Papers

The paper investigates Bayesian Model Averaging and Selection (BMA/S) under non-standard stochastic assumptions, focusing on stochastic frontier analysis (SFA). We propose fast, reliable procedures for inference in the normal-exponential stochastic frontier model and examine whether accounting for asymmetric disturbances affects model averaging and/or selection outcomes relative to the conventional Gaussian-error BMA/S. Particular attention is given to moderate-dimensional covariate selection problems typical in SFA applications. We demonstrate that, with appropriate search strategies and parallelization techniques, exhaustive model search can be computationally feasible and, in some cases, more practical than stochastic search alternatives. A Monte Carlo simulation study is used to compare the proposed SF-BMA/S procedure with standard Gaussian-error BMA/S under varying levels of inefficiency-to-noise ratio and signal strength with respect to the data generating process. The results show that accounting for stochastic frontier structures may affect posterior inference and model averaging outcomes, especially in scenarios where efficiency analysis is most sensible.

The Helmholtz equation governs time-harmonic wave propagation, and in dissipative media a complex modulus renders its squared wavenumber $\kappa^2$ complex. Inferring such fields from sparse, noisy data calls for solvers that also quantify their own uncertainty. Physics-informed Gaussian-process (GP) regression supplies this by returning a posterior over the solution, yet operator-conditioned formulations have been developed almost exclusively for real-valued fields. We extend operator-informed GP regression to complex-valued Helmholtz problems by realifying the complex operator into an equivalent coupled real block, which enables inference with standard real-valued GP conditioning. The construction admits a family of priors, from a proper diagonal prior to coregionalized and multiscale variants, and conditions on PDE residuals and boundary traces. On benchmark problems in one to three dimensions, the solver is competitive with finite-difference and neural-network baselines at a far smaller interior-constraint budget. Unlike those deterministic baselines, it returns a posterior over the complex wavefield rather than a point estimate. Applied to in vivo brain magnetic resonance elastography, a proper multiscale prior reconstructs the shear curl field to a correlation of $0.77$ with measurement, above a $0.75$ target. The gain arises from the multiscale kernel rather than from real–imaginary coupling. We further identify a low-frequency accuracy ceiling set by model mismatch and a posterior uncertainty that is not yet calibrated. Calibrated uncertainty therefore emerges as the central next step for probabilistic wavefield inference in dissipative media.

Amyotrophic lateral sclerosis (ALS) is a progressive and heterogeneous neurodegenerative disease in which predicting clinically meaningful milestones, such as assistive device use, remains challenging. We developed a time-to-event, digital-twin-inspired framework that integrates longitudinal ALS Functional Rating Scale-Revised (ALSFRS-R) trajectories with survival modeling to support individualized prediction of functional decline and assistive device utilization. We constructed a harmonized longitudinal dataset by integrating diagnosis records, ALSFRS-R assessments, activities of daily living, and demographic information, followed by preprocessing to ensure data quality, temporal alignment, and cohort consistency. Correlation-based clustering identified coherent functional domains spanning bulbar, upper limb, axial, lower limb, and respiratory systems. Generalized additive mixed models characterized nonlinear, domain-specific functional decline across all domains. In addition, a temporal machine learning model was developed to predict longitudinal functional decline and capture stage-dependent disease progression. Cox proportional hazards modeling further identified lower limb function, particularly walking and stair climbing, as the strongest predictors of earlier wheelchair access. Building on these results, we implemented a digital twin-inspired temporal machine learning-based time-to-event (TTE) model that generates individualized survival curves and dynamically predicts wheelchair-free survival. This framework provides a scalable, interpretable, and clinically actionable approach for linking ALS progression with personalized decision support, with applications in proactive care planning, clinical trial stratification, and precision medicine.

