Papers

The increasing availability of interventional data offers new opportunities for causal discovery, with gene perturbation studies providing a prominent example. Such data are typically count-valued and subject to substantial measurement error arising from technical variability and latent state heterogeneity. Motivated by these challenges, we study identification and estimation in latent linear structural causal models for interventional count data. We propose a latent linear Gaussian directed acyclic graph (DAG) model with Poisson measurement error that explicitly separates the latent causal structure from the observed counts. Under a mean-shift intervention design, we establish population-level identifiability of the latent causal DAG. Building on these identification results, we develop an estimation procedure based on sparse inverse matrix estimation and provide theoretical guarantees on estimation error and finite-sample causal discovery. Simulation studies and applications to Perturb-seq data demonstrate the practical effectiveness of the proposed method.

Variable-length Markov chains (VLMCs) are a flexible class of higher-order Markov models that admit a natural representation as context trees. Existing Bayesian methods for specifying prior distributions on trees rely on branching processes, but these suffer from a fundamental limitation: the connection between node-branching probabilities and the structural properties of the induced tree distribution is not straightforward, making it difficult to encode specific structural beliefs. We address this issue by introducing a novel representation of prior distributions on tree spaces, characterized by assigning weights to individual contexts through a function on nodes. In this way, our approach provides an intuitive mechanism for incorporating structural hypotheses into the prior while preserving computational tractability, allowing marginal likelihoods and posterior mode trees to be computed exactly via generalizations of the Context Tree Weighting (CTW) and Context Tree Maximizing (CTM) algorithms. By enabling exact Bayes factor calculations, our methodology provides a principled framework for model comparison over structural priors. We demonstrate the flexibility and effectiveness of our approach by comparing different prior specifications through simulation studies and an application to financial markets.

We provide explicit, finite-sample guarantees for learning causal representations from data with a sublinear number of environments. Causal representation learning seeks to provide a rigourous foundation for the general representation learning problem by bridging causal models with latent factor models in order to learn interpretable representations with causal semantics. Despite a blossoming theory of identifiability in causal representation learning, estimation and finite-sample bounds are less well understood. We show that causal representations can be learned with only a logarithmic number of unknown, multi-node interventions, and that the intervention targets need not be carefully designed in advance. Through a careful perturbation analysis, we provide a new analysis of this problem that guarantees consistent recovery of (a) the latent causal graph, (b) the mixing matrix and representations, and (c) unknown intervention targets.

We propose SAHMM-VAE, a source-wise adaptive Hidden Markov prior variational autoencoder for unsupervised blind source separation. Instead of treating the latent prior as a single generic regularizer, the proposed framework assigns each latent dimension its own adaptive regime-switching prior, so that different latent dimensions are pulled toward different source-specific temporal organizations during training. Under this formulation, source separation is not implemented as an external post-processing step; it is embedded directly into variational learning itself. The encoder, decoder, posterior parameters, and source-wise prior parameters are optimized jointly, where the encoder progressively learns an inference map that behaves like an approximate inverse of the mixing transformation, while the decoder plays the role of the generative mixing model. Through this coupled optimization, the gradual alignment between posterior source trajectories and heterogeneous HMM priors becomes the mechanism through which different latent dimensions separate into different source components. To instantiate this idea, we develop three branches within one common framework: a Gaussian-emission HMM prior, a Markov-switching autoregressive HMM prior, and an HMM state-flow prior with state-wise autoregressive flow transformations. Experiments show that the proposed framework achieves unsupervised source recovery while also learning meaningful source-wise switching structures. More broadly, the method extends our structured-prior VAE line from smooth, mixture-based, and flow-based latent priors to adaptive switching priors, and provides a useful basis for future work on interpretable and potentially identifiable latent source modeling.

