Papers

Trader-facing dynamic fees are increasingly proposed for automated market makers (AMMs), but historical data do not identify how order flow would respond: trader-facing fees do not vary, trader types are latent, and a replayed tape is not a sequential decision environment. We therefore construct a minimal closed-loop simulator in which the missing signal exists by construction: two constant-product pools repriced by an equilibrium-inspired dynamic-fee rule, fee-sensitive noise flow, and closed-form CEX–AMM arbitrage. Equilibrium is used as a closure principle, not as an object the trader learns. Against a tuned benchmark ladder of schedule, planning, lookahead, and tabular policies, a small DQN is the only evaluated valid policy whose paired improvement over tuned one-step routing excludes zero. On a reserved final block of 1{,}000 seeds with completion forced to 1.0 for every policy, it reduces implementation shortfall under every tested intra-step ordering, by $13.3\bps$ of order notional under the pre-specified agent-last ordering, and the edge is concentrated in, and learned from, dynamic-fee environments: under constant fees the paired difference is indistinguishable from zero. The result is model-conditioned counterfactual evidence about execution control in AMMs, not evidence about historical traders, equilibrium play, or deployable profit.

Standard learning rate schedules such as cosine annealing are tied to a fixed training horizon, limiting their ability to accommodate post hoc horizon extension. Warmup-stable-decay (WSD) partially addresses this issue by maintaining a long constant-rate phase before a short linear cooldown, allowing training to resume from a pre-decay checkpoint. However, its peak learning rate is still tuned based on the original training horizon and can become suboptimal when training is extended. Motivated by stochastic convex optimization, we propose WSqD (Warmup with Square-root base and linear Decay), a learning rate schedule that replaces WSD's constant stable phase with a shifted inverse-square-root base while retaining the final linear cooldown. In the stochastic convex setting, WSqD provably attains the minimax-optimal $O(1/\sqrt{T})$ last-iterate convergence rate. Importantly, its base learning rate schedule is horizon-independent, and the training horizon is needed only to determine when to begin the final cooldown. Empirically, on language-model pretraining using the SlimPajama corpus, WSqD matches or outperforms carefully tuned WSD and other baselines across multiple training horizons while reusing a single peak learning rate.

We introduce Sticky Jump Diffusions (SJDs), continuous-time Markov processes on $\mathbb R^d$ whose discrete anchors are token embeddings. In forward time, anchors release their mass at a hazard rate and the released mass diffuses in the continuous ambient space; time reversal couples a score-driven SDE with a sticky jump kernel whose rate and destination are fixed by flux balance with the forward law. We estimate the score and the per-anchor reverse hazards from a single denoising classifier via Denoising Hazard Matching, the hazard analogue of denoising score matching, with simulation-free cross-entropy training. SJD recovers masked diffusion, continuous diffusion, and hybrid diffusion as limits. Its reversal explains features that each family treats as given: the mask of masked diffusion carries no evidence about the source token because the unsticking kernel of every anchor collapses to the same absorbing point; the terminal projection of continuous diffusion is required due to the absence of atoms in its forward marginal, without which flux balance yields no reverse jumps; and the update rules of hybrid diffusion (commit rate, destination, and drift) all follow from flux balance rather than from separate design. Beyond these limits, the unsticking kernel becomes a design space: a cross-position blending corrupts each position toward a blend of its neighbors' clean values or embeddings, turning dependency structure such as spatial locality or a constraint graph into an inductive bias of the corruption itself, and improves over the identity-kernel hybrid on CIFAR-10, Text8, and Sudoku.

