Papers

We present a MATLAB package, which is the first of its kind, for Higher Order Markov Chains (HOMC). It can be used to easily compute all important quantities in our recent works relevant to higher order Markov chains, such as the $k$-step transition tensor, limiting probability distribution, ever-reaching probability tensor, and mean first passage time tensor. It can also be used to check whether a higher order chain is ergodic or regular, to construct the transition matrix of the associated reduced first order chain, and to determine whether a state is recurrent or transient. A key function in the package is an implementation of the tensor “box” product which has a probabilistic interpretation and is different from other tensor products in the literature. This HOMC package is useful to researchers and practitioners alike for tasks such as numerical experimentation and algorithm prototyping involving higher order Markov chains.

For many scientific questions, understanding the underlying mechanism is the goal. To help investigators better understand the underlying mechanism, variable selection is a crucial step that permits the identification of the most associated regression variables of interest. A variable selection method consists of model evaluation using an information criterion and a search of the model space. Here, we provide a comprehensive comparison of variable selection methods using performance measures of correct identification rate (CIR), recall, and false discovery rate (FDR). We consider the BIC and AIC for evaluating models, and exhaustive, greedy, LASSO path, and stochastic search approaches for searching the model space; we also consider LASSO using cross validation. We perform simulation studies for linear and generalized linear models that parametrically explore a wide range of realistic sample sizes, effect sizes, and correlations among regression variables. We consider model spaces with a small and larger number of potential regressors. The results show that the exhaustive search BIC and stochastic search BIC outperform the other methods when considering the performance measures on small and large model spaces, respectively. These approaches result in the highest CIR and lowest FDR, which collectively may support long-term efforts towards increasing replicability in research.

Ensuring reliability in modern software systems requires rigorous pre-production testing across highly heterogeneous and evolving environments. Because exhaustive evaluation is infeasible, practitioners must decide how to allocate limited testing resources across configurations where failure probabilities may drift over time. Existing combinatorial optimization approaches are static, ad hoc, and poorly suited to such non-stationary settings. We introduce a novel reinforcement learning (RL) framework that recasts configuration allocation as a sequential decision-making problem. Our method is the first to integrate Q-learning with a hybrid reward design that fuses simulated outcomes and real-time feedback, enabling both sample efficiency and robustness. In addition, we develop an adaptive online-offline training scheme that allows the agent to quickly track abrupt probability shifts while maintaining long-run stability. Extensive simulation studies demonstrate that our approach consistently outperforms static and optimization-based baselines, approaching oracle performance. This work establishes RL as a powerful new paradigm for adaptive configuration allocation, advancing beyond traditional methods and offering broad applicability to dynamic testing and resource scheduling domains.

For many students, placement into developmental education becomes a self-fulfilling prophecy. Placing college students into developmental education significantly negatively impacts student attainment, student probability of passing, and college credits earned. To combat these negative effects, many universities are investigating alternative placement mechanisms. Could directed self-placement be an effective alternative mechanism? Do students who self-place suffer the same negative impacts from placement recommendations as their traditionally placed counterparts? This paper uses longitudinal data with causal inference methods to examine whether directed self-placement has similar negative impacts on student grades and pass rates as mandatory placement schema. We begin with an analysis of over 20,000 student placement records into one of two different placement tracks for first-year writing. Longitudinal and institutional data allow us to control for characteristic variables such as student race, family income, and sex. The results of our regression discontinuity design show that directed self-placement does not negatively impact student grades or pass rate. This may be an improvement for students who place at or near the threshold for developmental/remedial education; However, class, race, and gender-based statistical differences persist in the program at-large, demonstrating that placement technique plays only one part in building a more equitable program.

