Papers

Active Inference (AIF) frames adaptive behavior as the minimization of expected free energy (EFE), combining epistemic and pragmatic objectives within a single variational principle. We frame AIF as policy optimization and show that, for closed-loop control policies, EFE minimization can be formulated as a convex Markov decision process (MDP). This perspective reveals that policy-dependent reward prediction errors transmit natural gradients of the expected free energy backwards in time rather than up a hierarchy. Finally, we show that coupling world-model learning with policy optimization gives active inference the structure of performative reinforcement learning. Together this places EFE minimization within modern reinforcement learning and optimization theory and opens a route toward principled algorithms for active inference.

We introduce the Directional Kernel Mean Difference (DKMD), a signed statistic for univariate distribution comparison that preserves the direction of distributional shifts. Unlike the squared Maximum Mean Discrepancy (MMD), which discards directional information by squaring the RKHS distance, DKMD integrates the difference of kernel mean embeddings against a fixed odd weighting function. This construction yields three structural properties: antisymmetry, immunity to symmetric distributional differences, and directional monotonicity under stochastic dominance. We derive a data-driven Riemann estimator that ensures asymptotic consistency with the continuous formulation, strictly preserving the theoretical guarantees of the signed statistic in empirical evaluations. To overcome the quadratic computational cost of kernel methods, we develop an $O(N \log N)$ prefix–suffix scanning algorithm that exploits the total order of the real line while requiring only $O(N)$ memory. Experiments on synthetic benchmarks demonstrate that DKMD correctly isolates directional shifts from symmetric perturbations, remains robust to heavy-tailed outliers that can flip the sign of the mean difference, and scales to millions of samples in seconds.

Non–negative matrix factorization (NMF) has become an established dimensionality reduction technique for extracting latent structures from non–negative data and has found widespread applications in fields such as bioinformatics, text mining, image analysis, and recommender systems. As the popularity of NMF has increased, numerous R packages implementing different optimization strategies and computational frameworks have been developed. Despite their widespread availability, comprehensive evaluations of these implementations under real–world data conditions remain limited. Consequently, researchers often lack objective guidance when selecting an appropriate package for practical applications. This study introduces a new R package for NMF and offers asystematic performance comparison with two widely available R packages for NMF analysis. Rather than relying on simulated datasets, the evaluation is conducted using real–world data to better reflect the complexity, heterogeneity, and noise characteristics encountered in practical analytical settings. The packages are assessed using a consistent experimental framework, with emphasis on computational efficiency, convergence behavior, reconstruction accuracy, memory utilization, and the stability of the resulting matrix factorization.

We present an R and Python package for fast online changepoint detection in univariate and multivariate data streams for a variety of models. The package implements the focus family of algorithms, which compute the Generalised Likelihood Ratio test for a single changepoint exactly and efficiently, with a per-iteration cost of approximately $\log(n)^d$ for a d-dimensional sequence, without introducing approximations. This is achieved by exploiting a connection between the location of the changepoint candidates and the geometry of the data. The package supports a broad range of models from the natural exponential family, including Gaussian, Poisson, Binomial, Exponential and Gamma distributions, as well as a non-parametric detector based on the empirical cumulative distribution function and a detector for autoregressive data.

We study horizon-free regret minimization for finite-horizon time-homogeneous tabular Markov decision processes with $S$ states, $A$ actions, horizon $H$, and per-trajectory total reward bounded by $1$. We propose a new algorithm and prove a regret upper bound \[\tilde O(\sqrt{SAK}+S^8A^3)\] with failure probability $\delta$, where $K$ is the number of episodes and $\tilde O(\cdot)$ hides $\mathsf{poly}\log(S,A,K,1/\delta)$. Thus, the regret is $H$-free and asymptotically optimal, matching the contextual-bandit lower bound $\Omega(\sqrt{SAK})$ up to logarithmic factors. This completely removes the $\log H$ dependence from the previous $\tilde O(\sqrt{SAK\log H}+S^2A\log H)$ guarantee of Zhang et al. (2021), and drastically improves the prior best horizon-free regret $\tilde O(\sqrt{S^9A^3K})$ of Zhang et al. (2022) asymptotically. The main technical difficulty is that the optimal value functions $\{V_h^*\}_{h=1}^H$ are time-inhomogeneous even though the transition kernel is time-homogeneous. A direct union bound over all value functions typically incurs an additional $\min\{\log H,S\}$ factor. We avoid this factor by (i) exploiting the monotonicity of $V_h^*$ in $h$ and (ii) non-trivially projecting the value functions onto an $S$-dimensional grid. Our analysis relies on three additional ingredients. First, we introduce a horizon-truncation argument that enables reward-based exploration and removes the cost of a separate reward-free exploration phase. Second, we design a cutting bonus that preserves both optimism and the monotonicity needed for planning. Third, we prove a new bound on total deviation for time-homogeneous MDPs, which controls the clipped variance terms in the cutting bonus with adjustable polynomial dependence on $S$ and without any dependence on $H$. Together, these tools yield an asymptotically optimal horizon-free regret guarantee.

