Papers

Political scientists increasingly use conversations as treatments. Sometimes these conversations are conducted by humans, but often and increasingly they will be conducted by generative artificial intelligence (AI). AI makes it possible to scale treatments that are responsive, and rich in real-world relevance. But this same interactivity creates specific challenges for causal inference. A respondent may be randomly assigned to a conversational condition, but the conversation that follows is not merely received by the respondent. It is generated jointly by the respondent and the conversational agent and is thus endogenous to who the respondent is. Consequently, when the theoretical object of interest is the conversation itself – or particular messages, features, or other attributes of that conversation – randomization of assignment does not necessarily identify the causal quantity the researcher seeks to estimate. This paper develops a potential outcomes framework for causal inference with conversations, with broad application but particular relevance to AI-mediated interaction. We distinguish among several causal objects: assignment to a conversational condition, assignment to a conversational policy, opening messages, messages within a conversation, realized conversational features, and the full realized conversation. Each corresponds to a distinct estimand and a different set of identifying assumptions. While some of these quantities are identified by standard randomized designs, others require additional assumptions or research designs, including sequential assumptions, representations of conversational histories, or explicit message-level interventions. The framework clarifies these distinctions and provides a common language for defining, interpreting, and designing conversational experiments as conversations increasingly become objects of causal inquiry.

Empirical Bayes methods are among the most widely used statistical methods for large-scale inference. A central paradigm is the NPMLE, whose theoretical guarantees are by now well understood for the independent Gaussian sequence model. In this paper, we study empirical Bayes estimation from dependent observations in the Gaussian sequence model. We show that the maximum Composite Marginal Likelihood (CML) estimator, which ignores all correlations in the likelihood, converges in weighted Hellinger distance at the rate $n_*^{-1/2}$, where $n_*=n/\kappa_0$ is the `effective sample size' determined solely by the number of observations $n$ and the spectral radius $\kappa_0$ of the correlation matrix of the Gaussian observations. A complementary minimax lower bound shows that $n_*$ indeed serves as the right complexity measure, and that the CML estimator is nearly rate optimal under general dependence. We consider two concrete applications. In the first, we consider Bayesian linear regression, where the signal prior is estimated via CML applied to the least squares estimator. In the second, we consider the more challenging Bayesian nonlinear single-index model, where prior is estimated by CML applied to a one-step debiased gradient descent. In both applications, although the full likelihood landscape can be arbitrarily complicated and intractable, our CML method is facilitated by exploiting the high-dimensional distribution of the auxiliary statistics through a correlated Gaussian sequence model. The key ingredient in the proof of our results is a sharp local maximal inequality for the log composite marginal likelihood process under dependent Gaussian observations. In contrast to standard empirical process methods, we prove this inequality by leveraging a recent geometric Brascamp-Lieb inequality for Gaussian measures.

Neyman–Pearson classification prioritizes one class by constraining its accuracy above a prespecified level, and then takes the accuracy of the other class as the utility objective. This paradigm is well suited for disease screening and diagnosis, among other applications. Statistical learning under this framework is complicated since classifier performance determines its acceptability. Furthermore, no learned classifier that is consistent for the oracle classifier can guarantee satisfaction of the control constraint in finite samples. Classical learning theory targets a control-relaxed empirical utility maximization (EUM) classifier. However, even the EUM classifier fails to achieve the desired control level on average. We conjecture that this under-control phenomenon is a manifestation of the over-optimism bias well known in standard statistical learning, and develop asymptotic theory to confirm it. Motivated by this insight, we propose refined learning procedures under two accuracy control strategies for the prioritized class: one controlling accuracy in expectation and the other with high probability. We further develop training-data-based methods to predict and infer class-specific accuracies of the resulting classifiers. Simulation studies demonstrate favorable finite-sample performance, and we illustrate the proposed methods with an application to cancer detection.