Linear Independent Component Analysis (ICA) recovers jointly independent source signals from their linear mixtures. To achieve this, classical ICA algorithms attempt to maximize non-Gaussianity, measured by negentropy, which is linked to independence by information theory. Because exact negentropy optimization is intractable, they rely on proxy contrast functions, such as fourth-order cumulants and parametric log-likelihoods. We propose instead to use the squared $L_2$-Wasserstein distance to a standard Gaussian as the ICA contrast. We show that the Wasserstein distance between a standard normal distribution and linear projections of the data is maximized when the projection recovers an independent component, and that under a regularity condition on the sources this maximum is separated from every genuine mixture by an explicit margin. We uncover the advantageous properties of the resulting estimator: for sources with a smooth density it is $\sqrt{N}$-consistent and asymptotically normal with a closed-form variance, whereas for a source with an atom the contrast has a kink at the true direction, which makes the estimator exact with probability tending to one. The proposed OT-ICA algorithm finds this projection by gradient-based optimization. Empirical evaluation on simulated data shows that OT-ICA outperforms proxy-based methods and that the $W_2^2$ contrast provides more robust signal than proxy contrasts in measuring non-Gaussianity for different distributional mixtures of the latent variables. Application to linear causal disentanglement and EEG artifact removal, along with further applications detailed in the appendix, confirms OT-ICA can be used for applied ICA tasks without distributional assumptions.

Speckle noise is a multiplicative noise commonly encountered in coherent imaging modalities such as synthetic aperture radar, optical coherence tomography, and digital holography. Although deep learning methods, in practice, have achieved state-of-the-art performance for speckle denoising, their fundamental statistical limits remain largely unexplored. Unlike additive noise models, multiplicative speckle noise makes the regression function unidentifiable from the conditional mean, rendering conventional least-squares-based deep learning approaches inapplicable. We study the minimax estimation of smooth nonparametric regression functions using likelihood-based deep neural network (DNN) estimators under a model with both multiplicative speckle noise and additive Gaussian noise. Our framework accommodates both low-dimensional and sparse high-dimensional features. We establish finite-sample upper bounds on the estimation error of the proposed DNN estimators and derive minimax lower bounds for nonparametric function recovery under our model, showing that they match up to logarithmic factors in the sample size. Moreover, these minimax rates coincide, up to logarithmic factors, with those for nonparametric regression under additive Gaussian noise alone, demonstrating that the intrinsic difficulty of estimation remains essentially unchanged despite the challenges posed by multiplicative speckle noise. Numerical experiments further supports consistency of our DNN-based despeckling methods and demonstrate their effectiveness.

Longitudinal tumor measurements, dropout information, and genetic covariates provide complementary information about treatment response, but integrating these data sources within a single population modeling framework remains challenging. We extend the empirical Bayes variational autoencoder (EB-VAE) framework to joint longitudinal and time-to-event modeling and evaluate it on tumor growth data. The framework represents inter-individual variability using latent individual effects regularized by a covariate-conditioned empirical Bayes prior, while a decoder maps these latent effects to tumor-volume trajectories. To account for informative dropout, the decoder was augmented with a hazard model, yielding joint predictions of tumor growth and time to dropout. We further compared fully neural and hybrid semi-mechanistic decoder formulations and incorporated genomic covariates through a genetics-conditioned prior adaptation. The hybrid decoder recovered treatment-effect parameters broadly consistent with previously reported nonlinear mixed-effects estimates, while achieving prior predictive performance comparable to the neural decoder. The joint model reproduced both tumor-volume distributions and dropout patterns in held-out individuals, and genetic conditioning improved individual-level prior predictions in both cutaneous melanoma and breast cancer experiments. Stability selection identified several biologically plausible genetic indicators, including alterations in BRAF, NRAS, NF1, and MDM2. These results demonstrate that EB-VAE provides a flexible probabilistic framework for combining neural dynamics, mechanistic structure, time-to-event modeling, and high-dimensional covariates in pharmacometric applications.

Whistleblowers are a key safeguard against organizational wrongdoing, but the threat of retaliation deters reporting. Existing whistleblower-protection proposals lack formal privacy guarantees, and existing differential privacy mechanisms do not directly target the natural threat model – one in which the audited organization itself observes auditor selection decisions and uses them to identify reporters. We formalize protection against a strong-adversary threat model as per-report $(0, \delta)$-differential privacy on the transcript of audit selections. Within this framework we prove that a natural approach – randomized response applied at the selection step – can never outperform uniform random auditing by more than $\delta$ at any horizon. We then give a generic mechanism that reduces private auditing to private continual counting: any $(0, \delta)$-DP continual counter plugs in by post-processing, and the audit transcript inherits the same per-report guarantee. Instantiating the reduction with a recent work in continual counting yields per-report $(0, \delta)$-DP with noise scaling as $O(\sqrt{\log T})$ across a horizon of $T$ audit decisions. A utility theorem shows that the selection error vanishes whenever the noisy report gap between the most-reported organization and the runner-up grows faster than $\sqrt{\log T}$. Simulations show a substantial improvement over randomized response.