Martingale posteriors quantify uncertainty by forward-imputing observations from one-step-ahead predictive distributions, but implementations stop after finitely many imputations. For the empirical Pólya-urn posterior of a quantile the law of the stopped state is derived. The quantile of the stopped urn measure keeps the familiar martingale tail-sum variance fraction; the deployed stochastic-approximation tracker with frozen gain $c$ does not. Its variance carries an explicit factor $G_a$ with $a=cf_0(q_\tau)$, which may fall below or exceed the tail fraction, and a density-adapted gain restores calibration through a density-free inflation. Shared urn innovations yield the joint law of finitely many quantile levels. For conditional quantile regression, a smoothed martingale posterior started at the ordinary quantile-regression estimator with a full inverse-Jacobian matrix gain satisfies a process Bernstein–von Mises theorem with calibrated finite-horizon bands; scalar or diagonal gains cannot match the sandwich covariance process.

We develop a theory of nonlinear shrinkage covariance estimation for nonparanormal (Gaussian-copula) models, in which each observed coordinate is an unknown strictly increasing transformation of a latent Gaussian vector. This model accommodates arbitrary marginal skewness and heavy marginal tails while retaining a Gaussian dependence structure, and it is the natural semiparametric setting for heavy-tailed, asymmetric financial returns. Our estimator, marginal-free nonlinear shrinkage (MENS), applies an oracle nonlinear shrinkage function to the eigenvalues of the normal-scores rank-covariance matrix. We give the almost-sure convergence of the empirical spectral distribution of the normal-scores covariance to the generalized Marchenko-Pastur law of Sigma, and asymptotic optimality of MENS among rotation-equivariant estimators under Frobenius loss. We establish a Baik-Ben Arous-Peche phase transition for spiked latent correlations. The MENS attains the robustness of rank-based estimation and the efficiency of nonlinear shrinkage at once within this class. We corroborate the theory with a simulation study that isolates the marginal-invariance property and the spiked transition. In an out-of-sample minimum-variance backtest on S&P 500 stocks, MENS delivers a better-conditioned covariance estimate, lower realized portfolio volatility, and lower turnover than linear shrinkage, illustrating its practical value for high-dimensional allocation and decision-making.

The 2026 FIFA World Cup was the first to mandate hydration breaks, brief stoppages near the twenty-second minute of each half, in every match regardless of weather. A widespread claim holds that these breaks blunt the momentum of whichever side is dominant. We test the claim with a within-match case-crossover design, using non-break minutes of the same match as self-matched controls. This differences out every match-level characteristic and adjusts only for game time, scoreline, and pre-break momentum state. The apparent post-break fade is not caused by the break: the dominant side's momentum decays at essentially the same rate whether or not a break occurs, reverting through the stoppage as if play had continued. What the break removes instead is the continuation of that side's pressure during the stopped minutes, and this leaves no trace in net expected goals. The average effect is only weakly identified, resting on a trend extrapolation into a window with no untreated minutes, whereas break-by-covariate interactions are stable; that average is small and near zero. With only 99 matches the design lacks power to reject a small effect, so we read the results by effect size and confidence interval. The estimates are not uniform across match states. The clearest modifier is team strength: the break effect shifts by about +1.6 momentum points per 100 Elo points of rating advantage, favouring a stronger in-form side over a weaker side that is momentarily dominant, and it is the only statistically significant interaction. A weaker pattern appears by scoreline, where a comfortably-leading side of average strength shows an implied loss near -4 points on a pre-break level of about +20. We report these state-dependent signals as exploratory and in need of replication.