A common approach for modeling extremes, such as peak flow or high temperatures, is the three-parameter Generalized Extreme-Value distribution. This is typically fit to extreme observations, here defined as maxima over disjoint blocks. This results in limited sample sizes and consequently, the use of classic estimators, such as the maximum likelihood estimator, may be inappropriate, as they are highly sensitive to outliers. To address these limitations, we propose a novel robust estimator based on the minimization of the density power divergence, controlled by a tuning parameter $\alpha$ that balances robustness and efficiency. When $\alpha = 0$, our estimator coincides with the maximum likelihood estimator; when $\alpha = 1$, it corresponds to the $L^2$ estimator, known for its robustness. We establish convenient theoretical properties of the proposed estimator, including its asymptotic normality and the boundedness of its influence function for $\alpha > 0$. The practical efficiency of the method is demonstrated through empirical comparisons with the maximum likelihood estimator and other robust alternatives. Finally, we illustrate its relevance in a case study on flood frequency analysis in the UK and provide some general conclusions in Section 6.

We develop a Bayesian spatio-temporal framework for extreme-value analysis that augments a hierarchical copula model with an autoregressive factor to capture residual temporal dependence in threshold exceedances. The factor can be specified as spatially varying or spatially constant, and the scale parameter incorporates scientifically relevant covariates (e.g., longitude, latitude, altitude), enabling flexible representation of geographic heterogeneity. To avoid the computational burden of the full censored likelihood, we design a Gibbs sampler that embeds amortized neural posterior estimation within each parameter block, yielding scalable inference with full posterior uncertainty for parameters, predictive quantiles, and return levels. Simulation studies demonstrate that the approach improves MCMC mixing and estimation accuracy relative to baseline specifications, particularly when using moderately more complex network architectures, while preserving heavy-tail behavior. We illustrate the methodology with daily precipitation in Guanacaste, Costa Rica, evaluating a suite of nested models and selecting the best-performing factor combination via out-of-sample diagnostics. The chosen specification reveals coherent spatial patterns in multi-year return periods and provides actionable information for infrastructure planning and climate-risk management in a tropical dry region strongly influenced by climatic factors. The proposed Gibbs scheme generalizes to other settings where parameters can be partitioned into inferentially homogeneous blocks and conditionals learned via amortized, likelihood-free methods.

Accurate prediction of dynamical response of structural system depends on the correct modeling of that system. However, modeling becomes increasingly challenging when there are many candidate models available to describe the system behavior. Furthermore, uncertainties can be present even for the parameters of these model classes. The plausibility of each input-output model class of the structures with uncertain components can be determined by a Bayesian approach from measured dynamic responses to one or more input records; predictions of the structural system response to alternate input records can then be made. However, this approach may require many model simulations, even though most of those model classes are quite implausible. An approach is proposed herein to use a bound, computed from the false discovery rate, on the likelihood of measured data to falsify models considering uncertainties in the passive control devices that do not reproduce the measured data to sufficient accuracy. Response prediction is then performed using the unfalsified models in an approximate Bayesian sense by assigning weights, computed from the likelihoods, only to the unfalsified models approach incurring only a fraction of the computational cost of the standard Bayesian approach. The proposed approach for response prediction is illustrated using three structural examples: an earthquake-excited four–degree-of-freedom building model with a hysteretic isolation layer; a 1623–degree-of-freedom three-dimensional building model, with tuned mass dampers attached to its roof, subjected to wind loads; and a full-scale four-story base-isolated building tested on world's largest shake table in Japan's E-Defense lab. The results exhibit accurate response predictions and significant computational savings, thereby illustrating the potential of the proposed method.

Deep neural networks excel in high-dimensional problems, outperforming models such as kernel methods, which suffer from the curse of dimensionality. However, the theoretical foundations of this success remain poorly understood. We follow the idea that the compositional structure of the learning task is the key factor determining when deep networks outperform other approaches. Taking a step towards formalizing this idea, we consider a simple compositional model, namely the multi-index model (MIM). In this context, we introduce and study hyper-kernel ridge regression (HKRR), an approach blending neural networks and kernel methods. Our main contribution is a sample complexity result demonstrating that HKRR can adaptively learn MIM, overcoming the curse of dimensionality. Further, we exploit the kernel nature of the estimator to develop ad hoc optimization approaches. Indeed, we contrast alternating minimization and alternating gradient methods both theoretically and numerically. These numerical results complement and reinforce our theoretical findings.