Serial verification gates are a core reliability primitive in LLM harnesses: a candidate answer is returned only if $k$ verifier calls all accept it. Under conditionally independent gates, the recent Odds Law (arXiv:2606.15712) shows that posterior log-odds grow linearly in $k$, so failure decays exponentially, and states that "a tight theory of partially correlated verifier cascades remains open." This note gives a minimal such theory. Modeling the per-instance false-accept rate on the generator's own errors as a latent variable $\alpha \sim G$ (de Finetti), the exact cascade posterior is $\ell_k = \ell_0 - \ln m_k$, with $m_k$ the $k$-th moment of $G$. Then: (i) $\ell_k$ is concave in $k$ for every non-degenerate $G$ – the Odds Law is its tangent at the first gate and an upper bound; (ii) for Beta$(a,b)$ latents, failure decays polynomially, $1-r_k \asymp k^{-b}$, with correlation parameter $\rho_v = 1/(a+b+1)$; (iii) a blind-spot atom of mass $1-\pi$ at $\alpha=1$ caps the evidence extractable from any number of gates at $-\ln(1-\pi)$ nats, so reliability saturates below 1; (iv) letting the true-accept rate also vary ($\beta \sim H$) yields a trichotomy – gates eventually always help, plateau, or actively harm – decided by the upper-tail exponents of $G$ and $H$, with closed-form crossover $k^\dagger$. The mechanism is survivorship: errors surviving gates are the high-$\alpha$ ones. The theory is measurable: $R$ repeated verdicts per instance identify the first $R$ moments of $G$, so two verdicts identify $\rho_v$; beta-binomial likelihood and NPMLE recover the reliability curve and the ill-posed ceiling. In synthetic tests, independence-based extrapolation underestimates failure by 20x at $k=5$ and ~3000x at $k=10$; the correlated fit at $R=8$ tracks held-out depths. The practical lever is decorrelation – changing model family, modality, or evidence source – not adding gates.

Artificial transaction generation remains an important source of potential market manipulation on cryptocurrency exchanges, as it may distort reported liquidity and reduce market transparency. This study proposes a diagnostic framework for detecting unusual trading patterns based on complexity and statistical-structure measures derived from high-frequency trade-level data. The analysis considers log-returns, trading volume, and transaction counts, using tail distributions, autocorrelation functions, multifractal characteristics, approximate entropy, and detrended cross-correlations. The methodology is applied to BTC, ETH, and XRP traded on Binance, Bitget, KuCoin, and Kraken over the period from April 1 to June 30, 2025. The results reveal a pronounced anomaly on Bitget for BTC and ETH after mid-May 2025. The number of transactions increases sharply, but there is no proportional increase in traded volume or return fluctuations. This regime is characterised by numerous low-volume trades, weaker autocorrelations, reduced multifractal organisation, higher short-pattern irregularity, and weaker cross-correlations involving the transaction-count series. These features are consistent with a noise-like component in trading activity and may indicate artificially increased transaction counts, although they do not provide direct proof of wash trading. The findings show that complexity-based indicators can be useful for detecting exchange-specific trading anomalies that remain hidden in price-based measures.

This paper presents a holistic systems informatics approach, i.e., Define, Measure, Analyze, Improve, and Control (DMAIC), for epidemic response and management through the intensive use of data, statistics and optimization. Despite the sustained successes of system informatics in a variety of established industries such as manufacturing, logistics, services and beyond, there is a dearth of concentrated review and application of the data-driven DMAIC approach in the context of epidemic outbreaks. First, we define specific challenges posed by epidemic outbreaks to populational health, health systems, as well as economic challenges to different industries such as retailing, education and manufacturing. Second, we present a review of medical testing and statistical sampling methods for data collection, as well as existing efforts in data management and data visualization. Third, we discuss the importance to realizing the full potential of data for epidemic insights, and emphasize the need to leverage analytical methods and tools for decision support. Fourth, an epidemic brings imperative changes to health systems. We discuss the new trend of healthcare solutions to improve system resilience, including telehealth, artificial intelligence, resource allocation, and system re-design. In closing, prescriptive approaches are discussed to optimize the health policies and action strategies for controlling the spread of virus. We posit that this work will catalyze more in-depth investigations and multi-disciplinary research efforts to accelerate the application of system informatics methods and tools in epidemic response and risk management.