Markov chain Monte Carlo (MCMC) methods remain the mainstay of Bayesian estimation of structural equation models (SEM), though they often incur a high computational cost. We present a bespoke approximate Bayesian approach to SEM, drawing on ideas from the integrated nested Laplace approximation (INLA; Rue et al., 2009, J. R. Stat. Soc., B: Stat. Methodol.) framework. After analytically integrating out the latent variables, we implement a simplified Laplace approximation that profiles the posterior using an efficient gradient-based volume correction, allowing for parametric skew-normal estimation of the marginals. A variational Bayes correction further refines the centre of the joint Gaussian approximation; marginal profiling implicitly recovers the same location correction to leading order. Essential quantities, including factor scores and model-fit indices, are obtained via a Gaussian copula sampling scheme. On a benchmark SEM, inference completes in seconds with close agreement to MCMC. A simulation study stresses the approximation along sample size, identification, boundary proximity, and model dimension. Accuracy remains high across the examined sample sizes and model dimensions, with degradation concentrated in weakly identified settings and in the lower tails of variances near the zero boundary.

Small, trade-dependent economies often exhibit limited maritime connectivity, yet empirical evidence on the structural configuration of their container systems remains limited. This study analyzes route concentration and node distributions in Mauritania's maritime container system during 2019-2022 using shipment-level data measured in forty-foot equivalent units (FFE). Routes, origin nodes, destination nodes, and industries are represented as FFE-weighted probability distributions, and concentration and divergence metrics are used to assess structural properties. The results show strong corridor concentration across the seven observed routes (HHI = 0.296), with the top three accounting for approximately 84% of total FFE. Node structures differ by direction: imports are associated with a highly concentrated set of destination nodes (HHI = 0.848), while exports originate from only two origin nodes (HHI = 0.567) and are distributed across a large number of destinations (HHI = 0.053). Industry distributions are more concentrated for exports (HHI = 0.352) than for imports (HHI = 0.096), with frozen fish and seafood accounting for more than 53% of export volume. Temporal analysis shows that route concentration remains stable over time (HHI ~ 0.293-0.303), while node distributions exhibit measurable variation, particularly for export destinations (JSD ~ 0.395) and import origins (JSD ~ 0.250).

We introduce a generalized Bayesian method for multiple changepoint analysis with a loss function inspired by multinomial logistic regression. The method does not require a specification of the data-generating process and avoids restrictive assumptions on the nature of changepoints. From the joint posterior distribution, we can make simultaneous inference on the locations of changepoints and the coefficients of a multinomial logistic regression model for distinguishing data across homogeneous segments. The multinomial logistic regression coefficients provide a familiar means of interpreting potentially complex changes. To select the number of changepoints, we leverage posterior summaries that measure whether the multinomial logistic classifier can distinguish data from either side of a potential changepoint. To simulate from the generalized posterior distribution, we present a Gibbs sampler based on Pólya-Gamma data augmentation. We assess the accuracy and flexibility of our method through simulation studies featuring different types of changes and demonstrate its interpretability through applications to financial network data and topological data derived from nanoparticle videos.

We study the unconstrained minimization of a smooth and strongly convex population loss function under a stochastic oracle that introduces both additive and multiplicative noise; this is a canonical and widely-studied setting that arises across operations research, signal processing, and machine learning. We begin by showing that standard approaches such as sample average approximation and robust (or averaged) stochastic approximation can lead to suboptimal – and in some cases arbitrarily poor – performance with realistic finite sample sizes. In contrast, we demonstrate that a carefully designed variance reduction strategy, which we term VISOR for short, can significantly outperform these approaches while using the same sample size. Our upper bounds are complemented by finite-sample, information-theoretic local minimax lower bounds, which highlight fundamental, instance-dependent factors that govern the performance of any estimator. Taken together, these results demonstrate that an accelerated variant of VISOR is instance-optimal, achieving the best possible sample complexity up to logarithmic factors while also attaining optimal oracle complexity. We apply our theory to generalized linear models and improve upon classical results. In particular, we obtain the best-known non-asymptotic, instance-dependent generalization error bounds for stochastic methods, even in linear regression.

We present an efficient algorithm for uniformly sampling from an arbitrary compact body $\mathcal{X} \subset \mathbb{R}^n$ from a warm start under isoperimetry and a natural volume growth condition. Our result provides a substantial common generalization of known results for convex bodies and star-shaped bodies. The complexity of the algorithm is polynomial in the dimension, the Poincaré constant of the uniform distribution on $\mathcal{X}$ and the volume growth constant of the set $\mathcal{X}$.

