Papers

In this paper, we introduce a general model for jointly modelling the nodal heterogeneity and covariates in weighted or unweighted bipartite networks, which contains two different types of nodes. The model has a degree heterogeneity parameter for each node and a fixed-dimensional regression coefficient for the covariates. We use the method of moments to estimate the unknown parameters. When the model belongs to the exponential family of distributions, the moment estimator is identical to the maximum likelihood estimator. We show the uniform consistency of the moment estimator, when the number of actors and the number of events both go to infinity under some conditions. Further, we derive an asymptotic representation of the moment estimator, which leads to their asymptotic normal distributions under some conditions. We present two applications to illustrate the unified results. Numerical simulations and a real-data analysis demonstrates our theoretical findings.

We develop a theoretical foundation for robust model comparison in a class of non-ergodic continuous volatility regression models contaminated by finite-activity jumps. Using the density-power weighting and the Hölder(-inequality)-based normalization of the conventional Gaussian quasi-likelihood function, we propose two Schwarz-type statistics and also establish their model selection consistency with respect to the minimal true parametric volatility coefficient. Numerical experiments are conducted to illustrate our theoretical findings.

This paper is the second part of our study on the non-parametric estimation of MS-NAR processes started with [L. Fermin et al. 2017]. We consider the Nadaraya-Watson type regression function estimator for non-linear autoregressive Markov switching processes. In this context the regression function estimator is interpreted as a solution of a local weighted We have introduced, in the first work, a restoration-estimation Robbins-Monro algorithm to approximate the estimator, and we proved identifiability of model and the consistency of the non-parametric estimator. In this work, we obtain the central limit theorem for the non-parametric estimator, whether the Markov chain is observed or not. Finally, we present a detailed simulation study illustrating the performances of our estimation procedure.

Bayesian inference for models with intractable likelihoods, such as Markov random fields, poses a fundamental computational challenge due to the tradeoff between inferential accuracy and computational cost. Various MCMC methods have been developed to address this challenge. The exchange algorithm targets the exact posterior, but requires an expensive perfect sampling step at each iteration, which is often infeasible in practice. In contrast, path sampling approximates the Metropolis acceptance ratio using a precomputed grid of likelihood values, but may introduce bias when the grid is poorly chosen. We introduce a novel amortized MCMC framework that retains the theoretical validity of exact methods while substantially reducing the computational burden. The proposed approach employs a gradient-informed grid selection procedure and constructs a surrogate likelihood via Hermite interpolation, yielding a smooth approximation with low error. A simulation study characterizes the rate at which inferential accuracy improves as the number of grid points increases. We further demonstrate the practical performance of the method through applications to a hidden Potts model for satellite imagery and an autologistic model for Arctic ice floes.

Considering a general framework of bootstrap with exchangeable weights, we show some concentration inequalities for the supremum of the bootstrap empirical process. On the one hand, we discuss the concentration of the bootstrap empirical process around its conditional expectation with respect to the original data, and on the other hand, the concentration of the latter quantity around its mean. For the concentration conditional on data, we build on Chatterjee's exchangeable pairs approach to concentration. To attain optimal concentration rates, we develop some refined arguments for the convergence of transposition walks on the symmetric group. The conditional expectation of the bootstrap empirical process is proved to be self-bounding, thus extending a well-known property for conditional Rademacher averages. To illustrate the interest of these concentration inequalities, we provide some new results pertaining to confidence regions for the estimation of a mean vector, as well as non-asymptotic bounds for the two-sample permutation test.

Tacho-less rotational speed estimation is critical for vibration-based prognostics and health management (PHM) of rotating machinery, yet traditional methods–such as time-domain periodicity, cepstrum, and harmonic comb matching–struggle under noise, non-stationarity, and inharmonic interference. Probabilistic tracking offers a principled way to fuse multiple estimators, but a major challenge is that heterogeneous estimators produce evidence on incompatible axes and scales. We address this with ARC (Alignment-based RPM Estimation with Curvature-adaptive Tracking) by unifying the observation representation. Each estimator outputs a one-dimensional evidence curve on its native axis, which is mapped onto a shared RPM grid and converted into a comparable grid-based log-likelihood via robust standardization and a Gibbs-form energy shaping. Standard recursive filtering with fixed-variance motion priors can fail under multi-modal or ambiguous evidence. To overcome this, ARC introduces a curvature-informed, state-dependent motion prior, where the transition variance is derived from the local discrete Hessian of the previous log-posterior. This design enforces smooth tracking around confident modes while preserving competing hypotheses, such as octave alternatives. Experiments on synthetic stress tests and real vibration-table data demonstrate stable, physically plausible trajectories with interpretable uncertainty, and ablations confirm that these gains arise from uncertainty-aware temporal propagation rather than per-frame peak selection or ad hoc rules.

