Standard conformal anomaly detection provides marginal finite-sample guarantees under the assumption of exchangeability . However, real-world data often exhibit distribution shifts, necessitating a weighted conformal approach to adapt to local non-stationarity. We show that this adaptation induces a critical trade-off between the minimum attainable p-value and its stability. As importance weights localize to relevant calibration instances, the effective sample size decreases. This can render standard conformal p-values overly conservative for effective error control, while the smoothing technique used to mitigate this issue introduces conditional variance, potentially masking anomalies. We propose a continuous inference relaxation that resolves this dilemma by decoupling local adaptation from tail resolution via continuous weighted kernel density estimation. While relaxing finite-sample exactness to asymptotic validity, our method eliminates Monte Carlo variability and recovers the statistical power lost to discretization. Empirical evaluations confirm that our approach not only restores detection capabilities where discrete baselines yield zero discoveries, but outperforms standard methods in statistical power while maintaining valid marginal error control in practice.

Tech firm'says goodbye' to Sora, made publicly available in 2024, just six months after its launch of a stand-alone app In an abrupt announcement on Tuesday, OpenAI said it was "saying goodbye" to its AI video generator Sora. The move comes just six months after the company's splashy launch of a stand-alone app with which people could make and share hyper-realistic AI videos in a scrolling social feed. "To everyone who created with Sora, shared it, and built community around it: thank you," the company wrote in a post on X . "What you made with Sora mattered, and we know this news is disappointing." OpenAI first made Sora publicly available in late 2024, but it wasn't until the company launched Sora 2 and its stand-alone app last September that the video generator reached mainstream attention.

Simulation-based inference (SBI) with neural networks has accelerated and transformed cognitive modeling workflows. SBI enables modelers to fit complex models that were previously difficult or impossible to estimate, while also allowing rapid estimation across large numbers of datasets. However, the utility of SBI for iterating over varying modeling assumptions remains limited: changing parameterizations, generative functions, priors, and design variables all necessitate model retraining and hence diminish the benefits of amortization. To address these issues, we pilot a meta-amortized framework for cognitive modeling which we nickname the CogFormer. Our framework trains a transformer-based architecture that remains valid across a combinatorial number of structurally similar models, allowing for changing data types, parameters, design matrices, and sample sizes. We present promising quantitative results across families of decision-making models for binary, multi-alternative, and continuous responses. Our evaluation suggests that CogFormer can accurately estimate parameters across model families with a minimal amortization offset, making it a potentially powerful engine that catalyzes cognitive modeling workflows.

Panel data methods are widely used in empirical analysis to address unobserved heterogeneity, but causal inference remains challenging when treatments are endogenous and confounding variables high-dimensional and potentially nonlinear. Standard instrumental variables (IV) estimators, such as two-stage least squares (2SLS), become unreliable when instrument validity requires flexibly conditioning on many covariates with potentially non-linear effects. This paper develops a Double Machine Learning estimator for static panel models with endogenous treatments (panel IV DML), and introduces weak-identification diagnostics for it. We revisit three influential migration studies that use shift-share instruments. In these settings, instrument validity depends on a rich covariate adjustment. In one application, panel IV DML strengthens the predictive power of the instrument and broadly confirms 2SLS results. In the other cases, flexible adjustment makes the instruments weak, leading to substantially more cautious causal inference than conventional 2SLS. Monte Carlo evidence supports these findings, showing that panel IV DML improves estimation accuracy under strong instruments and delivers more reliable inference under weak identification.

Causal representation learning (CRL) aims to learn low-dimensional causal latent variables from high-dimensional observations. While identifiability has been extensively studied for CRL, estimation has been less explored. In this paper, we explore the use of empirical Bayes (EB) to estimate causal representations. In particular, we consider the problem of learning from data from multiple domains, where differences between domains are modeled by interventions in a shared underlying causal model. Multi-domain CRL naturally poses a simultaneous inference problem that EB is designed to tackle. Here, we propose an EB $f$-modeling algorithm that improves the quality of learned causal variables by exploiting invariant structure within and across domains. Specifically, we consider a linear measurement model and interventional priors arising from a shared acyclic SCM. When the graph and intervention targets are known, we develop an EM-style algorithm based on causally structured score matching. We further discuss EB $g$-modeling in the context of existing CRL approaches. In experiments on synthetic data, our proposed method achieves more accurate estimation than other methods for CRL.