Multi-object detection and tracking from noisy point clouds remain challenging in many data-scarce radar applications. Current Bayesian trackers based on Poisson measurement models offer a training-free solution but struggle to achieve accuracy and efficiency under severe clutter, large object populations, and full-resolution Doppler point clouds. We address this with PiVoT, a fast, clutter-resilient multi-object tracker for both positional and Doppler measurements. PiVoT performs end-to-end detection and tracking of a large and time-varying number of objects without external clustering or detectors, through joint inference of object states, shapes, existence probabilities, data association, and measurement rates. Its efficiency is driven by several variational inference innovations, such as theoretically justified birth pruning, quadratic-to-linear complexity reductions for exact updates, and a computationally efficient Doppler Poisson model. Experiments show that PiVoT substantially outperforms existing Bayesian trackers in challenging scenes, while also demonstrating exceptional scalability to a thousand objects, robustness to clutter visually inseparable from objects, and real-time operation on full-scale modern automotive radar datasets, where it attains performance comparable to a deep-learning detection benchmark as a training-free joint detector and tracker.

We formalize verification in causal graphical models: deciding whether a given observational formula identifies a target interventional distribution. This opens a problem complementary to identification, asking not whether any identifying formula exists, but whether the given formula is identifying. We show that even sound and complete solutions to identification do not solve verification. We propose a falsifier as a first practical route forward, prove that it induces an almost-surely correct verifier for regular exponential-family models, and use the resulting verifier to develop the gateway test, which finds all sets admissible for use in a front-door formula.

In this paper we study the problem of change point detection in functional time series where the observations are allowed to vary on both sparse and dense support. We address the problem of mean shift as well as the process volatility. Our methodology is based on the maximization of the conditional probability of change point given all the other parameters. Further, it has been proved that the proposed estimator is consistent.

Relative importance (RI) analysis quantifies each predictor's contribution to the explained variance of a linear model. General Dominance (GD), a widely used benchmark, requires evaluating $2^p-1$ sub-models and becomes computationally intensive as the number of predictors $p$ grows. Orthogonalization-Reallocation Measures (ORMs), including Relative Weights (RW) and the Green–Carroll–DeSarbo measure (GCD), provide efficient alternatives by assigning importance to orthogonalized predictors and reallocating it to the original predictors. Each, however, has a structural limitation: RW exhibits a leveling problem that compresses differences among predictor importance values, whereas GCD exhibits an a priori bias that systematically favors certain predictors before a response is observed. We show that this bias is governed by the row-sums of the reallocation matrix. A closed-form analysis under compound symmetry relates the reallocations underlying GCD and RW to a GD-based benchmark, showing that homogeneous multicollinearity alone does not induce an a priori bias and formalizing RW's leveling problem as excess shrinkage relative to the benchmark. We correct GCD's bias by mapping its reallocation matrix to a doubly stochastic matrix using the Method of Alternating Projections (MAP) and the Sinkhorn–Knopp (SK) algorithm, yielding GCD-MAP and GCD-SK. Comprehensive simulations show that GCD-SK removes the structural row-sum bias, substantially improves upon GCD, and often outperforms RW when the first principal component is dominant. We conclude with empirical guidelines for selecting among the measures.

Heavy-tailed data arise in many domains where rare events carry disproportionate importance, such as imbalanced image datasets, financial returns, and weather extremes. Standard diffusion and flow-matching models typically begin from Gaussian noise or Gaussian source distributions, which yield tractable training targets but provide a poor inductive match for heavy-tailed data. We propose Heavy-Tailed Flow Matching via Random Clocks (HTFM), a framework that portrays heavy-tailed sources as mixtures of clock-conditioned Gaussian sources. Conditioning on a given clock path, the source distribution and flow are Gaussian; marginalizing over the clock gives a Gaussian scale mixture covering Gaussian, $\alpha$-stable, and Student-t families. To make the clock-conditioned vector field practical, we encode the path-valued clock using truncated logsignature features, allowing the velocity field to adapt to the realized conditional space with negligible overhead. Empirically, on 2D imbalanced $\alpha$-stable mixtures, CIFAR10-LT, and HRRR weather fields, HTFM improves mode coverage, sample quality, and tail-statistic recovery over Gaussian flow matching and competitive heavy-tailed baselines, while retaining the low-NFE sampling advantage of flow matching. Moreover, the random-clock formulation further provides a practical tail-control interface: by varying only the clock law or tail parameter, the same architecture can calibrate the “heaviness” of generated tails across different distribution families.

