, showcasing its utility in real-world applications.

Recent advances in interrupted time series analysis permit characterization of a typical non-linear interruption effect through use of generalized additive models. Concurrently, advances in latent time series modeling allow efficient Bayesian multilevel time series models. We propose to combine these concepts with a hierarchical model selection prior to characterize interruption effects with a multilevel structure, encouraging parsimony and partial pooling while incorporating meaningful variability in causal effects across subpopulations of interest, while allowing poststratification. These models are demonstrated with three applications: 1) the effect of the introduction of the prostate specific antigen test on prostate cancer diagnosis rates by race and age group, 2) the change in stroke or trans-ischemic attack hospitalization rates across Medicare beneficiaries by rurality in the months after the start of the COVID-19 pandemic, and 3) the effect of Medicaid expansion in Missouri on the proportion of inpatient hospitalizations discharged with Medicaid as a primary payer by key age groupings and sex.

Exact conditional tests for contingency tables require sampling from fibers with fixed margins. Classical Markov basis MCMC is general but often impractical: computing full Markov bases that connect all fibers of a given constraint matrix can be infeasible and the resulting chains may converge slowly, especially in sparse settings or in presence of structural zeros. We introduce a SAT-based alternative that encodes fibers as Boolean circuits which allows modern SAT samplers to generate tables randomly. We analyze the sampling bias that SAT samplers may introduce, provide diagnostics, and propose practical mitigation. We propose hybrid MCMC schemes that combine SAT proposals with local moves to ensure correct stationary distributions which do not necessarily require connectivity via local moves which is particularly beneficial in presence of structural zeros. Across benchmarks, including small and involved tables with many structural zeros where pure Markov-basis methods underperform, our methods deliver reliable conditional p-values and often outperform samplers that rely on precomputed Markov bases.

Inverse Game Theory (IGT) methods based on the entropy-regularized Quantal Response Equilibrium (QRE) offer a tractable approach for competitive settings, but critically assume the agents' rationality parameter (temperature $\tau$) is known a priori. When $\tau$ is unknown, a fundamental scale ambiguity emerges that couples $\tau$ with the reward parameters ($\theta$), making them statistically unidentifiable. We introduce Blind-IGT, the first statistical framework to jointly recover both $\theta$ and $\tau$ from observed behavior. We analyze this bilinear inverse problem and establish necessary and sufficient conditions for unique identification by introducing a normalization constraint that resolves the scale ambiguity. We propose an efficient Normalized Least Squares (NLS) estimator and prove it achieves the optimal $\mathcal{O}(N^{-1/2})$ convergence rate for joint parameter recovery. When strong identifiability conditions fail, we provide partial identification guarantees through confidence set construction. We extend our framework to Markov games and demonstrate optimal convergence rates with strong empirical performance even when transition dynamics are unknown.

Large health surveys increasingly collect high-dimensional functional data from wearable devices, and function on scalar regression (FoSR) is used to quantify the relationship between these functional outcomes and scalar covariates like age and sex. However, existing methods for FoSR fail to account for complex survey design. We introduce inferential methods for FoSR with complex survey designs. The approach combines fast univariate inference (FUI) developed for functional outcomes and survey sampling inferential methods developed for scalar outcomes. Our approach consists of three steps: (1) fit survey weighted GLMs at each point along the functional domain, (2) smooth coefficients along the functional domain, and (3) use balanced repeated replication (BRR) or Rao-Wu-Yue-Beaumont (RWYB) bootstrap to obtain pointwise and joint confidence bands for the functional coefficients. The approach is motivated by association studies between continuous physical activity data and covariates collected in the National Health and Nutrition Examination Survey (NHANES). A first-of-its-kind analytical simulation study and empirical simulation using NHANES data demonstrates that our approach performs better than existing methods that do not account for the survey structure. Finally, application of the approach in NHANES shows the practical implications of accounting for survey structure. The approach is implemented in the R package svyfosr.

We derive a deterministic, non-asymptotic upper bound on the Kullback-Leibler (KL) divergence of the flow-matching distribution approximation. In particular, if the $L_2$ flow-matching loss is bounded by $\epsilon^2 > 0$, then the KL divergence between the true data distribution and the estimated distribution is bounded by $A_1 \epsilon + A_2 \epsilon^2$. Here, the constants $A_1$ and $A_2$ depend only on the regularities of the data and velocity fields. Consequently, this bound implies statistical convergence rates of Flow Matching Transformers under the Total Variation (TV) distance. We show that, flow matching achieves nearly minimax-optimal efficiency in estimating smooth distributions. Our results make the statistical efficiency of flow matching comparable to that of diffusion models under the TV distance. Numerical studies on synthetic and learned velocities corroborate our theory.

