Papers

In this paper, we provide a novel measure for greenwashing – i.e., climate-related misinformation – that shows how polluting companies can use social media advertising related to climate change to redirect criticism. To do so, we identify greenwashing content in 11 million social-political ads in Meta's Ad Targeting Datset with a measurement technique that combines large language models, human coders, and advances in Bayesian item response theory. We show that what is called greenwashing has diverse actors and components, but we also identify a very pernicious form, which we call political greenwashing, that appears to be promoted by fossil fuel companies and related interest groups. Based on ad targeting data, we show that much of this advertising happens via organizations with undisclosed links to the fossil fuel industry. Furthermore, we show that greenwashing ad content is being micro-targeted at left-leaning communities with fossil fuel assets, though we also find comparatively little evidence of ad targeting aimed at influencing public opinion at the national level.

Deep graph learning has advanced Alzheimer's (AD) disease classification from MRI, but most models remain correlational, confounding demographic and genetic factors with disease specific features. We present Causal-GCN, an interventional graph convolutional framework that integrates do-calculus-based back-door adjustment to identify brain regions exerting stable causal influence on AD progression. Each subject's MRI is represented as a structural connectome where nodes denote cortical and subcortical regions and edges encode anatomical connectivity. Confounders such as age, sec, and APOE4 genotype are summarized via principal components and included in the causal adjustment set. After training, interventions on individual regions are simulated by serving their incoming edges and altering node features to estimate average causal effects on disease probability. Applied to 484 subjects from the ADNI cohort, Causal-GCN achieves performance comparable to baseline GNNs while providing interpretable causal effect rankings that highlight posterior, cingulate, and insular hubs consistent with established AD neuropathology.

Detecting heterogeneity in treatment response enriches the interpretation of gerontologic trials. In aging research, estimating the effect of the intervention on clinically meaningful outcomes faces analytical challenges when it is truncated by death. For example, in the Whole Systems Demonstrator trial, a large cluster-randomized study evaluating telecare among older adults, the overall effect of the intervention on quality of life was found to be null. However, this marginal intervention estimate obscures potential heterogeneity of individuals responding to the intervention, particularly among those who survive to the end of follow-up. To explore this heterogeneity, we adopt a causal framework grounded in principal stratification, targeting the Survivor Average Causal Effect (SACE)-the treatment effect among "always-survivors," or those who would survive regardless of treatment assignment. We extend this framework using Bayesian Additive Regression Trees (BART), a nonparametric machine learning method, to flexibly model both latent principal strata and stratum-specific potential outcomes. This enables the estimation of the Conditional SACE (CSACE), allowing us to uncover variation in treatment effects across subgroups defined by baseline characteristics. Our analysis reveals that despite the null average effect, some subgroups experience distinct quality of life benefits (or lack thereof) from telecare, highlighting opportunities for more personalized intervention strategies. This study demonstrates how embedding machine learning methods, such as BART, within a principled causal inference framework can offer deeper insights into trial data with complex features including truncation by death and clustering-key considerations in analyzing pragmatic gerontology trials.

