Papers

Policy learning aims to determine who should be treated based on individual characteristics. In high-stakes settings such as medicine and public policy where safety is a central concern, improving the average outcomes alone may not be sufficient: decision makers may also seek to protect individuals from harm, in line with the Hippocratic principle of “do no harm.” In this paper, we propose conformal policy learning (CPL), a policy learning procedure with a new distribution-free safety guarantee that controls the probability of assigning treatment to an individual who would be harmed relative to control. CPL views each treatment decision as testing a hypothesis of counterfactual harm and assigns treatment by thresholding conformal p-values. These p-values use observable proxies and selective calibration to address the challenge that the potential outcomes under comparison are never simultaneously observed. For randomized experiments, under standard exchangeability conditions, CPL provides finite-sample safety guarantee at a user-specified level, without imposing any outcome modeling assumptions. Moreover, when the outcome model is consistently estimated, CPL achieves asymptotically optimal welfare subject to the safety constraint. In observational studies, CPL with learn-then-balance weights achieves doubly robust safety guarantees. We evaluate CPL through extensive simulations and apply it to an empirical study of AI-powered interventions designed to reduce conspiracy beliefs.

Statistical heterogeneity limits federated learning when a single global classifier cannot represent client-specific label distributions. In this work, we propose Personalized Federated Knowledge Distillation with Head Adaptation (pFedKDH), which aggregates only the shared backbone, keeps persistent client-specific heads, and uses a recalibrated global head as a teacher during local training. Across MNIST, Fashion-MNIST, CIFAR10, and CIFAR100 under class-wise Dirichlet partitions, pFedKDH obtains the best accuracy in most settings, with accuracy gaps up to 37.67% over the weakest baseline and consistently low standard deviation across repetitions. Component-wise diagnostics and convergence results support the role of persistent heads and distillation-guided local optimization under label-skewed data.

High-dimensional data create challenges for causal effect estimation because identifying the covariates needed for correct model specification becomes increasingly difficult. Double/debiased machine learning (DML) facilitates the use of machine learning (ML) for causal inference by mitigating regularization and overfitting bias, but comparatively less attention has been given to covariate selection in relation to the double robustness (DR) property possessed by some DML estimators. In particular, ML-based covariate selection may result in differential covariate selection or in misspecification of both models, thereby limiting the practical utility of the DR property. To address these issues, we propose using the union of the covariates selected by the propensity score (PS) and outcome ML models to re-estimate both models. Simulation results show that using the union consistently reduces more confounding bias than using separate selected covariate sets. The results also show that ML-based estimation does not uniformly outperform conventional DR estimation, even under conditions favorable to the Lasso, and that post-Lasso reduces more confounding bias than standard Lasso. These findings demonstrate that successful use of ML for causal inference depends not only on the ML algorithm but also on how the information obtained through covariate selection is incorporated into causal effect estimation.

In various fields, such as medicine and marketing, accurately predicting individual treatment effects holds significant promise. However, achieving reliable predictions alone is often insufficient for making informed decisions; it is equally important to understand why the treatment effect is higher for some individuals than for others. To address this two-fold challenge of prediction and interpretation, we introduce an algorithm based on decision trees and random forests for estimating individual treatment effects. Our algorithm is simple: it operates exactly like a standard random forest, but with a different splitting criterion, and requires no additional workarounds such as double machine learning or orthogonalization as used in Generalized random forests. It handles observational studies with varying treatment propensities without requiring separate estimation of the full propensity function. This is achieved by combining two splitting criteria—one targeting heterogeneity in the treatment effect, the other targeting bias correction for the average treatment effect—which together improve split point selection and automatically distinguish confounders from features responsible for heterogeneity. As a result, interpretation follows directly from the fitted tree structure itself, that is, from which features the trees split on and with which split statistics, without requiring separate post-hoc analysis. For the theoretical analysis of this algorithm, we consider a change point model with step functions for potential outcomes and treatment propensity and provide insights into the theoretical underpinnings of our approach. Simulation studies show that our simple algorithm achieves comparable, and often better, prediction accuracy than existing methods, while substantially improving interpretability.