This work presents a Bayesian approach for parameter estimation in the class of Generalized Linear Autoregressive Moving Average (GLARMA) models, extending the methodology beyond the common exponential family setting. The proposed framework accommodates positive, double-bounded, and count time series through a unified MCMC-based estimation procedure implemented in nimble. We discuss prior specifications for the model parameters and conduct an extensive Monte Carlo simulation study to evaluate the finite-sample performance of the approach under three distinct data-generating mechanisms: Negative Binomial-GLARMA for count data, Beta-GLARMA for double-bounded outcomes, and Gamma-GLARMA for positive continuous time series. The simulation study assesses point and interval estimation, prior sensitivity, and the behaviour of the estimators under varying levels of temporal persistence, including challenging scenarios near the boundaries of the stationarity region. The practical utility of the proposed framework is illustrated through two empirical applications: analysing monthly net electricity generation by nuclear plants in the United States using a Gamma-GLARMA model with harmonic seasonal components; and modelling monthly hospital admissions due to chronic obstructive pulmonary disease in Belo Horizonte, Brazil, using a Negative Binomial-GLARMA model with principal components derived from air pollution covariates. The results demonstrate that the proposed Bayesian framework provides reliable and stable estimation across all settings, offering a flexible and practical tool for analysing non-Gaussian time series in a wide range of applications.

We show that projected Adam for online optimization with arbitrary moment decay parameters $\beta_1,\beta_2\in[0,1)$ can have average regret bounded away from zero. A similar result of Reddi-Kale-Kumar from 2018 required $\beta_1<\sqrt{\beta_2}$. Similar to their result, we use a three-periodic sequence of linear functions on $[-1,1]$ with slopes $c,-1,-1$, though we use $c$ slightly larger than $2$. This nonzero average regret result extends to Adam variants such as AdamW, RMSProp, NAdam, Adan, AdaMax, Muon, and to an i.i.d. variant of the three-periodic sequence of slopes for Adam.

When the standard of pointwise consistency for statistical inference – convergence to the truth in every possible state of the world – is provably unachievable, the usual responses are to change the inferential target or to strengthen background assumptions. This paper pursues a third: hold the inference problem fixed and identify the highest standard that remains achievable. I define a hierarchy of standards weaker than pointwise consistency, cast in topological terms, requiring convergence to the truth not everywhere but on a “large” set of probability measures. The main result is an impossibility theorem: for finite-precision tests, converging to the truth densely within each hypothesis already forces inconsistency on a comeager – “topologically almost all” – set of measures, whenever the two hypotheses are dense in their union. Distribution-free testing of conditional independence is one such case. Two further theorems characterize, in purely topological terms, exactly when each weaker standard is achievable, complementing Boeken et al.'s (2026) analysis of pointwise consistency.

Conjoint experiments provide an attractive way to assess the role of multiple attributes simultaneously on decision-making. However, the randomization of multiple attributes prevents understanding the causal mechanisms that, critically, depend on the relationship between attributes – e.g., how one attribute affects the respondent's belief as to another attribute. This is because conjoint experiments recover controlled effects whereas a substantively important estimand may be the total or indirect effect of one attribute. Unfortunately, existing experimental designs for conjoint experiments cannot estimate these effects. We provide an alternative framework that requires one additional, simple experiment to learn the relationship between attributes among respondents alongside the standard assumptions for causal mediation. Estimation of the relevant effects can be done in a doubly robust fashion using machine learning methods. We illustrate this by conducting a pre-registered experiment on candidate choice and disentangle the effect of different attributes by understanding their mediation through the candidate's party.