We propose a dense associative memory for empirical measures (weighted point clouds). Stored patterns and queries are finitely supported probability measures, and retrieval is defined by minimizing a Hopfield-style log-sum-exp energy built from the debiased Sinkhorn divergence. We derive retrieval dynamics as a spherical Hellinger Kantorovich (SHK) gradient flow, which updates both support locations and weights. Discretizing the flow yields a deterministic algorithm that uses Sinkhorn potentials to compute barycentric transport steps and a multiplicative simplex reweighting. Under local separation and PL-type conditions we prove basin invariance, geometric convergence to a local minimizer, and a bound showing the minimizer remains close to the corresponding stored pattern. Under a random pattern model, we further show that these Sinkhorn basins are disjoint with high probability, implying exponential capacity in the ambient dimension. Experiments on synthetic Gaussian point-cloud memories demonstrate robust recovery from perturbed queries versus a Euclidean Hopfield-type baseline.

Probability theory has become the predominant framework for quantifying uncertainty across scientific and engineering disciplines, with a particular focus on measurement and control systems. However, the widespread reliance on simple Gaussian assumptions--particularly in control theory, manufacturing, and measurement systems--can result in incomplete representations and multistage lossy approximations of complex phenomena, including inaccurate propagation of uncertainty through multi stage processes. This work proposes a comprehensive yet computationally tractable framework for representing and propagating quantitative attributes arising in measurement systems using Probability Density Functions (PDFs). Recognizing the constraints imposed by finite memory in software systems, we advocate for the use of Gaussian Mixture Models (GMMs), a principled extension of the familiar Gaussian framework, as they are universal approximators of PDFs whose complexity can be tuned to trade off approximation accuracy against memory and computation. From both mathematical and computational perspectives, GMMs enable high performance and, in many cases, closed form solutions of essential operations in control and measurement. The paper presents practical applications within manufacturing and measurement contexts especially circular factory, demonstrating how the GMMs framework supports accurate representation and propagation of measurement uncertainty and offers improved accuracy--compared to the traditional Gaussian framework--while keeping the computations tractable.

We study forward and inverse problems for time-dependent probability measures in Bayes--Hilbert spaces. On the forward side, we show that each sufficiently regular Bayes--Hilbert path admits a canonical dynamical realization: a weighted Neumann problem transforms the log-density variation into the unique gradient velocity field of minimum kinetic energy. This construction induces a transport form on Bayes--Hilbert tangent directions, which measures the dynamical cost of realizing prescribed motions, and yields a flow-matching interpretation in which the canonical velocity field is the minimum-energy execution of the prescribed path. On the inverse side, we formulate reconstruction directly on Bayes--Hilbert path space from time-dependent indirect observations. The resulting variational problem combines a data-misfit term with the transport action induced by the forward geometry. In our infinite-dimensional setting, however, this transport geometry alone does not provide sufficient compactness, so we add explicit temporal and spatial regularization to close the theory. The linearized observation operator induces a complementary observability form, which quantifies how strongly tangent directions are seen through the data. Under explicit Sobolev regularity and observability assumptions, we prove existence of minimizers, derive first-variation formulas, establish local stability of the observation map, and deduce recovery of the evolving law, its score, and its canonical velocity field under the strong topologies furnished by the compactness theory.

We propose a principled framework for unsupervised domain adaptation under covariate shift in kernel Generalized Linear Models (GLMs), encompassing kernelized linear, logistic, and Poisson regression with ridge regularization. Our goal is to minimize prediction error in the target domain by leveraging labeled source data and unlabeled target data, despite differences in covariate distributions. We partition the labeled source data into two batches: one for training a family of candidate models, and the other for building an imputation model. This imputation model generates pseudo-labels for the target data, enabling robust model selection. We establish non-asymptotic excess-risk bounds that characterize adaptation performance through an "effective labeled sample size", explicitly accounting for the unknown covariate shift. Experiments on synthetic and real datasets demonstrate consistent performance gains over source-only baselines.

Behavior cloning is a fundamental paradigm in machine learning, enabling policy learning from expert demonstrations across robotics, autonomous driving, and generative models. Autoregressive models like transformer have proven remarkably effective, from large language models (LLMs) to vision-language-action systems (VLAs). However, applying autoregressive models to continuous control requires discretizing actions through quantization, a practice widely adopted yet poorly understood theoretically. This paper provides theoretical foundations for this practice. We analyze how quantization error propagates along the horizon and interacts with statistical sample complexity. We show that behavior cloning with quantized actions and log-loss achieves optimal sample complexity, matching existing lower bounds, and incurs only polynomial horizon dependence on quantization error, provided the dynamics are stable and the policy satisfies a probabilistic smoothness condition. We further characterize when different quantization schemes satisfy or violate these requirements, and propose a model-based augmentation that provably improves the error bound without requiring policy smoothness. Finally, we establish fundamental limits that jointly capture the effects of quantization error and statistical complexity.