Papers

We prove the weighted Bayesian bootstrap, a method for approximate sampling of a posterior distribution, can be extended to sample from general constrained posterior distributions under mild assumptions. The method entails a simple algorithm that can take advantage of fast tools from convex optimization. Under regularity conditions, we show the asymptotic distribution of samples from the constrained weighted Bayesian bootstrap has a covariance matching the restricted maximum likelihood estimator, an efficient estimator. We assess the method empirically on a variety of constrained Bayesian problems, demonstrating broad applicability of the method as well as advantages over existing peer methods. The constrained weighted Bayesian bootstrap quickly samples from constrained posteriors, providing adequate uncertainty quantification for problems typically solved via optimization methods designed to deliver only a point estimate. As a case study, using constraints required in European-style option prices, uncertainty estimates of an option pricing surface are derived with constrained weighted Bayesian bootstrap.

Reliable, scalable detection of informal, small-scale environmental-health hazards (used lead-acid battery (ULAB) recycling, household-scale e-waste burning, indoor mercury amalgamation, brick kilns, small tanneries) remains an unsolved problem. These operations are invisible to satellites and absent from formal registries, yet disproportionately harm low-income populations in low- and middle-income countries. This paper articulates the problem class and explores a possible response: contextual geospatial features, with case-specific feature design informed by domain expertise. We use ULAB recycling as a demonstration case, drawing on 164 verified sites in Bangladesh and India from Pure Earth's Toxic Sites Identification Programme. At this sample size, five-fold cross-validation on the training set cannot statistically distinguish the engineered contextual features from a simple two-feature socio-demographic baseline. The added value only becomes visible when we evaluate outside the training set. On 172 held-out informal-recycling sites in non-NCR India and Bangladesh, the model assigns scores several times higher than to matched random urban controls; and on an independent set of 131 regulatory-confirmed formal recyclers, informal sites score materially higher than formal ones in non-NCR India, indicating that the model is picking up informal-recycler-specific structure rather than generic industrial signal. We frame these results as exploratory rather than confirmatory: label sparsity, gaps in point-of-interest coverage, and untested transfer beyond South Asia all remain open. We close with seven open problems and invite the environmental-health and geospatial machine-learning communities to engage with informal-hazard detection as a class of problems worth solving.

Existing analyses of the edge of stability (EoS) treat it as a global property of optimization. We show that it is also selective: the stability constraint redistributes learning across subsets of the training distribution, amplifying progress on some groups while suppressing progress on others. Using a branching intervention that enters or exits the EoS regime from the same training state, we causally demonstrate this trade-off and identify two necessary conditions for a group to benefit. First, its aggregate gradient must align with the top Hessian eigenvector. We isolate this mechanism with a controlled perturbation that preserves distance but randomizes direction, destroying alignment and eliminating the advantage. Second, the group must sustain non-vanishing gradient magnitude over time. Under cross-entropy loss, gradient saturation decouples confidently classified groups, shifting the advantage to output-outliers, whose gradients persist. Together, these results show that EoS functions not only as a stability boundary, but as a mechanism governing the allocation of learning across the data distribution.

We formulate the problem of exact unlearning in reinforcement learning, where the goal is to design an efficient framework that enables the removal of any user's data upon deletion request, i.e., the online learner's output after unlearning is indistinguishable from what would have been produced had the deleted user never interacted with the learner. For any $\rho >0$, we show that there exists a reinforcement learning (RL) algorithm that is $\rho$-TV-stable and supports an exact unlearning procedure whose expected computational cost is only a $\rho \sqrt{\ln T}$ fraction of the computational cost of retraining from scratch. We construct such a $\rho$-TV-stable RL algorithm for tabular Markov decision processes (MDPs), which achieves a regret bound of $\mathcal{O}(H^2 \sqrt{SAT} + H^3 S^2 A + {H^{2.5} S^2 A}/{\rho})$, where $S, A, H$, and $T$ denote the number of states, the number of actions, the episode horizon, and the number of episodes, respectively. We also establish a lower bound of $\Omega(H\sqrt{\!SAT}\! +\! {SAH}/{\rho})$ for $\rho$-TV-stable RL algorithms, showing that our algorithm is nearly minimax optimal.

