Papers

Understanding cognitive processes in major depressive disorder (MDD) often relies on behavioral tasks, which are typically analyzed separately, overlooking potential correlations and shared latent structure. To address this limitation, we propose the Shared Hidden-factor Information Framework for Multiple Behavioral Tasks (SHIFT), a joint modeling approach that leverages shared information across tasks, allowing each task to benefit from information learned by the others. SHIFT introduces subject-specific latent factors that capture cross-task dependencies while accommodating individual heterogeneity in decision-making, response times (RTs), and strategy switching. To address computational challenges without requiring high-dimensional integration, we develop an expectation-maximization with variational approximation algorithm that preserves both temporal structure and between-task dependencies. Through extensive simulation studies, we demonstrate that SHIFT substantially improves estimation accuracy and efficiency relative to single-task analyses. We then apply SHIFT to a study of MDD to jointly model the Probabilistic Reward Task (PRT) and the Flanker Task (FT). Results indicate that MDD participants show lower engagement in the PRT and reduced focus in the FT compared with healthy controls. Moreover, when individuals are engaged and focused, they exhibit longer RTs. Although observed RTs do not predict treatment response, the shared parameters recovered by SHIFT showed suggestive treatment-modulation patterns, indicating their potential as exploratory behavioral markers for therapeutic outcomes.

We generalize finite-sample bounds for convex clustering to the setting where affinity weights appearing in the objective correspond to a general connected graph. These bounds and their analysis lead to a better understanding of clustering behavior under various implied connectivity structures behind the data and to new rates of convergence for centroid recovery. The new theoretical framework is based on random walks, which allow application of concentration inequalities related to random graph models, and formalizes the relationship between the clustering performance and the connectivity of the graph structures. Through the form of the bound and empirical results, we argue proper tuning of hyperparameters to convex clustering problems should also include tuning of input affinity weights.

Selecting a finite dictionary of observables whose span is Koopman-invariant is a central challenge in data-driven Koopman operator approximation. We address this problem by exploiting zero-block structure in Extended Dynamic Mode Decomposition (EDMD) matrices. We show that any sub-dictionary whose span is Koopman-invariant induces an exact zero block in the EDMD matrix, even for finite data. We then show that such blocks can be detected by applying PageRank to a row-normalized EDMD matrix constructed from a large initial dictionary. The theory extends to approximately invariant subspaces and yields stronger guarantees for personalized PageRank (PPR) when the seed observables lie inside the target block and reach all observables in that block. Combining EDMD concentration bounds with PageRank perturbation theory gives end-to-end detection guarantees with $O(1/\sqrt{M})$ finite-sample scaling and explicit constants. More generally, without assuming an invariant subspace exists, high PPR mass on a sub-dictionary controls discounted multi-step leakage from the seed observables. Numerical experiments on the Duffing oscillator, Van der Pol oscillator, Lorenz system, and a three-well Ramachandran potential suggest that the method identifies compact, interpretable dictionaries with accurate predictions.

Quadratic regularization has emerged as a potential alternative to the popular entropic regularization in computational optimal transport, offering the theoretical advantage of producing sparse couplings through its hinge density structure. Despite recent progress in one-dimensional settings and general upper bounds, fundamental questions about the localization rate of QOT optimizers around the Monge coupling have remained open. In this work, we establish a general lower bound showing that the support of the QOT optimizer cannot concentrate around the Monge graph faster than order $\varepsilon^{\frac{1}{d+2}}$ in the directed Hausdorff distance, matching the conjectured optimal exponent under standard regularity assumptions in \citet{wiesel2025sparsity}. We also show that the QOT value gap controls the mean-squared deviation $\mathbb E_{\pi_\varepsilon}\|y-T(x)\|^2$ by the scale of $\varepsilon^{\frac{2}{d+2}}$. As a corollary, in the affine Brenier regime, which includes Gaussian-to-Gaussian transport, we derive a sharp pointwise tube bound of order $\varepsilon^{\frac{1}{d+2}}$ by reducing the problem to self-transport and applying recent self-transport sparsity results. Finally, we validate our theoretical bound with a synthetic experiment in high-dimensional settings.