Wasserstein gradient flow provides a general framework for minimizing an energy functional $J$ over the space of probability measures on a Riemannian manifold $(M,g)$. Its canonical time-discretization, the Jordan-Kinderlehrer-Otto (JKO) scheme, produces for any step size $\eta>0$ a sequence of probability distributions $\rho_k^\eta$ that approximate to first order in $\eta$ Wasserstein gradient flow on $J$. But the JKO scheme also has many other remarkable properties not shared by other first order integrators, e.g. it preserves energy dissipation and exhibits unconditional stability for $\lambda$-geodesically convex functionals $J$. To better understand the JKO scheme we characterize its implicit bias at second order in $\eta$. We show that $\rho_k^\eta$ are approximated to order $\eta^2$ by Wasserstein gradient flow on a modified energy \[ J^{\eta}(\rho) = J(\rho) - \frac{\eta}{4}\int_M \Big\lVert \nabla_g \frac{\delta J}{\delta \rho} (\rho) \Big\rVert_{2}^{2} \,\rho(dx), \] obtained by subtracting from $J$ the squared metric curvature of $J$ times $\eta/4$. The JKO scheme therefore adds at second order in $\eta$ a deceleration in directions where the metric curvature of $J$ is rapidly changing. This corresponds to canonical implicit biases for common functionals: for entropy the implicit bias is the Fisher information, for KL-divergence it is the Fisher-Hyvärinen divergence, and for Riemannian gradient descent it is the kinetic energy in the metric $g$. To understand the differences between minimizing $J$ and $J^\eta$ we study JKO-Flow, Wasserstein gradient flow on $J^\eta$, in several simple numerical examples. These include exactly solvable Langevin dynamics on the Bures-Wasserstein space and Langevin sampling from a quartic potential in 1D.

Projective shape analysis provides a geometric framework for studying digital images acquired by pinhole digital cameras. In the classical projective shape (PS) method, landmark configurations are represented in $(\RP^2)^{k-4}$, where $k$ is the number of landmarks observed. This representation is invariant under the action of the full projective group on this space and is sign-blind, so opposite directions in $\R^{3}$ determine the same projective point and front–back orientation of a surface is not recorded. Oriented projective shape ($\OPS$) restores this information by working on a product of $k-4$ spheres $\SP^2$ instead of projective space and restricting attention to the orientation-preserving subgroup of projective transformations. In this paper we introduce an extrinsic total-variance index for OPS, resulting in the extrinsic Fréchet framework for the m dimensional case from the inclusion $\jdir:(\SP^m)^q\hookrightarrow(\R^{m+1})^q,q=k-m-2$. In the planar pentad case ($m=2$, $q=1$) the sample total extrinsic variance has a closed form in terms of the mean of a random sample of size $n$ of oriented projective coordinates in $S^2$. As an illustration, using an oriented projective frame, we analyze the Sope Creek stone data set, a benchmark and nearly planar example with $41$ images and $5$ landmarks. Using a delta-method applied to a large sample and a generalized Slutsky theorem argument, for an OPS leave-two-out diagnostic, one identifies coplanarity at the $5\%$ level, confirming the concentrated data coplanarity PS result in Patrangenaru(2001)\cite{Patrangenaru2001}.

On many learning platforms, the optimization criteria guiding model training reflect the priorities of the designer rather than those of the individuals they affect. Consequently, users may act strategically to obtain more favorable outcomes. While past work has studied strategic user behavior on learning platforms, the focus has largely been on strategic responses to a deployed model, without considering the behavior of other users. In contrast, look-ahead reasoning takes into account that user actions are coupled, and – at scale – impact future predictions. Within this framework, we first formalize level-k thinking, a concept from behavioral economics, where users aim to outsmart their peers by looking one step ahead. We show that, while convergence to an equilibrium is accelerated, the equilibrium remains the same, providing no benefit of higher-level reasoning for individuals in the long run. Then, we focus on collective reasoning, where users take coordinated actions by optimizing through their joint impact on the model. By contrasting collective with selfish behavior, we characterize the benefits and limits of coordination; a new notion of alignment between the learner's and the users' utilities emerges as a key concept. Look-ahead reasoning can be seen as a generalization of algorithmic collective action; we thus offer the first results characterizing the utility trade-offs of coordination when contesting algorithmic systems.