Subspace identification methods (SIMs) have proven to be very useful and numerically robust for building state-space models. While most SIMs are consistent, few if any can achieve the efficiency of the maximum likelihood estimate (MLE). Conversely, the prediction error method (PEM) with a quadratic criteria is equivalent to MLE, but it comes with non-convex optimization problems and requires good initialization points. This contribution proposes a weighted null space fitting (WNSF) approach for estimating state-space models, combining some key advantages of the two aforementioned mainstream approaches. It starts with a least-squares estimate of a high-order ARX model, and then a multi-step least-squares procedure reduces the model to a state-space model on canoncial form. It is demonstrated through statistical analysis that when a canonical parameterization is admissible, the proposed method is consistent and asymptotically efficient, thereby making progress on the long-standing open problem about the existence of an asymptotically efficient SIM. Numerical and practical examples are provided to illustrate that the proposed method performs favorable in comparison with SIMs.

We introduce the Information-Estimation Metric (IEM), a novel form of distance function derived from an underlying continuous probability density over a domain of signals. The IEM is rooted in a fundamental relationship between information theory and estimation theory, which links the log-probability of a signal with the errors of an optimal denoiser, applied to noisy observations of the signal. In particular, the IEM between a pair of signals is obtained by comparing their denoising error vectors over a range of noise amplitudes. Geometrically, this amounts to comparing the score vector fields of the blurred density around the signals over a range of blur levels. We prove that the IEM is a valid global distance metric and derive a closed-form expression for its local second-order approximation, which yields a Riemannian metric. For Gaussian-distributed signals, the IEM coincides with the Mahalanobis distance. But for more complex distributions, it adapts, both locally and globally, to the geometry of the distribution. In practice, the IEM can be computed using a learned denoiser (analogous to generative diffusion models) and solving a one-dimensional integral. To demonstrate the value of our framework, we learn an IEM on the ImageNet database. Experiments show that this IEM is competitive with or outperforms state-of-the-art supervised image quality metrics in predicting human perceptual judgments.

Adaptive randomized pivoting (ARP) is a recently proposed and highly effective algorithm for column subset selection. This paper reinterprets the ARP algorithm by drawing connections to the volume sampling distribution and active learning algorithms for linear regression. As consequences, this paper presents new analysis for the ARP algorithm and faster implementations using rejection sampling.

Diffusion models have emerged as powerful generative frameworks with widespread applications across machine learning and artificial intelligence systems. While current research has predominantly focused on linear diffusions, these approaches can face significant challenges when modeling a conditional distribution, $P(Y|X=x)$, when $P(X=x)$ is small. In these regions, few samples, if any, are available for training, thus modeling the corresponding conditional density may be difficult. Recognizing this, we show it is possible to adapt the data representation and forward scheme so that the sample complexity of learning a score-based generative model is small in low probability regions of the conditioning space. Drawing inspiration from conditional extreme value theory we characterize this method precisely in the special case in the tail regions of the conditioning variable, $X$. We show how diffusion with a data-driven choice of nonlinear drift term is best suited to model tail events under an appropriate representation of the data. Through empirical validation on two synthetic datasets and a real-world financial dataset, we demonstrate that our tail-adaptive approach significantly outperforms standard diffusion models in accurately capturing response distributions at the extreme tail conditions.

We study empirical divergence-regularized optimal transport on arbitrary Polish spaces. For bounded continuous costs and dual-regular conjugates $\psi\in C^1(\mathbb R)$, we establish a dimension-free $n^{-1/2}$ bound for the empirical transport value using dual interpolation, Hoeffding projection, and bounded-difference arguments. For the asymptotic theory, we isolate the population identifiability condition needed for stability and give sufficient conditions for population uniqueness. In particular, active-set identifiability implies uniqueness of the canonical population potentials, and connectedness of either population support is sufficient. This condition requires neither compactness nor Euclidean structure and covers quadratic regularization, whose conjugate is $C^1$ but not $C^2$. We also give finite-support and large-regularization criteria. Under a bounded Lipschitz cost, the empirical potentials are stable, the transport value is asymptotically linear, and one- and two-sample central limit theorems hold with population centering. This includes noncompact and infinite-dimensional Polish state spaces.