We study the bandit-feedback version of online principal component analysis (Bandit PCA): in each round $t = 1,\dots,T$, the adversary selects a $d \times d$ symmetric gain matrix $G_t$ with spectrum in $[0,1]$ and rank at most $r$; the learner simultaneously selects a unit vector $w_t \in S^{d-1}$ and receives the reward $w_t^\top G_t w_t$. The learner receives no other feedback, and aims to minimize the regret against the best unit vector in hindsight. This problem was introduced by Kotlowski and Neu (2019), who gave an algorithm with regret $O(d\sqrt{rT \log T})$ and showed the lower bound of $\Omega(r\sqrt{T/\log T})$. We improve upon both of these bounds and essentially bridge the gap between them, establishing the minimax regret of order $r\sqrt{dT}$ up to polylogarithmic factors in $d$ and $T$. The upper bound is attained by a novel algorithm, which combines online mirror descent on the spectrahedron of (real) density matrices with a multiscale exploration scheme in which the eigenspaces with different spectral magnitudes are updated at different rates. For the lower bound, we construct an adaptive adversary that refines a hidden large-reward subspace based on the learner's actions, in such a way that low regret is impossible without estimating the subspace; as a result, lower-bounding the regret reduces to studying the arising subspace estimation problem. Finally, we discuss connections of Bandit PCA with adaptive-measurement quantum tomography.

Financial information rarely affects a single company in isolation. Earnings surprises, capital expenditure changes, supply constraints, and guidance revisions can propagate through networks of suppliers, customers, competitors, and technology ecosystems. Traditional financial NLP primarily measures document-level sentiment for the directly mentioned company and often ignores cross-entity information diffusion. This paper develops an LLM-based financial measurement and signal propagation framework. The LLM converts unstructured financial documents into structured economic state-change events and extracts explicit and implicit corporate relationships to construct a dynamic financial knowledge graph. Event signals are then propagated through the estimated network using a community-aware mechanism, allowing information to diffuse more strongly within dynamically detected economic communities than across community boundaries. We introduce Community Information Surprise, CIS, and Propagated Information Surprise, PIS, as network-based financial signals and develop corresponding econometric tests. Controlled simulations with time-varying economic communities show that the framework accurately recovers latent network structure, detects the emergence of new investment ecosystems, and generates propagated signals with incremental predictive power beyond sentiment and direct LLM event signals. Across repeated simulations, community-aware propagation achieves the strongest rank information coefficient and long-short Sharpe ratio among five nested benchmarks.A second Russell 1000 calibrated simulation confirms that the main results persist under sparser networks, heterogeneous news coverage, realistic large-cap volatility, and smaller effect sizes.

Decoding brain activity is useful for characterizing brain processes and understanding the functional architecture underlying cognition. However, the inter-individual variability in brain response patterns limits the development of decoders that generalize across individuals. A solution to this challenge is functional alignment: aligning functional data across individuals before training population-level decoders. The core issue is to strike the balance between aligning functional features and preserving the anatomical structure, while maintaining computational efficiency. We introduce a new functional alignment method for fMRI, SpectralOT, that embeds cortical geometry into Laplace-Beltrami eigenmodes along functional data to regularize the alignment.

Identifying heterogeneous treatment effects under unobserved confounding is central in observational causal inference. In proxy models with a discrete latent confounder, prior Synthetic Potential Outcomes (SPO) [Mazaheri-Squires-Uhler '25] recover the mixture of treatment effects through recursively constructed scalar moments. We show that this sequence is one projection of a more fundamental object. Under the same population factorization assumptions, there is an exact compressed observable operator: after projecting onto the shared proxy signal subspace, the difference of two treatment-arm quotient operators is similar to the diagonal matrix of latent treatment effects. Its eigenvalues are the latent effects; its lifted left eigenvectors, after anchor normalization, recover the target-proxy feature matrix and then the latent mixture proportions. Every scalar SPO moment is a bilinear functional of a power of this operator. The resulting estimator handles overcomplete proxy systems, replaces high-order scalar inversion with finite-dimensional spectral analysis, and admits high-probability first-order perturbation bounds for treatment effects, feature rows, and simplex-projected mixture weights.