Arnold & Manjunath (2021) claim that the bivariate pseudo-Poisson distribution is well suited to bivariate count data with one equidispersed and one overdispersed marginal, owing to its parsimonious structure and straightforward parameter estimation. In the formulation of Leiter & Hamdan (1973), the conditional mean of $X_2$ was specified as a function of $X_1$; Arnold & Manjunath (2021) subsequently augmented this specification by adding an intercept, yielding a linear conditional rate. A direct implication of this construction is that the bivariate pseudo-Poisson distribution can represent only positive correlation between the two variables. This study generalizes the conditional rate to accommodate negatively correlated datasets by introducing curvature. This augmentation provides the additional benefit of allowing the model to behave approximately linear when appropriate, while adequately handling the boundary case $(x_1,x_2)=(0,0)$. According to the Akaike Information Criterion (AIC), the models proposed in this study outperform Arnold & Manjunath (2021)'s linear models.

The Bayesian Optimal Phase II (BOP2) framework is a flexible trial design that can naturally facilitate complex adaptations due to its Bayesian setting. BOP2 uses equal randomisation and equally placed interim analyses in its design, but it is unclear whether these give the best operating characteristics. By incorporating Bayesian Response-Adaptive Randomisation (BRAR) and optimal interim analysis placement, we show that allocation to the best treatment and expected sample size can be improved with minimal impact on power. We discuss recommendations on implementing these adaptations, using simulation-based evidence, to give practical advice to practitioners. Reproducible code for the simulations is freely provided.

We establish the first global convergence result of neural networks for two stage least squares (2SLS) approach in nonparametric instrumental variable regression (NPIV). This is achieved by adopting a lifted perspective through mean-field Langevin dynamics (MFLD), unlike standard MFLD, however, our setting of 2SLS entails a bilevel optimization problem in the space of probability measures. To address this challenge, we leverage the penalty gradient approach recently developed for bilevel optimization which formulates bilevel optimization as a Lagrangian problem. This leads to a novel fully first-order algorithm, termed \texttt{F$^2$BMLD}. Apart from the convergence bound, we further provide a generalization bound, revealing an inherent trade-off in the choice of the Lagrange multiplier between optimization and statistical guarantees. Finally, we empirically validate the effectiveness of the proposed method on an offline reinforcement learning benchmark.

Disaster-induced power outages create cascading disruptions across urban lifelines, yet the timed coupling between grid failure and essential service access remains poorly quantified. Focusing on Hurricane Beryl in Houston (2024), this study integrates approximately 173000 15-minute outage records with over 1.25 million visits to 3187 food facilities to quantify how infrastructure performance and human access co-evolve. We construct daily indices for outage characteristics (intensity, duration) and food access metrics (redundancy, frequency, proximity), estimate cross-system lags through lagged correlations over zero to seven days, and identify recovery patterns using DTW k-means clustering. Overlaying these clusters yields compound power-access typologies and enables facility-level criticality screening. The analysis reveals a consistent two-day lag: food access reaches its nadir on July 8 at landfall while outage severity peaks around July 10, with negative correlations strongest at a two-day lag and losing significance by day four. We identify four compound typologies from high/low outage crossed with high/low access disruption levels. Road network sparsity, more than income, determines the depth and persistence of access loss. Through this analysis, we enumerate 294 critical food facilities in the study area requiring targeted continuity measures including backup power, microgrids, and feeder prioritization. The novelty lies in measuring interdependency at daily operational resolution while bridging scales from communities to individual facilities, converting dynamic coupling patterns into actionable interventions for phase-sensitive restoration and equity-aware preparedness. The framework is transferable to other lifelines and hazards, offering a generalizable template for diagnosing and mitigating cascading effects on community access during disaster recovery.

We develop methods for nonparametric uniform inference in cost-sensitive binary classification, a framework that encompasses maximum score estimation, predicting utility maximizing actions, and policy learning. These problems are well known for slow convergence rates and non-standard limiting behavior, even under point identified parametric frameworks. In nonparametric settings, they may further suffer from failures of identification. To address these challenges, we introduce a strictly convex surrogate loss that point-identifies a representative nonparametric policy function. We then estimate this representative policy function to conduct inference on both the optimal classification policy and the optimal policy value. This approach enables Gaussian inference, substantially simplifying empirical implementation relative to working directly with the original classification problem. In particular, we establish root-$n$ asymptotic normality for the optimal policy value and derive a Gaussian approximation for the optimal classification policy at the standard nonparametric rate. Extensive simulation studies corroborate the theoretical findings. We apply our method to the National JTPA Study to conduct inference on the optimal treatment assignment policy and its associated welfare.