Statistical inference in parametric models (e.g., the Bradley–Terry model and its variants) for paired-comparison data has been explored in the high-dimensional regime, in which the number of items involving in paired comparisons diverges. However, parametric models are highly susceptible to model misspecification. To relax the assumption of known distributions and provide flexibility, we propose a semiparametric framework for modeling the merits of items and covariate effects (e.g., home-field advantage) by introducing latent random variables with unspecified distributions. As the number of parameters increases with the number of items, semiparametric inference is highly nontrivial. To address this issue, we employ a kernel-based least squares approach to estimate all unknown parameters. When each pair of items has a fixed number of comparisons and the number of items tends to infinity, we prove the consistency of all resulting estimators and derive their asymptotic normal distributions. To the best of our knowledge, this is the first study to conduct a semiparametric analysis of paired comparisons with an increasing dimension. We conduct simulations to evaluate the finite-sample performance of the proposed method and illustrate its practical utility by analyzing an NBA dataset.

Clustering mixed-type data remains a major challenge in biomedical research to uncover clinically meaningful subgroups within heterogeneous patient populations. Most existing clustering methods impose restrictive assumptions like local independence, fail to accommodate censored biomarkers, or unable to quantify variable importance. We propose a Bayesian finite mixture model (BFMM) clustering framework that addresses these limitations. BFMM flexibly models both continuous and categorical variables, incorporates three covariance structures to capture cluster-specific dependencies among continuous features, and handles censored observations through likelihood-based imputation. To facilitate feature prioritization, BFMM uses spike-and-slab priors to estimate variable importance on a continuous 0-1 scale. Simulation studies demonstrate that BFMM outperforms existing methods in clustering accuracy, particularly given strong within-cluster correlation or censored variables, and reliably distinguishes informative features from noise under varying conditions. We applied BFMM to two real-world datasets: (1) the SENECA cohort integrating electronic health records from patients with Sepsis; and (2) the EDEN randomized trial of patients with acute lung injury. In both settings, BFMM identified clinically interpretable phenotypes and revealed variable-specific contributions to subgroup differentiation. In the EDEN trial, it also uncovered evidence of treatment heterogeneity. These findings validate BFMM as an effective, interpretable, and practically useful clustering tool for complex biomedical datasets.

Despite its extensive development for multivariate data, semi-supervised learning remains underdeveloped for functional data, especially under discrete and noisy observations. We develop a density-sensitive semi-supervised framework for functional data supported on a low-dimensional manifold by adapting the Fermat distance to reconstructed trajectories. The resulting pairwise distances are used to construct a weighted $k$-nearest-neighbor classifier and multidimensional-scaling-based classifiers. To accommodate massive datasets commonly seen in semi-supervised applications, we design a computationally efficient estimation procedure tailored for discrete and noisy functional observations. Theoretically, we establish exponentially decaying convergence rates of the $k$-NN classifier and the consistency of the estimated Fermat distance. Crucially, our results reveal that incorporating unlabeled data may not lead to improved classification accuracy without a sufficiently fast-growing individual sampling rate, precisely due to discrete and noisy observations. In most simulation settings satisfying the manifold and cluster assumptions, the proposed classifiers outperform the supervised benchmarks considered; in the Gaia spectra analysis, they attain higher agreement with high-confidence proxy labels.

We introduce BLOC (Black-box Optimization over Correlation matrices), a general framework for sparse covariance estimation with non-convex penalties. BLOC operates on the manifold of correlation matrices and reparameterizes it via an angular Cholesky mapping, transforming the positive-definite, unit-diagonal constraint into an unconstrained search over a Euclidean hyperrectangle. This enables gradient-free global optimization of diverse objectives, including non-differentiable or black-box losses, using a pattern search routine with adaptive coordinate polling, run-wise restarts to escape local minima, and leveraging up to $d(d-1)$ parallel threads when optimizing a $d$-dimensional correlation matrix. The method is penalty-agnostic and ensures that every iterate is a valid correlation matrix, from which covariance estimates are obtained. We establish convergence guarantees, including stationarity, probabilistic escape from poor local minima, and sublinear rates under smooth convex losses. From a statistical perspective, we prove consistency, convergence rates, and sparsistency for penalized correlation estimators under general conditions, extending sparse covariance theory beyond the Gaussian setting. Empirically, BLOC with nonconvex penalties such as SCAD and MCP outperforms leading estimators in both low- and high-dimensional regimes, achieving lower estimation error and improved sparsity recovery. A parallel implementation enhances scalability, and a proteomic network application demonstrates robust, positive-definite sparse covariance estimation.