The Lorenz curve is a fundamental tool for measuring inequality, but its extension to multivariate settings remains challenging due to the complex dependence structure among variables and the need to capture directional aspects of inequality. In this paper, we introduce a novel vector-valued bivariate Lorenz surface (VBLS) based on conditional distributions and conditional quantile functions. Unlike existing symmetric bivariate Lorenz surfaces, the proposed VBLS effectively captures the directional inequality arising from the conditional dependence between two variables. We establish several fundamental properties of the proposed surface and investigate its mathematical properties. The corresponding egalitarian surface is defined, leading to the development of associated vector-valued bivariate Gini measures for quantifying inequality. We further derive characterization results that demonstrate the uniqueness of the proposed VBLS within the underlying distributional framework. Nonparametric estimators of the VBLS are developed and their finite-sample performance is evaluated through a simulation study. The usefulness of the proposed methodology is also illustrated with applications to income inequality and actuarial data.

The wind energy industry relies on accurate power curve models to make power forecast, evaluate turbine performance, quantify upgrade, or support site-planning decisions. In this paper, we focus on site-planning power curves, i.e., we investigate how power curve models trained using turbine data on an operating wind farm can be transferred to a new, undeveloped farm. The traditional wisdom in the wind energy literature relies on distance, layout, or terrain characteristics for making cross-farm power curve transfer. Through the lens of domain adaptation, we propose a more reliable transfer learning approach for cross-farm power curve modeling. In the cross-farm applications, a domain is specified by the temporal environmental variates and spatial terrain variables. Domain adaptation is to find a capable similarity metric to adapt the domain on the new farm to that on the existing farm. Empirical results show that our domain adapted power curve consistently outperforms competing approaches by an appreciable margin for site-planning power predictions.

Estimating population abundance from field surveys is often complicated by interference between multiple survey protocols. In this paper, we propose a two-stage estimation framework for abundance models in which detection processes interact, leading to both missed detections and sample loss caused by survey procedures. Our approach separates the calibration of sample loss from the estimation of detection probability, thereby avoiding the feedback and weak identifiability that can arise in fully joint hierarchical models. We further derive a sandwich-type robust variance estimator that propagates first-stage uncertainty into the second stage and remains valid under certain forms of model misspecification. Simulation studies demonstrated that the proposed method provides more reliable uncertainty quantification than a Bayesian hierarchical joint model, which tends to underestimate uncertainty even under correct specification. We illustrate the practical utility of the method using ectoparasite abundance data from the invasive Pallas's squirrel Callosciurus erythraeus.

LLMs can be prohibitively expensive and slow to run at scale, especially for applications that invoke an LLM per sample over millions of inputs. A natural way to scale is to cluster the inputs, run the LLM only on cluster representatives, and propagate the outputs to other cluster members. However, the outputs a member receives are only as good as its match to the representative. Off-the-shelf clustering methods optimize an aggregate objective, targeting average-case quality without per-sample guardrails. As a result, members can be assigned to poorly-matched representatives, and the inherited outputs – though appropriate for the representative – may be irrelevant or even unsafe for the member. For example, a parent of a toddler grouped with parents of older children could receive age-inappropriate recommendations. Most clustering methods also scale poorly to millions of inputs in runtime and memory, limiting their use at industry scale. We propose a scalable two-stage clustering algorithm with provable per-sample guardrails: every sample is guaranteed to share a user-specified minimal embedding similarity and exact attribute match with its representative. The algorithm first generates initial clusters with Mini-batch K-Means, then greedily selects representatives within each to satisfy the guardrails. We provide theoretical guarantees, complexity analysis, and benchmarks against common methods on internal and public datasets. Our method delivers per-sample guardrails while running substantially faster and scaling to data sizes where most standard methods become intractable. We demonstrate its impact in a real-world deployment clustering 38 million customers, reducing downstream LLM cost and runtime by 50-fold while preserving personalization. This unblocked the launch of a persona-based recommender system that delivers significant gains in revenue and engagement in an A/B test.