Two-phase sampling designs have been widely adopted in epidemiological studies to reduce costs when measuring certain biomarkers is prohibitively expensive. Under these designs, investigators commonly relate survival outcomes to risk factors using the Cox proportional hazards model. To fully utilize covariates collected in phase 1, multiple imputation (MI) methods have been developed to impute missing covariates for individuals not included in the phase 2 sample. However, MI becomes computationally intensive in large-scale cohorts, particularly when rejection sampling is employed to mitigate bias arising from nonlinear or interaction terms in the analysis model. To address this issue, Borgan et al. (2023) proposed a random supersampling (RSS) approach that randomly selects a subset of cohort members for imputation, albeit at the cost of reduced efficiency. In this study, we propose an influence function-based supersampling (ISS) method with weight calibration. The method achieves efficiency comparable to imputing the entire cohort, even with a small supersample, while substantially reducing computational burden. We further demonstrate that the proposed method is especially advantageous when estimating hazard ratios for high-dimensional expensive biomarkers. Extensive simulation studies are conducted, and a real data application is provided using the National Institutes of Health-American Association of Retired Persons (NIH-AARP) Diet and Health Study.

Attention is the brain's ability to selectively focus on a few specific aspects while ignoring irrelevant ones. This biological principle inspired the attention mechanism in modern Transformers. Transformers now underpin large language models (LLMs) such as GPT, but at the cost of massive training and inference energy, leading to a large carbon footprint. While brain attention emerges from neural circuits, Transformer attention relies on dot-product similarity to weight elements in the input sequence. Neuromorphic computing, especially spiking neural networks (SNNs), offers a brain-inspired path to energy-efficient intelligence. Despite recent work on attention-based spiking Transformers, the core attention layer remains non-neuromorphic. Current spiking attention (i) relies on dot-product or element-wise similarity suited to floating-point operations, not event-driven spikes; (ii) keeps attention matrices that suffer from the von Neumann bottleneck, limiting in-memory computing; and (iii) still diverges from brain-like computation. To address these issues, we propose the Spiking STDP Transformer (S$^{2}$TDPT), a neuromorphic Transformer that implements self-attention through spike-timing-dependent plasticity (STDP), embedding query–key correlations in synaptic weights. STDP, a core mechanism of memory and learning in the brain and widely studied in neuromorphic devices, naturally enables in-memory computing and supports non-von Neumann hardware. On CIFAR-10 and CIFAR-100, our model achieves 94.35% and 78.08% accuracy with only four timesteps and 0.49 mJ on CIFAR-100, an 88.47% energy reduction compared to a standard ANN Transformer. Grad-CAM shows that the model attends to semantically relevant regions, enhancing interpretability. Overall, S$^{2}$TDPT illustrates how biologically inspired attention can yield energy-efficient, hardware-friendly, and explainable neuromorphic models.

Global sensitivity metrics are essential tools for assessing parameter importance in complex models, particularly when precise information about parameter values is unavailable. In many cases, such metrics are used to provide parameter rankings that allow for necessary dimension reduction in moderate-to-high dimensional systems. However, globally-derived sensitivity results may obscure localized variability in parameter sensitivities, resulting in misleading conclusions about parameter importance and ensuing consequences for subsequent tasks such as model calibration and surrogate model construction. In this study, we illustrate how discrepancies between globally- and locally-based sensitivity information may arise for an emerging sensitivity metric based on active subspace methodology, as well as for other commonly used sensitivity techniques. In response, we outline a framework that exploits the active subspace to evaluate the stability of parameter sensitivities over the admissible parameter space. This analysis allows one to determine the subregions of the parameter space in which a globally-derived sensitivity metric may be trustworthy. The proposed framework is illustrated on a collection of simple examples for ease of visualization, as well as the highly-applicable Lotka-Volterra model, for which we demonstrate how these issues may be exacerbated in higher dimensions. Our findings suggest that globally-derived sensitivity information should be treated with caution, and that incorporating analysis on local subregions may improve robustness and accuracy in downstream modeling tasks.