We study a distributional generalization of the matrix completion problem in which each entry of the target matrix is a probability distribution rather than a scalar. In this setting, only a subset of matrix entries is observed, and even for observed entries, the underlying distributions are not directly accessible; instead, we observe finitely many samples drawn from them. To represent distributional entries, we employ kernel mean embeddings and introduce a notion of Tucker rank for distribution-valued matrices to capture their low-rank structure. The infinite-dimensional nature of kernel embeddings poses significant methodological challenges. To address this, we introduce functional unfolding operators that link the proposed distributional low-rank structure to the classical Tucker rank for finite-dimensional tensors. Based on this framework, we propose a novel estimator for distributional matrix completion. We establish non-asymptotic error bounds that characterize the statistical performance of the estimator. Extensive experiments on synthetic data and a real-world application demonstrate the effectiveness of the proposed method.

Cellular heterogeneity is a hallmark of biological tissues and plays a central role in disease progression, diagnosis, and prognosis. Yet, accurately characterizing this heterogeneity from bulk molecular profiles remains challenging because observed signals arise from mixtures of multiple cell populations. Cell deconvolution aim to recover the relative abundance of constituent cell types from such heterogeneous measurements, but most existing approaches implicitly rely on restrictive assumptions on residual errors, including independence, homoscedasticity, and normality. These assumptions are rarely satisfied in omics data, which are inherently bounded and overdispersed. In this work, we show that whole-genome cell-type specific DNA methylation profiles exhibit latent group structures that can substantially impair deconvolution accuracy when ignored. We therefore propose a mixture of non-negative Beta regression models estimated through an Expectation-Maximization algorithm for DNA methylation rates. Our framework naturally incorporates a feature selection mechanism through mixture component identification, making component selection a critical step of the inference procedure. We further propose a dedicated criterion for component selection and assess the performance of the approach through an extensive comparative study across several in vitro benchmark datasets. Our results demonstrate that deconvolution accuracy is highly sensitive to latent component structure and show that explicitly modeling this heterogeneity yields substantial improvements over standard whole-genome deconvolution strategies. Altogether, this work establishes mixture modeling of DNA methylation data as a powerful new direction for robust and accurate cell deconvolution.

Wildfires threaten biodiversity, carbon stocks, and management capacity in the Brazilian Cerrado, where Conservation Units and their official buffer zones must allocate prevention resources under a strong dry-season fire regime. This work develops a retrospective daily active-fire detection benchmark for the Cerrado portion of Minas Gerais, Brazil, using INPE BDQueimadas reference satellite labels (AQUA_M-T), constrained pseudo absences with same-year MapBiomas Collection 9 land-cover filtering, and four nested covariate stages extracted through Google Earth Engine. Logistic Regression, Random Forest, and XGBoost are evaluated under five-fold time-series cross-validation on a global training base and on independent imbalanced test sets spatially held out to Parque Estadual do Pau Furado and Parque Estadual da Serra do Cabral with their official buffer zones. AUC-PR is the primary metric, with AUC-ROC, threshold precision and recall, SHAP explanations, and retrospective score maps used as complementary diagnostics. Temporal cross-validation showed the highest mean AUC-PR at the complete temporal-memory stage for all three model families. Held-out AOI tests were weaker under the stricter 1:100 prevalence design: Random Forest peaked at Stage 3 in both AOIs, while XGBoost maps exposed high-recall, high-warning-volume behavior. The resulting baseline provides a reproducible reference for comparing atmospheric, surface, static spatial, and short-term memory covariates in daily CU-scale active-fire detection ranking. Because several stages use same-day covariates, the study is a retrospective classification benchmark rather than a prospective forecast.

