ALT Model selection and hyperparameter tuning pose a central challenge in off-policy evaluation (OPE) because errors of fitted Q-functions and occupancy-ratio estimates cannot be directly evaluated from held-out transitions. Bellman-residual and minimax validation methods often require auxiliary regressions or optimization over separate critic classes, adding computational and tuning costs. We introduce pairwise Bellman validation (PBV), a tuning-free minimax procedure for selecting among finite classes of fitted Q-functions and occupancy-ratio estimators using held-out transitions. PBV constructs critics from pairwise candidate differences, requiring only finitely many empirical moment calculations without auxiliary validation models or separate critic optimization. We establish finite-sample oracle inequalities relative to the best available candidate, even under candidate-class misspecification. Our key insight is that Q-function errors and log ratios between candidate and true occupanc

ALT Standard reinforcement learning (RL) algorithms based on Markov Decision Processes (MDPs) are vulnerable to sim-to-real gaps. To address this issue, distributionally robust RL algorithms based on robust MDPs (RMDPs) have been proposed, for ensuring that agents can perform reliably to unpredictable conditions in real-world environments. Despite of the rich literature, revisionan efficient model-free method is still lacking for robust RL, particularly for Markovian data, which is more relevant in practical applications. In this work, we take a step towards settling this problem by proposing a sample efficient (asynchronous Q-learning) algorithm for robust RL. In particular, consider a γ-discounted infinite-horizon RMDP with state space S and action space A, where the uncertainty set is specified by the total variation (TV) distance with uncertainty level σ. Assuming access to a single trajectory of Markovian samples induced by a behavior policy and the nominal transition kernel, the samp

ALT Neural scaling laws describe the predictable power-law dependence of model performance on training time, dataset size, and model scale, with the exponents quantifying how performance changes with resources. Recent theory has shown how scaling exponents are shaped by the data distribution and the structure of the learning task, but whether network depth can improve training-time scaling has remained unsettled. Through a refined analysis of deep linear networks, we clarify that the task spectrum determines when increasing network depth improves training-time scaling. For spectrally difficult tasks, increasing depth improves the asymptotic training-time scaling exponent, whereas for easy tasks, the exponent remains independent of depth, with depth affecting only a logarithmic correction at the boundary between these regimes. Remarkably, we find that a reparameterization of time governed by the predictor norm provides a unified description of the dynamics across task difficulties. Under th

ALT Structured sparse learning is a leading paradigm for high-dimensional data modeling, as it enables rigorous integration of domain-validated structural priors into the learning process. Among these priors, pre-defined grouped structure and piecewise smoothness are ubiquitous in real-world applications. However, most existing structured regularization methods are built on squared loss and convex penalties, rarely jointly model these two complementary structural priors, and suffer from two key limitations. Their optimal tuning parameters are sensitive to the unknown noise level σ due to the squared loss. Meanwhile, convex penalties induce inherent estimation bias and severe over-shrinkage of large magnitudes. To address these issues, we propose a knowledge-driven Nonconvex Structured Smooth Adjustment for Square-Root Regularization (NS³R), which unifies the σ-free square-root loss with a joint nonconvex ℓ2,q penalty (0 < q < 1) to simultaneously encode group sparsity and structured smooth

ALT Source selection often favors similar data, yet marginal proximity need not identify the most useful pretraining source. We motivate a conditional alternative through domain-adaptation theory and a regression example in which broader source variation improves estimation despite increasing Wasserstein distance. We examine five-day cryptocurrency volatility using ten Binance spot assets, six forecaster families, three seeds, and shared temporal cutoffs. Selecting the three farthest rather than nearest Gaussian-Wasserstein sources improves mean persistence-relative skill by 12.52 percentage points for MLP and 20.90 for Transformer, with positive post-hoc paired date-block intervals. Forward pilot selection improves mean skill over random transfer in all six families. Compact recurrent models achieve the lowest absolute mean errors, separating selection utility from forecasting quality. Retrospective five-candidate screening shows additional gains from farthest-first geometry before pilot