In causal inference, interference occurs when the treatment of one unit may affect the outcomes of other units. The goal of this work is to serve as a guide to the use of linear outcome modeling for estimating causal effects in settings where interference may pose a challenge to identification and estimation, such as spatial and network data. We demonstrate that, under a linear model, causal effects of binary and continuous treatments can be identified in terms of regression coefficients under totally and partially known interference structures. Our work constructs unbiased and consistent point and variance estimators for these effects under one or more possible fixed or random interference networks. A chief advantage is that this approach can be implemented using standard linear regression software, and is easily augmented with random effects and heteroscedastic or autocorrelation consistent standard errors. Numerical experiments and an example data analysis demonstrate the efficacy of this approach in eliminating interference bias.

When estimating population prevalence from a non-random sample, it is important to adjust for differences between sample and population. However, adjustment for multiple factors requires analysis that can be difficult to understand and validate. In this manuscript, we explore an unexpected downward trend of estimates when covariates are added sequentially to a Bayesian hierarchical model for the estimation of the prevalence of SARS-CoV-2 specific antibodies in an Australian city in late 2020. We compare our data analysis to results from a simulation study to understand four potential contributors to this effect: (i) correction for differences between sample and population, (ii) rare-events bias in logistic regression, (iii) inclusion of the uncertainty of test sensitivity and specificity in a multilevel model, and (iv) increasing model dimensionality. We find that weak prior distributions on the logistic regression coefficients lead to a systematic increase in the amount of partial pooling across adjustment cells-the prior becomes stronger as model dimensionality increases-which in turn feeds through to the estimated assay specificity, which then feeds back to the model and results in lowering the estimated prevalence. Our paper contributes three elements: (i) immediate and longer-term recommendations for using these types of models, (ii) simulation studies to explore the impact of the contributors to this effect, and (iii) a worked example of investigation of unexpected results in a model with multiple adjustment factors.

In this paper, we consider the sphericity test for a one-sample problem under high-dimensional two-step monotone incomplete data. Existing asymptotic expansions for the null distributions of the likelihood ratio test (LRT) statistic and modified LRT statistic deteriorate in high-dimensional settings. Therefore, we derive an Edgeworth expansion for the null distribution of the LRT statistic in such settings and obtain its computable error bounds. Furthermore, we demonstrate that our proposed Edgeworth expansion provide better approximation accuracy than the existing asymptotic expansion. We also conduct numerical experiments using Monte Carlo simulations to evaluate the maximum absolute error between the distribution function of the standardized test statistic and the Edgeworth expansion for the null distribution of the LRT statistic, as well as to assess the performance of the computable error bounds. Finally, by deriving a Cornish-Fisher expansion for the null distribution of the LRT statistic in high-dimensional settings, we evaluate the empirical Type I error rates via Monte Carlo simulations.

This study addresses the challenge of estimating average treatment effects (ATEs) for advertising campaigns in online marketplaces where complete randomized experimentation is infeasible. We propose two key innovations: (1) a shrinkage estimator that optimally combines observational and experimental data without assuming smooth treatment effects across campaigns, and (2) a Bayesian adaptive experimental design framework that efficiently selects campaigns for randomized evaluation that minimizes cumulative risk. Our shrinkage estimator achieves lower risk compared to existing methods by balancing bias-variance tradeoffs, while our adaptive design significantly reduces the costs of campaign randomization. We establish theoretical guarantees including asymptotic normality and regret bounds. In an application to Amazon Ads data analyzing 2,583 campaigns, our approach achieves equivalent estimation precision while requiring only half of the randomized experiments needed by random sampling, the standard method widely used in practice today. The proposed method serves as a practical solution for marketplace platforms to efficiently measure advertising effectiveness while managing experimentation costs.