We consider the problem of uncertainty quantification for prediction in a time series: if we use past data to forecast the next time point, can we provide valid prediction intervals around our forecasts? To avoid placing distributional assumptions on the data, in recent years the conformal prediction method has been a popular approach for predictive inference, since it provides distribution-free coverage for any iid or exchangeable data distribution. However, in the time series setting, the strong empirical performance of conformal prediction methods is not well understood, since even short-range temporal dependence is a strong violation of the exchangeability assumption. Using predictors with "memory" – i.e., predictors that utilize past observations, such as autoregressive models – further exacerbates this problem. In this work, we examine the theoretical properties of split conformal prediction in the time series setting, including the case where predictors may have memory. Our results bound the loss of coverage of these methods in terms of a new "switch coefficient", measuring the extent to which temporal dependence within the time series creates violations of exchangeability. Our characterization of the coverage probability is sharp over the class of stationary, $\beta$-mixing processes. Along the way, we introduce tools that may prove useful in analyzing other predictive inference methods for dependent data.

The aim of this note is to overview some of our work in Chernikov, Towsner'20 (arXiv:2010.00726) developing higher arity VC theory (VC$_n$ dimension), including a generalization of Haussler packing lemma, and an associated tame (slice-wise) hypergraph regularity lemma; and to demonstrate that it characterizes higher arity PAC learning (PAC$_n$ learning) in $n$-fold product spaces with respect to product measures introduced by Kobayashi, Kuriyama and Takeuchi'15. We also point out how some of the recent results in arXiv:2402.14294, arXiv:2505.15688, arXiv:2509.20404 follow from our work in arXiv:2010.00726.

Preserving correlation in synthetic data is of interest in several applications. Existing approaches mainly address correlation preservation during the generation procedure. Here, we instead consider it as a postprocessing problem. Given original and synthetic tabular data, we seek the smallest change to the synthetic dataset that restores the Pearson correlation matrix of the original data. Under suitable assumptions, we derive a unique explicit solution to the minimization problem. We also provide a bound on the size of the correction in terms of the initial correlation error. On the numerical side, across several datasets and generation methods, the proposed approach largely preserves marginal distributions, t-SNE geometry, and classification performance. The method is generator-independent and can be applied after synthesis without modifying the generation procedure.

Diffusion models have achieved state-of-the-art performance, demonstrating remarkable generalisation capabilities across diverse domains. However, the mechanisms underpinning these strong capabilities remain only partially understood. A leading conjecture, based on the manifold hypothesis, attributes this success to their ability to adapt to low-dimensional geometric structure within the data. This work provides evidence for this conjecture, focusing on how such phenomena could result from the formulation of the learning problem through score matching. We inspect the role of implicit regularisation by investigating the effect of smoothing minimisers of the empirical score matching objective. Our theoretical and empirical results confirm that smoothing the score function – or equivalently, smoothing in the log-density domain – produces smoothing tangential to the data manifold. In addition, we show that the manifold along which the diffusion model generalises can be controlled by choosing an appropriate smoothing.

While continuous diffusion models have achieved remarkable success, discrete diffusion offers a unified framework for jointly modeling text and images. Beyond unification, discrete diffusion provides faster inference, finer control, and principled training-free guidance, making it well-suited for posterior sampling. Existing approaches to posterior sampling using discrete diffusion face severe challenges: derivative-free guidance yields sparse signals, continuous relaxations limit applicability, and split Gibbs samplers suffer from the curse of dimensionality. To overcome these limitations, we introduce Anchored Posterior Sampling (APS), built on two key innovations: quantized expectation for gradient-like guidance in discrete embedding space, and anchored remasking for adaptive decoding. APS achieves state-of-the-art performance among discrete diffusion samplers on both linear and nonlinear inverse problems across the standard image benchmarks. We demonstrate the generality of APS through training-free stylization and text-guided editing. We further apply APS to a large-scale diffusion language model, showing consistent improvement in question answering.