Feature-based multi-product pricing uses customer characteristics to identify demand heterogeneity and tailor prices across products. Choice model trees segment customers through interpretable feature rules and fit a demand model within each leaf. Existing methods typically construct these trees greedily, selecting one myopic split at a time. We develop optimal choice model trees with multinomial logit leaves (OCMT-MNL), jointly optimizing the tree and leaf models within a prescribed depth. Our exact dynamic program derives closed-form Fenchel lower bounds during constrained Newton iterations and propagates them across nested and disjoint customer subsets, avoiding new fits and resuming unfinished fits without repeating completed work. In synthetic experiments, it reduces exact leaf fits by 99.98% and leaf evaluations by 86.13%, achieving up to 7.15-fold speedups over unpruned dynamic programming. One-dimensional lookup tables translate offline estimation into real-time pricing, with a revenue-loss bound quadratic in grid spacing under the fitted model. Compared with greedy trees, OCMT-MNL achieves lower revenue loss with fewer leaves on synthetic data and better predictive fit on real data. In a 23-week randomized experiment on ancillary seat pricing across 48 airline markets and 190,220 passengers, OCMT-MNL increases seat revenue per passenger by a statistically significant 11.3% over static pricing.

We propose Low-Rank Quantile Surfaces (LRQS), a bivariate causal model in which, in the causal direction, an unknown monotone transformation of the conditional quantile surface admits a low-rank functional decomposition. LRQS subsumes location-scale noise models and post-nonlinear heteroscedastic noise models, while allowing multiple quantile bases to represent changes beyond location-scale effects. We prove generic identifiability of LRQS: the transformed quantile surface is low rank in the causal direction, whereas reverse representability under the corresponding constraints occurs only for exceptional, fine-tuned cause marginals. We provide a simple-yet-powerful causal score using a nonparametric fitting procedure that alternates between rank-constrained approximation of discretized quantile surfaces and isotonic estimation of the unknown monotone transformation. Experiments on synthetic mechanisms with higher-rank distributional shape variation and strong nonlinear distortions, together with standard bivariate benchmarks, show that LRQS is especially effective when conditional distributional shape or observation distortion goes beyond existing location-scale assumptions.

Hyperbolic geometry provides a natural inductive bias for genomic representation learning, but existing hyperbolic genomic models primarily use Lorentz convolutions to learn local sequence representations, while their residual pathways do not directly aggregate full Lorentz representations. We propose HyCoSeq, a contextual hyperbolic representation learning framework for genomic sequences. HyCoSeq incorporates weighted Lorentzian residual aggregation into multi-curvature Lorentz encoding, allowing full Lorentz representations to participate directly in geometry-consistent local aggregation. It further introduces a bidirectional long short-term memory network that integrates information from both sequence directions to learn contextual relationships among local representations at different positions within a genomic sequence, thereby extending local hyperbolic convolutional encoding to sequence-level contextualized representations. Extensive experiments across diverse genomic tasks show that HyCoSeq outperforms existing hyperbolic baselines and, without large-scale genomic pretraining, achieves competitive performance against substantially larger pretrained DNA language models.

Weighted majority votes are central to many successful ensemble methods. PAC-Bayesian theory provides tight generalization guarantees for such models by analyzing the expected risk of stochastic classifiers, while analyzing the risk of deterministic majority votes relies on surrogate bounds. To avoid these surrogates, Zantedeschi et al. ( 2021) introduced guarantees for stochastic majority votes, but the resulting models remain randomized. In this paper, we propose a derandomization framework for stochastic majority votes. To do so, we apply recent advances in disintegrated PAC-Bayesian theory directly to the space of majority vote weight vectors, transforming stochastic guarantees into certificates for a single deterministic majority vote. We derive two families of high-probability generalization bounds, covering both data-independent and data-dependent constructions of the ensemble, which naturally lead to a self-bounding learning algorithm optimizing deterministic majority vote guarantees.