An Automated Sliced Gibbs framework is proposed for fully automated Markov chain Monte Carlo sampling from arbitrary finite dimensional probability kernels. The method targets unnormalized, non-smooth, heavy tailed, and highly multimodal densities. A Cauchy transformation based effective support estimator is combined with slice driven Gibbs updates. This construction removes the need for user specified truncation bounds, proposal scales, step-size tuning, or conditional optimization. Unlike existing slice samplers, ASG does not require manually chosen bracket widths or geometric insight into the support. All calibration is performed automatically within each Gibbs cycle. The resulting Markov chain preserves invariance and ergodicity. Automated support detection allows efficient movement across disconnected high density regions. The sampler adapts to sharp curvature and irregular geometry without gradient information. Extensive numerical experiments evaluate performance on complex kernels, including univariate Beta mixtures, multivariate Rosenbrock and Ackley benchmarks, and non-smooth kernels derived from generalized LASSO type loss functions. Across these challenging settings, ASG consistently achieves higher effective sample size per second and faster decorrelation than Random Walk Metropolis Hastings, adaptive Gibbs variants, and some recently proposed slice based methods. The framework provides a scalable and general-purpose solution for sampling from complicated probability kernels where existing algorithms require substantial tuning or exhibit slow mixing.

Standard macroeconomic frameworks have correctly identified Japan's government debt - now exceeding 240% of GDP - as carrying substantial fiscal risk. Yet FRED data from 2013 to 2026 present an empirical record inviting a complementary perspective: debt ratios have stabilized, nominal GDP has exceeded 670 trillion yen (SAAR), and unemployment has remained near 2.6-2.7%. This paper formalizes these channels through the Japanese Financial Repression r-g (JFR-rg) model. Building on Blanchard (2019), the framework incorporates a financial repression bias (epsilon_t = pi_t - r^n_t, directly observable from FRED) and a non-linear exchange-rate channel. Three theoretical contributions extend the literature: (i) the Debt Sustainability Corridor, a characterization of stability in (epsilon_t, g^n*_t) space; (ii) the Normalization Ratchet, a path-dependence theorem showing that temporary policy errors generate persistently higher debt trajectories; and (iii) the Captive Financial System Parameter (phi_t), which endogenizes the institutional precondition for JFR-rg stability. Appendices H-L provide supporting empirical evidence (VAR, ARDL, Local Projections) showing the framework's claims are empirically disciplined and falsifiable. The core debt-dynamics propositions are anchored in the consolidated government budget identity (Layer L1), while selected propositions additionally rely on minimal structural assumptions; identification concerns apply only to the empirical Layer L2. Counterfactual simulations illustrate a Normalization Trap: aggressive rate hikes can produce counterproductive debt dynamics. For high-debt, low-growth economies sharing Japan's institutional characteristics, strategically deploying the resulting Repression Dividend into productivity-enhancing investment may represent a regime-contingent equilibrium possibility, conditional on the captive system condition being maintained.

Many natural systems posses, and can transition between, multiple alternative states. For example, a climate “tipping element” is a climate component that can transition to an alternative steady state due to an external perturbation such as global warming. Despite the potential impact, existence of alternate states in realistic, complex simulations (e.g. climate models) remain poorly understood. Arguably a reason for this is the lack of applicable methodology that explicitly targets finite yet high-dimensional datasets. In this work we utilize recent progress in computational nonlinear dynamics to formulate a workflow that analyses potentially multi-state simulation data and decides algorithmically what are the alternate states contained within, if any are clearly distinguishable. The framework undergoes an optimization routine that showcases which observables in the data best differentiate the alternate states, and which ones do not differentiate at all, which could be used to guide monitoring and early-warning for multistable components in climate or ecosystems. Finally, once the alternate states have been found, we define an indicator called “intermingledness”. It quantifies differences and similarities between alternate states, as well as for their basins of attraction (if applicable), across various diagnostic variables. We analyse and present results using three diverse climate datasets: Atlantic ocean circulation, atmospheric midlatitude flow, and habitability of exoplanets. The method is not exclusive to climatic data, but applicable to a variety of cases, including complex networks such as power grids or biological networks. We also provide easy-to-use open source code for applying the workflow to new data.