This paper introduces an adaptive framework for leverage correction in heteroskedasticity-consistent covariance matrix estimation for ordinary least squares regression. Unlike existing heteroskedasticity-consistent estimators, which rely on predetermined leverage adjustment functions, the proposed approach introduces an adaptive leverage correction calibrated to the empirical leverage structure of the design matrix. It replaces the conventional leverage-based adjustment used in existing heteroskedasticity-consistent estimators with a data-driven correction derived from a fitted Beta distribution. The Beta parameters are estimated from the observed leverage values, allowing the adjustment factors to adapt automatically to the leverage structure of the sample. By exploiting information from the entire leverage configuration rather than from individual leverage values alone, the proposed estimator accommodates heterogeneous leverage patterns while avoiding the excessive growth of adjustment factors that may arise with some existing methods. Monte Carlo simulations show that the proposed estimator yields accurate finite-sample inference and confidence interval coverage while retaining the desired asymptotic properties. Empirical applications further illustrate its practical advantages in the presence of influential observations, particularly in situations where existing estimators exhibit overshooting of leverage adjustment factors. To facilitate its adoption, an open-source R package, hcinfer, has been developed and made publicly available.

Small-data inverse design is challenging in engineering informatics when observations are heterogeneous, mixed-type, and constrained by physical relations among design variables. This work proposes a topology-aware surrogate framework guided by an Incremental Transformer (INCRT) for physics-constrained inverse design, applied to geopolymer mixture design. The method integrates intrinsic-dimensionality analysis, mixed-variable design-space representation, tabular surrogate prediction, INCRT-based manifold rationalisation, and constrained inverse optimisation. Using a public benchmark of fly-ash and slag-based geopolymer concrete mixtures with compressive-strength and carbon-emission targets, the high-dimensional design space proves strongly redundant, organising around fewer effective mixture regimes. Compressive strength requires nonlinear tabular surrogates, while carbon emission is largely determined by composition and well recovered by regularised linear models. INCRT thus acts not as a replacement for tabular predictors but as a rationalisation layer providing prototype regimes and a manifold-support score for inverse design. Three strategies are compared: unconstrained surrogate optimisation, physics-constrained optimisation, and topology-aware physics-constrained optimisation. Unconstrained optimisation can match target strength but may yield physically invalid or off-manifold candidates; physics-only constraints do not always ensure data support. The topology-aware strategy yields candidates balancing target compliance, carbon reduction, physical admissibility, and proximity to the learned feasible manifold. The framework aims not to replace experimental validation but to support screening of credible candidate mixtures from small, mixed, physically constrained engineering datasets.

Sustainable user growth in online platforms depends not only on acquiring new users but also on reactivating and engaging existing ones through social sharing features. A well-designed sharing feature can trigger a self-reinforcing “flywheel effect”: reactivated users become potential sharers whose engagement propagates through the network over multiple rounds, amplifying total engagement. Measuring the causal impact of such sharing features is challenging, as their effects unfold through complex social networks and temporal cascades, violating the no-interference assumption underlying classical A/B testing. We develop a framework for experiments on sharing features that accounts for interference caused by the flywheel effect and targets a global treatment effect on share-induced engagement. Our estimator is motivated by a flow-balance identity and interprets share-induced engagement as a geometric amplification process, yielding a closed-form propagation adjustment that accounts for multi-round diffusion using commonly available attribution logs. Under mild conditions, we establish consistency of the proposed estimator and develop a valid A/A testing procedure for pipeline validation. Simulation studies show that our method substantially reduces bias relative to the difference-in-means estimator and first-order adjustments, while the proposed A/A test maintains nominal Type I error. We also extend the framework to a user-level reactivation metric via a Poisson approximation. Finally, we demonstrate the approach on a real-world large-scale online platform and discuss empirical implications for evaluating sharing feature designs.