We study the power and limitations of subset selection in statistical estimation through the framework of super-teaching, where a teacher selects a subset of i.i.d. data to optimize a learner's estimator. Unlike prior work focused on specific distributions or fixed subset sizes, we develop a general theory under minimal assumptions. For mean estimation, we prove that super-teaching is possible for any distribution whose density is bounded away from zero in some neighborhood of the mean, allowing subset sizes growing as $k = o(n^{1/3})$ and achieving error on the order of roughly $k!/n^{k}$. This significantly extends existing results on admissible distributions and subset scaling. We also extend the analysis to parameters expressed as smooth functionals of expectations, such as variance and scale parameters in classical parametric families, including settings with heavy tails. Moreover, we show that super-teaching can greatly improve estimation rates for nonlinear estimators like the sample median, achieving rates beyond classical asymptotics. Through examples, including cases where maximum likelihood estimators are inconsistent or fail to be asymptotically normal, we demonstrate that super-teaching can succeed even when standard statistical guarantees break down. Our results establish a unified theory of data selection to enhance statistical efficiency.

Policy learning has received substantial attention with the goal of learning policies from observational data for decision-making. A majority of work in this space has focused on developing algorithms for computing policies that minimize regret compared to the optimal policy. However, in many practical settings, there is insufficient data to obtain low regret. As a result, recent work has shifted attention to alternative objectives, most notably, studying whether it is possible to learn an improving policy that statistically significantly outperforms baseline policies. We argue that there is substantial merit in studying a broader range of policy learning problems. When there is insufficient data to learn an improving policy, there may still be useful questions that can be answered. To this end, we provide a mathematical framework for studying the relationships between policy learning problems. We formalize three problems within our framework: beyond the optimal policy problem and the improving policy problem, we also propose the policy existence problem, which aims to determine if an improving policy exists. Within our framework, we show that the policy existence problem reduces to the improving policy problem, which in turn reduces to the optimal policy problem; these reductions prove that each problem is at least as easy as the next one (in sample complexity). A key question remains: is this hardness strict? We provide partial answers. First, the gap between the optimal policy and improving policy problems is strict. For the improving policy and policy existence problems, we prove that a sublinear polynomial gap exists under natural conditions on improving policy learning algorithms. Thus, we may be able to answer questions about the existence of an improving policy even when we cannot find one. These results highlight the value in studying a broader range of policy learning problems.

Kernel Stein Discrepancy (KSD) compares a sample to a fixed target distribution known only through its score, and is widely used for goodness-of-fit testing, sample quality assessment, and approximate inference. We study the estimation of $\operatorname{KSD}(P_0,P)$ from $n$ independent observations and identify the sharp spectral constant governing the minimax risk: it is the Hilbert-Schmidt norm of the Stein covariance operator $C_\star$, giving the minimax scale $\sqrt{\|C_\star\|_{\mathrm{HS}}/n}$. This scale is attained by the positive-part square-root U-statistic, whereas the standard plug-in V-statistic remains at the trace scale $\sqrt{\operatorname{tr}(C_\star)/n}$ and is therefore suboptimal by the fourth root of the effective rank of $C_\star$; for a Gaussian target with a fixed-bandwidth Gaussian kernel this factor is exponential in the dimension.

We propose CaSPECT, a causal spectral clustering framework for discovering causally homogeneous subgroups from observational data. Rather than clustering in covariate space, CaSPECT defines similarity through the topology of a learned directed acyclic graph (DAG); a bootstrap-stabilised PC algorithm recovers the causal skeleton; a novel Orientation Validation Score (OVS) combines PC bootstrap evidence with DirectLiNGAM to orient edges robustly; directed edges are weighted by backdoor-identified average treatment effects estimated via OLS or double machine learning. Chung's directed Laplacian provides a spectral embedding in which individuals close together share the same causal propagation pathways. We establish almost-sure consistency of the full pipeline and validate the method through a controlled simulation study and on LaLonde CPS1, IHDP, and 401(k) datasets, where CaSPECT recovers a positive and statistically significant treatment effect within the causally comparable subpopulation and corrects for severe confounding without requiring a pre-specified propensity score model.