ALT We develop a derivative-free temporal-difference (TD) framework for calibrating black-box simulators using one-step transitions from a target system and noisy simulator-generated continuation values. The calibration parameter is defined through Bellman orthogonality, recovering the physical parameter under correct simulator specification and yielding a near-optimal L₂ approximation of the policy value under misspecification. We propose three TD algorithms based on random-direction finite differences, distinguished by their query costs and reuse of noisy simulator evaluations. We establish almost-sure convergence, last-iterate mean-square error bounds, and central limit theorems for Polyak-Ruppert averages across four query-noise regimes. Our analysis reveals a specification-dependent bias phenomenon: for two algorithms, the finite-difference bias of the TD estimating equation vanishes at the calibration target under correct specification, even when the gradient surrogate remains biased

ALT Embedding-based verification often calibrates a false-accept threshold from all impostor pairs among m identities, although these pairs share identities. We characterize a worst-case limit: when hub identities score highly against a fraction ρ of the population, a calibration-only threshold with marginal false-accept rate (FAR) at most α under every identity-exchangeable law reaches the hub score on hub-free calibration sets with probability at most (m+2)α/(2ρ). Uniformly accepting near that score at levels well below ρ/m therefore requires trial information. We propose COVE, which ranks the trial pair among all N=binomm+22 pairs formed by augmenting the calibration units with the probe and reference. Under identity exchangeability, its marginal FAR is at most ⌊αN⌋/N, with first possible acceptance at 1/N=O(1/m²). The rule also retains this guarantee with a fixed symmetric cohort-normalized score using an independent cohort. On 6 benchmarks and 8 frozen encoders, realised FAR was consi

ALT Disseminating synthetic data in place of original ones is a promising way to enforce privacy while complying with open science principles, especially in the healthcare domain. To keep pace with the rate at which researchers collect such data, there is a need for fast and flexible synthesis procedures. A popular class of such procedures is based on models of conditional distributions induced by decision trees. Such models can be combined into a synthetic distribution following two main approaches: sequential specification and fully conditional specification. However, there is currently no recommendation on which specification to use to optimize the risk-utility tradeoffs. In this work, we use both specifications to synthesize medical datasets by combining tree-based models of conditional distributions. We compare the quality of the resulting synthetic data using several metrics of risk and utility. Our results indicate no general superiority of either specification over the other. Seque

ALT Conformal Risk Control (CRC) extends conformal prediction beyond the coverage setting to the control of general monotone loss functions, in a distribution-free and modelagnostic fashion. This makes it well-suited to problems with high-dimensional targets, such as the semantic segmentation task addressed in this work. However, CRC guarantees only marginal control, meaning that the risk is controlled on average over the data distribution. Under imbalanced distributions, the risk on inputs that contain rare objects may therefore remain uncontrolled, even when the marginal guarantee holds. We propose a new method that controls the risk on average over user-defined groups of the domain, drawing on Mondrian conformal prediction and macro-coverage algorithms. The method relies on a taxonomy, that is, a function that assigns a group to each data point, and reweights each point's risk by a coefficient that depends on its group probability, so that rare points contribute more than common ones. W

ALT Clean-image prediction (x-prediction) and noise prediction yield equivalent population-optimal denoisers, yet can perform very differently in finite diffusion networks. For noisy input Yₜ with noise standard deviation σₜ, a noise predictor fε,ₜ induces the clean-image estimate X̂₁=Yₜ-σₜ fε,ₜ(Yₜ). This reveals a noise-transmission burden: the predictor must preserve information needed to cancel the input corruption. Under Gaussian corruption of d-dimensional data, a linear input bottleneck of rank r<d imposes a denoising-error floor σₜ²(d-r) even with unrestricted downstream computation, while the corresponding optimal risk for image prediction remains bounded. EDM attenuates this bottleneck contribution at high noise; exact preconditioning cancels it at every noise level. Without an input bottleneck, assuming exact affine recovery of the noisy patch from the model representation, we characterize how the covariance spectrum of corrections beyond linear denoising determines the width req