We present an estimation procedure of spatial and temporal effects in spatiotemporal autoregressive panel data models using the Least Absolute Shrinkage and Selection Operator, LASSO (Tibshirani, 1996). We assume that the spatiotemporal panel is drawn from a univariate random process and that the data follows a spatiotemporal autoregressive process which includes a regressive term with space-/ time-varying exogenous regressor, a temporal autoregressive term and a spatial autoregressive term with an unknown weights matrix. The aim is to estimate this weight matrix alongside other parameters using a constraint penalised maximum likelihood estimator. Monte Carlo simulations showed a good performance with the accuracy increasing with an increasing number of time points. The use of the LASSO technique also consistently distinguishes between meaningful relationships (non-zeros) from those that are not (existing zeros) in both the spatial weights and other parameters. This regularised estimation procedure is applied to hourly particulate matter concentrations (PM10) in the Bavaria region, Germany for the years 2005 to 2020. Results show some stations with a high spatial dependency, resulting in a greater influence of PM10 concentrations in neighbouring monitoring stations. The LASSO technique proved to produce a sparse weights matrix by shrinking some weights to zero, hence improving the interpretability of the PM concentration dependencies across measurement stations in Bavaria

In certain fields where compositional data are studied, the compositional components, called parts, can be combined into certain subsets, called amalgamations, that are based on domain knowledge. Furthermore, these subsets can form a natural hierarchy of amalgamations subdividing into sub-amalgamations. The authors, a statistician and a biochemist, demonstrate how to create a hierarchy of amalgamations in the context of fatty acid compositions in a sample of marine organisms. Following a tradition in compositional data analysis, these amalgamations are transformed to logratios, and their usefulness as new variables is quantified by the percentage of total logratio variance that they explain. This method is proposed as an alternative method of variable selection in compositional data analysis.

In the Chilean local alcohol industry (pisco indus- try), for one liter of alcohol produced 10-15 liters of vinasse as the main wastewater of the process. To comply with industrial waste regulations, vinasse must be stored, which enables evaporation, leaving behind a residual sludge. However, treating vinasse remains an environmental and industrial challenge, having a high nutrient concentration and acidity that can degrade soil quality and harm surrounding vegetation. While previous studies have modeled sludge generation and transport in urban water systems, research on industrial wastewater, such as the alcohol industry, remains limited, affecting the search for opportunities to improve the treatment process.. This paper proposes a System Dynamics Model (SDM) to assess the costs associated with three management strategies: natural drying of vinasse, relocation to an alternative site, and implementation of a coagulation- flocculation treatment to accelerate sludge production. This paper makes two contributions. First, we describe a pioneer SDM applicable to sludge management, which includes variables such as sludge transport, coagulant quantity, and ambient temperature to make hypothetical scenarios that affect the treatment processes of vinasse. Second, we present the expected results of the associated costs of the scenarios proposed in the model, helping decision-makers to manage vinasse. The model is calibrated with historical data provided by a company in the North of Chile, helping to improve the decision-making for vinasse treatment.