Parameters of interest in causal inference, such as treatment or policy effects, can often be expressed as linear functionals of an outcome regression function. Automatic debiased machine learning (AutoDML) is a unified framework for obtaining asymptotically normal estimators of such parameters, which requires estimation of both a regression function and a Riesz representer. Existing AutoDML neural network architectures, such as RieszNet and MADNet, use a shared intermediate covariate representation. However, it remains unclear whether this shared representation should be predictive of the Riesz representer or the outcome. We show that a shared representation of the covariates that preserves predictive power of the outcome while discarding information about the Riesz representer is asymptotically more efficient than the baseline AutoDML estimator that uses all covariates. Motivated by these results, we propose the outcome-adapted AutoDML estimator and establish its asymptotic behavior in a sample splitting framework. We provide a neural network implementation of the estimator that learns a sparse representation of the covariates that is predictive of the outcome but not predictive of the Riesz representer. We demonstrate the efficiency gains of our estimator over existing alternatives on synthetic data and achieve state-of-the-art estimation accuracy on the semi-synthetic IHDP benchmark dataset.

We consider the Multiscale Single-Index Model (MSIM), first introduced in \cite{oymak2021learning}, as a stylized model for hierarchical learning with scale separation. Each layer extracts a shared single-index feature at one physical scale and passes it to the next, thus defining a tractable setting in which to study how deep architectures learn multiscale representations. Under non-degeneracy and delocalization assumptions on the link function and planted features respectively, for fixed depth $K$ and local scale $d$, the first Wiener chaos of the target behaves as a perturbed spiked tensor, where the perturbation of order $d^{-1/2}$ comes from the non-linearity – revealing the MSIM as a natural non-linear analogue of the Tensor PCA model \cite{montanari2014statistical}. While this perturbative picture is sufficient to enable efficient spectral recovery based on Tensor unfolding (as already observed in \cite{oymak2021learning}), it is not precise enough for the analysis of backpropagation gradient-based methods. In this work, we address this limitation by performing a fine-grained analysis of the Wiener chaos using Edgeworth expansions. In the first chaos, this gives a finite-rank hierarchy at scales $d^{-q/2}$. In higher chaoses, balanced flattenings exhibit staircase singular-value plateaus of size $d^{-\rho/2}$ and multiplicity $d^{\rho}$ under a natural higher-chaos non-cancellation condition. Using this higher-chaos structure, and under an additional slow Hermite-energy tail condition, we first establish shallow-network approximation lower bounds, quantifying the benefit of depth in this model. Next, and most importantly, we prove that online SGD on the correlation objective, where all layers evolve in the same timescale, achieves $1 - o_d(1)$ recovery with $n = \widetilde{O}( d^{K-1})$ samples, recovering the same sample complexity as in the linear counterpart.

A BHEP test for the null hypotesis of multivariate normality on the basis of incomplete data is introduced. Estimators for the underlying unknown parameters in this situation are suggested. The test uses characteristic functions and circumvents the problem of singular covariance matrix estimates. As the sample size tends to infinity, an almost sure limit of the test statistic is obtained under the null hypothesis and under alternatives. The convergence in distribution under the null hypothesis is also proved. Critical values can be obtained using a bootstrap procedure. Simulation studies investigate size and power of the test and confirm the adequacy of the approach. A real data example demonstrates the application of the test.