We propose a general robust prediction framework, termed conformity-based projective prediction (CPP), that integrates Bayesian predictive modeling with ideas from conformity-based conformal prediction. Rather than assessing conformity through residual-based scores, the CPP criterion defines conformity distributionally: a candidate value for a future response is considered conforming to the extent that its inclusion in the data leaves the leave-one-out predictive distributions of the observed responses undisturbed. The framework requires only that the leave-one-out and swapped predictive distributions are available in closed form and that the swapped predictive mean is differentiable in the candidate value. Under these conditions, we establish a general bounded-influence proposition and a general local convexity lemma, and prove that CPP dominates any plug-in predictor with unbounded influence in asymptotic variance under $\epsilon$-contamination models. When the posterior mean is linear in the observations – as in Gaussian linear models, basis-expansion regression, and Gaussian process regression – the swapped predictive mean is affine in the candidate value, yielding closed-form or one-dimensional optimization solutions and an efficient rank-two computational update; all general theoretical results specialize to explicit corollaries in this setting. Simulation experiments and two data analyses under the Gaussian linear model illustrate the finite-sample advantages of the proposed method, confirming the theoretical predictions across contamination levels, sample sizes, and predictor dimensions.

Low-light, long-exposure defocus deblurring remains a challenging problem due to the simultaneous presence of severe blur and complex biased noise. Existing methods typically rely on simplified noise assumptions, which limits their effectiveness under realistic imaging conditions. In this work, we propose Physen-Noise2Noise, a self-supervised deblurring framework guided by the physical model of defocus imaging, which leverages noisy multi-frame observations without requiring clean reference images. Unlike conventional Noise2Noise-based approaches that assume zero-mean noise, we derive a frequency-domain constraint inherent to the defocus imaging process and incorporate it into the learning framework via a learnable noise bias parameter. In addition, a multi-frame noisy initialization strategy is introduced to suppress complex biased noise prior to deblurring, providing a more stable starting point for reconstruction. This formulation explicitly models biased noise and enables joint bias correction and high-frequency detail recovery during training. Furthermore, we develop a pretrain-finetune variant to enhance robustness and generalization under challenging noise conditions. Extensive experiments on both simulation and real-world datasets demonstrate that the proposed method consistently outperforms state-of-the-art self-supervised approaches for defocus deblurring in the presence of complex biased noise.

In high-dimensional clustered data, covariates whose distributions differ across clusters can act as proxies for unobserved cluster effects. We show that the marginal-model LASSO implicitly uses sparse combinations of such covariates to shift the estimation target from structural coefficients to a contaminated vector, which inflates false selections. We therefore propose the Synthetic Heterogeneous-Effects LASSO (SHEL), which augments the regression design with separately penalized, outcome-independent, cluster-constant synthetic covariates to correct the cluster-induced target shift. Under a fixed nuisance-effects formulation, we derive oracle properties and establish consistency of the structural coefficients when the residual heterogeneity is weakly aligned with the augmented design. We also demonstrate the distinction between the structural parameter under small residual heterogeneity and the population working parameter when residual heterogeneity persists. Further, we develop a debiased estimator with a cluster-robust sandwich variance, and establish asymptotic results. Simulations show far fewer false selections than the marginal LASSO, and an analysis of longitudinal neutrophil transcriptomic data from hospitalized COVID-19 patients yields a more parsimonious gene set that retains the severity markers of the original study.

Comparing a model's internal activations before and after alignment is a natural way to ask what safety training changes: one forms the matrix of paired aligned-minus-base activations on safety-relevant inputs and reads off its effective rank or top direction. We show the obvious way to form this matrix is confounded. The aligned model is evaluated under a chat template the base model never saw, so the naive difference conflates the alignment shift with chat formatting. We introduce a four-variant decomposition of the modification matrix (naive, template-controlled, within-aligned, and difference-in-differences, DiD) that separates the two effects. Template control alone removes a 2.0-3.9x inflation of the measured effective rank across Llama-3.1-8B, Gemma-2-9B, and Qwen-2.5-7B; the DiD contrast is what recovers the refusal direction of Arditi et al. (2024), lifting its cosine alignment from 0.18-0.39 to 0.50-0.86. Projection-ablation across the three families confirms the recovered subspace is behaviorally active and that singular-value order is not causal order. We validate the protocol on a controlled testbed and distill it into measurement recommendations for activation-difference studies of alignment.