Bayesian methods provide a natural framework for estimating a parameter in non-linear inverse problems and quantifying uncertainty in the estimation. However, when the forward model for such non-linear inverse problems is given by some Partial Differential Equation (PDE), Bayesian inference is typically carried out by resorting to MCMC methods. Since each MCMC iteration requires solving a PDE, these methods become computationally expensive and are often impractical for large-scale imaging problems. In this work, we develop a computationally efficient Bayesian framework for two such nonlinear imaging inverse problems: Quantitative Photoacoustic Tomography (QPAT) and Electrical Impedance Tomography (EIT). Building on a recently proposed two-stage pushforward methodology, we first formulate a Bayesian regression problem for an auxiliary variable whose posterior is available in closed form. This posterior is then pushed forward through a deterministic reconstruction map to obtain a posterior on the unknown parameter, avoiding MCMC sampling. We give a rigorous measure-theoretic justification to interpret the induced posterior as a Bayesian posterior and derive posterior contraction rates for both QPAT and EIT. Numerical results show that the proposed method provides accurate reconstructions and reliable uncertainty estimates at a arguably lower computational cost than standard Bayesian approaches.

We develop a systematic approach to quantify $L^2$-relaxation times for non-reversible Markov processes based on the singular value gap of the generator introduced by Chatterjee. The inverse of the singular value gap is equivalent to the relaxation time of the time-averaged transition semigroup. We show that, moreover, the inverse singular value gap of the two-point motion is equivalent to the relaxation time of the non-averaged transition semigroup, and that it provides a lower bound on the usual spectral gap of the generator. We then introduce a method for deriving lower bounds on singular value gaps for Markov processes with degenerate noise that is based on the concept of a first- and second-order collapse of the generator. It follows ideas from hypocoercivity developed in a previous series of works but is simpler and more broadly applicable. In contrast to previous results, it includes settings with non-vanishing first-order collapse, and thus applies directly to Markov chains (in continuous time), but also to diffusion processes and piecewise-deterministic Markov processes. Our approach yields sharp upper and lower bounds for several classes of examples. First applications include the proof of a conjecture by Diaconis and Miclo on a square-root speed-up for lifted random walks on abelian groups, as well as bounds on relaxation times of switching flows perturbed by noise and of non-reversible diffusion processes.

Mendelian Randomization (MR) has been widely used as a standard approach for identifying causal effects in biomedical research. When the true exposure and outcome variables are unknown among many potential candidates, a common but problematic practice is to first screen for associations and then evaluate causal effects only among exposure-outcome pairs that show significant correlations. We demonstrate that the classical MR ratio estimator suffers from severe type I error inflation under this selection procedure. To address this issue, we propose a novel robust MR test that remains valid regardless of the prior association screening step when there is no true causal effect. We show that the proposed test consistently maintains the correct type I error rate, independent of the association test results. Furthermore, our method can incorporate summary statistics from previous association studies to improve the power of causal effect detection. Extensive simulation studies illustrate the advantages of the proposed method compared with the classical MR approach.

We build GNet, a scalable and flexible Gaussian process network with nonparametric activation functions. The key computational contribution is to make estimation of GP activations computationally scalable without forming covariance matrices explicitly. We provide theoretical studies comparing function classes with a fixed architecture, and derive predictive risk bounds for GNets. Using essentially the same architecture and optimization settings, GNet shows competitive performance across a diverse range of test problems, including predicting nonlinear functions, nonparametric regression of real-world data, and predicting one-body direct correlation functions with high-dimensional inputs in classical density functional theory. The strong performance of GNet suggests that flexible nonparametric neurons can substantially reduce the number of trainable parameters while remaining computationally scalable.