Conventional wisdom in deep learning optimization dictates updating all layers at every step-a principle followed by all recent state-of-the-art optimizers such as Muon. In this work, we challenge this assumption, showing that full-network updates can be fundamentally suboptimal, both in theory and in practice. We introduce a non-Euclidean Randomized Progressive Training method-Drop-Muon-a simple yet powerful framework that updates only a subset of layers per step according to a randomized schedule, combining the efficiency of progressive training with layer-specific non-Euclidean updates for top-tier performance. We provide rigorous convergence guarantees under both layer-wise smoothness and layer-wise $(L^0, L^1)$-smoothness, covering deterministic and stochastic gradient settings, marking the first such results for progressive training in the stochastic and non-smooth regime. Our cost analysis further reveals that full-network updates are not optimal unless a very specific relationship between layer smoothness constants holds. Through controlled CNN experiments, we empirically demonstrate that Drop-Muon consistently outperforms full-network Muon, achieving the same accuracy up to $1.4\times$ faster in wall-clock time. Together, our results suggest a shift in how large-scale models can be efficiently trained, challenging the status quo and offering a highly efficient, theoretically grounded alternative to full-network updates.

Many time series applications require access to multi-step forecast trajectories in the form of sample paths. Recently, time series foundation models have leveraged multi-step lookahead predictions to improve the quality and efficiency of multi-step forecasts. However, these models only predict independent marginal distributions for each time step, rather than a full joint predictive distribution. To generate forecast sample paths with realistic correlation structures, one typically resorts to autoregressive sampling, which can be extremely expensive. In this paper, we present a copula-based approach to efficiently generate accurate, correlated sample paths from existing multi-step time series foundation models in one forward pass. Our copula-based approach generates correlated sample paths orders of magnitude faster than autoregressive sampling, and it yields improved sample path quality by mitigating the snowballing error phenomenon.

Imputation methods play a critical role in enhancing the quality of practical time-series data, which often suffer from pervasive missing values. Recently, diffusion-based generative imputation methods have demonstrated remarkable success compared to autoregressive and conventional statistical approaches. Despite their empirical success, the theoretical understanding of how well diffusion-based models capture complex spatial and temporal dependencies between the missing values and observed ones remains limited. Our work addresses this gap by investigating the statistical efficiency of conditional diffusion transformers for imputation and quantifying the uncertainty in missing values. Specifically, we derive statistical sample complexity bounds based on a novel approximation theory for conditional score functions using transformers, and, through this, construct tight confidence regions for missing values. Our findings also reveal that the efficiency and accuracy of imputation are significantly influenced by the missing patterns. Furthermore, we validate these theoretical insights through simulation and propose a mixed-masking training strategy to enhance the imputation performance.

Arctic warming threatens over 100 billion in permafrost-dependent infrastructure across Northern territories, yet existing risk assessment frameworks lack spatiotemporal validation, uncertainty quantification, and operational decision-support capabilities. We present a hybrid physics-machine learning framework integrating 2.9 million observations from 171,605 locations (2005-2021) combining permafrost fraction data with climate reanalysis. Our stacked ensemble model (Random Forest + Histogram Gradient Boosting + Elastic Net) achieves R2=0.980 (RMSE=5.01 pp) with rigorous spatiotemporal cross-validation preventing data leakage. To address machine learning limitations in extrapolative climate scenarios, we develop a hybrid approach combining learned climate-permafrost relationships (60%) with physical permafrost sensitivity models (40%, -10 pp/C). Under RCP8.5 forcing (+5C over 10 years), we project mean permafrost fraction decline of -20.3 pp (median: -20.0 pp), with 51.5% of Arctic Russia experiencing over 20 percentage point loss. Infrastructure risk classification identifies 15% high-risk zones (25% medium-risk) with spatially explicit uncertainty maps. Our framework represents the largest validated permafrost ML dataset globally, provides the first operational hybrid physics-ML forecasting system for Arctic infrastructure, and delivers open-source tools enabling probabilistic permafrost projections for engineering design codes and climate adaptation planning. The methodology is generalizable to other permafrost regions and demonstrates how hybrid approaches can overcome pure data-driven limitations in climate change applications.