Learning reproducible and generalizable optimal treatment policies for chronic diseases requires large, representative populations with long-term follow-up. Administrative health data provide a natural starting point, but their use is often limited by unmeasured confounding. We address this by proposing a novel framework based on Instrumented Difference-in-Differences (iDID) to estimate optimal policies for recurrent event outcomes subject to a terminating event. The iDID design is particularly useful in this setting because it leverages policy-induced treatment variation while allowing for persistent unmeasured differences across populations, relying on assumptions that are more plausible for administrative health data than those required by conventional IV or DID approaches. A key feature of our approach is that it explicitly addresses the fundamental challenge of avoiding policies that trivially reduce recurrent adverse events by increasing mortality. We derive two distinct Inverse Probability Weighted identifications and develop a multiply robust estimator that achieves consistency if any one of several subsets of nuisance models is correctly specified. We establish the estimator's consistency and asymptotic normality through large-sample theory and demonstrate its superior finite-sample performance over existing methods via simulation. Finally, we apply this framework to a national Medicare dataset to optimize first-line Type 2 Diabetes strategies, specifically targeting the minimization of disease-related hospitalizations while accounting for survival.

This paper studies quantile regression in a data-limited setting where the gold-standard outcome is available only for a limited number of observations, whereas a surrogate outcome is widely available. Such settings are becoming increasingly common with the availability of low-cost predictions from modern AI, motivating a growing line of research on "prediction-powered inference," for improved statistical inference. Naively extending this framework to quantile regression, however, raises two challenges: computational difficulties due to the discontinuity of the subgradient, and overly conservative confidence intervals. To address these issues, we propose a convolution-based smoothing of the check-loss objective and develop two variants of the estimator. The proposed estimators are computationally tractable, and our numerical studies show that they mitigate overcoverage. As a theoretical contribution, we establish the asymptotic distributions of the proposed estimators under a possibly misspecified linear quantile regression model. We further propose an ensemble of the two estimators and illustrate the proposed methods through simulations and an application to a local housing dataset.

Whether global mean surface temperature has accelerated has received opposite answers in quick succession, reported as undetectable on data to 2023 and as significant on data to 2024. This raises two questions: since when is acceleration detectable, and how far does the answer depend on the test used? We show that structural-break tests, often used for this purpose, cannot reliably date the onset of a continuously accelerating warming rate. We therefore test for curvature directly, under specifications whose null is exactly a constant warming rate and whose alternative is curvature rather than a break. One is a linearithmic trend, which grows faster than linear but more slowly than any polynomial of degree greater than one; the other estimates the curvature freely from the data. We report alongside them the quadratic trend used in the recent literature. Over 1970-2025, in a single full-sample test, the linearithmic and quadratic coefficients are positive and statistically significant in all five major temperature datasets once El Niño and solar variability are controlled for. The onset of acceleration is dated by re-estimating over expanding windows and correcting for multiple testing. Under the linearithmic specification, acceleration first becomes detectable in windows ending in mid-2023 for NOAA, late 2023 for GISTEMP and mid-2024 for ERA5, and not yet in HadCRUT or Berkeley. The free-curvature specification agrees on direction but rejects in fewer datasets, since estimating the shape costs precision. The linearithmic specification implies the least curvature of the three, with an acceleration that declines over time, and so the lowest warming of the three when extended to 2050.

Online evaluation of ranking and retrieval systems often relies on downstream monetization metrics such as app revenue or creator earnings. These metrics are typically heavy-tailed, with a small fraction of users dominating both mean and variance, leading to low statistical power and unreliable conclusions in A/B experiments – especially under limited traffic. We present a practical framework for variance reduction in online experiments by combining post-stratification with CUPED. Our approach leverages pre-experiment covariates to improve the sensitivity of monetization experiments without requiring additional traffic. Deployed at ShareChat across ranking-driven monetization experiments, the method substantially reduces variance and improves decision stability, achieving equivalent statistical confidence with ~45% less traffic than standard metrics. We further discuss practical design choices, guardrails, and limitations, providing guidance on when post-stratification is appropriate for real-world information retrieval and Recommendation systems.

This paper proposes a two-stage pseudo anomaly-guided anomaly detection method (Two-stage Pseudo Anomaly-guided Anomaly Detection, TPA-AD) for axle-box bearing time-series anomaly detection (time series anomaly detection, TSAD) under the setting where only normal samples are available for training. The method first generates pseudo-anomalous windows near the normal boundary using a reconstruction model and per-feature target-error control. It then learns anomaly-sensitive representations through contrastive learning between normal and pseudo-anomalous windows, and finally produces window-level and point-level anomaly scores using k-nearest neighbors (KNN). Compared with existing methods that rely on known fault categories, real anomaly priors, or random anomaly injection, TPA-AD improves the separability of the normal boundary by constructing pseudo-anomalies in boundary neighborhoods and can jointly handle continuous and discrete features in mixed-variable scenarios. The main experiments are conducted on bearing fault detection datasets and degradation-process datasets, with an additional exploratory extension on $13$ public TSAD datasets. The results show that the proposed method yields relatively stable anomaly responses, is sensitive to degradation evolution, and demonstrates a certain degree of broader applicability on public TSAD benchmarks and real high-speed-train-related bearing data.