The Normalized Maximum Likelihood (NML) codelength, or stochastic complexity, represents a principled criterion for universal coding. While recent coarea-based formulations provided a calculation method for smooth models, this framework collapses for the non-smooth estimators ubiquitous in modern machine learning (e.g., Lasso, Sparse SVMs). In this work, we provide a rigorous framework for computing the NML for regular path-differentiable Lipschitz (PDL) estimators. By applying classical geometric measure theory and bridging the coarea formula with conservative Jacobians, we prove that the stochastic complexity for non-smooth models is well-posed and theoretically consistent with the outputs of modern Automatic Differentiation. To compute this quantity exactly, we introduce the Propose-and-Project Metropolis-Hastings (PDL-PPMH) sampler, a geometric MCMC algorithm capable of traversing the non-differentiable level sets of the maximum likelihood estimator. We theoretically justify its components, including a stochastic tangent space proposal and a provably convergent non-smooth projection solver. We demonstrate the method's robustness by sampling from a high-dimensional Lasso posterior ($P=2000$), while simultaneously quantifying the computational scaling that governs the trade-off between exactness and mixing time. Crucially, we empirically demonstrate that our exact NML criterion provides a highly data-efficient alternative to cross-validation, achieving statistically indistinguishable predictive optima without requiring data splitting. Altogether, our work paves the way for the theoretical analysis of the NML codelength for regular non-smooth models.

We establish Chernoff-type bounds for the largest eigenvalue of sums of Hermitian random matrices generated by a time-inhomogeneous Markov chain. Our primary regime assumes a compact state space and contractivity of each Markov kernel in Wasserstein distance, i.e., positive Ollivier-Ricci curvature. This assumption is convenient to verify in inhomogeneous settings and is satisfied by several chains of practical interest, such as stochastic gradient descent on strongly convex smooth objectives. We also develop analogous bounds for noncompact state spaces under a notion of spectral gap for inhomogeneous chains introduced by Saloff-Coste and Zuniga. Finally, we illustrate the utility of our results through an analysis of the Elo rating system, a popular method for ranking players in sports analytics, under a dynamic version of the Bradley-Terry-Luce model.

Stochastic Dominance (SD) theory provides a rigorous framework for selecting superior assets tailored to the asset allocation needs of investors with varying risk preferences (i.e., risk-averse, risk-seeking, and risk-neutral). However, traditional stock clustering methods typically rely on geometric metrics such as Euclidean distance, which often fail to effectively capture the intrinsic risk dominance relationships among assets. To address this limitation, this paper proposes an innovative clustering analysis framework based on SD test statistics. Methodologically, this study deeply integrates SD theory with machine learning algorithms. Transcending the limitations of traditional reliance on geometric distance, we innovatively utilize test statistics from first-, second-, and third-order SD to construct a "Stochastic Dominance Coefficient Matrix." Building upon this matrix, we modify the classic K-means and Hierarchical Clustering algorithms. Specifically, we derive 12 distinct algorithm variants tailored to different orders of SD relationships. Simultaneously, we construct the SD-SC coefficient and the SD-DBI index as specialized validity indices to evaluate the clustering performance. Empirically, we analyze constituent stock data from a representative developed market (the US NASDAQ Index) and an emerging market (China's CSI 100 Index). The results verify the effectiveness and robustness of the proposed method. Furthermore, we apply the clustering results to the modification of the Single Index Model and the construction of Global Minimum Variance Portfolios (GMVP). The findings demonstrate that the proposed method effectively facilitates customized asset allocation for investors, holding significant theoretical value and practical implications.