We investigate the problem of estimating the structure factor, or spectra, of stationary spatial point processes. In the first part, we establish a minimax lower bound for this estimation problem, using an approach tailored to second-order properties of spatial point processes. Although not the main focus, this methodology also extends naturally to a minimax lower bound for the estimation of the pair correlation function of spatial point processes. In the second part, we construct a multitaper estimator that achieves the optimal rate of convergence in squared risk. Under a Brillinger-mixing condition, we further establish a chi-square-type concentration bound. Finally, we propose a data-driven procedure for selecting the number of tapers, supported by an oracle inequality, and we demonstrate the practical effectiveness of the method through numerical experiments.

Despite its evanescent nature, statistical power is crucial for planning Partial Least Squares Structural Equation Modelling (PLS-SEM) studies. This brief paper introduces PLS-SEM-power, a Shiny Application and R package that implements the inverse square root method by Kock and Hadaya (2018) to calculate both the minimum required sample size (a priori analysis) and the Minimum Detectable Effect Size (MDES, sensitivity analysis), given a chosen significance level (alpha level) and desired statistical power (1 - beta), set to 0.80 by default. The software supports both one-tailed and two-tailed calculations, with one-tailed calculations as the default following the formulation of Kock and Hadaya (2018), and provides an intuitive user interface, facilitating reproducible and easily accessible analyses in diverse research contexts.

Structural nested mean models (SNMMs) are a principled approach to estimate the treatment effects over time. A particular strength of SNMMs is to break the joint effect of treatment sequences over time into localized, time-specific “blip effects”. This decomposition promotes interpretability through the incremental effects and enables the efficient offline evaluation of optimal treatment policies without re-computation. However, neural frameworks for SNMMs are lacking, as their inherently sequential g-estimation scheme prevents end-to-end, gradient-based training. Here, we propose DeepBlip, the first neural framework for SNMMs, which overcomes this limitation with a novel double optimization trick to enable simultaneous learning of all blip functions. Our DeepBlip seamlessly integrates sequential neural networks like LSTMs or transformers to capture complex temporal dependencies. By design, our method correctly adjusts for time-varying confounding to produce unbiased estimates, and its Neyman-orthogonal loss function ensures robustness to nuisance model misspecification. Finally, we evaluate our DeepBlip across various clinical datasets, where it achieves state-of-the-art performance.

In this paper we examine the effectiveness of five mathematical models used to predict the outcomes of amateur darts games. These models not only predict the outcomes at the start of the game, but also update their estimations as the game score changes. The models were trained and tested on a dataset consisting of games played by amateur players involving students, faculty, and staff at Roanoke College. The five models are: the null model, which is based only on the live scores, a logistic regression model, a basic simulation model, a time-adjusted simulation model, and a new variation of the Massey model which updates based on the current score. We evaluate these models using two approaches. First, we compare their Brier scores. Second, we conduct head-to-head comparisons in a betting game in which one model sets the betting odds while the other places bets. In both cases, model performance is assessed not only at the start of the game but also at the start of each round. Across both evaluation methods, the score-dependent Massey model performs the best. We conclude by illustrating how this score-dependent Massey model framework can be adapted to other competitive settings beyond darts.

We propose a spatio-temporal data-fusion framework for point data and gridded data with variables observed on different spatial supports. A latent Gaussian field with a Matérn-SPDE prior provides a continuous space representation, while source-specific observation operators map observations to both point measurements and gridded averages, addressing change-of-support and covariate misalignment. Additionally incorporating temporal dependence enables prediction at unknown locations and time points. Inference and prediction are performed using the Integrated Nested Laplace Approximation and the Stochastic Partial Differential Equations approach, which delivers fast computation with uncertainty quantification. Our contributions are: a hierarchical model that jointly fuses multiple data sources of the same variable under different spatial and temporal resolutions and measurement errors, and a practical implementation that incorporates misaligned covariates via the same data fusion framework allowing differing covariate supports. We demonstrate the utility of this framework via simulations calibrated to realistic sensor densities and spatial coverage. Using the simulation framework, we explore the stability and performance of the approach with respect to the number of time points and data/covariate availability, demonstrating gains over single-source models through point and gridded data fusion. We apply our framework to soil moisture mapping in the Elliot Water catchment (Angus, Scotland). We fuse in-situ sensor data with aligned and misaligned covariates, satellite data and elevation data to produce daily high resolution maps with uncertainty.