We study simultaneous alternating power iteration for fixed-order asymmetric rank-one spiked tensor models. Our main contribution is a finite-iteration local theory that is independent of any particular initialization. Once the iterates enter a sufficiently small neighborhood of the planted rank-one direction, their error decomposes into a geometrically decaying transient and an intrinsic noise floor caused by fixed orthogonal noise contractions at the planted point. The deterministic finite-sample conditions are stated explicitly, but under a coarse fixed-order multilinear noise event they reduce to a conservative high-signal regime for fixed or slowly expanding local radii. We then separate the warm-start mechanism from any specific spectral construction. A generic one-sweep principle shows that, if a sign-compatible initializer has correlation \(\gamma_N\), first-sweep noise level \(a_N\), and \(a_N/(\gamma_N^{d-1}\omega_{N,d})\to0\), then one can choose an expanding radius \(r_N=o(\omega_{N,d})\) for which the first sweep enters the local basin. After entry, the local affine contraction yields convergence to the unique informative local fixed point in that basin. For centered-Gram initialization, we verify the required correlation and same-sample first-sweep noise bound under i.i.d. finite-fourth-moment noise by a signal-preserving noise-only leave-one comparison and an averaged leave-one slice-contraction estimate, which we call a pressed-back estimate. The leave-one comparison keeps the spike fixed and averages over the deleted coordinate, so planted coordinates enter through \(\ell_2\)-weighted sums rather than worst-case incoherence bounds.

We show that the lower bound in the majorizing measures theorem holds for a large class of random vectors. Specifically, suppose $X \sim \mu$ is a centered random vector in $\mathbf{R}^n$ with \[ C_{\mathrm{KL}}(\mu) = \sup_{\substack{\theta \neq \eta \\ \theta, \eta \in \mathbf{R}^n}} \frac{\mathrm{KL}(\mu_\theta \| \mu_\eta)}{\|\theta - \eta\|_2^2} < \infty, \] where $\mu_\theta$ denotes the law of the translate $\theta + X$. Then, for every nonempty, bounded $T \subset \mathbf{R}^n$, \[ \sqrt{C_{\mathrm{KL}}(\mu)}\, \mathbf{E}_\mu \Big[\sup_{t \in T} \, \langle X, t \rangle \Big] \gtrsim \gamma_2(T), \] where the righthand side denotes Talagrand's generic chaining functional. This result recovers, as a special case, the lower bound in the majorizing measures theorem for centered Gaussian processes. Our argument critically relies on the rate-distortion integral, recently introduced by J. Liu.

Aggregated relational data (ARD) consists of survey responses to questions of the form “how many people do you know who~$X$?” and is widely used in survey statistics for indirect inference about populations and social networks. The dominant ARD inference target is hidden-population size estimation via the Network Scale-Up Method (NSUM), but ARD is also used for personal-network-size estimation, mixing-pattern recovery, and inference about latent network structure. Bayesian inference for ARD almost universally assumes that, conditional on a respondent's degree, the counts reported for different subpopulations are independent. There are, however, reasons to question this assumption, as homophily, latent-space clustering, and imperfect recall may all induce cross-population dependence. We develop a simulation-based neural estimation framework for ARD which requires only a simulator, so it can be applied to generative models whose likelihood cannot be written down or efficiently evaluated. The framework trains a permutation-invariant neural Bayes estimator that returns, for each marginal parameter, a posterior median and a 95% credible interval, by minimising a multi-quantile pinball loss with a cumulative-gap construction that rules out quantile crossing by design. We demonstrate the framework on three structurally distinct intractable extensions of NSUM-style ARD inference: a stochastic block model, a latent-space model, and a recall-subset model. We apply the framework to ARD Household Survey collected in Rwanda. The framework provides inference on any new survey drawn from the training distribution, and extends the reach of ARD modelling to network-structure and cognitive-process assumptions beyond those currently accessible to likelihood-based inference.