Time series forecasting drives operational decisions in areas like finance, transportation, and energy. While supervised learning approaches achieve strong performance, they require domain-specific training, feature engineering, and ongoing maintenance. Large-scale foundation models have recently emerged as a zero-shot alternative, avoiding task-specific training much like LLMs. In this work, we evaluate foundation models against standard supervised approaches. Rather than focusing solely on aggregate accuracy, we analyze performance across four operational regimes: periodic human-centric systems, physically constrained processes, stochastic financial markets, and heterogeneous demand forecasting. Our results characterize optimal deployment areas. Foundation models perform well in domains with transferable periodic structures and are efficient for cold-start or long-tail scenarios. Conversely, supervised specialists maintain higher precision in systems governed by strict physical constraints. In financial domains, newer foundation models are rapidly closing the performance gap with supervised specialists. We further quantify trade-offs in inference latency, data drift adaptability, and deployment constraints. Finally, we propose a Complexity Router that assigns each series to the optimal model class using empirical features. We demonstrate that this selective routing achieves higher accuracy and significantly lower inference costs compared to deploying a universal foundation model, providing a practical framework for balancing generalization and efficiency.

Real-World Data (RWD), with its large sample sizes and rich clinical detail, offers a compelling alternative to randomized controlled trials (RCTs) for studying treatment effects in diverse and complex patient populations. However, its observational nature introduces confounding that prevents straightforward comparative effectiveness research. Target trial emulation leverages RWD to estimate average treatment effects (ATE) at the population scale and diversity that RCTs cannot achieve, yet its validity depends critically on unbiased ATE estimation under high-dimensional confounding. Many causal inference pipelines address high-dimensional confounding through machine learning and artificial intelligence (ML/AI) outcome regression. However, commonly used ML/AI regression models exhibit systematic prediction bias, with predicted outcomes shrinking toward the marginal outcome mean. This structural bias propagates into ATE estimation and cannot be corrected by cross-fitting, ensemble methods, or any standard ML practice. In this work, we first quantitatively characterize how systematic prediction bias in ML/AI outcome regression leads to biased ATE estimates in causal inference models. We further propose an unbiased ML/AI regression-based causal inference framework to ensure unbiased ATE estimation for observational studies. We demonstrate our approach by studying the effects of opioids on cardiovascular health in patients with chronic pain using UK Biobank data.

Multicalibration extends classical calibration by requiring predictions to be unbiased over a rich collection of functions, encompassing both prediction slices and subpopulations. It has emerged as a powerful framework for fairness, robustness, and reliable prediction, yet the theoretical understanding of multicalibration boosting (MCBoost) remains fragmented and often relies on restrictive assumptions. In this work, we develop a unified and refined perspective on MCBoost that subsumes existing variants, including multiaccuracy, BatchGCP, and BatchMVP. We uncover several phenomena that provide new insights into its practical behavior: even highly accurate and flexible predictors can remain substantially miscalibrated; enforcing multicalibration introduces a calibration-risk trade-off; and early stopping plays a central role in controlling this trade-off. On the theoretical side, we establish a general framework for MCBoost under weaker and more realistic conditions. We show that the boosting iterates converge to a Bregman projection of the population-optimal predictor onto the cumulative span generated by the audit class, thereby explicitly characterizing the function space on which multicalibration is achieved. We further derive convergence rates under different smoothness assumptions, finite-sample guarantees, and principled stopping rules that ensure multicalibration at termination. Finally, we extend the theory of universal adaptability under covariate shift, providing more general transfer guarantees and clarifying when multicalibrated predictors generalize across domains. These results provide a more complete theoretical foundation and practical guidance for multicalibration boosting, positioning it as both a unifying framework and a reliable post-processing approach for modern predictive models.

The global push for electric vehicles (EVs) has sharply increased demand for critical minerals such as cobalt and lithium, creating a tension between rapid industrial growth and long-term sustainability. Extraction is concentrated in a few regions – notably the Democratic Republic of Congo (DRC), Chile, and Argentina – where it has produced serious socio-environmental harms, including ecosystem degradation, labour exploitation, and the displacement of Indigenous communities. In the DRC, cobalt mining is frequently linked to child labour and hazardous working conditions; in Chile, lithium extraction intensifies water scarcity and threatens local agriculture and biodiversity. Policy instruments such as the U.S. Inflation Reduction Act (IRA) seek to promote ethical sourcing, but an extraction-driven model continues to deepen global inequalities. This chapter examines the contested temporalities of the transition, in which the short-term economic incentives of extraction conflict with longer-term environmental and social goals. It argues for a place-based framework built on community-centred governance, sustainable mining practices, and circular-economy strategies, including recycling and material substitution, to align resource security with equity and ensure that the shift to EVs does not reproduce the injustices it aims to address.