Pre-trained Time Series Foundational Models (TSFMs) represent a significant advance, capable of forecasting diverse time series with complex characteristics, including varied seasonalities, trends, and long-range dependencies. Despite their primary goal of universal time series forecasting, their efficacy is far from uniform; divergent training protocols and data sources cause individual TSFMs to exhibit highly variable performance across different forecasting tasks, domains, and horizons. Leveraging this complementary expertise by arbitrating existing TSFM outputs presents a compelling strategy, yet this remains a largely unexplored area of research. In this paper, we conduct a thorough examination of how different TSFMs exhibit specialized performance profiles across various forecasting settings, and how we can effectively leverage this behavior in arbitration between different time series models. We specifically analyze how factors such as model selection and forecast horizon distribution can influence the efficacy of arbitration strategies. Based on this analysis, we propose Synapse, a novel arbitration framework for TSFMs. Synapse is designed to dynamically leverage a pool of TSFMs, assign and adjust predictive weights based on their relative, context-dependent performance, and construct a robust forecast distribution by adaptively sampling from the output quantiles of constituent models. Experimental results demonstrate that Synapse consistently outperforms other popular ensembling techniques as well as individual TSFMs, demonstrating Synapse's efficacy in time series forecasting.

Physics-informed deep learning has emerged as a promising framework for solving partial differential equations (PDEs). Nevertheless, training these models on complex problems remains challenging, often leading to limited accuracy and efficiency. In this work, we introduce a hybrid adaptive sampling and weighting method to enhance the performance of physics-informed neural networks (PINNs). The adaptive sampling component identifies training points in regions where the solution exhibits rapid variation, while the adaptive weighting component balances the convergence rate across training points. Numerical experiments show that applying only adaptive sampling or only adaptive weighting is insufficient to consistently achieve accurate predictions, particularly when training points are scarce. Since each method emphasizes different aspects of the solution, their effectiveness is problem dependent. By combining both strategies, the proposed framework consistently improves prediction accuracy and training efficiency, offering a more robust approach for solving PDEs with PINNs.

Off-dynamics reinforcement learning (RL), where training and deployment transition dynamics are different, can be formulated as learning in a robust Markov decision process (RMDP) where uncertainties in transition dynamics are imposed. Existing literature mostly assumes access to generative models allowing arbitrary state-action queries or pre-collected datasets with a good state coverage of the deployment environment, bypassing the challenge of exploration. In this work, we study a more realistic and challenging setting where the agent is limited to online interaction with the training environment. To capture the intrinsic difficulty of exploration in online RMDPs, we introduce the supremal visitation ratio, a novel quantity that measures the mismatch between the training dynamics and the deployment dynamics. We show that if this ratio is unbounded, online learning becomes exponentially hard. We propose the first computationally efficient algorithm that achieves sublinear regret in online RMDPs with $f$-divergence based transition uncertainties. We also establish matching regret lower bounds, demonstrating that our algorithm achieves optimal dependence on both the supremal visitation ratio and the number of interaction episodes. Finally, we validate our theoretical results through comprehensive numerical experiments.

We establish non-asymptotic efficiency guarantees for tensor decomposition-based inference in count data models. Under a Poisson framework, we consider two related goals: (i) parametric inference, the estimation of the full distributional parameter tensor, and (ii) multiway analysis, the recovery of its canonical polyadic (CP) decomposition factors. Our main result shows that in the rank-one setting, a rank-constrained maximum-likelihood estimator achieves multiway analysis with variance matching the Cramér-Rao Lower Bound (CRLB) up to absolute constants and logarithmic factors. This provides a general framework for studying "near-efficient" multiway estimators in finite-sample settings. For higher ranks, we illustrate that our multiway estimator may not attain the CRLB; nevertheless, CP-based parametric inference remains nearly minimax optimal, with error bounds that improve on prior work by offering more favorable dependence on the CP rank. Numerical experiments corroborate near-efficiency in the rank-one case and highlight the efficiency gap in higher-rank scenarios.

We establish parameter inference for the Poisson canonical polyadic (PCP) model of tensor count data through a latent-variable formulation. Our approach exploits the property that any random tensor that follows the PCP model can be derived by marginalizing an unobservable random tensor of one dimension larger. The loglikelihood of this larger dimensional tensor, referred to as the "complete" loglikelihood, is comprised of multiple loglikelihoods corresponding to rank one PCP models. Using this methodology, we first demonstrate that several existing algorithms for fitting non-negative matrix and tensor factorizations are Expectation-Maximization algorithms. Next, we derive the observed and expected Fisher information matrices for the PCP model by leveraging its latent-variable formulation. The Fisher information provides us crucial insights into the well-posedness of the tensor model, such as the role that the rank of parameter tensor plays in identifiability and indeterminacy. For the special case of PCP models with rank one parameter tensors, we demonstrate that these results are greatly simplified.

Tests of goodness of fit are used in nearly every domain where statistics is applied. One powerful and flexible approach is to sample artificial data sets that are exchangeable with the real data under the null hypothesis (but not under the alternative), as this allows the analyst to conduct a valid test using any test statistic they desire. Such sampling is typically done by conditioning on either an exact or approximate sufficient statistic, but existing methods for doing so have significant limitations, which either preclude their use or substantially reduce their power or computational tractability for many important models. In this paper, we propose to condition on samples from a Bayesian posterior distribution, which constitute a very different type of approximate sufficient statistic than those considered in prior work. Our approach, approximately co-sufficient sampling via Bayes (aCSS-B), considerably expands the scope of this flexible type of goodness-of-fit testing. We prove the approximate validity of the resulting test, and demonstrate its utility on three common null models where no existing methods apply, as well as its outperformance on models where existing methods do apply.