Background: Linear mixed-effects models are central for analyzing longitudinal continuous data, yet many learners meet them as scattered formulas or software output rather than as a coherent workflow. There is a need for a single, reproducible case study that links questions, model building, diagnostics, and interpretation. Methods: We reanalyze a published mouse body-weight experiment with 31 mice in three groups weighed weekly for 12 weeks. After reshaping the data to long format and using profile plots to motivate linear time trends, we fit three random-intercept linear mixed models: a common-slope model, a fully interacted group-by-time model, and a parsimonious model with group-specific intercepts, a shared slope for two groups, and an extra slope for the third. Models are compared using maximum likelihood, AIC, BIC, and likelihood ratio tests, and linear contrasts are used to estimate group differences in weekly means and 12 week gains. Results: The parsimonious model fits as well as the fully interacted model and clearly outperforms the common-slope model, revealing small and similar gains in two groups and much steeper growth in the third, with highly significant contrasts for excess weight gain. Interpretation: This case study gives a complete, executable workflow for longitudinal linear mixed modeling, from raw data and exploratory plots through model selection, diagnostics, and targeted contrasts. By making explicit the mapping from scientific questions to model terms and estimable contrasts, and by providing R code and a stepwise checklist, it serves as a practical template for teaching and applied work in biostatistics, epidemiology, and related fields

Spatio-temporal Hawkes point processes are a particularly interesting class of stochastic point processes for modeling self-exciting behavior, in which the occurrence of one event increases the probability of other events occurring. These processes are able to handle complex interrelationships between stochastic and deterministic components of spatio-temporal phenomena. However, despite its widespread use in practice, there is no common and unified formalism and every paper proposes different views of these stochastic mechanisms. With this in mind, we implement two simulation techniques and three unified, self-consistent inference techniques, which are widely used in the practical modeling of spatio-temporal Hawkes processes. Furthermore, we provide an evaluation of the practical performance of these methods, while providing useful code for reproducibility.

We introduce conditional push-forward neural networks (CPFN), a generative framework for conditional distribution estimation. Instead of directly modeling the conditional density $f_{Y|X}$, CPFN learns a stochastic map $\varphi=\varphi(x,u)$ such that $\varphi(x,U)$ and $Y|X=x$ follow approximately the same law, with $U$ a suitable random vector of pre-defined latent variables. This enables efficient conditional sampling and straightforward estimation of conditional statistics through Monte Carlo methods. The model is trained via an objective function derived from a Kullback-Leibler formulation, without requiring invertibility or adversarial training. We establish a near-asymptotic consistency result and demonstrate experimentally that CPFN can achieve performance competitive with, or even superior to, state-of-the-art methods, including kernel estimators, tree-based algorithms, and popular deep learning techniques, all while remaining lightweight and easy to train.

To distinguish Markov equivalent graphs in causal discovery, it is necessary to restrict the structural causal model. Crucially, we need to be able to distinguish cause $X$ from effect $Y$ in bivariate models, that is, distinguish the two graphs $X \to Y$ and $Y \to X$. Location-scale noise models (LSNMs), in which the effect $Y$ is modeled based on the cause $X$ as $Y = f(X) + g(X)N$, form a flexible class of models that is general and identifiable in most cases. Estimating these models for arbitrary noise terms $N$, however, is challenging. Therefore, practical estimators are typically restricted to symmetric distributions, such as the normal distribution. As we showcase in this paper, when $N$ is a skewed random variable, which is likely in real-world domains, the reliability of these approaches decreases. To approach this limitation, we propose SkewD, a likelihood-based algorithm for bivariate causal discovery under LSNMs with skewed noise distributions. SkewD extends the usual normal-distribution framework to the skew-normal setting, enabling reliable inference under symmetric and skewed noise. For parameter estimation, we employ a combination of a heuristic search and an expectation conditional maximization algorithm. We evaluate SkewD on novel synthetically generated datasets with skewed noise as well as established benchmark datasets. Throughout our experiments, SkewD exhibits a strong performance and, in comparison to prior work, remains robust under high skewness.