We describe how the target trial framework can be used to plan and report analyses that attempt to answer causal questions by combining information from multiple, diverse sources. Such analyses may involve comparisons of treatments evaluated in different populations, for example when an index trial is combined with other data sources in external comparator analyses, or when extending causal inferences from a randomized trial to a new target population in generalizability and transportability analyses. When planning such analyses, the specification of the target trial supports the explicit definition of the target population with an associated sampling model. We propose this as an additional component for the target trial framework, especially relevant for analyses that combine information, because it influences the choice of eligibility criteria, the specification of the causal model, the choice of causal contrasts, and reasoning about identification strategies. Furthermore, the framework encourages careful mapping of data elements from multiple data sources to a single target trial. This mapping process can highlight potentially irreconcilable misalignments between data sources with respect to specific components of the framework – for example, in the definitions of eligibility criteria, treatment assignment, and treatment receipt. Such misalignments can arise when attempts to specify a target trial that aligns with a specific data source introduce or worsen misalignments with other proposed data sources. The extent of such misalignments may warrant switching to other data sources, or prospectively obtaining data, to emulate the proposed target trial. We conclude that the target trial framework promotes transparent discussion about the design of and assumptions made in analyses that answer causal questions by combining information from diverse sources.

Context or prompt-level reweighting has emerged as a central algorithmic lever in Reinforcement Learning with Verified Rewards (RLVR) for improving the reasoning capability of large language models, yet the principle determining what constitutes an optimal weighting remains poorly understood. We address this gap by formulating prompt reweighting as a functional derivative of a utility functional defined in the pass-rate function space, yielding a unified optimality framework that accommodates existing schemes, including REINFORCE and GRPO. Building on this optimality framework, we propose a distribution-aware prompt reweighting approach, called CurveRL, based on a quantile coordinate transform, in which the weight assigned to each prompt depends not on the absolute value of pass rates but on its rank and density to reflect the distributional structure of the pass rates in the learning dynamics. Extensive experiments across multiple benchmarks demonstrate that our proposed CurveRL consistently outperforms GRPO and other RLVR baselines. Our study identifies context-distribution control as a principled axis for analyzing and designing prompt-reweighted RLVR algorithms. The code is released in https://github.com/zhyzmath/CurveRL.

Softmax attention-based transformers and recurrent memory-based models (e.g., state space models (SSMs)) form the foundation of modern sequence models. Hybrid architectures aim to combine the expressivity from attention and the computational efficiency from recurrent memory, yet so far common practices simply stack both attention and recurrent layers. We propose Interdomain Attention (IA) as a novel hybrid attention architecture that mixes attention and recurrent memory in the same layer. Motivated by a kernel regression view of softmax attention, IA compresses values and kernel features of keys into a recurrent memory parameterized by an SSM. Then IA approximates dot-product attention by implicitly reconstructing the attention matrix and values from memory states; importantly this construction maintains SSM's computational efficiency advantage. We demonstrate IA's efficacy by designing and pre-training IA network architectures, where ablation studies identify attention-like readout as the primary source of gain over SSMs. Across 125M-1.3B models pre-trained on text data, IA improves over an S4D baseline at matched memory size. It also outperforms softmax attention-based Transformer in perplexity and accuracy on common-sense reasoning tasks. Based on Caduceus backbone, IA matches or outperforms the original SSM-based architecture in both perplexity and downstream tasks on genomic data.

Explainability of deep learning algorithms is critical for computer-vision applications with high-stakes decisions. Concept bottleneck models (CBM) have recently shown promising performance to provide explainable and accurate predictions for classification problems, based on a bottleneck of high-level concepts. Existing CBM methods rely on a linear aggregation of the concept scores to compute predictions. However, a large number of concepts is often used in this linear approach, which undermines explainability and favors information leakage. In general, the underlying relation between concepts and output logits is not linear. Therefore, we introduce Hoeffding Concept Bottleneck Models (HCBM), which build on the Hoeffding functional decomposition of gradient-boosted trees to provide non-linear and sparse aggregations of concept scores, and generate compact predictions using prime implicants. HCBM have strong theoretical properties of robustness to interconcept leakage, and outperform sparse linear CBM in practice, as shown in extensive experiments. Beyond classification, HCBM can be adapted to object detection, and we focus on a challenging case with overhead images to show the high performance of HCBM in these settings.