Flatness of the loss landscape has been widely studied as an important perspective for understanding the behavior and generalization of deep learning algorithms. Motivated by this view, we propose Flatness-Aware Stochastic Gradient Langevin Dynamics (fSGLD), a first-order optimization method that biases learning its dynamics toward flat basins while retaining the computational and memory efficiency of SGD and SGLD. We provide a non-asymptotic theoretical analysis showing that fSGLD targets a flatness-biased Gibbs distribution under a theoretically prescribed coupling between the noise scale $\sigma$ and the inverse temperature $\beta$, together with explicit excess risk guarantees. We empirically evaluate fSGLD across standard optimizer benchmarks, Bayesian image classification, uncertainty quantification, and out-of-distribution detection, demonstrating consistently strong performance and reliable uncertainty estimates. Additional experiments confirm the effectiveness of the theoretically prescribed $\beta$-$\sigma$ coupling compared to decoupled choices.

In fields such as hydrology and climatology, modelling the entire distribution of positive data is essential, as stakeholders require insights into the full range of values, from low to extreme. Traditional approaches often segment the distribution into separate regions, which introduces subjectivity and limits coherence. This is especially true when dealing with multivariate data. In line with multivariate extreme value theory, this paper presents a unified, threshold-free framework for modelling marginal behaviours and dependence structures based on an extended generalized Pareto distribution (EGPD). We propose decomposing multivariate data into radial and angular components. The radial component is modelled using a semi-parametric EGPD and the angular distribution is permitted to vary conditionally. This approach allows for sufficiently flexible dependence modelling. The hierarchical structure of the model facilitates the inference process. First, we combine classical maximum likelihood estimation (MLE) methods with semi-parametric approaches based on Bernstein polynomials to estimate the distribution of the radial component. Then, we use multivariate regression techniques to estimate the angular component's parameters. The model is evaluated through synthetic simulations and applied to hydrological datasets to exemplify its capacity to capture heavy-tailed marginals and complex multivariate dependencies without threshold specification.

We introduce Action-Triggered Sporadically Traceable Markov Decision Processes (ATST-MDPs), a reinforcement learning framework for partial observability in which full state observations occur stochastically at each step, with probability determined by the chosen action. We derive Bellman equations tailored to this setting and establish the existence of an optimal policy. Exploiting the fact that sporadic observations reveal the full state, we provide an equivalent formulation in which agents commit to action-sequences between consecutive observations. Under the linear MDP assumption, we show that the value function over such action-sequences admits a linear representation in a finite-dimensional feature map, enabling standard regression-based methods. As an application, we derive ATST-LSVI-UCB, an optimistic algorithm achieving regret $\widetilde{O}(\sqrt{Kd^3(1-\gamma)^{-3}})$ for episodic learning with geometrically distributed horizons, where $K$ is the number of episodes, $d$ the feature dimension, and $\gamma$ the discount factor (episode continuation probability), matching the known rate for linear MDPs with full observability.

Peer review in academic research aims not only to ensure factual correctness but also to identify work of high scientific potential that can shape future research directions. This task is especially critical in fast-moving fields such as artificial intelligence (AI), yet it has become increasingly difficult given the rapid growth of submissions. In this paper, we investigate an underexplored measure for identifying high-impact research: authors' own rankings of their multiple submissions to the same AI conference. Grounded in game-theoretic reasoning, we hypothesize that self-rankings are informative because authors possess unique understanding of their work's conceptual depth and long-term promise. To test this hypothesis, we conducted a large-scale experiment at a leading AI conference, where 1,342 researchers self-ranked their 2,592 submissions by perceived quality. Tracking outcomes over more than a year, we found that papers ranked highest by their authors received twice as many citations as their lowest-ranked counterparts; self-rankings were especially effective at identifying highly cited papers (those with over 150 citations). Moreover, we showed that self-rankings outperformed peer review scores in predicting future citation counts. Our results remained robust after accounting for confounders such as preprint posting time and self-citations. Together, these findings demonstrate that authors' self-rankings provide a reliable and valuable complement to peer review for identifying and elevating high-impact research in AI.