Take a look around you – in your family, your school or workplace, in the streets, and you see boys & girls in about equal proportion, and without any easily visible gender patterns in case of siblings. So, to the famous first order of statistical approximation, we're all the results of hierarchical cascades of independent coin tosses through history, with each little fate determined by a 0.50-0.50 coin. This is not entirely correct, as one discovers with careful analysis and enough data: the coins of fate are (a little) imbalanced; they vary (a little) from family to family; there is a (slight) dependence in your children's gender sequence; and there are (slightly) more only-girls and only-boys families than predicted from binomial conditions. In this article I use the opportunity to talk also about how sample sizes influence p-values and statistical detection power.

Despite there now being more than 1,000 FDA-authorised AI medical devices, formal equity assessments – whether model performance is uniform across patient subgroups – are rare. Here, we evaluate the equity of 18 open-source brain tumour segmentation models across 648 glioma patients from two independent datasets (n = 11,664 model inferences) along distinct univariate, Bayesian multivariate, spatial, and representational dimensions. We find that patient identity consistently explains more performance variance than model choice, with clinical factors, including molecular diagnosis, tumour grade, and extent of resection, predicting segmentation accuracy more strongly than model architecture. A voxel-wise spatial meta-analysis identifies neuroanatomically localised biases that are compartment-specific yet often consistent across models. Within a high-dimensional latent space of lesion masks and clinic-demographic features, model performance clusters significantly, indicating that the patient feature space contains axes of algorithmic vulnerability. Although newer models tend toward greater equity, none provide a formal fairness guarantee. Lastly, we release Fairboard, an open-source, no-code dashboard that lowers barriers to equitable model monitoring in medical imaging.

Mediation analysis for complex, non-Euclidean data, such as probability distributions, compositions, images, and networks, presents significant methodological challenges due to the inherent nonlinearity and geometric constraints of such spaces. Existing approaches are often restricted to Euclidean settings or specific data types. We propose Random Object Mediation Analysis (ROMA), a unified framework that simultaneously accommodates object-valued exposures, mediators, and outcomes, enabling the analysis of nonlinear causal pathways in general metric spaces. ROMA leverages an additive Reproducing Kernel Hilbert Space (RKHS) operator model to rigorously disentangle direct and indirect causal pathways, which is a significant advancement over existing single-predictor or purely predictive additive frameworks. Theoretically, we establish the nonparametric identification of causal effects and derive global asymptotic normality for our estimators. Crucially, this theoretical foundation enables the construction of simultaneous confidence bands and global test statistics without the need for computationally intensive resampling. We demonstrate the practical utility of ROMA through simulations and real-world applications involving compositional mediators and distributional outcomes, extending the scope of mediation analysis.

In many statistical problems, the data distribution is specified through a generative process for which the likelihood function is analytically intractable, yet inference on the associated model parameters remains of primary interest. We develop a likelihood-free inference framework that combines score matching with gradient-based optimization and bootstrap procedures to facilitate parameter estimation together with uncertainty quantification. The proposed methodology introduces tailored score-matching estimators for approximating likelihood score functions, and incorporates an architectural regularization scheme that embeds the statistical structure of log-likelihood scores to improve both accuracy and scalability. We provide theoretical guarantees and demonstrate the practical utility of the method through numerical experiments, where it performs favorably compared to existing approaches.

We investigate the behavior of the length of the longest weakly increasing subsequences (weak LIS) of $n$-step random walks with nonzero integer increments $k = \pm 1, \pm 2, \dots$ given by a symmetric heavy tailed mass distribution proportional to $|k|^{-1-\alpha}$ for several values of the real parameter $\alpha > 0$ together with that of the simple random walk ($k=\pm 1$), to which the $n$-step heavy tailed walks reduce when $\alpha$ grows large enough that step jumps beyond $\pm 1$ become essentially absent on the scale of $n$. By means of exploratory fits, weighted nonlinear least squares, and nested-model comparisons, we found that the sample average length $\langle{L_{n}}\rangle$ scales like $\langle{L_{n}}\rangle \sim \sqrt{n}\log{n}$ when the distribution of increments has finite variance ($\alpha > 2$) and $\langle{L_{n}}\rangle \sim n^{\theta}$ with a varying exponent $\theta > 0.5$ when the variance is infinite ($\alpha \leq 2$). Distributional diagnostics indicate that the bulk of the $L_{n}$ distribution is very well-approximated by a lognormal model, though systematic deviations are observed in the tails. Our results corroborate and expand upon previous results for the LIS of other types of heavy-tailed random walks and raise a conjecture as to whether the distribution of $L_{n}$ is given, or can be effectively described, by a lognormal distribution.