A key capability of modern neural networks is their capacity to simultaneously learn underlying rules and memorize specific facts or exceptions. Yet, theoretical understanding of this dual capability remains limited. We introduce the Rules-and-Facts (RAF) model, a minimal solvable setting that enables precise characterization of this phenomenon by bridging two classical lines of work in the statistical physics of learning: the teacher-student framework for generalization and Gardner-style capacity analysis for memorization. In the RAF model, a fraction $1 - \varepsilon$ of training labels is generated by a structured teacher rule, while a fraction $\varepsilon$ consists of unstructured facts with random labels. We characterize when the learner can simultaneously recover the underlying rule - allowing generalization to new data - and memorize the unstructured examples. Our results quantify how overparameterization enables the simultaneous realization of these two objectives: sufficient excess capacity supports memorization, while regularization and the choice of kernel or nonlinearity control the allocation of capacity between rule learning and memorization. Experiments on a CIFAR10-based RAF task show that the qualitative trade-off persists for fixed kernels, whereas representations learned by deeper neural networks substantially mitigate it, preserving factual recall while improving generalization. The RAF model provides a theoretical foundation for understanding how modern neural networks can infer structure while storing rare or non-compressible information.

Tensors provide a structured representation for multidimensional data, yet discretization discards the underlying continuous structure when the data originate from continuous processes. We address this limitation by introducing a functional Tucker decomposition (FTD) that embeds a mode-wise continuity constraint directly into the factorization. The FTD models the continuous mode as a function in a reproducing kernel Hilbert space (RKHS), avoiding a prespecified basis while preserving the multilinear subspace structure of the Tucker model. We derive a reconstruction error bound for the continuous mode that quantifies the approximation quality when a subspace estimated on one domain is reused on another. This bound provides theoretical justification for subspace transfer, whose practical value we demonstrate on cross-domain classification tasks in hyperspectral imaging and multivariate time-series analysis.

In this paper I develop a breakdown frontier approach to assess the sensitivity of Local Average Treatment Effects (LATE) estimates to violations of monotonicity and independence of the instrument. I parametrize violations of independence using the concept of $c$-dependence from Masten & Poirier (2018) and allow for the share of defiers to be greater than zero but smaller than the share of compliers. I derive identified sets for the LATE and the Average Treatment Effect (ATE) in which the bounds are functions of these two sensitivity parameters. Using these bounds, I derive the breakdown frontier for the LATE, which is the weakest set of assumptions such that a conclusion regarding the LATE holds. I derive consistent sample analogue estimators for the breakdown frontiers and provide a valid bootstrap procedure for inference. Monte Carlo simulations show the desirable finite-sample properties of the estimators and an empirical application shows that the conclusions regarding the effect of family size on unemployment from Angrist & Evans (1998) are highly sensitive to violations of independence and monotonicity.

We propose a method for constructing distribution-free prediction intervals in nonparametric instrumental variable regression (NPIV), with finite-sample coverage guarantees. Building on the conditional guarantee framework in conformal inference, we reformulate conditional coverage as marginal coverage over a class of IV shifts $\mathcal{F}$. Our method can be combined with any NPIV estimator, including sieve 2SLS and other machine-learning-based NPIV methods such as neural networks minimax approaches. Our theoretical analysis establishes distribution-free, finite-sample coverage over a practitioner-chosen class of IV shifts.

Model retraining is usually treated as an ongoing maintenance task. But as Harrison Katz now argues, retraining can be better understood as approximate Bayesian inference under computational constraints. The gap between a continuously updated belief state and your frozen deployed model is "learning debt," and the retraining decision is a cost minimization problem with a threshold that falls out of your loss function. In this article Katz provides a decision-theoretic framework for retraining policies. The result is evidence-based triggers that replace calendar schedules and make governance auditable. For readers less familiar with the Bayesian and decision-theoretic language, key terms are defined in a glossary at the end of the article.