Conventional uniform convergence bounds and empirical risk minimization break down in massive over-parameterized models, such as large language transformers and biological sequence networks. With near-infinite unconstrained internal degrees of freedom, their optimization landscapes develop flat vertical gauge valleys, rendering classical generalization metrics vacuous and inducing severe pathologies, specifically generative hallucination and catastrophic forgetting. We introduce the Statistically Meaningful Geometry (SMG) framework, an information-geometric paradigm lifting deterministic parametric models into infinite-dimensional non-parametric Orlicz statistical manifolds. Modeling the total state space as a differential fiber bundle ($\mathcal{M}, \mathcal{B}, \pi, \mathcal{V}, \mathcal{H}, \omega$), we establish a Two-Fold Inference Paradigm. We formalize an Ehresmann connection 1-form $\omega$ as a dynamic geometric filter that strips away vertical gauge noise (Structural Internal Directions, or SID) and isolates learning trajectories along the strictly non-degenerate horizontal distribution (Statistical Variational Directions, or SVD$\chi$). We prove that under connection-filtered pre-training, out-of-distribution predictive variance is strictly upper-bounded by the finite diameter of the identifiable quotient base manifold $\mathcal{B}$, establishing a hard geometric containment of generative hallucinations. By projecting downstream updates onto the orthogonal complement of the historical horizontal carriage, we formalize the SMG Sequential Adaptation Flow, proving the total non-asymptotic elimination of catastrophic forgetting. SMG replaces empirical fine-tuning heuristics with coordinate-free topological constraints, bridging advanced differential geometry with structural reliability in AI.

Multivariate generalized Pareto distributions arise as limits of threshold exceedances and form a central model class for multivariate extremes. Existing inference methods based on the extremal variogram condition on the value of a single component, which can be statistically suboptimal. We generalize this approach by conditioning the multivariate generalized Pareto random vector $Y$ to lie on arbitrary half-spaces. Specifically, for a direction vector $v$, we introduce the random vector $Y^v = (Y \mid v^\top Y > 0)$ and define the associated $v$-variogram $\Gamma_{ij}^v=\mathrm{Var}(Y_i^v-Y_j^v)$. We establish the decomposition $Y^v \stackrel{d}{=} W^v+E\mathbf{1}$ into the so-called $v$-extremal function $W^v$ and an independent exponential random variable $E$, and derive several results relating these random variables to each other. For logistic, Dirichlet, and Hüsler-Reiss multivariate generalized Pareto models, we derive closed-form expressions for $\Gamma^v$. In the Hüsler-Reiss case, we further derive new density representations and identify a distinguished resistance-curvature vector $v_0$ that uniquely centers the Gaussian law of $W^{v_0}$ while characterizing the least-mass half-space. On the statistical side, we introduce empirical $v$-variograms and show in a simulation study that the choice of $v$ induces a pronounced bias-variance trade-off that is strongly related to the mass of the conditioning half-space. Moreover, combining information across multiple directions $v$ can substantially reduce estimation variance relative to methods based on a single vector.

We present a new quadratic model for the certification problem in adversarial robustness, which simultaneously accounts for all possible target classes. Building on this model, we propose a novel semidefinite programming (SDP) relaxation for incomplete verification. A key advantage of our approach is that it certifies robustness in a single optimization, avoiding the need for a separate resolution per class. This yields a significant computational speed-up and enables scalability to large datasets with many classes. To further improve efficiency, we also propose an effective pruning strategy of active neurons, thus reducing the problem dimensionality and accelerating convergence.

Sign-flipping score tests provide robust inference in generalized linear models under variance misspecification and form the basis of two recent inferential frameworks: post-selection inference in multiverse analysis (PIMA) and the sign-flipping score-based two-stage summary-statistics approach (flip2sss). PIMA provides asymptotically valid inference across a multiverse of model specifications, whereas flip2sss extends sign-flipping score testing to longitudinal and hierarchical data through cluster-level summary statistics. In this paper, we combine these two approaches to develop PIMAX, a multiverse inferential framework for clustered observations. The resulting method extends post-selection inference to clustered-data settings, accommodating heteroscedasticity, unbalanced designs, and within-cluster dependence. Given a multiverse of candidate specifications, PIMAX provides a global p-value for testing whether any specification exhibits a non-zero effect (weak control of the family-wise error rate, FWER), lower confidence bounds on the number of true discoveries, and multiplicity-adjusted p-values for identifying the specific contributing specifications (strong FWER control). By avoiding inference based on a fully specified random-effects covariance structure, PIMAX solves a key source of type I error inflation due to random-effects misspecification while enabling inference across a multiverse of fixed-effects specifications.