We introduce Self-Similar Generative Estimation (SS-GEN), a method for simulating multivariate tail events and estimating rare-event probabilities in both heavy and light-tailed settings. SS-GEN exploits asymptotic tail structure to decompose the tail distribution into an explicit radial component and a nonparametric angular component, reducing tail learning to a compact-domain problem that can be handled by off-the-shelf deep generative models. The resulting sampler generates representative extreme scenarios and supports probability estimation far beyond the observed data. Under mild nonparametric tail assumptions, we show that the SS-GEN density is asymptotically exact in the tail, with vanishing uniform relative error for regularly varying distributions and vanishing uniform log-relative error for Weibull-type distributions. Unlike existing approaches that rely on specialized architectures or parametric tail specifications, SS-GEN leverages asymptotic tail structure to enable standard generative models to generate representative extreme samples and estimate rare-event probabilities beyond the observed data.

In this paper, we provide a systematic investigation of SO(2) theory to machine learning interatomic potentials (MLIPs) and identify the limitations of conventional SO(2) Linear architectures relative to SO(3) Clebsch-Gordan Tensor Products (CGTP). Building on these insights, we propose direct Cartesian construction and recursive Clebsch-Gordan construction of Wigner D-matrices and introduce two novel interaction building blocks. First, we propose the Edge Complex Product Basis based on Generalized Asymmetric Contraction, a new formulation for many-body expansion that directly constructs higher-order interactions on edges through complex-valued equivariant multiplications. Second, we introduce Radial Rotary Complex Attention(RRA), which enhances extrapolation performance and surpasses existing attention vector formulations. We also introduce several improvements to the Atomic Cluster Expansion module. Building on these advances, we train our models on OMat24, sAlex, and MPTrj, and introduce TECE-OAM-RRA-1.0, which achieve state-of-the-art (SOTA) performance on the Matbench Discovery.

Supply-demand mismatch represents a fundamental challenge in supply chain management, yet its direct measurement remains particularly elusive for small and medium-sized enterprises (SMEs).These firms typically lack systematic inventory records, leaving labeled training data critically scarce. Conventional supervised learning methods rely heavily on labeled samples, rendering them ill-equipped to reliably validate firm-level predictions under such data-scarce conditions. To resolve this unlabeled-data dilemma, we develop a multi-agent semi-supervised inference framework that reframes the label-scarcity problem as a structured, collaborative task distributed across specialized agents. We first construct a production-function-constrained graph machine learning model that infers firm-level inventory changes directly from supply chain network topology. A dedicated econometric validation agent then concurrently loads five econometric models (spanning spatial spillovers, dynamic persistence, causal direction, shock transmission, and supply-demand forecasting) to generates structured economic evidence from complementary dimensions. An expert review agent synthesizes the structured econometric evidence and produces a unified consistency assessment by resolving cross-agent inconsistencies. Empirical results demonstrate stable predictive performance on inventory-change forecasting tasks. Multi-agent econometric validation further confirms that predicted inventory dynamics align closely with established economic theory in terms of causal structure and network transmission mechanisms. Critically, the proposed agent framework enables effective prediction verification even when ground-truth observations are unavailable.

K-fold cross-validation assumes exchangeable observations, violated by the stratification, clustering, and unequal weights of complex sample surveys. Design-respecting "survey CV" exists, but the question of when the extra care changes any conclusion has remained open. We answer it before validating any model, with two inexpensive diagnostics: the within-cluster intraclass correlation (ICC) of the outcome and of a preliminary linear predictor. A simulated positive control demonstrates their sensitivity, with naive cross-validation growing optimistic about new-cluster performance as the ICC rises while cluster-level folds stay honest. We then evaluate paired naive-versus-design-respecting cross-validation in three national health surveys (chronic-pain, diabetes, and adolescent-suicidality prediction; penalized and random-forest learners, plus an unpenalized comparator) - one reanalysis, one prospective application, and one prespecified screen. In all three the diagnostics correctly anticipated the outcome: no scheme difference of practical size, and the only interval excluding zero showed pessimism, not the optimism that cluster leakage produces - even where the design effect was large (which, unlike the ICC, is not the right trigger). We also show the stratified recipe is often infeasible in public-use designs and give a fallback hierarchy, and we document weight-handling errors whose order-of-magnitude artifacts dwarfed any fold-scheme effect. Reproducible code accompanies the paper.