ALT Simulation-based inference often encodes observations Y into a fixed-dimensional summary S, with the posterior conditioning only on S. While exact preservation often requires infinite information, any such summary imposes a finite information budget on inference which is rarely an explicit choice or measurement. In this paper, we make the budget explicit by modeling the summary as a lossy channel from Y to S, and ask two questions: how large must the budget be, and how best is it spent? First, we show for parametric models that this budget, measured by the mutual information I(Y;S), grows unboundedly as the posterior concentrates, even when fixed-dimensional sufficient statistics exist. More generally, the required budget is set by the distribution of the random posterior, and we bound it from above by quantizing posteriors and from below by converses that weight each posterior state by its probability. Second, we show that a finite budget is best spent stochastically. Under a common-s

ALT Spatio-temporal graph neural networks combine a node's history with information from graph neighbors. The central question is whether graph neighbors provide predictive information beyond each node's own history. Forecast accuracy depends on both the choice of neighbors and the way graph messages enter the temporal model. We study these choices as graph construction and graph exposure on U.S. state unemployment, traffic speed, and electricity demand. Our diagnostic design uses two comparisons: varying exposure while holding the domain graph fixed, and varying construction while holding late gated integration fixed. A GRU using only each node's own history and randomized graph controls help assess what the graph contributes. Under a common change forecasting protocol, the same domain graph can improve or worsen error relative to the GRU across integration designs. Late integration alone is insufficient, while adding a fusion gate yields lower mean error in all three tasks. With late gat

ALT Foundation models provide powerful representations for unstructured data, such as text and images, and parameter-efficient fine-tuning (PEFT) makes their adaptation to downstream tasks increasingly practical. For neural estimators that lack a tractable sampling distribution, resampling-based procedures offer a flexible route to statistical inference, but they often require hundreds of model fits, making them computationally prohibitive at foundation-model scale. We introduce HIFI, a two-stage fine-tuning framework for statistical inference on parameters such as conditional means. Stage 1 adapts a foundation model once on a larger sample, capturing the complex structure of the data and controlling estimation bias through a single fit. Stage 2 applies a resampling inference procedure to a smaller independent sample, concurrently fitting multiple lightweight PEFT estimators to the residual to quantify estimation variability without relearning the full task. HIFI accommodates a broad class

ALT Kernel techniques are among the most powerful methods in data science and statistics. One of the key properties of kernels contributing to their numerous successful applications is that the associated reproducing kernel Hilbert space is expressive enough to encode probability distributions without loss of information or to capture the joint independence of M≥ 2 random variables, under mild conditions. Computationally, these measures (i) rely on the so-called Gram matrix which contains the pairwise similarity of sample points, and (ii) converge at a rate O (n⁻¹⁄₂), where n denotes the sample size. We focus on measuring the independence of latent position random graphs (LPRGs), a model widely-applied for instance in neuroscience, sociology, and epidemiology. In LPRGs a latent representation is associated to each node. The similarity of these representations (meant via a kernel) determines whether two nodes are connected, making the Gram matrices only implicitly observable and the estimat

ALT A scalar measurement can determine a robust decision without identifying the latent covariance or every decision risk. We study finite Gaussian projection experiments with a fixed mean-plus-standard-deviation target. The observation laws define a set of indistinguishable moment models. We exhibit decisions that agree throughout that set despite unidentified risk values, and give a confidence-set certificate that returns a decision or an unresolved outcome. We prove soundness, necessary abstention for indistinguishable models with incompatible optima, and a fixed-checkpoint certification guarantee. A scalar profile reduces nonlinear risk comparisons to convex inner problems. Across seven synthetic instances, jointly calibrated moment regions give sufficient budgets 21 to 52 times explicit expected-sample information lower bounds. Separately measured stopping times are lower, with zero decision errors in 1,900 simulated streams. These comparisons do not constitute matching bounds, and th