We develop an efficient online algorithm to sample a sequence of discrete random variables using an entropy source of i.i.d. fair coin flips, in a standard model of real computation where real-valued probabilities are represented by rational approximations. For any sequence $F_1, F_2, \dots$ of probability distributions, our sampler generates $n$ outputs $X_1 \sim F_1, \dots, X_n \sim F_n$ using at most $\mathbb{E}\left[H(F_1) +\dots + H(F_n)\right] + O(\log n)$ coin flips in expectation while carrying $O(\log n)$ bits of persistent space, where $H$ is the Shannon entropy. Under standard assumptions, we prove that the space used by our sampler to achieve this information-theoretically optimal entropy rate is asymptotically optimal. The key idea is to replace the global arithmetic-decoding sampling scheme of Han and Hoshi (1997) with a local discrete uniform state, yielding an exponential reduction in space for a given entropy loss. Our approach applies to distributions with irrational probabilities and countably infinite supports, generalizing recent randomness-recycling methods beyond finite rational distributions with bounded denominator.

We study likelihood-ratio tests for the hypothesis that a positive-semidefinite matrix has rank at most a prescribed value. The null hypothesis is stratified: points of maximal allowed rank lie on a regular boundary stratum, whereas lower-rank points are singular. Consequently, the usual chi-bar-square calibration on the top stratum does not by itself describe the whole composite null, especially along sequences whose rank changes at the local $n^{-1/2}$ scale. After profiling regular nuisance parameters, we derive a common reduced Gaussian experiment for every fixed null rank and for all admissible local rank transitions. On the top stratum, the classical chi-bar-square law is recovered. At lower ranks, the limit generally involves projection onto a nonconvex rank-constrained semidefinite set. Our main calibration result shows that, under isotropy, the top-stratum law is least favourable over all fixed null strata and all local null rank transitions. We also prove the corresponding transition dominance under arbitrary anisotropy when the active corank is one. Finally, on the top stratum, we obtain a conditional shape derivative for the limiting distribution and its critical value. Gaussian covariance models and finite-sample experiments illustrate nuisance profiling, rank transitions, anisotropy, and orientation sensitivity.

Neural networks trained on modular arithmetic exhibit grokking, a delayed transition from memorisation to generalisation known to depend on model capacity: too little and the network memorises slowly or not at all, too much and it generalises almost immediately. What happens at the extreme of this spectrum, when the architecture's expressible function class collapses to a finite-dimensional algebraic variety? We study two-layer networks with a holomorphic monomial activation sigma(z)=z^k, trained on modular tasks encoded via roots of unity. Here the network output, regardless of hidden width, is confined to a (k+1)-dimensional subspace of characters of (Z_p)^2, an O(k/p^2) slice of the full function space. We give a complete algebraic characterisation of this subspace: a task is representable if and only if its discrete Fourier support lies on the diagonal u+v = k (mod p), which for linear-phase targets reduces to the arithmetic criterion m+n=k. This is not merely a constraint on eventual generalisation but on memorisation itself: because the outputs are algebraically confined, a non-representable target cannot be fit even on the training set, and we prove a positive lower bound on the training loss, independent of width. Across 585 runs the algebraic prediction matches the observed outcome with 99.8% accuracy, with no memorisation regime and no grokking; outcomes split cleanly into instant success and outright failure. This binary behaviour is the limiting case of the capacity-grokking relationship: when the expressible class shrinks to a fixed algebraic object, the question of when a network will grok dissolves into whether it can represent the target at all. A bottleneck ablation connects this extreme to standard networks, tracing a continuous path from representational failure, through memorisation without generalisation, to grokking with a shrinking gap as capacity grows.