The fraction of variance explained (FVE) in a linear model quantifies the extent to which predictors account for outcome variability. In high-dimensional settings, where traditional FVE estimators do not apply, modern FVE estimators such as GWASH or linear mix-effect model estimated through the restricted maximum likelihood (LMM-REML) struggle with strong correlation among predictors, often found, for example, in brain imaging data. We propose a decomposition framework that partitions the FVE into two components: a low-dimensional component capturing the strong correlation, estimable by low dimensional methods, and a high-dimensional component with remaining weak correlation, estimable by high dimensional methods. Simulations demonstrate that decomposing dominant principal components (PCs) and estimating the high-dimensional FVE using GWASH or LMM-REML leads to improved bias reduction compared to directly applying standard approaches such as GWASH and LMM-REML. Our method shows consistent performance asymptotically as both the number of predictors and the number of samples increase. We illustrate the method in an analysis of the Adolescent Brain Cognitive Development (ABCD) brain imaging dataset, capturing nuanced heritability signals in the FVE of cognitive measures predicted by high-resolution brain imaging data.

Advertising platforms use randomized lift tests to measure incrementality, but privacy-preserving reporting systems degrade the observed signal through match-rate loss, linkability loss, attribution-window loss, aggregation-threshold suppression, randomized reporting noise, and segment-heterogeneous signal loss. This paper formulates privacy-constrained advertising measurement as a robust causal decision problem under the mentioned signal losses. Given a randomized experiment and an ambiguity set for privacy-induced degradation, the framework projects the observation-compatible fiber of clean/unfiltered experimental worlds onto the incrementality functional and returns certified, rejected, and unresolved decisions. The main result gives a sharp decision frontier. Reports outside the frontier support uniformly valid certification or rejection, whereas reports inside it contain too little information for any method to uniformly distinguish above-threshold incrementality from non-incrementality. Supporting results give finite-sample certification, sample-complexity guarantees, a minimax lower bound showing that signal loss reduces effective information, and a reporting-granularity tradeoff. On 2.0M Criteo Uplift rows and the 64K-row Hillstrom email experiment, clean conversion lift is positive in both datasets, with lifts 0.00112 and 0.00495, respectively. Population certification survives mild degradation in Criteo and severe degradation in Hillstrom, while all considered finite-sample stress settings in both datasets remain unresolved after simultaneous uncertainty and reporting noise are included. Overall, the research contributes a decision-theoretic layer for privacy-aware incrementality measurement whose output is the strongest causal-claim justified by degraded ads signals.

The precise definition of a primary estimand, accounting for intercurrent events (IEs) as per the ICH E9(R1) addendum, is fundamental to the design and interpretation of clinical trials. Conventional power and sample size calculations, however, often do not adequately incorporate the impact of IEs and their corresponding handling strategies, creating a risk of over- or under-powered studies. While simulation-based approaches can address this complexity, they are often computationally intensive and may only explore a limited set of scenarios. In this paper, we introduce a set of formulae for calculating power for estimands with time-to-event endpoints. We focus on estimands that use treatment policy, hypothetical, composite, or a combination of strategies for handling IEs, assuming constant hazards and that a participant's risk of experiencing an IE is unrelated to their risk of other IEs or the primary endpoint, while the effect of an IE on the endpoint is determined by the chosen handling strategy. Simulation is used to assess the accuracy of calculated power in a variety of settings, and we explore deviations in power estimates in scenarios where event times for outcomes and IEs are dependent, hazards are non-constant, or follow-up times vary. We illustrate the practical application of our approach through a case study in nasal polyposis, examining the sensitivity of sample size requirements to varying IE rates and their impacts on post-IE outcomes. The proposed formulae facilitate rapid and accurate power and assurance calculations, enabling clinical trial designs to be more closely aligned with the estimand of interest.