We consider the recovery of a pair of sparse vectors from a limited number of nonlinear observations of their superposition: $y_i=g(\inner{\ba_i}{\bPhi\bw^\ast+\bPsi\bz^\ast})+e_i$, $i=1,\dots,m$, with $m\ll n$, incoherent orthonormal bases $\bPhi,\bPsi$, a scalar link $g$, and noise $e_i$ that may be heavy-tailed or contaminated. We propose a regularization-based framework combining a Huberized data fidelity with generalized folded-concave penalties (SCAD, MCP), and a two-block proximal alternating algorithm with backtracking (NLD-PALM) whose whole iterate sequence provably converges to critical points under the Kurdyka–Łojasiewicz property, with local linear rates. On the statistical side we establish restricted strong convexity of the Huberized nonlinear loss through an exact sign-definite decomposition, and derive estimation error bounds of order $\sigma\sqrt{s\log(n)/m}$ that hold at every localized stationary point, an oracle rate $\sigma\sqrt{s/m}$ free of $\log n$ and shrinkage bias under a beta-min condition, and a co-equal recovery theorem for unknown monotone links via a linear surrogate and a clipped Plan–Vershynin decoupling. The estimator requires no knowledge of the sparsity levels, and its guarantees hold under symmetric noise with only finite variance. Experiments at $n=512$ under a frozen data-driven regularization rule show an earlier phase transition than convex $\ell_1$ demixing and greedy hard-thresholding baselines, a $35\times$ accuracy advantage over squared-loss estimation under $5\%$ gross outliers, and successful demixing of spike-plus-background signals observed through a saturating amplifier.

This paper proposes a network-adjusted generalized method of moments (NA-GMM) estimator for social interaction models when the observed network may differ from the true interaction network. NA-GMM is a novel penalized GMM approach that allows the elements of the observed interaction matrix to be modified to improve the fit of the moment conditions. To avoid unrestricted network adjustments, the NA-GMM criterion introduces a penalty on the amount of adjustment. Since NA-GMM does not aim to estimate the true interaction network itself, the estimator generally converges to a pseudo-true parameter. For a linear spatial autoregressive model, we prove that the NA-GMM estimator is consistent for the pseudo-true parameter and is asymptotically normally distributed under general moment misspecification. We also prove that a fixed-weight version of the NA-GMM estimator has a desirable bias reduction property relative to conventional GMM without network adjustment. An empirical application to U.S. county-level COVID-19 infection data demonstrates the usefulness of the proposed method.

In contrast to most studies on neural network approximation theory that characterize results through a single parameter, such as the total number of network parameters, \cite{shen2020deep} pioneered the characterization of approximation rates as a joint function of the width parameter $N$ and the depth parameter $L$, thereby granting greater architectural flexibility. Existing works using the $(N,L)$-characterization focus on function classes with finite smoothness $s$, establishing a typical approximation rate of $\mathcal{O}\left(N^{-2s/d}L^{-2s/d}\right)$ with $d$ denoting the input dimension, which indicates that network depth and width play symmetric roles for these classes. In contrast, this paper establishes upper bounds for the approximation of analytic functions, which possess infinite smoothness, via ReLU networks under the $(N,L)$-characterization. Specifically, we derive approximation rates of $\mathcal{O}\left(N^{-C L^{\tau}}\right)$, where $C>0$ is some constant and $\tau>0$ is a parameter influenced by the relation between $L$ and $N$. In particular, $\tau=1$ if $N$ scales roughly as $L^d$. Our findings reveal that depth plays a more critical role than width in the context of analytic function approximation. The main technical difficulty of obtaining such upper bounds lies in the trade-off between the smoothness parameters and the approximation accuracy. To overcome this difficulty, we employ refined constructions of several ReLU networks to approximate power functions, multivariate multiplication, and polynomials, which may be of independent interest.