Observational causal analyses increasingly pool records across sites, vendors, and collection systems, creating vulnerability to append-only attacks in which plausible records are strategically selected to alter a reported treatment effect. We develop a data-poisoning audit for augmented inverse-probability-weighted estimation. The analyst specifies a finite catalog of feasible records, an append budget, and nested source capacities, and the adversary selects a feasible subset to maximize movement in a prespecified direction. With preprocessing and nuisance fits held fixed, we propose a greedy scan that computes the exact finite-sample worst-case movement at every append budget. To account for nuisance refitting, we go on to derive a total-influence score combining each record's direct contribution with its effect through the propensity and outcome models. We further obtain a conservative finite-budget bound for the fully refitted estimate. Extensive simulations validate the exact result and show that total influence improves local refit prediction, while multisite and public-data analyses demonstrate material sensitivity at small append budgets. By translating adversarial data-composition risk into movement curves and critical budgets, the framework supports more reliable causal reporting and the design of source-level safeguards.

We study the problem of recalibrating an online predictor [KE17, OKS24]: given an arbitrary "hint" sequence of forecasts, the learner must output new predictions that are calibrated while incurring small excess error relative to the original forecasts, under a proper loss. We give an online algorithm that achieves $(\varepsilon, \varepsilon^2)$-recalibration for Lipschitz proper losses in $T \approx \varepsilon^{-3}$ rounds, using an imbalanced extension of the recent simultaneous Blackwell approachability reduction framework of [HTY26]. We show that this tradeoff is optimal by proving a matching lower bound for recalibrating against the squared loss. We also prove a companion $\mathcal{K}_2$-recalibration theorem that obtains the same tradeoffs up to a logarithmic factor. As our main application, we show how our recalibration algorithms can be combined with the online refinement method of [FH23] to obtain simultaneous $\varepsilon$-calibration and $\varepsilon^2$-calibeating for smooth proper losses at the same asymptotic rate, improving upon prior works that achieved these properties separately or with a worse $\varepsilon$ dependence. In particular, the $\mathcal{K}_2$ variant answers a question of [CHJL26] on simultaneously achieving near-optimal calibeating and calibration rates. We also derive extensions to settings with multiple hint sequences. Finally, we empirically evaluate our algorithms on a classification dataset undergoing distribution shift.

Complex risk arises when interacting hazards, infrastructures, ecological systems, institutions, and human behaviors produce nonlinear impacts that cannot be inferred from any component in isolation. We call the study of these dynamics complex risk science. Flourishing is the actualization of all beings toward their good–individually and collectively–answering the question of `how do we live well with and for each other?'. In science as in society, the tendency to reduce, segregate, specialize, and settle has precluded embracing the concept of flourishing as a guiding principle. We describe how complex risk science reframes risk science research so that it can promote the flourishing of socio-ecological-technological systems, and explore how its practice may point society toward a more flourishing future. Our exploration mirrors the unsettled and searching nature of flourishing: examine ideologies traditionally believed to be rigidly in opposition and consider what emerges in the space(s) and conversation between them. We call this a dialectical approach: not a means of resolving contradiction, but a practice of sustaining it, so that systems, and our understanding of them, remain capable of reframing as conditions change. Within this dialectical paradigm, we revisit longstanding tensions in risk science: physical|social, determinism|uncertainty, and contextuality|generality. Examining the conversation among these tensions reveals five seeds that are dispositions for practicing complex risk science: interdependence, responsivity, participation, pluralism, and ongoingness. They can support any scientific endeavor to embrace complexity and promote flourishing. Practicing these seeds at scale will depend on institutional reform: creating collectives toward complex risk science, supporting them with skillfully governed commons, and centering care in our research and evaluation.