Time-warping estimation is a fundamental problem in signal processing with applications in bioacoustics, radar, and biomedical analysis. This paper introduces a Time-Warping Estimation Trainable (TWET) model for estimating timewarping functions from a single observation. The proposed approach formulates time-warping estimation as a stationarization problem in the wavelet domain and leverages a hierarchical dilated convolutional architecture to estimate the time-warping functions. A differentiable stationarity criterion is introduced for end-to-end optimization. TWET is compared with existing approaches. Experimental results show improved deformation reconstruction accuracy together with significantly reduced computation time, making the framework compatible with low-latency applications.

Parameter estimation in finite mixture models can exhibit highly heterogeneous convergence behavior: locally isolated components may be estimated substantially faster than groups of competing components. Existing analyses based on Wasserstein distances typically characterize only the worst-case rate and therefore do not fully capture this local heterogeneity. In this paper, we introduce a Voronoi-based partial optimal transport (VPOT) framework for obtaining refined local and global convergence guarantees for the maximum likelihood estimator of the mixing measure. The key geometric idea is to localize the comparison of two mixing measures to extended Voronoi neighborhoods and use partial optimal transport to accommodate the unequal masses of their local restrictions. Within each neighborhood, the first-order POT discrepancy is raised to a power determined by the number of locally competing atoms, allowing the resulting loss to adapt to the local degree of singularity. Under suitable regularity and strong identifiability conditions, we establish uniform local and global upper bounds for a maximum likelihood estimator under the VPOT loss. These bounds reveal a configuration-dependent form of parameter estimation: less singular local configurations admit faster convergence, whereas the most singular configuration recovers the classical worst-case behavior characterized by Wasserstein-based analyses. We further establish a minimax lower bound showing that the convergence rate for estimating the mixing measure under the VPOT loss is optimal. Our results hold in arbitrary fixed dimension without requiring mixing proportions to be uniformly bounded away from zero or prior knowledge of the true number of mixture components. Overall, VPOT provides a configuration-adaptive framework for capturing heterogeneous parameter-estimation behavior in finite mixture models.

Neural PDE solvers provide efficient surrogates for time-dependent physical systems, but autoregressive prediction over long horizons remains challenging because local errors can induce distribution shift and accumulate under recursive deployment. We develop a variational approach to this problem by introducing latent Markov dynamics in which physical states are represented by latent distributions and evolved through probabilistic transitions. The framework is formulated directly on function spaces and specialized to functional Gaussian models, where structured latent perturbations induce a spectral geometry and variational transition alignment regularizes the learned dynamics. We further analyze how these mechanisms affect autoregressive error propagation, providing a theoretical connection between variational training and long-horizon prediction. We instantiate the framework as the Variational Autoencoding Markov Operator (VAMO), which combines spatially resolved latent fields, structured Gaussian perturbations, and a neural-operator transition. Empirically, we demonstrate the effectiveness of VAMO on several fluid-dynamics benchmarks with prediction horizons extending substantially beyond those represented during training, where it consistently reduces error accumulation and improves rollout stability over several deterministic and noise-injection baselines. Overall, these results highlight variational modeling as a complementary approach to robust long-horizon neural PDE dynamics.

The chain ladder's volume-weighted pattern minimises an explicit loss function, yet is rarely booked as such. Practitioners adjust the pattern and record the final adjusted ratios. This paper treats the chain ladder's pattern selection as a supervised-learning problem. Judgement on pattern adjustments becomes a framework of defined penalties and hyperparameters on the chain ladder's loss function, treated here as an objective function in machine learning. Data weights are generalised with a decay and a power parameter for recency and volume weighting. Benchmark shaping and smoothness enter through a reference penalty and Whittaker-Henderson smoothing. The assembled objective is strictly convex and minimised by a single linear system. Each hyperparameter becomes an interpretable adjustment in its own right, declarable by judgement and categorised as an experience or a prospective adjustment. Experience adjustments can be set more objectively by a proposed training loop and a reserve validation score on held-out calendar diagonals. Further hyperparameter-based adjustments are written as almost-everywhere differentiable penalties that re-time or reshape the pattern. A worked example carries one real Schedule P triangle through an incurred and then a paid training stage, demonstrating the workflow.