We study stochastic multi-armed bandits on dynamic graphs, where arms correspond to the vertices of a network with time-varying edges. In this setting, the learner is restricted to local movement, selecting only its current node or an immediate neighbor at each round. This constraint decouples best-arm identification from exploitation: even after the optimal arm is identified, the learner may remain unable to reach it through the evolving topology. We identify a process-agnostic structural condition, based on sliding-window mixing, that ensures the graph's intrinsic walk remains stable for both exploration and navigation. Under this regime, we analyze a family of local explore-then-commit algorithms and establish sublinear expected regret. Our framework includes a reward-aware strategy, for which we prove a worst-case safety theorem and a separate performance gain theorem.

With the development of generative AI, watermarking techniques have been widely used to detect the authenticity of AI-generated data and protect the rights of users and creators. While it is already well applied in data types including imaging and text data, watermarking tabular data is still under-explored. Existing methods primarily focus on numerical data, leaving discrete, categorical, and mixed data less studied. In this work, we propose STAMP (Single-observation Tabular Attribution and Marking Procedure), a novel framework for watermarking tabular data that can accommodate and preserve a wide range of distributions. We also develop a corresponding detection mechanism, which can reliably identify watermarks even when the sample size is as small as one. We establish theoretical guarantees for asymptotic consistency and detection accuracy. Finally, through extensive simulation studies and two real-data applications, we demonstrate that the proposed method is effective and robust to subsetting, while maintaining data fidelity and a high detection rate.

Pseudo-labeling based on Optimal Transport (OT) has become an effective mechanism for enhancing short text clustering. Existing OT methods are short in modeling semantic consistencies between samples, which may assign different pseudo-labels to semantically similar samples. These erroneous pseudo-labels can cause the model to produce inferior clusters. This paper proposes a novel short text clustering framework, which remedies the neglect of semantic consistency in existing OT methods, generating reliable pseudo-labels to facilitate clustering. Specifically, the proposed approach first designs an instance-level attention mechanism to capture semantic relationships between samples, which are then integrated into the OT formulation to endow the transport process with neighborhood semantic awareness. By solving the proposed OT formulation, reliable pseudo-labels are obtained that simultaneously account for sample-to-sample semantic consistency and sample-to-cluster global structure information. These pseudo-labels are then used as supervisory signals to guide the model to achieve accurate clustering. Extensive experiments demonstrate that the proposed approach outperforms state-of-the-art methods. The code is available at: \href{https://github.com/YZH0905/CAOT-STC}{https://github.com/YZH0905/CAOT-STC}.

We propose a two-stage estimator for structural mediation parameters that combines deep representation learning with G-estimation under the "no essential heterogeneity" (NEH) assumption. We call the method UNIT. In the first stage,TARNet estimates the heterogeneous effect of a randomized treatment on a mediator by learning a shared covariate representation across treatment arms.The resulting conditional average treatment effect (CATE) estimate provides a plug-in approximation to the heterogeneity-dependent component of the weight function entering the G-estimating equation of Zheng and Zhou (2015), which identifies the structural parameters even in the presence of unmeasured mediator-outcome confounding. We show that more accurate first-stage representation learning can yield a more informative plug-in weight and thereby improve the precision of the structural parameter estimator. In simulations with non-Gaussian covariates and nonlinear mediator effects, TARNet weights reduce the Stage-2 standard error of the mediation coefficient by a factor of $1.45$ to $1.51$ (median across replications, $n \ge 2000$) relative to the classical approach, at no cost to bias or coverage.

Rolling and expanding windows are widely used in age-specific demographic modeling and forecasting. Building on these approaches, we propose a simple combination method that assigns equal weight to the forecasts from both schemes. Our focus is on evaluating and comparing the forecast accuracy of the two window types in modeling age-specific mortality and fertility. Based on the multi-country comparison, the superior performance of one method often persists across different forecast horizons. In the absence of prior information, our combined approach offers a robust and practical alternative.