We study statistical estimation in a student–teacher setting, where predictions from a pre-trained teacher are used to guide a student model. A standard approach is to train the student to directly match the teacher's outputs, which we refer to as student soft matching (SM). This approach directly propagates any systematic bias or mis-specification present in the teacher, thereby degrading the student's predictions. We propose and analyze an alternative scheme, known as residual-as-teacher (RaT), in which the teacher is used to estimate residuals in the student's predictions. Our analysis shows how the student can thereby emulate a proximal gradient scheme for solving an oracle optimization problem, and this provably reduces the effect of teacher bias. For general student–teacher pairs, we establish non-asymptotic excess risk bounds for any RaT fixed point, along with convergence guarantees for the student-teacher iterative scheme. For kernel-based student–teacher pairs, we prove a sharp separation: the RaT method achieves the minimax-optimal rate, while the SM method incurs constant prediction error for any sample size. Experiments on both synthetic data and ImageNette classification under covariate shift corroborate our theoretical findings.

In a dataset of 423 patients who had had radical prostatectomy for localised prostate cancer we estimated the apparent Shannon information (ASI) about time to biochemical recurrence in various subsets of the available pre-op variables using a Bayesian Gamma-power-mixture survival regression model. In all the subsets examined the ASI was positive with posterior probability greater than 0.975 . Using only age and results of pre-operative blood tests (PSA and biomarkers) we achieved 0.232 (0.180 to 0.290) nats ASI (0.335 (0.260 to 0.419) bits) (posterior mean and equitailed 95% posterior confidence intervals). This is more than double the mean posterior ASI previously achieved on the same dataset by a subset of the current authors using a log-skew-Student-mixture model, and is greater than that previous value with posterior probability greater than 0.99 . Additionally using pre- or post-operative Gleason grades, operative findings, clinical stage, and presence or absence of extraprostatic extension or seminal vesicle invasion did not increase the ASI extracted. However removing the blood-based biomarkers and replacing them with either pre-operative Gleason grades or findings available from MRI scanning greatly reduced the available ASI to respectively 0.077 (0.038 to 0.120) and 0.088 (0.045 to 0.132) nats (both less than the values using blood-based biomarkers with posterior probability greater than 0.995). A greedy approach to selection of the best biomarkers gave TGFbeta1, VCAM1, IL6sR, and uPA in descending order of importance from those examined.

In this applied paper, we address the difficult open problem of when to discharge patients from the Intensive Care Unit. This can be conceived as an optimal stopping scenario with three added challenges: 1) the evaluation of a stopping strategy from observational data is itself a complex causal inference problem, 2) the composite objective is to minimize the length of intervention and maximize the outcome, but the two cannot be collapsed to a single dimension, and 3) the recording of variables stops when the intervention is discontinued. Our contributions are two-fold. First, we generalize the implementation of the g-formula Python package, providing a framework to evaluate stopping strategies for problems with the aforementioned structure, including positivity and coverage checks. Second, with a fully open-source pipeline, we apply this approach to MIMIC-IV, a public ICU dataset, demonstrating the potential for strategies that improve upon current care.

Probabilistic forecasts provide a principled representation of forecast uncertainty through predictive distributions. Directly propagating predictive distributions with conventional physical models requires solving distributional evolution equations, a task well-known to be computationally prohibitive for high-dimensional nonlinear systems. Consequently, multi-step predictive distributions are commonly approximated using ensembles or sampled trajectories. A novel distribution-to-distribution (D2D) neural probabilistic forecasting framework is proposed with compatible distributional encoding and decoding interfaces around a replaceable neural forecasting module. Kernel mean embeddings represent input distributions, while mixture density networks parameterise outputs, enabling recursive multi-step forecasting in distributional form. The framework is demonstrated on the Lorenz63 system. Results show that the D2D model captures nontrivial distributional evolution, produces skillful probabilistic forecasts without explicit ensemble simulation, and remains competitive with a naively initialised perfect-model benchmark. This provides proof-of-concept evidence that predictive distributions can be recursively propagated through a neural forecasting model and evaluated in terms of probabilistic forecast performance.