Single-cell perturbation experiments provide causal information on gene regulation, whereas population-scale single-cell studies characterize gene expression and phenotypes in human populations. We develop a framework that integrates these complementary data sources for causal path analysis. Rather than assuming that a perturbational gene network transfers directly to the target population, we use externally learned ancestral relationships to constrain the network topology and re-estimate its direct edges and effects from population data. To address latent heterogeneity and measurement error in multiscale single-cell measurements, we develop a surrogate-variable procedure operating at both the cell and subject levels, combined with errors-in-variables correction for network and outcome regressions. We establish theoretical guarantees for confounder recovery and high-dimensional estimation of network and gene-outcome effects. Simulations demonstrate the importance of jointly correcting confounding and measurement error. An application to acute myeloid leukemia identifies distinct regulatory pathways linking transcriptional regulators to blast count.

We develop a certified continuation framework for inference and training in deep equilibrium networks (DEQs), with training posed as interpolation to accuracy $2^{-b}$. For inference, input homotopy selects an equilibrium branch from a supplied start root, and a rounded tracker follows it under quantitative conditioning, derivative, boundary, and tube-radius certificates. The framework includes structured factorized certificates, sequential block elimination, inheritance of contraction guarantees in adapted coordinates, and bordered continuation through simple folds. For smooth multidimensional DEQs, including tanh networks, rational local tests can construct and validate oriented continuation charts under explicit geometric promises. For training, programmable dormant bilinear rank-one channels provide output-preserving residual-aligned repairs. Loaded Tikhonov solves diagnose insufficient parameter-to-output directions, while certified gate realization, column stability, well-posed inference, and finite-update error budgets control each pass. Under polynomially bounded certificate, encoding, precision, and backend costs, both inference and training have bit complexity $O(\mathrm{poly}(L+b))$, where $L$ is the encoded instance length; training uses $O(b+\ell)$ passes and reserve channels from an initial residual bounded by $2^\ell$. A budgeted implementation returns either certified success or inconclusive termination. The quantitative core and local certificate machinery are machine-checked in Lean 4, while numerical experiments illustrate the training mechanism.

Deep spline superposition networks face a tension between approximation order and stability across depth. We study approximation under a hard layerwise Lipschitz budget, and organise it around two quantities: the factorisation stability complexity of a given deep factorisation, and the budget-compatible approximation complexity of a discretisation operator. First, we solve exactly the finite-depth diagonal balancing problem for a fixed chain of nonnegative envelope matrices: the optimal uniform layer budget equals $\|M_{L-1}\cdots M_0\|_{\infty\to\infty}^{1/L}$, attained by an explicit one-pass minimiser, for rectangular layers, with a complete treatment of degeneracies and non-attainment. The optimum can be arbitrarily larger than the Lipschitz constant of the network itself, because passing to envelopes destroys sign cancellation. Second, we give a constructive spline discretisation theorem preserving the budget up to a controlled slack, with an explicit grid threshold. Conversely, for linear spline-valued operators that preserve the budget exactly, we prove budget-compatible minimax lower bounds on classes constrained simultaneously in the first and third derivative norms – a constraint pair that is forced by the problem and that rules out the usual scaling escapes. Finally, we show that the corresponding layer errors need not cancel under composition: for every operator of the class there is a stable depth-$L$ tower realising a constant fraction of the accumulated error, so the linear-in-depth accumulation of the upper bound is not a proof artefact.