This paper investigates non-stationary online learning using the metric of interval regret, which requires an online algorithm to perform well over every time interval. We propose the first online learning algorithm that achieves an interval regret bound scaling with gradient variation, a fundamental measure of the cumulative change in online function gradients, which relates to various problem-dependent quantities and is closely connected to stochastic optimization and other problems. Our method employs a simple and efficient two-layer online ensemble structure that achieves strong theoretical guarantees. Specifically, it enjoys a regret bound that simultaneously adapts to various problem-dependent quantities while also preserving the minimax-optimal rate in the worst case. Moreover, recognizing the challenge of hyperparameter tuning, we introduce a Lipschitz- and smoothness-agnostic variant that automatically adapts to these potentially unknown constants. This is primarily enabled by a novel Lipschitz-adaptive meta algorithm, which may be of independent interest. Beyond interval regret, our method also yields broader implications: it provides versatile bounds for interval dynamic regret, a stronger measure that competes with changing comparators over any interval, and yields the first piecewise characterization for stochastic extended adversarial optimization. Theoretical findings are validated by experiments.

Realized volatility has become a standard tool for measuring latent variation in financial assets, and its forecasting is crucial for a wide range of financial applications. We propose a network-based model for forecasting a vector of realized variance processes through the heterogeneous autoregressive (HAR) approach. The generalised network HAR (GNHAR) model incorporates cross-sectional spillovers through a directed graph inferred from Granger-causality tests or connectedness indices, yielding a parsimonious multivariate time series model specification. In an application to ten equities over tranquil and crisis regimes, the proposed GNHAR model improves upon common HAR model benchmarks under both short- and long-term forecasting. We also compare the network-based specification when the jump-continuous decomposition or node-specific option-implied variances are considered. Finally, unlike overparameterised models, our approach yields a concise set of parameters that track the strengthening or weakening of cross-market dependencies, providing a time-varying quantitative assessment of market stability.

We develop a quantitative framework for diffusion distillation by viewing few step sampling as approximation through compositions of learned flow maps. For trajectory distillation of the probability flow ODE, we show that low noise multimodal regimes separate score approximability from dynamical stability: the score remains efficiently approximable, while small local errors may be strongly amplified by stiff flow dynamics. In a Gaussian mixture Ornstein–Uhlenbeck model, we prove time uniform \(L^p(p_t)\) score approximation by ReLU and ReQU networks with explicit polylogarithmic complexity, and derive a computable Lipschitz bound \(L(t)\) for the flow velocity. The stability factor \(\exp\bigl(\int_s^t L(u)\mathrm du\bigr)\) can grow exponentially as noise decreases and mixture separation increases. Comparing this certificate with a certified local Lipschitz budget for one step students identifies regimes of direct distillation difficulty, without implying an approximation lower bound. We also show that deep residual compositions control global transport error through propagated local errors, and that equalizing cumulative stability yields an optimal nonuniform segmentation. With eight segments, this grid reduces final mean relative MSE by up to \(51.9\%\) versus uniform grids.

Paired comparison models are useful for estimating latent abilities or preferences from binary outcomes, but maximum likelihood estimation can be unstable or fail when the comparison graph is disconnected or nearly separated. Ridge regularization addresses these difficulties by shrinking ability parameters toward a common center, but it can obscure the simple likelihood interpretation that makes Bradley-Terry and Thurstone-Mosteller models attractive to practitioners. This paper describes two data-augmentation perspectives on regularization. The first adds fractional pseudo-games between every pair of competitors. The second adds a fixed-strength phantom player and gives each real competitor a weighted pseudo-win and pseudo-loss against that player. Both approaches yield finite, shrunken estimates; the phantom-player construction also resolves the usual location nonidentifiability without an explicit linear constraint. For the Bradley-Terry model, the two augmentations lead to transparent penalty functions that can be compared directly with ridge penalties. An application to the 2025 Major League Baseball regular season illustrates that tuned pseudo-game and phantom-player regularization can closely reproduce ridge-regularized strength estimates while retaining an intuitive augmented-data representation.