We propose PACE-GGM, a data-adaptive differentially private method for covariance estimation that concentrates its privacy budget on the most informative entries of the empirical covariance matrix, rather than perturbing all entries. This applies in the natural setting where the modeler supplies separate bounds for each variable, so that individual entries can be measured with less noise than the full matrix. In each round, our method selects a poorly approximated entry, measures it using the Gaussian mechanism, and then reconstructs a full covariance matrix using a maximum-entropy reconstruction objective, leading to a Gaussian graphical model structure. Experiments on diverse real-world datasets demonstrate consistent improvements in estimation error with respect to the Gaussian mechanism and other baselines, particularly in high-dimensional and low-to-moderate privacy regimes.

This paper studies the joint role of long-memory dynamics,rough-volatility behavior, and persistence-based forecasting features in equity volatility modeling. We combine semiparametric long-memory estimation, rough-volatility diagnostics, and structured forecasting regressions to examine whether persistence measures contain economically meaningful forecasting information beyond conventional volatility predictors. Using a panel of 115 S&P500 constituents from November 2001 through April 2026, we document that volatility proxies exhibit substantial long-memory behavior and locally rough dynamics. The cross-sectional mean Geweke-Porter-Hudak estimate of the memory parameter is $\hat{d} = 0.226$, while the corresponding local-Whittle estimate is $\hat{d} = 0.440$, with statistical significance observed across nearly the entire panel. Rolling estimates of persistence rise substantially during the global financial crisis and the COVID period and display a positive contemporaneous association with the VIX. We then examine whether persistence-related features improve out-of-sample volatility forecasts beyond standard HAR and HAR-X benchmarks. Incorporating cross-sectional persistence aggregates, sectoral persistence measures, and persistence-by-stress interaction terms produces moderate but statistically significant forecasting improvements, particularly at longer horizons and during stress regimes. Forecast gains are strongest during periods of elevated market volatility and in volatility-managed portfolio applications. The results suggest that persistence measures may serve as useful reduced-form indicators of the duration and propagation of uncertainty in financial markets, although the paper does not claim structural identification of the economic mechanisms generating persistence.

This study presents the development and application of a scalable non-ergodic ground motion model (NGMM) for the Los Angeles area. The NGMM is trained and validated on physics-based simulated ground-motion data from a recent Statewide California Earthquake Center (SCEC) CyberShake study. The NGMM is formulated as a Gaussian Process (GP) regression model, where the prior median is defined as the ASK14 ergodic ground-motion model and the posterior median is obtained by learning the non-ergodic effects embedded in the training data. These non-ergodic effects include systematic site and path effects, which are represented in the GP using Matérn and specialized covariance kernels that explicitly characterize path vectors. Implementing the NGMM requires hyperparameter tuning and inference on large datasets (on the order of one million data points or more), posing significant computational challenges for conventional GP approaches. To address this scalability issue, this paper presents a suite of computational strategies, including sparse Cholesky inversion, parallel computing, GPU acceleration, and stochastic gradient descent minimization. Despite these advances, the full CyberShake dataset (on the order of hundreds of millions of data points) remains computationally prohibitive. Therefore, aleatory variability is modeled separately using a mixed-effects formulation to represent within-event and between-event variability. The developed NGMM has two primary applications: interpolation of partially observed ground-motion fields and predictive modeling for ground motions in unobserved earthquake scenarios. Validation results on independent datasets demonstrate accurate performance in both applications. A case study of power transmission network assessment in an Mw 6.7 Puente Hill scenario further demonstrated that the developed NGMM closely reproduces physics-based simulation results.