Goal-conditioned reinforcement learning hinges on how the goal is encoded. Contrastive, metric, temporal-distance and information-theoretic encoders disagree on the objective. They agree on one thing. None of them sees the current state, so the embedding cannot mark which part of the goal still needs action, and the policy must recover that cue by inverting both encoders. We propose DAGR, which refines the static embedding of any late-fusion encoder into a state-conditioned one through multi-scale gated cross-attention. A gated residual holds the refinement near the base, and a difference-aware attention rule biases the scores by a per-token state-goal mismatch. A single condition decides what such a refinement can guarantee, namely whether the block returns its input at closed gates. We prove that the usual post-norm placement violates it, measure the consequence on frozen checkpoints, and recover part of the resulting loss by restoring the condition. On OGBench DAGR improves navigation and matches or trails the base elsewhere. Our ablations trace the gain to the gated residual rather than to the difference bias that names the method. Code is available at https://github.com/leixingxing1/DAGR

Large-scale approximate nearest neighbor search commonly relies on partitions for indexing: database vectors are partitioned into clusters, and for each query a probing function selects the clusters to be scanned. The query probing function and the database partition are rarely treated as separate entities: most techniques assign queries with the same assignment function as the database vectors, which is suboptimal especially when database and query distributions differ. This paper introduces CwA (Cluster with Auctions), which addresses this limitation by jointly learning a balanced database partition and a neural probing function. CwA optimizes search performance directly for the query distribution. It minimizes its objective by alternating two steps: (i) gradient descent on the neural network of the probing function, and (ii) a large-scale combinatorial optimization of the cluster assignment for the database vectors. We solve the latter with a parallelizable auction algorithm that balances the partition by design. To further scale CwA, we extend the method to a Cartesian product of clusters that increases the partition's granularity. When database and query distributions differ, CwA achieves up to 4.7$\times$ throughput over the state-of-the-art at equal recall. In the in-distribution (ID) setting, even a simple linear probing function trained with CwA outperforms competing deep neural methods.

After COVID epidemic has ravaged the world, around 20% of infected subjects continue to manifest symptoms several months after their cure. This disorder is called long COVID. This paper presents a study carried out at the University Hospital of Ourense with the aim of establishing a relationship among the disease and variations in Heart rate variability (HRV) parameters using machine learning (ML). Five heart rate recordings were obtained per subject, both at rest and under conditions of physical effort and stress. Each record was processed and 15 HRV indices were extracted, giving 75 features per patient. Of these features, 16 were selected to train 10 different ML models: Support Vector Classification, Linear Support Vector Classification, Logistic Regression, Linear Discriminant Analysis, Stochastic Gradient Descent, Multiple Layer Perceptron, Naive Bayes, Random Forest, and Gradient and ADA Boost Classifiers. Results show that the best model, Gradient Boost, achieves an accuracy of 85.2%, F1-score of 84.9%, and an Area Under the Receiver Operating Characteristic Curve (AUC) of 0.907, and that all models exceed 0.833 AUC. This study demonstrates an association between long COVID and heart rate variability (HRV), highlighting the utility of machine learning models in identifying this relationship and supporting its diagnose.

Fréchet means and $L^p$ centres of mass provide notions of average location in metric spaces. On finite-dimensional spheres, existence follows from compactness. On infinite-dimensional spheres, it is not known whether a centre of mass always exists. We show that this is not always the case, and give a simple assumption under which a centre of mass exists. We then show that finding the sample centre of mass of data $x_1, \ldots, x_n$ on the sphere is always an optimisation problem on a subsphere of manifold dimension at most $n$, regardless of the potentially infinite dimension of the sphere. We conclude with some statistical implications.

Recovering a latent potential from observed flow on a directed graph (a discrete Poisson problem with Dirichlet boundaries) is ill-posed, and the standard fix backfires: ridge regularization shrinks toward a gauge-meaningless origin, collapsing and reversing the recovered ordering ($+0.81\to-0.42$ rank correlation against a planted ground truth). The gauge-invariant graph Dirichlet energy removes the hazard and delivers parameter-insensitivity: the estimate is stable across four orders of magnitude in $\lambda$, whereas ridge inverts the ordering for every $\lambda>0$. We prove the reduced solve is SPD and preserves dynamic range exactly where ridge collapses it, and localize absorbing boundaries from flow alone via a Poisson residual. The $H^1$ seminorm is classical; what is new is the gauge diagnosis, the parameter-insensitivity it buys, and an ablation showing the result is robust to the extraction method. On three public clickstream corpora the gauge-invariant estimate retains $28$–$41\%$ of the interior dynamic range while ridge collapses to as little as $0.2\%$. The same gauge invariance carries into graph neural networks – neutralizing the constant mode per layer prevents the oversmoothing that collapses a deep directed GCN – linking this classical inverse problem to a central question in graph learning.