Online debate platforms offer a window into whether exposure to diverse crowds changes how people reason: they capture political preferences, the perceived quality of arguments, and the ideological diversity of the audience. Drawing on theories of deliberative democracy and cross-cutting exposure, I develop a Bayesian logistic regression model that decomposes voting behaviour in online debates into three components: conviction (agreement between a user's prior beliefs and a debate's stance), persuasiveness (perceived argument quality), and cross-cutting exposure (the ideological diversity of a debate's prior voters). I apply this framework to the DDO dataset: approximately 341k votes across 78k debates on 48 socio-political topics. As the platform provides no predefined topic labels, I infer topic and stance from debate text using large language models. I test whether a more ideologically diverse prior audience weakens a voter's conviction, a central claim from the cross-cutting exposure literature. Persuasiveness is the strongest and most consistent predictor of vote choice, never outweighed by conviction, though conviction remains a credible predictor on several topics tied to personal freedoms. Cross-cutting exposure moderates conviction on 4 of 47 topics, though these results are sensitive to topic classification and sparse coverage, with implications for the design of deliberative platforms.

Outliers are known to significantly distort the results of many commonly used clustering methods, often leading to unreliable partitions. To address this issue, several robust clustering approaches have been developed that not only reduce their influence but also facilitate the detection of meaningful outliers. This presentation focuses on robust clustering methods based on trimming, especially TCLUST, which extends the type of trimming used by MCD in one-population problems to the more general case of multiple and unknown clusters. While TCLUST performs well on low-dimensional data, it struggles with high-dimensional datasets due to the complexity of estimating a large number of parameters. The Robust Linear Grouping (RLG) method offers an alternative by assuming clusters lie near lower-dimensional subspaces, thereby combining clustering with dimensionality reduction. However, RLG has limitations when subspaces intersect and assumes overly simplistic isotropic orthogonal errors. A robust clustering method extending TCLUST will be presented, building on the High Dimensional Data Clustering (HDDC) approach by incorporating trimming and eigenvalue constraints. This new approach, called tHHDC, combines TCLUST and RLG, requiring careful modification and integration of both methodologies within that HDDC framework. A study of the theoretical properties of this approach, together with a feasible algorithm for its implementation, will be presented. The interest of the proposed methodology, along with the issue of selecting input parameters, will be illustrated through a simulation study and a real-data example.

We study dynamic pricing over a finite selling horizon when limited resource capacity determines revenue and the observations available for inference at a prespecified price. Resource depletion can remove the target neighborhood from the feasible price set, changing the experiment generated by the pricing policy. We develop inference-aware re-solving controllers that check target-band feasibility before current covariates arrive and log the pricing mixture. Target-reserved and smooth controllers take population mean-pair geometry as a predeployment input; learned barycentric re-solving instead estimates stationary mean-consumption vectors of predeclared component kernels. On an affine binding-capacity family, an exact-input target-reserved controller assigning mass $t^{-\gamma}$ obtains an information clock of order $T^{1-\gamma}$ in probability, radius $O_p\{T^{-(1-\gamma)/2}\}$, and, under an exposed-face reward identity, a signed fluid-benchmark gap bounded above by $O(\log T+T^{1-\gamma})$. Under the exogenous affine-face condition, predeclared target support, and polynomial error spending with exponent greater than one, learned barycentric re-solving has a linear information clock in probability and an $O(\log T)$ signed-gap upper bound; centered local pricing has the same orders under slack capacity and global target optimality. An exact-input, target-compatible smooth alternative without reservation gives a linear clock in probability, an $O_p(T^{-1/2})$ deterministic-envelope radius with unconditional coverage and reporting probability tending to one, and an $O(\log^2 T)$ signed-gap upper bound. Boundary results show when physical support is lost and why a $1/t$ target branch yields only $O_p(1)$ information if it is the sole target-local source. The policy reports an interval when its prespecified support and information conditions hold and otherwise abstains.

Large Language Models remain plagued by hallucinations. Recent work has sought to tame their prevalence using statistical techniques based on conformal prediction, with both theoretical and empirical success. However, these methods operate in a post-hoc fashion, treating the sampling procedure itself as atomic and then surgically altering samples to remove hallucinated claims. This disconnect between filtering and generation can result in samples that are incoherent, inconsistent, or simply unlikely under the model itself. Moreover, post-hoc surgery is unable to shift probability mass towards more useful and helpful responses. To address these issues, we propose to instead sample from approximations to an LLM posterior, where the conditioning event corresponds to a calibrated, high-scoring region. We develop a calibration procedure tailored to the setting of conditional sequential generation that effectively identifies this region and achieves target risk control. Empirically, we apply our method to case studies focused on open-ended biography generation and mathematical problem solving; compared to prior work, we obtain the same statistical guarantees, with higher downstream utility.