Li and Matin (2005a, 2005b) reported three regularities of the induced visually-perceived vertical (VPV), the direction judged upright. For small tilts, a peripheral line shifts it nearly linearly with tilt, two lines combine nearly linearly, and mirror-image tilts cancel. Each line votes at twice its angle, weighted by its strength. The votes' vector sum $c_1$ is the first circular moment of the doubled angles; half its angle, $\phi=\tfrac12\arg c_1$, is the induced vertical, a stimulus axis, not the judged upright. This is the orientation order-parameter model (PLUMB). We prove that $c_1$ is, up to a constant factor, the only additive summary of axes (lines without arrowheads) that scales with line strength and turns twice as far as the field rotates. With Li and Matin's own length gain and no per-configuration fit, the model matches their multiline coefficients in-sample. Their data rule out complete summation but not simple averaging for long lines. But a line's effect is fourfold (period $90^\circ$): it reverses past $45^\circ$ (Li and Matin, 2005a; Vingerhoets et al., 2009), and near-horizontal lines shift VPV as near-vertical ones do, which $c_1$ forbids. In a two-harmonic fit to Li and Matin's data, $c_1$ carries an estimated 2–4% of a near-vertical line's slope and a fourfold term the rest. To first order in tilt, for near-vertical segments, the readout equals the committee rule Shavit, Li, and Matin (2026) fit to eight line-array experiments, with its drives read as concentrations. If the half-fields' signals are read as sum and difference, perceived eye level (VPEL) is the difference, recovering Shavit, Li, and Matin's (2013) reversed integration rules; a fourfold term gives the same signals, so this does not single out $c_1$. Re-analysed data (30 observers) show the predicted signs and nulls, an internal check only; the cross-field gain is fitted.

In multivariate extreme value analysis, the tail dependence between some of the risk variables at hand may be weak, even when other variables do tend to become large simultaneously. Weak tail dependence may induce a substantial bias in estimation procedures based on the limiting multivariate (generalized) Pareto distribution of excesses over high thresholds. We consider a Hüsler–Reiss multivariate generalized Pareto model and, motivated by this issue, propose first- and second-order moment estimators of its variogram matrix constructed from a lower-tail-clipped version of the underlying random vector. The asymptotic normality of the proposed estimators is established. We demonstrate by simulation studies that they have lower bias than the empirical variogram estimator in certain cases, particularly when the dependence between components is weak. The estimators are applied to flood discharge data from the Danube river basin and the US flight delay data, showing that the tail dependence structure implied by the fitted model based on the first-order clipped moment estimator aligns more closely with the empirical tail dependence of the data than that based on the empirical variogram estimator.

Difference-in-differences with staggered adoption identifies group-time average treatment effects ATT(g,t) by comparing each cohort to units not yet treated, which avoids the "forbidden comparisons" that bias two-way fixed-effects estimators when effects are heterogeneous. This paper studies the covariate-conditional version of that object, tau_{g,t}(x), and estimates it with a fixed-effects causal forest. Within each (g,t) comparison block, the outcome and treatment are residualized on unit and period fixed effects inside each tree node, and honest causal trees split on treatment-effect heterogeneity in the covariates. The estimand is not new: Hatamyar, Kreif, Rocha and Huber (2023) introduced it using a doubly-robust R-learner, and Imai, Qin and Yanagi (2023) study it for a single continuous covariate. What we add is a different way to estimate it. Where those methods remove confounding by modeling nuisance functions, we remove it by differencing out unit and period effects within each tree node, following the fixed-effects residualization of Kattenberg, Scheer and Thiel (2023) and Gavrilova, Langorgen and Zoutman (2025) and carrying it into the Callaway-Sant'Anna group-time structure. In Monte Carlo experiments the estimator is the only forest-based method that stays unbiased and correctly covered for the overall effect under staggered timing with cohort-varying effects; two-way fixed effects and a pooled causal forest inherit large forbidden-comparison bias. We apply the method to the Callaway-Sant'Anna minimum-wage panel as a validation and to the staggered county-level rollout of the ACA Medicaid expansion, where it recovers an average 2.25 percentage-point fall in the uninsured rate and a conditional surface on which poorer and lower-income counties gained substantially more coverage – heterogeneity measured along socioeconomic covariates that are not lags of the outcome.