We explore whether survival model performance in underrepresented high- and low-risk subgroups - regions of the prognostic spectrum where clinical decisions are most consequential - can be improved through targeted restructuring of the training dataset. Rather than modifying model architecture, we propose a novel risk-stratified sampling method that addresses imbalances in prognostic subgroup density to support more reliable learning in underrepresented tail strata. We introduce a novel methodology that partitions patients by baseline prognostic risk and applies matching within each stratum to equalize representation across the risk distribution. We implement this framework on a cohort of 1,799 patients with resected colorectal liver metastases (CRLM), including 1,197 who received adjuvant chemotherapy and 602 who did not. All models used in this study are Cox proportional hazards models trained on the same set of selected variables. Model performance is assessed via Harrell's C index, time-dependent AUC, and Integrated Calibration Index (ICI), with internal validation using Efron's bias-corrected bootstrapping. External validation is conducted on two independent CRLM datasets. Cox models trained on risk-balanced cohorts showed consistent improvements in internal validation compared to models trained on the full dataset while noticeably enhancing stratified C-index values in underrepresented high- and low-risk strata of the external cohorts. Our findings suggest that survival model performance in observational oncology cohorts can be meaningfully improved through targeted rebalancing of the training data across prognostic risk strata. This approach offers a practical and model-agnostic complement to existing methods, especially in applications where predictive reliability across the full risk continuum is critical to downstream clinical decisions.

Conjoint experiments have become central to survey research in political science and related fields because they allow researchers to study preferences across multiple attributes simultaneously. Beyond estimating main effects, scholars increasingly analyze heterogeneity through subgroup analysis and contextual variables, raising methodological challenges in detecting and interpreting interaction effects. Statistical power constraints, common in survey experiments, further complicate this task. This paper addresses the question: how can both main and interaction effects be reliably inferred in conjoint studies? We contribute in two ways. First, we conduct a systematic evaluation of leading approaches, including post-hoc corrections, sparse regression methods, and Bayesian models, across simulation regimes that vary sparsity, noise, and data availability. Second, we propose a novel black-box inference framework that leverages machine learning to recover main and interaction effects in conjoint experiments. Our approach balances computational efficiency with accuracy, providing a practical tool for researchers studying heterogeneous effects.

This paper addresses the problem of inverse covariance (also known as precision matrix) estimation in high-dimensional settings. Specifically, we focus on two classes of estimators: linear shrinkage estimators with a target proportional to the identity matrix, and estimators derived from data augmentation (DA). Here, DA refers to the common practice of enriching a dataset with artificial samples–typically generated via a generative model or through random transformations of the original data–prior to model fitting. For both classes of estimators, we derive estimators and provide concentration bounds for their quadratic error. This allows for both method comparison and hyperparameter tuning, such as selecting the optimal proportion of artificial samples. On the technical side, our analysis relies on tools from random matrix theory. We introduce a novel deterministic equivalent for generalized resolvent matrices, accommodating dependent samples with specific structure. We support our theoretical results with numerical experiments.

We study structure learning for linear Gaussian SEMs in the presence of latent confounding. Existing continuous methods excel when errors are independent, while deconfounding-first pipelines rely on pervasive factor structure or nonlinearity. We propose DECOR, a single likelihood-based and fully differentiable estimator that jointly learns a DAG and a correlated noise model. Our theory gives simple sufficient conditions for global parameter identifiability: if the mixed graph is bow free and the noise covariance has a uniform eigenvalue margin, then the map from $(\B,\OmegaMat)$ to the observational covariance is injective, so both the directed structure and the noise are uniquely determined. The estimator alternates a smooth-acyclic graph update with a convex noise update and can include a light bow complementarity penalty or a post hoc reconciliation step. On synthetic benchmarks that vary confounding density, graph density, latent rank, and dimension with $n<p$, DECOR matches or outperforms strong baselines and is especially robust when confounding is non-pervasive, while remaining competitive under pervasiveness.