This paper studies the degree to which a bivariate copula fails to be symmetric under coordinate permutation, a property known as non-exchangeability. Working within an axiomatic framework that quantifies this asymmetry through a family of $L^p$-based measures, we establish sharp bounds linking non-exchangeability to classical dependence and concordance measures, prove exact scaling laws under convex mixing that enable explicit construction of copulas with any prescribed degree of asymmetry, and characterise the class of maximally non-exchangeable copulas together with the feasible range of asymmetry–concordance pairs. On the inferential side, we propose a nonparametric permutation test for exchangeability with exact finite-sample error control and consistency against all asymmetric alternatives, validated by Monte Carlo simulation and illustrated on a real data set.

Efficient global optimization (EGO) is one of the most widely used noise-free Bayesian optimization algorithms.It comprises the Gaussian process (GP) surrogate model and expected improvement (EI) acquisition function. In practice, when EGO is applied, a scalar matrix of a small positive value (also called a nugget or jitter) is usually added to the covariance matrix of the deterministic GP to improve numerical stability. We refer to this EGO with a positive nugget as the practical EGO. Despite its wide adoption and empirical success, to date, cumulative regret bounds for practical EGO have yet to be established. In this paper, we present for the first time the cumulative regret upper bound of practical EGO. In particular, we show that practical EGO has sublinear cumulative regret bounds and thus is a no-regret algorithm for commonly used kernels including the squared exponential (SE) and Matérn kernels ($\nu>\frac{1}{2}$). Moreover, we analyze the effect of the nugget on the regret bound and discuss the theoretical implication on its choice. Numerical experiments are conducted to support and validate our findings.

Classical estimation outputs a single point estimate of an unknown $d$-dimensional vector from an observation. In this paper, we study \emph{$k$-list estimation}, in which a single observation is used to produce a list of $k$ candidate estimates and performance is measured by the expected squared distance from the true vector to the closest candidate. We compare this centralized setting with a symmetric decentralized MMSE benchmark in which $k$ agents observe conditionally i.i.d.\ measurements and each agent outputs its own MMSE estimate. On the centralized side, we show that optimal $k$-list estimation is equivalent to fixed-rate $k$-point vector quantization of the posterior distribution and, under standard regularity conditions, admits an exact high-rate asymptotic expansion with explicit constants and decay rate $k^{-2/d}$. On the decentralized side, we derive lower bounds in terms of the small-ball behavior of the single-agent MMSE error; in particular, when the conditional error density is bounded near the origin, the benchmark distortion cannot decay faster than order $k^{-2/d}$. We further show that if the error density vanishes at the origin, then the decentralized benchmark is provably unable to match the centralized $k^{-2/d}$ exponent, whereas the centralized estimator retains that scaling. Gaussian specializations yield explicit formulas and numerical experiments corroborate the predicted asymptotic behavior. Overall, the results show that, in the scaling with $k$, one observation combined with $k$ carefully chosen candidates can be asymptotically as effective as – and in some regimes strictly better than – this MMSE-based decentralized benchmark with $k$ independent observations.

Households represent a key unit of interest in infectious disease epidemiology, in both empirical studies and mathematical modelling. The within-household transmission potential of a disease is often summarised by a secondary attack ratio (SAR). Despite its widespread use, the SAR depends on the household size distribution (HHSD) seen during the study period, making it difficult to generalise to new contexts. Extending estimates of transmission potential to new populations instead requires estimates of person-to-person transmission rates which can be convoluted with data on population structure to parametrise mechanistic transmission models. In this study we present a new Bayesian inference method which uses an MCMC algorithm to infer the transmission intensity by imputing the unreported household structure underlying the epidemic. This method can be run on household epidemiological data reported at varying levels of resolution. For synthetic data from a realistic underlying HHSD, we were able to achieve over 90% coverage in our estimates of transmission rate consistently. We were also able to consistently achieve over 90% coverage for data generated with a pathological underlying HHSD, given strong information about the HHSD. Using an existing dataset which recorded micro-scale household epidemiological outcomes during the COVID-19 pandemic, we show that stratifying observed SARs by household size substantially reduces the uncertainty in estimates. Our findings suggest that researchers conducting household epidemiological studies can improve the utility of results for infectious disease modellers by reporting household-stratified estimates. These results aim to encourage the reporting of higher resolution outputs in epidemiological field work as, in the absence of strong priors, transmission parameters were not easily identifiable from low resolution datasets, which are often reported.