Linear probing is the standard instrument for detecting social biases in the hidden representations of large language models. Yet reported probe accuracies come almost exclusively from counterfactual evaluations in which every input carries an explicit demographic marker. Once only a fraction $\alpha$ of inputs carries demographic information, performance degrades sharply, and a weak probe may reflect either an unbiased model or an underpowered detector. We develop a theory that resolves this ambiguity. Modeling representations as two class-conditional clusters with Mahalanobis separation $s$ on a manifold of curvature $\kap$, we prove: (i) a finite-sample generalization bound governed by the manifold's extrinsic radius with a matching $\smash{\sqrt{\dB/n}}$ minimax lower bound; (ii) an exact purity law for the maximum linear-probe AUC, strictly increasing in $\alpha$; (iii) a curvature ceiling: ambient chordal separation on a space form cannot exceed $2/\sqrt{\kap}$; and (iv) a detectability threshold below which no audit can distinguish probe output from chance. Every theorem is validated on synthetic manifolds with known ground truth and on six open-weight models $\times$ four bias dimensions, where the purity law predicts entire AUC–$\alpha$ curves from a single cross-fitted $\hat s$ measured at $\alpha=1$, with no parameters fitted to those curves. The framework turns bias auditing into a power analysis: given a target purity and effect size, it prescribes the sample budget $n(\alpha)$ for a conclusive audit.

We develop nonparametric inference for reliability indicators of discrete-time semi-Markov systems from independent trajectories observed over a common fixed horizon. Augmenting the physical state by the backward recurrence time yields a finite coupled Markov representation on the observed age range. We distinguish the resulting age-restricted failure-or-exit time from calendar truncation, since these two finite-horizon quantities coincide only in special cases. The framework covers restricted factorial moments and moment characteristics, calendar-truncated failure-time summaries, and the discrete-time intensity of the hitting time. Under explicit row-exposure conditions, strong consistency and joint asymptotic normality are established for the empirical initial law, the required transition rows and the corresponding plug-in functionals. The Gaussian random-matrix representation gives pointwise and joint covariance formulas, simultaneous confidence envelopes, Wald procedures for linear summaries, and curvature-adjusted Gaussian approximations. Restriction diagnostics and a target-specific horizon-selection rule based on exposure, boundary interaction and nested-horizon stability are developed separately. Numerical experiments assess the inferential formulas and the diagnostics, while a complete-case illustration from the European Group for Blood and Marrow Transplantation reports calendar-truncated failure-time summaries and finite-dimensional hitting intensities.

Refinement operators generate many functions used in wavelet constructions, subdivision schemes, and geometric modeling. Their finite iterates can develop rapidly increasing numbers of linear pieces, making them a natural test case for the expressive power of deep neural networks. Earlier work showed that, for scalar binary refinement with a finitely supported mask, every compactly supported continuous piecewise linear seed has finite refinement iterates that admit exact ReLU realizations of fixed width and depth growing linearly with the number of refinement steps. The present paper gives a new construction of this known theorem. The difficulty is that the refinement cascade is driven by discontinuous binary digit choices, whereas ReLU networks produce continuous piecewise linear maps. We represent the residual dynamics on a polygonal model of the circle and describe each residual position in two overlapping coordinate systems, one ordinary and one shifted by one half. Their discontinuities occur at different points. The network switches between the two descriptions only where both are valid and the corresponding fixed linear cascade updates agree, so the switch is exact and requires no multiplication by a variable selector. The construction also gives exact readout of every continuous piecewise linear circle function satisfying the natural endpoint compatibility condition. Localized seeds are handled by a two-pass network, and translation covariance, finite decomposition, and gluing extend the result to arbitrary compactly supported continuous piecewise linear seeds in a preserved support window.

Existing adaptive inference methods for Large Language Models rely on observational heuristics, such as hidden-state similarity or activation magnitudes, to drop redundant modules. However, these correlation-based metrics often fail to capture subtle, non-linear structural computations vital for semantic accuracy. We introduce CausalGate, an intervention-guided framework for compute-efficient transformer inference. During a calibration phase, CausalGate isolates individual Attention and MLP sub-layers, zeros out their respective outputs, and measures the exact semantic damage via the Kullback-Leibler divergence of the final logit distribution. To eliminate runtime routing overhead, this structural importance hierarchy is distilled into a global set of static, lightweight scalar gates using an Exponential Moving Average smoothing objective paired with a differentiable pairwise ranking loss. Evaluated on TinyLlama-1.1B, Qwen2.5-3B, and Llama-3.1-8B across language modeling and commonsense reasoning benchmarks, CausalGate consistently outperforms prominent dynamic routing and layer-skipping baselines, translating theoretical compute savings into concrete hardware latency reductions with zero operational overhead.