Uncertainty quantification of hydrological predictions is necessary to inform operational decisions. Recent generative machine-learning methods have advanced probabilistic streamflow prediction, but have remained confined to lumped models that predict a basin outlet directly. At the same time, deterministic LSTM runoff models are increasingly applied at grid or catchment scale and routed through river networks to produce spatially continuous, physically consistent discharge fields. This technical note argues that moving probabilistic prediction from lumped to distributed models introduces a specific new requirement: the joint distribution of upstream runoff generation must be sampled jointly. In lumped inference, the model predicts the outlet distribution directly and can modulate spread from basin attributes. In distributed inference, downstream discharge is obtained by routing many upstream runoff predictions, so independent local sampling averages uncertainty away. Using Japan as a case study, we train two probabilistic basin-scale runoff LSTMs and route their runoff through a Hayami routing scheme. Randomly matching upstream ensemble members produces severely under-dispersed downstream ensembles, whereas a simple quantile matching strategy restores much of the spread of the direct basin-scale reference. The shift from lumped to distributed probabilistic hydrology therefore requires explicit attention to the spatial joint structure of runoff uncertainty.

Origin-destination (OD) flow prediction is central to urban analytics, yet deep models trained on raw counts remain vulnerable to distribution shift. The core problem is that raw count supervision cannot distinguish transferable choice mechanisms from environment-specific shortcuts. Raw OD count mixes two objects: how much demand an origin produces and how that demand is allocated across destinations. We argue that the transferable object is the exposure-to-choice law that maps spatial conditions to relative destination preferences. We propose OpFlow, a mechanism-constrained framework that learns row-centered choice potentials and reconstructs flows by combining the induced allocation with a separately calibrated origin scale. Under distribution shift, spatial exposures and the induced allocations are allowed to vary; what transfers is the conditional map from exposure states to relative choice potentials. Theoretically, we characterize the identifiable row-centered potential and show that classical spatial interaction laws are restricted log-potential cases. Controlled synthetic shifts and a real-world experiment show OpFlow improves robustness under environment shifts.

Random walks are commonly used to model movement throughout the sciences, from the motion of particles and molecules to the observed behaviour of animals and crowds. The correlated random walk, which assumes a level of persistence between movement directions, has become ubiquitous in the analysis and modelling of movement in recent times. Whilst many properties of the correlated random walk are known, there are still many which are not fully understood and, therefore, under utilised in movement data analysis. Here we consider the effect that sub-sampling has on the descriptive distributions of correlated random walks. Our work demonstrates the connection between the distributions of turning angles and step-lengths that characterise a correlated random walk, along with the resulting distributions found after sub-sampling. We provide examples for where this approach could aid in movement analysis as well as determining future ways the work could be extended.

In selective deployment, practitioners act only on a model-chosen subset of individuals based on predicted conditional average treatment effects, but marginal conformal guarantees need not control reliability on that selected subset. We study reliable selection for black-box CATE predictors: selecting candidates whose CATE errors are below a tolerance while controlling the false discovery rate (FDR). Since CATE errors are unobservable, we construct doubly robust proxy errors from pseudo-outcomes; however, naive proxies can lose power under heteroskedasticity because variance overwhelms the reliability signal. We propose Denoised Conformal Alignment, which subtracts an estimated conditional variance component and combines conformal calibration with Benjamini–Hochberg selection. Our analysis shows that validity is governed by stability of proxy/oracle threshold labels, rather than pointwise perfection of the variance estimator. Experiments show substantially improved power while maintaining FDR control across challenging settings.