Input-convex neural nets parametrize the convex potentials of density models and transport maps, and their convexity requires the inter-layer weights to be non-negative. Projected gradient descent enforces this by projecting after each step, and due to mini-batch noise the boundary is re-crossed indefinitely, which leads to an active set the projection never identifies. The differentiable alternative, direct softplus, optimizes a free latent weight through a softplus positivity map whose derivative attenuates the gradient exponentially where the weight is negative—the shoulder—so a coordinate that reaches it stays for an exponentially long time. To keep this unconstrained parametrization without its slow escape, we propose the lift, which replaces the free latent weight by a learnable slack plus an unconstrained network—the body—that takes a permutation-invariant summary of the training batch as input. The latent weight thus varies with the batch before the positivity map, and couples to the gradient formed on it. We show that this coupling enters the variance of the update to the latent weight at first order in the fluctuation, and that the slack, the batch dependence and the shared batch are each needed for it to act. Where the coupling aligns positively with the loss curvature, that variance is larger under the lift than under direct softplus, and a coordinate leaves the shoulder sooner. We compare the lift with the two existing methods on several applications. Where a constrained weight of direct softplus reaches the shoulder and does not leave, the lift fits the target more closely and reaches the same reconstruction about three times sooner. Where almost none reaches it, the methods agree.

Low-dimensional embeddings are widely used as visual summaries of high-dimensional data and to enable downstream scientific discoveries. Yet, popular nonlinear dimension reduction methods, such as t-SNE and UMAP, are often selected based on visual appeal alone and without rigorous quantitative validation. A major reason is that manifold embeddings typically do not provide an out-of-sample map nor an inverse back to the original feature space; this makes held-out validation, the gold standard in supervised learning, all but impossible. To address these challenges, we develop a novel framework, MEDAL (Manifold Embedding Distillation via Autoencoder Learning), which distills a fitted manifold embedding into a reusable encoder–decoder model. MEDAL trains a constrained autoencoder whose bottleneck exactly matches any teacher embedding while the decoder reconstructs the original input; this yields an explicit map for new samples, an approximate inverse, and a pointwise reconstruction-based measure of distortion in the manifold space. This converts static manifold embeddings into models that can be evaluated on held-out data, enabling quantitative validation including comparing different dimension reduction methods as well as hyperparameter tuning. Across multiple benchmark and scientific case studies, we show that MEDAL enables held-out validation to determine optimal manifold embeddings and hyperparameters, reveals biologically coherent regions that are difficult to preserve in two dimensional embeddings, and detects distribution shift when new samples are mapped into a fixed reference manifold. MEDAL provides a general validation wrapper to any existing dimension reduction technique that will improve the rigor and reliability of dimension reduction in scientific workflows.

In 3D scene understanding, deep learning models rely on large models and extensive training to capture basic geometric structures that are present in the 3D data. However, existing methods lack explicit mechanisms to incorporate geometric information, such as learnable primitive shapes, often necessitating large models and more training data which in turn increases cost and can limit generalization. We introduce GIBLy, a lightweight geometric inductive bias layer that integrates learnable geometric priors into 3D segmentation pipelines. GIBLy enhances existing architectures – whether MLP-based, convolution-based, or transformer-based – by providing features aligned with simple geometric shapes (and thus human-interpretable) that improve segmentation performance with minimal computational overhead. We validate our approach across multiple 3D semantic segmentation benchmarks, demonstrating consistent performance gains, including up to +11.5% mIoU on TS40K with PTV3, while adding only 58K extra parameters. Our results highlight the benefit of explicitly encoding geometric structure to support accurate and efficient 3D scene understanding, with a lightweight add-on layer