TThis paper develops a Dynamic Mini-Max (DMM) framework for repeated surveys comprising a Dynamic Mini-Max Design and a Sequential Hierarchical Bayes Update (SHBU). The DMM jointly optimizes sample size and wave overlap subject to simultaneous precision constraints for levels and movements, a respondent burden limit, and a fieldwork budget. The methods are illustrated using 2021 Australian Census data (t = 1) and simulated waves t = 2, 3, 4. Both the DMM and the classical design start from the same 5% proportional allocation of n_A = 42,018 units. The DMM reduces this to n* = 40,251 while meeting all precision constraints, achieving a cost saving of approximately 6.3%. Level coverage is comparable between the two designs (maximum absolute relative error (MARE) ratio 0.844–1.263). Movement coverage diverges markedly: the DMM achieves 100% across all 27 domain-variable cells, while the classical design achieves only 82%–96% (87.5%–95.0% nationally). The classical confidence interval understates movement uncertainty because it addresses sampling variance only and does not account for the model variance component V_mod_hat. Additional benefits of the DMM framework – including coherent joint inference for levels and movements, sequential updating without ad hoc composite-estimator chaining, and small area estimation – are outlined in the paper.

We study projection-based diagnostics for distinguishing directional asymmetry from tail-ratio departure in multivariate data. The procedure reduces the problem to one-dimensional projections and computes two quantile-based summaries: a directional skewness measure evaluated over several quantile levels, and an interquantile tail-ratio evaluated relative to a chosen benchmark. The two summaries lead to a four-regime classification: symmetric benchmark-tail, symmetric tail-departed, skewed benchmark-tail, and skewed tail-departed. The quantile formulation avoids relying on third and fourth moments, which can be unstable in heavy-tailed settings. We establish population properties under central symmetry and ellipticity, uniform finite-sample bounds over the searched directions, and consistency of the threshold classifier under separated regimes. A sparse rank-one calculation is also used to show why coordinate directions can complement random directions in high dimensions. The resulting diagnostic is meant to guide subsequent modelling choices, for example whether a symmetric, skewed, tail-departed, or combined multivariate model is appropriate.

High-dimensional time series regressions are often regularized to produce sparse coefficients. We show that temporal aggregation provides a powerful alternative to reduce dimensionality in high-order autoregressions and mixed-frequency regressions. To this end, we propose StarTime (Sparse Tree-based Aggregation for Time Series), a convex penalization method that uses a temporal tree to arrange lags hierarchically from high to low frequency. StarTime then flexibly selects coefficients to be aggregated at possibly varying frequencies, sparse or a combination thereof. We provide new error bounds for StarTime, demonstrate improved estimation accuracy and recovery of aggregation and sparsity in simulations relative to benchmarks, and illustrate StarTime's relevance for financial and macroeconomic applications.

Prediction performance metrics such as accuracy and the F1 score are typically reported as single numbers, with no measure of uncertainty. The omission has been tolerable in exploratory settings, where model evaluation is used for informal comparison rather than formal decision-making. But as machine learning is deployed in real-world applications, evaluation results are increasingly used to support binary decisions – whether a model meets a required standard or not – making uncertainty quantification essential. The problem is compounded when data are dependent, as in repeated measurements, clustered subjects, or time series, where variability is harder to assess and easy to underestimate. We develop a unified framework that links a broad class of performance metrics through their representation as smooth functionals of confusion-matrix probabilities. This representation allows the use of the cluster-robust sandwich variance estimator to obtain asymptotically valid confidence intervals, hypothesis tests, and paired model comparisons for both binary and multiclass problems under clustered data. We also provide power and sample size approximations based on pilot data, enabling principled study design for model evaluation. Simulations show that the proposed methods achieve near-nominal coverage across a range of dependence structures, while naive methods underestimate variability. A real-data application further illustrates how accounting for clustering can materially change conclusions. These results offer a practical foundation for uncertainty quantification and study design in prediction performance evaluation, in settings where decisions should be justified under dependent and clustered data.