The informativeness of a training set is as consequential as its size, yet most sampling strategies remain agnostic to the intrinsic geometry of the data distribution. We introduce CuBAS (Curvature-Based Adaptive Sampling), an information-geometric framework for adaptive data selection in supervised classification, grounded in the q-state Potts Markov random field (MRF) model. The central insight is that a labeled dataset can be viewed as a statistical manifold, on which local curvature, estimated via the ratio of second to first-order observed Fisher information, faithfully encodes the geometric complexity of the data distribution. We construct a k-nearest-neighbor graph over the labeled data and derive a closed-form curvature score at each vertex from the Potts sufficient statistics. This curvature signal partitions the graph into two complementary regimes: low-curvature regions, corresponding to smooth, homogeneous clusters, and high-curvature regions, concentrated around decision boundaries that are disproportionately informative for classification. By selecting nodes from both regimes, CuBAS constructs compact yet maximally informative training subsets. Empirical evaluation across more than 60 benchmark datasets demonstrates consistent and statistically significant improvements over random sampling and uncertainty-based baselines, across a wide range of labeling budgets and classifier architectures. CuBAS is computationally efficient (linear in the number of k-NN graph edges), theoretically grounded in the differential geometry of statistical manifolds, and interpretable in terms of the local shape operator of the data manifold.

Fuzzy clustering is used to identify overlapping geometric cluster structures through partial memberships. However, classical methods are limited by the assumption of equal variable importance and by sensitivity to the fuzzifier parameter. These limitations may yield equal cluster membership probabilities, which we refer to as the uniform solution. To address these issues, we propose Kernel Fuzzy Relational Clustering (KFRC) equipped with a bandwidth selection algorithm tuned via the spectral properties of the induced kernel Gram matrix. The KFRC framework implicitly performs unsupervised kernel metric learning by controlling the geometric embedding of the data through adjustable bandwidth parameters. We conduct a formal stability analysis to identify the exact theoretical conditions under which relational clustering collapses, thereby ensuring the stable performance of KFRC. We find that our two-stage bandwidth selection procedure adapts to the data structure while actively avoiding the uniform solution. Furthermore, this theoretical analysis leads to the proposal of a novel fuzzifier function that presents distinct advantages over the power fuzzifier function. We conduct experiments on several synthetic and publicly available data sets to demonstrate that the proposed framework consistently recovers complex structures that traditional methods fail to resolve, while ensuring a purely fuzzy solution.

We revisit random projections for reducing the dimension of high-dimensional polygonal curves. Drawing from the toolbox of randomized linear algebra, we give a considerably simplified proof of the known $O(\varepsilon^{-2}\log(nm))$ bound on the target dimension of a random projection that preserves the continuous Fréchet distance of polygonal curves up to a factor $(1\pm\varepsilon)$. Our proof is based on the concept of sparse oblivious subspace embeddings. While previous techniques were limited to the case of the Fréchet distance, our techniques are fairly general and extend to all possible distance measures that involve the maximum, a sum or an integral over Euclidean distances between pairs of points on both input curves. We define a generalized dissimilarity measure for curves that includes several popular measures such as Fréchet, $q$-DTW, Hausdorff, etc. as special cases and show that the same dimension reduction technique works for this generalized dissimilarity measure. Finally, we apply the same framework for dimension reduction to piecewise linear surfaces, after extending the distance measure suitably to such surfaces.

Silicon sampling-using large language models (LLMs) to simulate human survey respondents-has emerged as a promising approach for augmenting traditional survey research. However, most evaluations rely on distributional comparisons rather than individual-level prediction, which risks conflating pattern matching with coherent respondent-level prediction. We propose cross-survey transfer, a more rigorous evaluation framework in which an LLM is given a respondent's answers to one set of questions and must predict their answers to entirely different questions from the same survey. Using data from the Taiwan Election and Democratization Study (TEDS) 2024, three open-weight LLMs (27B-120B parameters), and supervised machine learning baselines, we find that: (1) zero-shot LLMs achieve 52% accuracy on genuinely unseen items, closing to within 6 percentage points (pp) of a supervised random forest trained on same-population data; (2) a stable construct predictability hierarchy emerges, from 67% for partisan attitudes to 23% for sovereignty; and (3) variance collapse and safety alignment effects-two commonly cited LLM limitations-turn out to be more nuanced than previously reported, with variance collapse affecting supervised models as well and alignment effects varying dramatically across model families. These findings clarify both the promise and boundaries of silicon sampling.