Deploying clinical prediction models across healthcare systems often fails when key training covariates are unavailable at deployment and labeled outcomes are limited in the target domain. For example, high-performing models for out-of-hospital cardiac arrest (OHCA) rely on detailed prehospital measurements routinely collected in high-resource settings but unavailable in many international registries. Existing methods either discard missing covariates, sacrificing predictive information, or rely on untestable assumptions about their target distribution. We propose DRUM (\underline{D}istributionally \underline{R}obust \underline{U}nsupervised transfer learning with structurally \underline{M}issing covariates), a framework that transfers prediction models to target populations where certain covariates are structurally absent and outcome labels are unavailable. DRUM partitions covariates into shared components ($X$), observed across all settings, and missing components ($A$), observed only in the source. Rather than imputing missing covariates, DRUM optimizes worst-case predictive performance over the unknown target distribution of $A \mid X$ using a neural network generator, with a robustness parameter controlling allowable deviation from the source conditional. We further develop a bias correction procedure that reduces sensitivity to nuisance estimation error. Simulations show substantial improvements in both mean and worst-case prediction error under distribution shift. Applied to cross-national OHCA prediction, transferring models from a US registry to multiple Asian registries where prehospital variables are unrecorded, DRUM yields better-calibrated predictions and improved clinical classification performance across sites.

What functions can Neural Processes represent? We analyze the representational capacity of popular NP architectures: Conditional Neural Processes (CNPs), Attentive Neural Processes (ANPs), Transformer Neural Processes (TNPs), and their latent variants. We prove these architectures form a strict hierarchy. CNP-representable functions are exactly those depending on finitely many expected features of the context distribution. ANPs strictly generalize CNPs via query-dependent reweighting, enabling kernel smoothers. ConvCNPs and ANPs are incomparable; each contains functions outside the other, separated by stationarity versus translation equivariance. TNPs with $L$ self-attention layers capture $L$-hop context interactions. For latent NPs, we show finite-dimensional latents provide coherent sampling but do not circumvent encoder limitations; matching GP posterior distributions requires latent dimension scaling with context size. These results provide a theoretical foundation for architecture selection based on task structure.

This article addresses issues of model criticism and model comparison in Bayesian contexts, and focusses on the use of the so-called posterior predictive p-values (ppp values). These involve a general discrepancy or conflict measure and depend on the prior, the model, and the data. They are used in statistical practice to quantify the degree of surprise or conflict in data, and for purposes of comparing different combinations of prior and model. The distribution of such ppp values is however far from uniform, as we demonstrate for different models, making their interpretation and comparison a difficult matter. We propose a natural calibration of the ppp values, where the resulting cppp values are uniform on the unit interval under model conditions. The cppp values, which in general rely on a double simulation scheme for their computation, may then be used to assess and compare different priors and models. Our methods also make it possible to compare parametric with nonparametric model specifications, in that genuine `measures of surprise' are put on the same canonical uniform scale. Our techniques are illustrated for some applications to real data. We also present supplementing theoretical results on various properties of the ppp and cppp.

Longitudinal modified treatment policies (LMTP) are a class of interventions that allow the definition, identification, and estimation of causal effects in general settings, such as with continuous or multivariate exposures, treatment regimens that require grace periods. Targeted machine learning estimators (i.e., double/debiased) have been formulated for LMTPs that assign the exposure at time $t$ as a function of the natural value of treatment at time $t$. However, important applications such as estimating the effect of a delay in the start of a treatment require formulating LMTPs that depend not only on the natural value of treatment at time $t$ but also on the history of the natural value of treatment prior to time $t$. This paper develops targeted learning estimators for this general case. We discuss the definition of the effects, and propose estimators that use an augmented-data version of the sequential regression form of the longitudinal g-computation formula. Our estimators are based on the efficient influence function and provide $\sqrt{n}$ inference under standard doubly robust rate assumptions on the convergence of the outcome and treatment regressions. We apply the new estimators to assess the effect of delaying a risky pain treatment by one month on 12-month incidence of opioid use disorder.

We study the generalized dynamic factor model in a long-memory setting. Unlike most recent work, which assumes a finite-dimensional factor space and short memory, our framework allows the factor space to be infinite-dimensional and the common components to exhibit long memory. We employ the two-sided estimation method of Forni, Hallin, Lippi and Reichlin (2000, Review of Economics and Statistics) to recover the common component. The long memory structure of the common component poses a challenge, as it introduces unboundedness/discontinuity in the spectral density. We address this issue by leveraging two key facts: First, the estimated operator is a projection onto the leading eigenspace and thus the eigengap provides an intrinsic scaling that partially mitigates the blow-up. Second, we perform most of our estimation in $L^p$-norm, rather than pointwise. Experimental results are presented to provide evidence supporting the theory, as well as potential improvements to it.