Classification and regression trees are typically constructed using a greedy splitting rule that maximizes the immediate reduction in prediction error at each node. Although this strategy is computationally efficient, it can miss splits that yield small short-term gains but create substantial downstream improvements after further partitioning. We propose a look-ahead tree-building method that evaluates each candidate split by the prediction error reduction achieved after growing a conventional CART subtree below that split. Because the full look-ahead procedure can be computationally expensive, we also describe a smart look-ahead algorithm that learns downstream split values using node-level features. The proposed framework preserves the interpretability of recursive partitioning while improving split selection in hierarchical or interaction-driven settings. We conduct a simulation study comparing conventional, full look-ahead, and smart look-ahead methods under several settings and apply the proposed methods to analyze two real data examples demonstrating the merit of the new methods.

Class-balanced learning and label noise create a coupled failure mode: frequency correction prevents majority classes from dominating the decision rule, but can amplify incorrectly labeled minority examples. We introduce BARGE (Bounded Adjustment with Reliability-Guided Embeddings), a single-stage objective combining a bounded, prior-adjusted density-power score with reliability-guided angular geometry. Its classification score is strictly proper in the adjusted probability space and recovers balanced Bayes ordering under clean supervision and the true class prior. Under label contamination, its finite range bounds classification-risk perturbation at a fixed predictor, while its logit gradient redescends when the model confidently contradicts the supplied label. The adjusted target probability also weights class-equal feature compactness, and a one-sided separation term discourages aligned class directions. BARGE requires neither a noise rate nor a transition matrix, uses one network, and leaves inference unchanged. We evaluate it on CIFAR-10, CIFAR-100, and Tiny ImageNet under long-tail and step imbalance, clean labels, and 20% and 40% random incorrect-label replacement. Across 12 clean settings, BARGE ranks second overall and attains the lowest error in four. Under corruption, it achieves the lowest mean balanced error in all six dataset-corruption settings, reducing the six-setting average from 72.32% for the strongest competitor to 70.00%. It also obtains the highest macro-F1 and macro-AUPRC in every corrupted-label setting. Ablations show that class-equal angular compactness improves on the bounded score alone. These results support bounded predictive influence and reliability-guided geometry as complementary mechanisms for imbalanced learning with uncertain labels.

Real-world datasets often exhibit long-tailed class distributions, where a few head classes contain a large number of training samples while a large number of tail classes have only a few. The composition of each mini-batch, determined by the sampling strategy, governs which classes contribute to the stochastic gradient estimate, and therefore affects convergence behaviour and generalisation across the whole class spectrum. We provide a systematic theoretical and empirical comparison of four mini-batch sampling strategies for long-tailed image classification: uniform instance sampling, class-balanced sampling, square-root sampling, and progressively balanced sampling. We place all four in a unified bias-variance framework describing their effect on gradient estimation, which exposes the tension between unbiased optimisation of the empirical loss and fair representation of rare classes. We then evaluate them under controlled conditions using ResNet-32 on CIFAR-100-LT at three imbalance ratios (rho = 10, 50, 100), with every strategy sharing the same long-tailed subsets and initialisation within a seed. Progressive sampling improves tail-class accuracy by 25% relative to the uniform baseline at rho = 100 (13.5% versus 10.8%), consistently across all three seeds, while its overall accuracy is not distinguishable from that of uniform sampling given the seed-to-seed variation (40.0% versus 39.7%); the tail-class gain, not the overall gain, is the robust effect. At rho = 100, class-balanced sampling degrades accuracy on every class group, including the tail classes it is designed to help, which we attribute to overfitting caused by extreme oversampling of scarce data; at rho = 50 this failure is confined to head and medium classes. These results indicate that when rebalancing is applied during training matters as much as how much rebalancing is applied.