Systematic comparisons between current situations and structurally similar past events in the historical, i.e., historical analogies, is among the most powerful tools for foresight analysis. In this work, we present a new task called Analogical Deep Research (ADR) to Large Language Model (LLM) agents and construct the first ADR benchmark ADR-bench to study whether LLM agents are able to find and leverage historical analogies when doing foresight analysis. Our investigation reveals a key obstacle: LLM agents are poor at finding analogies because they match on surface features rather than underlying mechanisms. We argue that ADR is inherently a causal question as it requires understanding why the event occurred. Based on our theoretical analysis, we propose two principles required for ADR, including the mechanism alignment and cross-analogy confirmation. Built upon our theoretical results, we propose a new agentic framework called Causal Analogical Researcher (CANA) that guides LLMs to find and integrate historical analogies. CANA incorporates a simple yet effective structural decomposition representation, and integrates structural feedback for reflective improvements of historical analogy identification and integration. We show that CANA brings up to 10% improvements in historical analogy generation, and surpasses the state-of-the-art deep research agents in the ADR-bench. Case studies with the ongoing events confirm the effectiveness of CANA in leveraging historical analogies.

This paper addresses the problem of running variable manipulation in Regression Discontinuity Designs. Leveraging the observation that manipulation often alters the density balance around the cutoff, we detect these structural imbalances using Benford's Law -a natural statistical regularity widely applied in fraud detection. Our framework serves as a vital precautionary safeguard alongside traditional McCrary-type tests. It eliminates researcher-chosen parameters that can skew outcomes, while delivering a deeper diagnostic breakdown of the density's behavior. Crucially, whereas the classic McCrary test can overlook systemic imbalances due to its rigid symmetric setup, our method separates the data into directional components. This allows researchers to pinpoint the exact origin of a deviation and spot hidden manipulation that standard frameworks fail to capture. To achieve this, we introduce an innovative method for selecting a bandwidth consistent with BL, and construct two distinct, complementary tests using threshold values adapted from Nigrini (2012) that successfully transition the law's application from digits to probabilities. Empirical applications confirm the enhanced protective value of this diagnostic framework.

Boosting is one of the most successful learning techniques for standard classification and regression tasks. Its extension to multi-output prediction problems has found an increasing number of applications in recent years. Among them is the prediction of entire conditional distributions rather than single functionals, which can often be framed as a multi-output regression problem, for example multiple quantile regression. Addressing such problems with classical implementations of boosting is computationally challenging, because usually one base model is trained for each target at every iteration. More efficient variants of boosting have been proposed to speed up training, but they tend to be tied to specific loss functions and classes of base learners, usually decision trees. In this work, we study a modification of the gradient boosting algorithm, which we call parallel gradient boosting, designed to circumvent all these limitations. The core idea is to use a common descent direction for all training observations. By doing so, only one base model is needed at each iteration, regardless of the number of targets, which allows for considerable performance gains. We establish sufficient conditions for the convergence of the algorithm, whose practical use is introduced via the multiple quantile regression setting. We show that in such a setting, it provides predictions of similar quality to state-of-the-art boosting libraries such as XGBoost, while being faster by several orders of magnitude. Then, we evaluate the properties of the resulting conditional distribution estimator, which is shown empirically to outperform other nonparametric and semiparametric estimators, especially in high-dimensional settings and in the presence of mixed and/or missing covariates.