Estimating causal effects under interference is a common problem in social science and economics. However, it is challenging due to the complex dependency structure induced by network connections. In this paper, we propose GAUGER, a Generalized regression Adjustment framework via Graph-weighted Exposure-level Residualization for design-based causal inference under general interference. We first reveal a surprising mismatch between accuracy and efficiency in this setting: model adjustments that minimize prediction error (e.g., MSE) do not necessarily lead to the most variance reduction of the treatment effect estimator. To address this mismatch, we propose a two-step approach: (1) leveraging a strong prediction model to learn outcome patterns from the network and covariates, and (2) applying a novel calibration scheme called Graph-weighted Exposure-level Residualization (GER) that directly targets variance reduction. The resulting estimator is consistent for target causal parameters, enjoys provable variance reduction, and is asymptotically normal with a conservative variance estimator for valid statistical inference. As a practical implementation of the pipeline, we present a scheme that leverages Graph Neural Networks (GNNs) to construct the prediction model and use GER to steer the model adjustment for better variance reduction. Numerical studies show substantial efficiency gains over existing methods.

Meta-analysts routinely test for publication bias, but a nonsignificant test is inconclusive because it may be a Type 2 error. In a large factorial simulation, I show that publication-bias tests have low power even with 1,000 studies once effect sizes are heterogeneous and the data do not meet the model's assumptions. I argue that the goal should shift from detecting bias to estimating it with confidence intervals. A confidence interval does not only bound the hypothesis that bias is absent; its upper bound also indicates how much bias remains compatible with the data. When the interval is wide, the upper bound does not exclude a large amount of bias, even if the formal test is nonsignificant. I then show that confidence intervals from step-function selection models are too narrow, covering the true amount of bias only about half the time. In contrast, z-curve's confidence interval obtained by transforming the expected discovery rate into a selection weight parameter has nominal coverage. Z-curve is therefore a valuable tool for examining publication bias in meta-analyses, especially when heterogeneity is high. I illustrate the implications of bias estimation with a meta-analysis of social priming and a set of applied-psychology meta-analyses.

The shape of a planar curve is the geometric information that remains once translation, rotation, scale and reparametrisation are removed and is of interest in many health applications, e.g. in neuroimaging. We propose a deep shape regression model for open planar curves that admits multimodal and high-dimensional covariates. Representing curves as complex-valued functions, we show that the conditional full Procrustes mean is the leading eigenfunction of the conditional covariance. To estimate this covariance surface, we propose a novel deep conditional covariance smoother with modality-specific encoders - e.g. splines for scalar covariates and convolutional networks for images, which classical spline smoothers cannot accommodate. Our model is by construction invariant to the translation, rotation and scaling of the input curves and handles sparsely and irregularly sampled curves. We further provide an algorithm for elastic mean estimation that also removes parametrisation by iterating covariance smoothing, rotational alignment and parametrisation alignment. We illustrate the method on simulated outlines with known conditional mean and multimodal covariates, and give a first application to hippocampal outlines from the ADNI cohort, recovering covariate effects consistent with the literature. Code is available at https://github.com/mpff/dnn-shapes.

We study the positive Grassmannian through the lens of algebraic statistics. A closed formula is presented for the maximum likelihood degree of the Grassmannian of lines. We study the real and positive critical points for the Grassmannian of lines in 3-space.