Adaptive experiments optimize their design throughout data collection, which can bring substantial benefits compared to conventional experimental settings. Potential applications include, among others, computerized adaptive testing (when selecting informative tasks in ability measurements), adaptive treatment assignment (when searching for experimental conditions maximizing certain outcomes), and active learning (when choosing optimal training data for machine learning algorithms). However, implementing these techniques in real time poses substantial computational and technical challenges. In this paper, we introduce a practical and unified approach to real-time adaptive experiments that can encompass these scenarios across textual, visual, and audio tasks. Our strategy combines active inference, a Bayesian framework inspired by cognitive neuroscience, with Pyro, a probabilistic programming library, and PsyNet, a modular Python package for large-scale online behavioral experiments. Active inference provides a task-agnostic optimization objective and efficient inference strategies; probabilistic programming makes the computations practical, reducing implementation costs; and PsyNet makes the resulting procedure deployable with humans in real time across diverse behavioral paradigms. We illustrate this approach through two concrete examples: (1) an adaptive testing experiment estimating participants' ability by selecting optimal challenges, reducing the number of trials required by 30–40%; and (2) an adaptive treatment assignment strategy that identifies the optimal treatment up to three times as accurately as a fixed design. We provide instructions to facilitate adoption of the workflow.

The use of transfer learning within Bayesian optimization addresses the disadvantages of the so-called cold start problem by using source data to aid in the optimization of a target problem. We present a method that leverages an ensemble of surrogate models using transfer learning and integrates it in a constrained Bayesian optimization framework. We identify challenges particular to aircraft design optimization related to heterogeneous design variables and constraints. We propose the use of a partial-least-squares dimension reduction algorithm to address design space heterogeneity, and a meta data surrogate selection method to address constraint heterogeneity. Numerical benchmark problems and an aircraft conceptual design optimization problem are used to demonstrate the proposed methods. Results show significant improvement in convergence in early optimization iterations compared to standard Bayesian optimization, with improved prediction accuracy for both objective and constraint surrogate models.

Motivated by the prevalence of environments in which data is abundant while resources for storage and/or transmission might be scarce, we study linear regression when predictors, their squares, and responses are subject to single-bit dithered quantization. An estimator relying on plug-in estimation of the quadratic and linear terms in the quadratic program formulation of the least squares problem is proposed. We provide a non-asymptotic bound on the $\ell_2$-estimation error of this estimator and obtain its asymptotic distribution when the number of predictors is fixed, which can be used for inference and an investigation of the mean-square error efficiency relative to the ordinary least squares estimator. It is shown that for the quantization protocol under consideration, substantial improvements over the proposed estimator cannot be expected. A compression pipeline in which the underlying data is first subject to sketching and subsequently quantization can be studied within our framework as well. We also present an extension to address high-dimensional predictors. Numerical experiments with synthetic data complement our theoretical findings.

Aircraft design relies heavily on solving challenging and computationally expensive Multidisciplinary Design Optimization problems. In this context, there has been growing interest in multi-fidelity models for Bayesian optimization to improve the MDO process by balancing computational cost and accuracy through the combination of high- and low-fidelity simulation models, enabling efficient exploration of the design process at a minimal computational effort. In the existing literature, fidelity selection focuses only on the objective function to decide how to integrate multiple fidelity levels, balancing precision and computational cost using variance reduction criteria. In this work, we propose novel multi-fidelity selection strategies. Specifically, we demonstrate how incorporating information from both the objective and the constraints can further reduce computational costs without compromising the optimality of the solution. We validate the proposed multi-fidelity optimization strategy by applying it to four analytical test cases, showcasing its effectiveness. The proposed method is used to efficiently solve a challenging aircraft wing aero-structural design problem. The proposed setting uses a linear vortex lattice method and a finite element method for the aerodynamic and structural analysis respectively. We show that employing our proposed multi-fidelity approach leads to $86\%$ to $200\%$ more constraint compliant solutions given a limited budget compared to the state-of-the-art approach.