ALT Broad classes of deep generative models (DGMs) operate by learning to map a simple source distribution, such as a standard Gaussian, to a complex high-dimensional target distribution. Despite their success, DGMs often empirically struggle to accurately represent distributions with heavy tails or well-separated modes. In this work, we show that these difficulties reflect intrinsic properties of the underlying transport problem rather than particular neural network architectures or training procedures. We establish quantitative lower bounds on the gradients and Jacobians of pushforward mappings that transport log-concave source distributions to such targets. For heavy-tailed target distributions, the required gradient magnitude grows as the target develops increasingly large moments. For multimodal target distributions, the low-probability regions between well-separated modes similarly force large gradients in the transport map. We discuss how such large derivatives relate to trade-offs

ALT Time Series Foundation Models have demonstrated that pretraining on diverse datasets enables effective transfer to new forecasting tasks. Classical methods like ARIMA, however, remain configured and trained independently for each series, discarding knowledge from previous experiments. Consequently, selecting and training an ARIMA configuration remains challenging and often relies on heuristic approaches based on in-sample goodnessof-fit measures. We propose MetaARIMA, a pretrained configuration policy based on metalearning that brings transfer learning to classical statistical forecasting at the configuration level rather than the model level. The policy learns from historical experiments which ARIMA configurations achieve top-quantile performance, and recommends promising candidates for new series while preserving interpretability and local estimation. At inference, it selects a diverse set of candidates via maximal marginal relevance and efficiently identifies the final configuration

ALT Off-policy evaluation (OPE) is essential for assessing decision policies before deployment when online experimentation is costly or unsafe. Accurate estimation remains difficult when behavior-policy data are limited and the target policy favors states and actions rarely observed in those data. We propose InCOPE, a prior-data fitted network that learns a shared policy-value prediction rule across synthetic OPE tasks. We construct an OPE task prior over Markov decision processes and behavior-target policy pairs, generating behavior-policy datasets and exact target-policy values for pretraining. For a new tabular decision problem, the pretrained network uses the behavior-policy dataset, target policy, and known task settings as context to predict the policy's expected return without task-specific parameter updates. Experiments across four tabular domains, including a semi-synthetic clinical setting, demonstrate InCOPE's effectiveness for policy-value estimation.

ALT With the rapid development of modern scientific research, tensor data have become increasingly prevalent across a wide range of fields. How to effectively characterize the relationship between tensor predictors and a response while preserving the intrinsic structure of tensor data has therefore become an important problem in high-dimensional statistical analysis. Existing tensor regression methods mainly focus on conditional means or conditional quantiles. When the response distribution is asymmetric, heavy-tailed, or contaminated by outlying observations, the conditional modal provides a robust and interpretable alternative characterization. In this paper, we propose a partial modal tensor regression (PMTR) method. The proposed method constructs the partial modal tensor covariance, which incorporates information on the conditional modal to guide tensor dimension reduction, and subsequently establishes a modal tensor regression model in the reduced tensor space. This strategy alleviate

ALT Federated learning trains a shared model across clients without exchanging their data, yet the updates they transmit still leak information about individual records. Enforcing differential privacy is harder still when the model parameters lie on a Riemannian manifold. Existing methods rebuild the noise added for privacy in the geometry of each new iterate, aggregate through intrinsic maps that often lack a closed form, and prove convergence only in restricted regimes. We introduce DP-RFedProj, a record-level differentially private federated learning method for compact submanifolds that aggregates through closed-form projections and privatises gradients in a fixed ambient geometry. Each client may run any stochastic first-order optimiser, take several local steps, and participate only intermittently. An explicit record-level f-DP guarantee holds for the entire training transcript, independently of the manifold, the aggregation scheme and the local optimiser. We establish convergence of