We introduce RELTA-SGLD, a taming scheme that stabilizes superlinear stochastic-gradient updates while reducing unnecessary suppression of the original learning drift. A threshold determines where the taming turns on, while a relative-growth principle derived from the one-step Lyapunov stability condition determines the required taming strength. Together, they produce a lighter $\lambda$-scale denominator and preserve a nonvanishing far-tail return. As a consequence, we prove polynomial moment stability and first-order stationary accuracy in both $W_1$ and $W_2$ for nonconvex SGLD with superlinearly growing stochastic-gradient oracles, improving the corresponding half-order and quarter-order bounds for comparable stochastic-gradient tamed schemes. On Fashion-MNIST under active stabilization pressure, RELTA improves the mean learning metrics over both untamed SGLD and TUSLA and remains competitive with a tuned AdamW reference. In an ordinary-training regime, its lighter localized denominator reduces unnecessary perturbation of the original update and maintains nearly untamed learning dynamics.

Most 3D properties relevant to molecular design, including free energies and shape descriptors, are $\textit{expectations}$ over the Boltzmann distribution over 3D configurations of a molecular graph. However, existing property-guided generative models tie each property to a single structure, ignoring the underlying ensemble. We recast 3D molecular design as $\textbf{Boltzmann-expected design}$ and realise it with $\textbf{DECAF}$ (Decoupled Annealing Flows), which factorise the joint distribution over graphs and coordinates into two conditional flow models: a graph-conditioned flow $p(x\mid\mathcal{G})$, acting as a $\textit{Boltzmann emulator}$, and a coordinate-conditioned flow $p(\mathcal{G}\mid x)$, proposing new graphs from 3D information. By alternating the two flows, DECAF optimises molecular graphs with a simulated-annealing acceptance rule whose scoring function is evaluated on ensembles drawn from $p(x\mid\mathcal{G})$, making ensemble statistics, not single-conformer properties, the design target. The resulting loop requires no retraining to change objectives. On GEOM-Drugs, we show that ensemble-aware optimisation produces graphs whose mean radius of gyration and solvent-accessible surface area consistently shift toward targets, while single-conformer optimisation degrades on larger drug-like molecules where Boltzmann distributions are broadest. DECAF extends to multi-objective trade-offs and, uniquely among 3D generative models, to $\textbf{higher-moment design}$: jointly optimising an ensemble property's variance and skewness to produce flexible molecules biased to a prescribed conformational regime: we verify the conformational distributions of these higher-moment designs with all-atom MD simulations.

Probabilistic extreme event attribution aims to quantify how anthropogenic climate change has altered the likelihood or intensity of a class of extreme events. Existing studies commonly combine evidence from observational products and climate-model ensembles by first estimating attribution measures, such as probability ratios or intensity changes, for each data source and then synthesizing the resulting estimates. We critically assess this approach, identify potential shortcomings of a respective benchmark procedure from the literature, and propose both targeted modifications and a new parameter-level synthesis method. The latter combines estimates of the underlying nonstationary distributional regression parameters, thereby enabling inference across multiple event thresholds and counterfactual climate conditions. In controlled simulation studies, the proposed modifications substantially improve upon the benchmark procedure, while parameter-level synthesis provides competitive overall performance. The practical usefulness is illustrated through a case study of the heavy precipitation associated with Storm Boris in September 2024.

Modern LLM deployments use a number of implementation choices and inference optimizations (e.g., batching, custom kernels, and quantization) on top of fixed weights, so two engines serving "the same model" can produce meaningfully different distributions. We study the problem of estimating the total variation (TV) distance between two length-$n$ autoregressive distributions to additive error $\varepsilon$, under three access models. (1) Under sample access, we use $\widetilde{O}(n^2 K/\varepsilon^2)$ queries, where $K$ is the maximum support of the next-token distribution. This improves upon the $\widetilde{O}(n^3 m/\varepsilon^5)$-query estimator of Meel et al. (2025), where $m \geq K$ is the total size of the token alphabet. (2) Under logit access, we use $O(n/\varepsilon^2)$ queries, and this is tight. (3) Under noisy logit access, we smoothly interpolate between the above two guarantees: if probability values are given to relative error $\sigma$, we use $\widetilde{O}((n+n^2\sigma^2)/\varepsilon^2)$ queries. We complement our theoretical results with an empirical evaluation of our algorithms, for example measuring the distance between SGLang and vLLM serving identical weights. Our experiments highlight the robustness and practicality of estimating the total variation distance, which remains estimable where the KL divergence is infinite. Our code is available at https://github.com/XunZhiyang/llm-tv-estimation.