Bell inequalities characterize the boundary of the local-realist correlation polytope – the set of joint probability distributions achievable by classical hidden-variable models. Quantum mechanics exceeds this boundary through non-commutativity, reaching the Tsirelson bound $2\sqrt{2}$ for CHSH. We show that this polytope structure is not specific to quantum foundations: it appears identically in the causal inference literature, where the instrumental inequality, the Balke–Pearl linear programming bounds, and the Tian–Pearl probabilities of causation all arise as facets of the same marginal compatibility polytope. Fine's theorem – that CHSH inequalities hold if and only if a joint distribution exists – is precisely the pivot: the instrumental variable model in causal inference is structurally equivalent to the Bell local hidden-variable model, with the instrument playing the role of the measurement setting and the latent confounder playing the role of the hidden variable $\lambda$. We develop this correspondence in detail, extending it to algorithmic (Kolmogorov complexity) and entropic formulations of Bell inequalities, the NPA semidefinite programming hierarchy, and the MIP$^*$=RE undecidability result. We further show that the Born-rule / Bayes-rule duality underlying quantum Bayesian computation exploits the same non-commutativity that enables Bell violation, providing polynomial speedups for posterior inference. The framework yields a concrete dictionary between quantum information theory, causal econometrics, and Bayesian computation, and suggests new directions including NPA-based quantum causal inference algorithms and quantum architectures for function approximation.

Geofencing surveillance poses a dynamic spatial sampling problem. Police agencies must select a surveillance site, choose a geofence perimeter from a set of alternatives, and identify potential suspects through reverse location warrants. At the same time, warrant magistrates must impose constraints that curtail the reach of police surveillance efforts. This sampling problem emerges because agencies commonly use fixed geofence boundaries that ignore how humans move about a chosen surveillance site (i.e., pedestrian flows or traffic patterns). This further exacerbates privacy concerns and increases the risk of selective expansion where agencies extend their data collection efforts beyond the parameters outlined in their warrant. Given the Court's recent ruling in Chatrie, there is currently a need to establish a measurable process that allows magistrates to quantify and evaluate the potential impacts of a warrant proposal. In this paper, we take the first step in introducing a set of optimal radius estimators that measure how geofence perimeters adapt to their local context. Given a surveillance site and some privacy constraint, these estimators generate surveillance perimeters whose size changes with local population densities. This allows magistrates to quantify tradeoffs between local privacy intrusions with law enforcement's surveillance needs. We discuss the properties of these estimators, their underlying assumptions, and the potential consequences of using algorithms to better protect the privacy of its citizens.

The minimum-norm interpolator (MNI) framework has recently attracted considerable attention as a tool for understanding generalization in overparameterized models, such as neural networks. In this work, we study the MNI under a $2$-uniform convexity assumption, which is weaker than requiring the norm to be induced by an inner product; in this setting, the MNI typically does not admit a closed-form solution. At a high level, we show that this condition yields an upper bound on the MNI bias in both linear and nonlinear models. We further show that this bound is sharp for overparameterized linear regression when the norm's unit ball is in isotropic or John's position and the covariates are i.i.d.\ sub-Gaussian, for example, when each covariate vector has i.i.d. Rademacher entries. Finally, under the same assumption on the covariates, we prove sharp generalization bounds for the $\ell_p$-MNI when $p \in \bigl(1 + C/\log d, 2\bigr]$. To the best of our knowledge, this is the first work to establish sharp bounds for non-Gaussian covariates in linear models when the norm is not induced by an inner product. This work is deeply inspired by classical work on $K$-convexity and recent work on the geometry of $2$-uniformly convex and isotropic convex bodies.

Given two functions $\mathbf{a}\!:\! [n] \rightarrow [n]$ and $\mathbf{b}\!:\! [n] \rightarrow [n]$ chosen uniformly at random, any word $w=w_1w_2\dots w_k\in \{a,b\}^k$ induces a random function $\mathbf{w}\!:\! [n] \rightarrow [n]$ by composition, i.e. $\mathbf{w}=\phi_{w_k}\circ \dots \circ \phi_{w_1}$ with $\phi_a=\mathbf{a}$ and $\phi_b=\mathbf{b}$. We study the following question: assuming $w$ is fixed but unknown, and $n$ goes to infinity, does the random function $\mathbf{w}$ carry enough information to (partially) recover the word $w$ with good enough probability, in one or several i.i.d. samples? We prove that the random functions stemming from two non-isomorphic words can be discriminated with probability arbitrarily close to $1$ with a bounded number of samples, when $n$ goes to infinity. Equivalently, the total variation distance between their distributions is bounded away from zero. The proof relies on the study of certain auto-correlation functions appearing in the variance of the weighted number of quasi-leaves. Whether the total variation distance goes to 1, or equivalently, whether one sample is enough to distinguish the words with high probability, is the major question we leave open. We show that this is the case when the two words have different lengths or different exponents.