Non-expansive two-time-scale stochastic approximation is governed by a slow stochastic Krasnoselskii–Mann fixed-point iteration rather than by contraction to a unique equilibrium. We study this regime under a contractive fast map and a non-expansive reduced slow map. We first prove a finite-horizon lower bound showing that, for any prescribed slow stepsize schedule $(\beta_k)$, the classical KM residual scale $(\sum_{i<N}\beta_i(1-\beta_i))^{-1}$ is worst-case sharp for the corresponding unregularized KM update. Combined with the raw fast-tracking leakage scale, this explains the previously observed $k^{-1/4+o(1)}$ last-iterate mean-square residual exponent. We then introduce a residual-preconditioned slow oracle that cancels the first-order dependence on the fast tracking error. In a nested Tikhonov-KM algorithm, the uncorrected oracle yields total-sample rate $T^{-1/4+o(1)}$, while the corrected oracle yields $T^{-1/3+o(1)}$. This improvement comes from changing the slow-oracle bias from first order to second order in the fast error after all inner-loop samples are counted. Finally, we show that the repeated inner-loop cost of the nested method can be avoided in a smooth derivative-oracle model. A single-loop algorithm that tracks both the fast equilibrium and the leakage preconditioner online achieves $T^{-1/2+o(1)}$ with $O(1)$ primitive samples per iteration.

In bandit problems, standard regret-minimizing algorithms treat exploration as an amortized cost, which can expose early participants to unfair ex-ante losses in settings such as clinical trials. Recent work addresses this by evaluating the sequence of per-round expected rewards through the generalized $p$-mean, interpolating between utilitarian welfare ($p=1$), Nash welfare ($p\to0$), and Rawlsian fairness ($p\to-\infty$). Although tight guarantees are known for $p\ge0$, the strictly fair regime $q=-p>0$ remains unresolved because negative-power means are dominated by the smallest per-round rewards. For $\sigma$-sub-Gaussian rewards with nonnegative means, the best prior algorithm relied on uniform early exploration and achieved regret $O(k^{(q+1)/2}/\sqrt{T})$, while the only general lower bound was the classical $\Omega(\sigma\sqrt{k/T})$. Thus it was unclear whether the extra dependence on $k$ was intrinsic to strict fairness or an artifact of uniform exploration. We close this gap by identifying the exact polynomial price of strict fairness. Using a needle-in-haystack construction, we prove an algorithm-independent lower bound $\Omega(\sigma\sqrt{k^{\max(1,q)}/T})$; for $q>1$, this shows that the penalty $k^{q/2}$ is information-theoretically unavoidable. We then introduce UCB-HARE (Harmonic Anchored Rank Exploration), which replaces uniform exploration with an inverse-weighted harmonic rank schedule protected by a certified positive-mean anchor. Its regret is $\widetilde{O}(\sigma\sqrt{k^{\max(1,q)}/T})$, matching the lower bound up to logarithmic factors. Experiments on synthetic instances confirm that UCB-HARE improves over uniform-exploration baselines, with gains increasing as $q$ grows.

We propose an interpretable machine-learning framework for dynamic hedging using the Itô signature transform, which turns asset-price paths into a set of linear features that universally represent nonlinear functions on time-series. We show that each discretized Itô signature component can be perfectly replicated by a simple self-financing strategy using only the underlying assets and cash, which turns Itô signature components into tradable and transparent hedging bases. This allows nonlinear derivative payoffs to be approximated by linear combinations of signature terms and hedged through the corresponding combination of trading strategies. We further establish a new approximation result for the Itô signature and derive theoretical bounds for both in-sample and out-of-sample hedging errors. Our method is computationally efficient, easy to implement, and avoids the estimation of future conditional expectations, which makes it attractive for real-world applications. In simulations, our method delivers strong sample efficiency at substantially lower computational cost than neural-network benchmarks. In an empirical study of S&P 500 index options, it performs robustly across vanilla and path-dependent contracts, with the signature-kernel weighted version providing further gains by localizing estimation to similar historical market paths. Overall, the paper identifies the Itô signature as a practical, transparent, and model-agnostic implementation framework for dynamic hedging.

XGBoost is a very popular and powerful method for prediction. It iteratively fits simple decision trees to the residuals of the previous step. An efficient and scalable implementation is available. The standard loss function for XGBoost is the quadratic loss, but a Huber loss can also be used. In this paper, we study the robustness of XGBoost and show that its performance can be affected by vertical outliers and leverage points. To address this, we explore alternative loss functions, based on M-, S-, and {\tau} -estimators from robust regression. Our results indicate that a two-step procedure, referred to as MM-XGBoost, provides the best trade-off between robustness and prediction accuracy.