Pretraining followed by fine-tuning introduces a compute-allocation problem: under a fixed training budget, compute spent improving the upstream objective reduces the compute available for downstream adaptation. Despite its practical importance, this trade-off is not yet well understood theoretically, even in simple models. In this paper, we cast this allocation as a compute-split problem under a two-stage pretrain–fine-tune procedure with fixed total optimisation budget, using regularised least squares trained by gradient descent as a tractable setting. We characterise the optimal split under data-dependent evaluation geometries induced by the fine-tuning problem. Our results show that the allocation depends on how pretraining directions affect fine-tuning predictions and how fine-tuning shifts are seen through downstream data geometry. In particular, the relevant quantities are determined by prediction-relevant spectral components of the pretraining and fine-tuning empirical covariances. Technically, the analysis relies on a basis-invariant, eigenspace-level spectral decomposition, together with perturbative control of the non-commuting pretraining and fine-tuning dynamics.

Diagnostic errors and mislabeling are common in biomedicine, which compromise the reliability of predictive models and data-driven outcomes. Stratifying unlabeled biomedical data based on complex relationships between features eliminates the need for data labels and overcomes the limitations of supervised learning. Traditional clustering methods assume restrictive data distributions, making them suboptimal for capturing complex dependencies in high-dimensional biomedical data. This paper introduces a novel cluster-friendly data presentation framework that integrates the non-Gaussian and non-linear feature dependence of copula models with an ensemble of causal structure discovery (CSD) methods based on Directed Acyclic Graphs (DAGs). While copulas model flexible multivariate distributions by relaxing assumptions related to multivariate normality, linear dependence, and symmetric relationships, an ensemble of DAG-based CSD methods identifies stable causal relationships between features. When clustered using K-means, the new data representation obtained by the proposed copula-adapted DAG (CopDAG) ranks first among the 12 methods in normalized clustering accuracy and adjusted Rand index across 16 biomedical datasets. Our CopDAG method predicts ground-truth class labels directly from feature relationships without data annotations and supervised learning, while also providing cluster visualizations and explainable causal structures of the biomedical data features.

Prototype reduction replaces a training set with a smaller representation, and the established methods return a finite set of points. We propose Skeletal Prototypes on Iterative Nerve Expansions (SPINE). The model for each class is an embedded 1-complex rather than a point set. Its initial edge set is a class-conditional Mapper graph, so the data decide which localized clusters are joined. Later phases fit the vertices under a classification objective, and an observation is assigned to the class whose complex is nearest. The segments therefore enter the decision rule and not only the fitting. We evaluate SPINE on seventeen benchmark datasets under stratified 10-fold cross validation, against seven other prototype reduction methods at a matched budget. SPINE attains the highest mean accuracy and the best average rank. It is significantly better than five of the seven competitors under Wilcoxon signed-rank tests with Holm correction. A budget sweep shows that the decision rule using the entire graph segments contribute most when prototypes are scarce, while the method as a whole competes best at moderate budgets. Construction cost places SPINE with the discriminative methods, and it is faster than generalized learning vector quantization on fourteen of the seventeen datasets.

Some of the sharpest challenges in sampling from the energy functions of physical systems arise at phase transitions, where the density of states changes abruptly and many sampling algorithms stall. Nested sampling is a particle method that traverses the density of states under a hard energy constraint and is known to be robust to such transitions, but its application in high dimension is limited by the difficulty of sampling under that constraint. In this work we introduce Quenched Ensemble Sampling, which generalises the hard constraint to a family of repulsive potentials at the energy boundary. This preserves the quenched path of monotonically decreasing energy while making the constrained target amenable to scalable gradient-based kernels. We demonstrate on synthetic models of phase transitions that our method estimates the marginal likelihood and draws posterior samples across a first-order transition where popular alternatives such as tempering fail. We apply the procedure to marginal likelihood estimation in Bayesian neural networks, enabling model comparison between network architectures. Finally, in a high-dimensional continuous lattice field theory, we show that this method traverses a first-order transition and estimates the partition function.