Demographic parity (DP) is a widely used group fairness criterion requiring predictive distributions to be invariant across sensitive groups. While natural in classification, full distributional DP is often overly restrictive in regression and can lead to substantial accuracy loss. We propose a relaxation of DP tailored to regression, enforcing parity only at a finite set of quantile levels and/or score thresholds. Concretely, we introduce a novel (${\ell}$, Z)-fair predictor, which imposes groupwise CDF constraints of the form F f |S=s (z m ) = ${\ell}$ m for prescribed pairs (${\ell}$ m , z m ). For this setting, we derive closed-form characterizations of the optimal fair discretized predictor via a Lagrangian dual formulation and quantify the discretization cost, showing that the risk gap to the continuous optimum vanishes as the grid is refined. We further develop a model-agnostic post-processing algorithm based on two samples (labeled for learning a base regressor and unlabeled for calibration), and establish finite-sample guarantees on constraint violation and excess penalized risk. In addition, we introduce two alternative frameworks where we match group and marginal CDF values at selected score thresholds. In both settings, we provide closed-form solutions for the optimal fair discretized predictor. Experiments on synthetic and real datasets illustrate an interpretable fairness-accuracy trade-off, enabling targeted corrections at decision-relevant quantiles or thresholds while preserving predictive performance.

Recent vision backbones, such as Transformer families and state-space models like Mamba, have achieved remarkable progress on image recognition. Despite their empirical success, these architectures remain far from the computational principles of the human brain, often demanding enormous amounts of training data while offering limited interpretability. We propose the Vision Hopfield Memory Network (V-HMN), a brain-inspired vision backbone that integrates hierarchical memory mechanisms across layers with iterative refinement updates. Specifically, V-HMN incorporates local Hopfield modules that provide associative memory dynamics at the image patch level, global Hopfield modules that function as episodic memory for contextual modulation, and a predictive-coding-inspired refinement rule for iterative error correction. By organizing these memory-based modules hierarchically, V-HMN captures both local and global dynamics in a unified framework. Memory retrieval exposes the relationship between inputs and stored patterns, providing a prototype-based form of interpretability through explicit memory retrieval, while the reuse of stored patterns improves data efficiency. This brain-inspired design therefore enhances data efficiency and provides a prototype-based form of interpretability compared to existing self-attention- or state-space-based approaches. We conducted extensive experiments on public image classification benchmarks. V-HMN achieves strong performance on small- and medium-scale benchmarks, and remains competitive with widely adopted backbone architectures on ImageNet despite minimal architectural tuning, while offering improved data efficiency and a prototype-based form of interpretability. These findings highlight the potential of V-HMN as a memory-centric alternative to standard vision backbones, thereby bridging brain-inspired computation with modern machine learning.

In the present paper, we discuss for the first time the theoretical Kendall correlation coefficient for non-identical bivariate data. In the non-identical case, we first introduce a theoretical Kendall correlation coefficient $\tau_n$ and show that the expected value of the rank Kendall correlation coefficient $\tilde{\tau}_n$ is equal to $\tau_n$. We then prove that $\tilde{\tau}_n$ converges in probability to $\tau=\lim_{n\rightarrow\infty} \tau_n$. These facts enable us to state that $\tau_n$ is a correctly defined theoretical Kendall correlation coefficient for the non-identical case. We also support our theoretical results by simulation experiments.

Under network interference, a unit's observed outcome depends on the treatment assignment of its neighboring units in an exposure graph. Existing design-based asymptotic theory typically considers local interference by restricting neighborhood sizes in the exposure graph. Such methods do not apply to dense exposure graphs, so prior work has often adopted a superpopulation approach instead, imposing regularity through random-graph models. In this paper, we introduce a notion of convergence for a sequence of finite populations under anonymous interference. Building on the graph limit framework of Lovász and Szegedy, we show that large-scale geometry of the exposure graph can provide a source of regularity beyond sparsity assumptions or random-graph modeling. Under Bernoulli assignment, our convergence notion yields asymptotic normality of standard estimators for the average direct effect, even on dense, non-random exposure graphs. As a special case, graphon-based random-graph models studied in prior work generate finite populations that converge in our sense. Under these models, graph randomness generates exposure graphs with stable large-scale geometry, while first-order uncertainty in average direct effect estimation is driven by treatment assignment.