Alterations in functional brain connectivity characterize neurodegenerative disorders such as Alzheimer's disease (AD) and frontotemporal dementia (FTD). As a non-invasive and cost-effective technique, electroencephalography (EEG) is gaining increasing attention for its potential to identify reliable biomarkers for early detection and differential diagnosis of AD and FTD. Considering the behavioral similarities of signals from adjacent EEG channels, we propose a new spectral dependence measure, the nonlinear vector coherence (NVC), to capture beyond-linear interactions between oscillations of two multivariate time series observed from distinct brain regions. This addresses the limitations of conventional channel-to-channel approaches and defines a more natural region-to-region connectivity framework in the frequency domain. As a result, the NVC measure offers a new approach to investigate dependence between brain regions, which then enables to identify altered functional connectivity dynamics associated with AD and FTD. We further introduce a rank-based inference procedure that enables fast and distribution-free estimation of the proposed measure, as well as a fully nonparametric test for spectral independence. The empirical performance of our proposed inference methodology is demonstrated through extensive numerical experiments. An application to resting-state EEG data reveals that our novel NVC measure uncovers distinct and diagnostically meaningful connectivity patterns which effectively discriminate healthy individuals from those with AD and FTD.

This paper studies the asymptotic distribution of a constrained lasso-type estimator for denoising signals defined on the nodes of a graph, where the underlying structure encodes relationships between variables. We show that, under suitable assumptions on the penalization parameters, the limiting distribution of the estimator is obtained by applying the corresponding constrained procedure to the asymptotic distribution of the unrestricted estimator. Thus, the constrained estimator shares the same convergence rate as the unrestricted estimator. Without the fusion penalty, the limiting distribution is obtained by applying individual nearly isotonic estimators to the corresponding sub-vectors of the unrestricted estimator's asymptotic distribution, similarly to the limiting behavior of isotonic regression.

We develop algorithms for detecting multiple changepoints in functional data when the number of changepoints is unknown (unsupervised case), when it is specified apriori (supervised case), and when certain bounds are available (semi-supervised case). These algorithms utilize the maximum mean discrepancy (MMD) measure between distributions on Hilbert spaces. We develop an oracle analysis of the changepoint detection problem which reveals an interesting relationship between the true changepoint locations and the local maxima of the oracle MMD curve. The proposed algorithms are shown to detect general distributional changes by exploiting this connection. In the unsupervised case, we test the significance of a potential changepoint and establish its consistency under the single changepoint setting. We investigate the strong consistency of the changepoint estimators in both single and multiple changepoint settings. In both supervised and semi-supervised scenarios, we include a step to merge consecutive groups that are similar to appropriately utilize the prior information about the number of changepoints. In the supervised scenario, the algorithm satisfies an order-preserving property: the estimated changepoints are contained in the true set of changepoints in the underspecified case, while they contain the true set under overspecification. We evaluate the performance of the algorithms on a variety of datasets demonstrating the superiority of the proposed algorithms compared to some of the existing methods.

Structural equation modeling (SEM) is a statistical method used to investigate relationships among latent variables. In SEM, the model must be specified in advance. However, in practice, statisticians often have several candidate models and need to select the most appropriate one. Consequently, model selection is a key issue in SEM, and information criteria are commonly used to address this issue. In this study, we develop an Akaike-type information criterion of SEM for jump-diffusion processes, which enables model selection for SEM based on high-frequency data with jumps. Simulation studies are conducted to illustrate the finite-sample performance of the proposed method.