Spectral features can remain optimal under strongly uneven task preferences when they retain the directions most useful to the tasks. In a local-task model, expected probing gain depends on the task prior only through its covariance $\Lambda$: with $B$ recording dependence between views, $k$ spectral features span the leading eigenspace of $BB^\top$, while task-optimal features span that of $B\Lambda B^\top$. We derive alignment-dependent regret bounds, matching worst-case lower bounds for a flat leading spectrum, and bounds using the leading $2k$ directions with a spectral-tail term; a spectral gap makes the bound quadratic in small anisotropy. We also bound the imbalance from random preference patterns and from averaging independent tasks with an isotropic population covariance. With known $\Lambda$, changing one term of the spectral contrastive loss selects task-optimal features; with a labelled task bank, we propose a diagnostic and test correction without retraining. Correction reduces synthetic held-out regret from $0.858$ to $0.003$ with $2000$ tasks when less task-relevant directions dominate, and on CIFAR-100 lowers empirical regret by $0.031$–$0.053$ on held-out fine-label tasks using the same images. With a small task bank, however, correction can hurt.

We study density ratio estimation and importance-weighted regression under target shift with continuous outputs. Under target shift, the conditional distribution of the inputs given the outputs remains invariant across the training and test distributions, while the output marginal distribution may change. Although this problem has been extensively studied for discrete outputs, the continuous setting is substantially less understood: the importance weights are determined by an unknown density ratio function, for which existing estimation methods lack explicit finite-sample convergence rates. We propose a spectral regularization method in a reproducing kernel Hilbert space (RKHS) for estimating the continuous density ratio from labeled training samples and unlabeled test inputs. Under a source condition with regularity parameter $\iota>0$, we establish high-probability finite-sample guarantees and show that the estimator achieves the capacity-independent minimax-optimal RKHS-norm rate $O(n_\eta^{-\iota/(2\iota+2)})$. We then incorporate the estimated density ratio into importance-weighted regression and characterize the propagation of density-ratio estimation error to the final predictor. When sufficiently many samples are available for density ratio estimation, the resulting regression estimator attains the minimax-optimal rates of standard kernel regression. These results establish a finite-sample theory for continuous density ratio estimation and importance-weighted learning under target shift.

Keyed watermark detection tests dependence between observed tokens and pseudorandom variables reconstructed from a secret key. Building on the pivotal framework of Li et al. (2025), we construct predictive likelihood ratios that average over uncertain probability deficits and residual-tail distributions. The aim is robust detection power across alternative specifications without requiring a single signal-strength tuning. A mixture prior combines tail shape and effective width; hierarchical extensions allow within-document variation in deficit or width. The test maximizes prior-averaged power at a fixed size, but is not generally uniformly most powerful or minimax. Under the exact conditional pivot null, normalized predictive alternatives selected before each observation yield a Bayes factor that is also a test martingale: Type I error control is unaffected by alternative misspecification and remains valid under optional stopping. This guarantee does not cover violations of the conditional null, and the interpolated implementation has no certified anytime guarantee. Gumbel marginal likelihoods are evaluated by fixed quadrature. Across the evaluated tail-shape and tail-width alternatives and three horizons, the union-tail mixture has maximum observed Type II error regret .0080, compared with .0962 for the equal-tail mixture, relative to the best tested rule. On temperature-matched outputs from two open models, it improves AUC over the equal-tail baseline in all eight non-saturated model-temperature cells, although the leading reference score generally has higher AUC. Supplementary experiments show retained power under independent null-like replacement and smaller changes from hierarchical dependence modeling. The evidence supports robustness across the evaluated alternatives, not uniform power guarantees or resistance to arbitrary text edits.

This paper studies the detection of multiple simultaneous (systematic) change points for high-dimensional nonstantionary economic and financial time series data. The analytic framework used is based on the standard and adaptive fused group lasso method, where the mixed L_{2,1} penalty is either uniform or re-weighted by data-dependent weights. This paper shows that, under appropriate conditions, this approach is L_2 consistent and, by adopting the data-dependent weights, could correctly select the change points with probability approaching unity (L_0 consis- tency). It quantifies the conditions on the interplay among the averaged minimum magnitude of structural changes, the number of change points and the number of observations for consistently discovering the change points. The performance of this approach is illustrated via an analysis of a large panel of U.S. economic and financial time series data over the past 50 years.