As a representative continuous-depth neural network approach, stochastic differential equation (SDE)-based Bayesian neural networks (BNNs) have attracted considerable attention due to their solid theoretical foundations and strong potential for real-world applications. However, their reliance on numerical SDE solvers inevitably incurs a large number of function evaluations (NFEs), resulting in high computational cost and occasional convergence instability. To address these challenges, we propose a Nesterov-accelerated gradient (NAG) enhanced SDE-BNN model. By integrating NAG into the SDE-BNN framework along with an NFE-dependent residual skip connection, our method accelerates convergence and substantially reduces NFEs during both training and testing. Extensive empirical results show that our model consistently outperforms conventional SDE-BNNs across various tasks, including image classification and sequence modeling, achieving lower NFEs and improved predictive accuracy.

Causal representation learning seeks to uncover causal relationships among high-level latent variables from low-level, entangled, and noisy observations. Existing approaches often either rely on deep neural networks, which lack interpretability and formal guarantees, or impose restrictive assumptions like linearity, continuous-only observations, and strong structural priors. These limitations particularly challenge applications with a large number of discrete latent variables and mixed-type observations. To address these challenges, we propose discrete causal representation learning (DCRL), a generative framework that models a directed acyclic graph among discrete latent variables, along with a sparse bipartite graph linking latent and observed layers. This design accommodates continuous, count, and binary responses through flexible measurement models while maintaining interpretability. Under mild conditions, we prove that both the bipartite measurement graph and the latent causal graph are identifiable from the observed data distribution alone. We further propose a three-stage estimate-resample-discovery pipeline: penalized estimation of the generative model parameters, resampling of latent configurations from the fitted model, and score-based causal discovery on the resampled latents. We establish the consistency of this procedure, ensuring reliable recovery of the latent causal structure. Empirical studies on educational assessment and synthetic image data demonstrate that DCRL recovers sparse and interpretable latent causal structures.

We propose a Bayesian propensity score-augmented latent factor model for causal inference with time-series cross-sectional data. The framework explicitly models the treatment assignment mechanism by incorporating latent factor loadings, while the outcome model flexibly incorporates the propensity score, for example through stratification. Relative to existing approaches, the proposed method provides greater flexibility and captures additional heterogeneity across propensity-score strata, enabling more credible comparisons between treated and control units within each stratum. For estimation and inference, we adopt an approximate Bayesian procedure to address the model feedback problem common in Bayesian propensity score analysis. We demonstrate the performance of the proposed method through Monte Carlo simulations and an empirical application examining the effect of political connections on firm value.

The validity of assessments, from large-scale AI benchmarks to human classrooms, depends on the quality of individual items, yet modern evaluation instruments often contain thousands of items with minimal psychometric vetting. We introduce a new family of nonparametric scalability coefficients based on interitem isotonic regression for efficiently detecting globally bad items (e.g., miskeyed, ambiguously worded, or construct-misaligned). The central contribution is the signed isotonic $R^2$, which measures the maximal proportion of variance in one item explainable by a monotone function of another while preserving the direction of association via Kendall's $\tau$. Aggregating these pairwise coefficients yields item-level scores that sharply separate problematic items from acceptable ones without assuming linearity or committing to a parametric item response model. We show that the signed isotonic $R^2$ is extremal among monotone predictors (it extracts the strongest possible monotone signal between any two items) and show that this optimality property translates directly into practical screening power. Across three AI benchmark datasets (HS Math, GSM8K, MMLU) and two human assessment datasets, the signed isotonic $R^2$ consistently achieves top-tier AUC for ranking bad items above good ones, outperforming or matching a comprehensive battery of classical test theory, item response theory, and dimensionality-based diagnostics. Crucially, the method remains robust under the small-n/large-p conditions typical of AI evaluation, requires only bivariate monotone fits computable in seconds, and handles mixed item types (binary, ordinal, continuous) without modification. It is a lightweight, model-agnostic filter that can materially reduce the reviewer effort needed to find flawed items in modern large-scale evaluation regimes.