A large literature in econometrics proposes decision rules with optimality guarantees based on ex ante criteria, such as minimax regret. We develop a framework for analyzing the dynamic consistency of such rules and show that, in many empirically relevant settings, the researcher may wish to deviate from the interim prescription of ex ante optimal rules after observing the data realization. To address this problem, we propose and axiomatize two classes of optimality criteria that yield dynamically consistent decision rules.

Unobserved confounding is a fundamental obstacle in causal inference problems. In the graphical modeling literature, a general theory has been developed that allows identification in the presence of hidden variables, with some limitations. In particular, Pearl's celebrated front-door criterion allows nonparametric identification in the presence of unobserved common causes of the treatment and the outcome, however it requires the presence of an unconfounded variable that mediates all causal influence from the treatment to the outcome. This stringent requirement limits the applicability of the front-door criterion. We propose proximal generalizations of the front-door criterion, allowing both arbitrary treatment/outcome confounding, and unobserved confounders of the mediator, provided informative proxies for the latter type of confounders are observed. In addition to deriving three new identification strategies in this setting, we provide plug-in and influence function-based estimation strategies for the resulting functionals, and evaluate their performance through simulations.

Bayesian structure learning for directed acyclic graphs (DAGs) is a central tool for reconstructing biological networks, yet it often assumes the data are jointly Gaussian. In motivating proteomic applications, this assumption is routinely violated by skewed and heavy-tailed data, causing Gaussian DAGs to recover spurious or misdirected edges. We develop a fully Bayesian framework for DAG learning in the nonparanormal family, replacing Gaussianity with the weaker requirement that unknown strictly increasing marginal transformations are jointly Gaussian. Working on the modified Cholesky parameterization of the latent precision matrix, we introduce two innovation-variance priors: a non-conjugate Normal-Gamma prior, which decouples coefficient shrinkage from variance regularization, and a conjugate Normal-Inverse-Gamma prior. For both, we obtain the node-wise marginal likelihood in closed form – through a modified Bessel function of the third kind for the Gamma prior and a Student-$t$ form for the Inverse-Gamma prior – allowing MCMC sampler moves to be scored without numerical integration. Exploiting these, we build a locally-balanced informed sampler and a Bessel-free score that scales the sampler to hundreds of nodes. On simulated data, our nonparanormal samplers match Gaussian methods when data are Gaussian and dominate them sharply when margins are skewed. On human T-cell protein-signalling data, they recover well-established interactions at high posterior probability, clearly outperforming constraint-based competitors and performing comparably to a Gaussian Bayesian model.

Bayesian structure learning of directed acyclic graphs (DAGs) is central to high-dimensional causal discovery, yet existing methods mostly assume multivariate Gaussian data, which is routinely violated by measurements displaying heavy tails, skewness, or bounded support. We address this by introducing NPN-DAG-HS, a fully Bayesian semiparametric DAG model coupling the nonparanormal family with horseshoe shrinkage on Cholesky off-diagonals via an extended-rank likelihood. This handles arbitrary unknown monotone marginal transformations without estimating them, preserving exact-zero shrinkage and conditionally conjugate posteriors for practical inference in large dimensions. Our method uses a partially collapsed Metropolis-within-Gibbs sampler that augments rank-likelihood Gaussian copies and alternates score-based DAG moves with horseshoe Gibbs updates. Theoretically, in the high-dimensional regime ($p \to \infty$ with $\log p / n \to 0$), we establish posterior contraction at the rate $\sqrt{(s_0+p)\log p/n}$, strong skeleton selection consistency, and a parametric Bernstein-von Mises theorem for smooth total causal-effect functionals, yielding asymptotic frequentist calibration of credible intervals. Simulations confirm our method outperforms Gaussian baselines and standard frequentist learners. Applied to an acute myeloid leukaemia dataset, it recovers a sparse, interpretable network, pruning unsupported edges declared by Gaussian analyses and illustrating the value of our semiparametric relaxation.