End-to-end Supervised Graph Prediction (SGP) requires a permutation-invariant loss to compare predicted and target graphs with arbitrary node orderings. Such losses typically involve a costly graph-matching problem. We first study three Optimal Transport relaxations of this problem and show, theoretically and empirically, that the Gromov-Wasserstein (GW) objective is the most suitable for SGP. Then, to avoid solving the resulting inner optimization for every training example, we propose to amortize the graph matching (node alignment) problem. For each training sample, the loss function leverages a transport plan provided by a parametric matcher based on the differentiable Sinkhorn algorithm applied on empirical node distributions. The graph prediction module and the matcher are jointly learned. We showcase the efficiency of this approach on toy and real world SGP problems of increasing complexity including a novel Mass-spectra to Scaffold task that we introduce.

We study the uniform approximation of smooth scalar-valued functionals on an infinite-dimensional separable Hilbert space by ReLU neural networks. A key feature in deep learning for functional data is the varying importance of different coordinates/dimensions. Representing the functional input in a basis expansion, we quantify the importance of each coordinate through both the magnitude of its corresponding basis score and the directional sensitivity of the target functional. Our analysis combines coordinate truncation, anisotropic partitioning, local Taylor approximation, and ReLU network realization, while allowing unrestricted interactions among the retained coordinates. We establish a general nonasymptotic upper bound for the uniform approximation error and a complementary pseudo-dimension-based lower bound for the worst-case approximation error. Under generalized exponential coordinate decay $w_ds_d\asymp\exp(-cd^\rho)$, with $\rho>0$, the upper and lower bounds match at the leading order, which is stretched-exponential in the logarithm of the network size budget, and thus yield the nearly optimal approximation rate. This is the first work to characterize neural network approximation error for infinite-dimensional functional inputs explicitly through the joint dimensional decay of coordinate magnitudes and directional sensitivities.

Conformal counterfactual prediction constructs prediction sets with finite-sample coverage guarantees for counterfactual outcomes and individual treatment effects under the no-interference assumption. In this work, we relax this assumption by allowing each unit's potential outcomes to depend on other units' treatments and covariates. In this setting, propensity-score reweighting does not restore weighted exchangeability, and existing methods may fail to achieve valid coverage. To address this issue, we develop interference-adjusted weighted conformal prediction that accounts for interference by constructing an observable upper bound on the ideal and unobserved conformal $p$-value under the target intervention. The resulting prediction sets provide finite-sample marginal coverage guarantees for counterfactual outcomes and individual treatment effects in both transductive and inductive settings. We also derive a sharper construction when intervention-induced changes in nonconformity scores are bounded. Numerical experiments show that our methods preserve nominal coverage, whereas existing methods may not.

A learner probes at most $k$ of $n$ arms each round, receives the maximum of their rewards in $[0,1]$, and competes with the best fixed arm. When does the probing advantage pay for learning? We determine two minimax laws. Under independent stochastic rewards with winner feedback (the maximum and a winning label), or on arbitrary fixed sequences given a single signed contrast between block maxima, the minimax regret has order $\Phi_{n,k}(T)=\min\{\frac{n-k}{n}T,\frac{n-k}{k}\}$, $2\le k<n$. Under winner feedback, both arbitrary joint i.i.d. rewards and fixed sequences have minimax regret of order $R_{n,k}(T)=\frac{n-k}{n}\min\{T,\frac{n+T}{k},\sqrt{\frac{nT}{k}}\}$. Both laws have universal constants and anytime upper bounds. The first reduces regret to a pure coverage cost: same-round contrasts absorb the stability cost, and independence permits exact resampling whose gains fund sample advancement. The second adds a learning cost that becomes comparable to coverage at horizon $n$; beyond $nk$, numerical maxima improve over labels alone. The lower bound allows every adaptive action size.