In many modern experiments, latent interactions drive multicomponent stochastic systems, yet the data are available only as pooled measurements that obscure these dependencies. Whether such interactions can be identified and inferred from aggregate signals remains largely unexplored. Motivated by multi-channel electrophysiological recordings, we address this problem by introducing sum-dependent Markov chains, a class of finite-state continuous-time multivariate Markov processes whose transition rates encode interactions through the aggregate state. Under natural structural conditions, we establish identifiability of the latent dynamic parameters from the aggregate process. We define a cooperativity index that distinguishes positive cooperativity, negative cooperativity and independence, and construct its consistent estimators. For discretely and noisily observed pooled data, we develop likelihood-based inference through a hidden Markov model, address the associated embedding problem, and prove consistency and asymptotic normality. We further propose a stepdown test for cooperativity with asymptotic size control and power guarantees. Simulations and real-data analyses, demonstrate the scope and effectiveness of the methodology.

In high-dimensional Ising model estimation, target sample sizes are often limited, and effectively using auxiliary binary datasets of unknown relevance remains challenging. To address this, we propose Trans-Ising, a transfer learning method that combines a loss-based source screening rule with a two-stage estimation procedure. The method first identifies informative auxiliary sources using held-out target pseudolikelihood to prevent negative transfer. It then computes an initial estimator via pooled nodewise $\ell_1$-regularized logistic regression, followed by a target-only correction step using a folded-concave penalty. Theoretically, we establish fixed-node $\ell_2$ and $\ell_1$ error bounds, exact graph selection consistency, and the conditional consistency of the screening rule. Through extensive simulations and real-data analyses, we demonstrate that Trans-Ising achieves lower estimation errors than both target-only estimation and naive data pooling.

Weighted observations on the unit sphere arise in importance sampling, quadrature, and attention-weighted embeddings. Directional uncertainty is often summarized through a von Mises-Fisher (vMF) fit and its concentration or entropy. This summary uses only mean-direction information. It can miss antipodal, axial, girdle-like, or multimodal structure. We introduce geometric information decomposition (GID), which fits nested maximum-entropy projections to spherical features. Each gap measures the entropy reduction contributed by one feature level. The first gap is the fitted vMF distribution's KL divergence from uniformity. The second measures residual quadratic information, including Fisher-Bingham anisotropy. Later gaps describe finer angular structure. We establish invariance, consistency, alternative-regime asymptotic normality, and quadratic-form null calibration. Circular and spherical experiments include importance-weight calibration and a query-weighted digit projection. The results separate settings where vMF uncertainty is adequate from settings with higher-order structure.

This paper asks whether modern NBA shot selection can be evaluated as a dynamic portfolio problem rather than as a collection of isolated shot attempts. We combine a possession-level Markov reward process with both a mean-variance shot allocation objective and a defense response cost. The model separates rim attempts, midrange attempts, corner threes, and noncorner threes, then values each candidate shot diet by immediate scoring, continuation after offensive rebounds, empirical game-level variance, and a timeout-response stability cost. Because fastbreak value depends on geometry that is not fully observed in standard play-by-play, we optimize the no-fastbreak sample first and then add back observed fastbreak shot selection as a fixed transition component. Our results indicate that the league aggregate operates near the efficient frontier, with marginal improvements to be made by slightly decreasing perimeter volume and mid range attempts while increasing rim attempts. Team-level analyses reflect this general trend. Ultimately, these findings suggest the three-point revolution has pushed volume slightly past its optimal boundary. By incorporating outcome variance and continuation effects, we show that optimizing solely for expected value mathematically overstates the benefit of perimeter shots.