Papers

This work on gap acceptance is based on the premise that the decision to accept/reject a gap happens in a person's mind and therefore must be based on the perceived gap and not the measured gap. The critical gap must also exist in a person's mind and hence, together with the perceived gap, is a latent variable. Finally, it is also proposed that the critical gap is influenced by various exogenous variables such as subject and opposing vehicle types, and perceived waiting time. Mathematical models that (i) incorporate systematic and random distortions during the perception process and (ii) account for the effect of the various influencing variables are developed. The parameters of these models are estimated for two different gap acceptance data sets using the maximum likelihood technique. The data is collected as part of this study. The estimated parameters throw valuable insights into how these influencing variables affect the critical gap. The results corroborate the initial predictions on the nature of influence these variables must exert and give strength to the gap acceptance decision-making construct proposed here. This work also proposes a methodology to estimate a measurable/observable world emulator of the latent variable critical gap. The use of the emulator critical gap provides improved estimates of derived quantities like the average waiting time of subject vehicles. Finally, studies are also conducted to show that the number of rejected gaps can work as a reasonable surrogate for the influencing variable, waiting time.

This technical note considers the sampling of outcomes that provide the greatest amount of information about the structure of underlying world models. This generalisation furnishes a principled approach to structure learning under a plausible set of generative models or hypotheses. In active inference, policies - i.e., combinations of actions - are selected based on their expected free energy, which comprises expected information gain and value. Information gain corresponds to the KL divergence between predictive posteriors with, and without, the consequences of action. Posteriors over models can be evaluated quickly and efficiently using Bayesian Model Reduction, based upon accumulated posterior beliefs about model parameters. The ensuing information gain can then be used to select actions that disambiguate among alternative models, in the spirit of optimal experimental design. We illustrate this kind of active selection or reasoning using partially observed discrete models; namely, a 'three-ball' paradigm used previously to describe artificial insight and 'aha moments' via (synthetic) introspection or sleep. We focus on the sample efficiency afforded by seeking outcomes that resolve the greatest uncertainty about the world model, under which outcomes are generated.

A shortcoming of black-box supervised learning models is their lack of interpretability or transparency. To facilitate interpretation, post-hoc global variable importance measures (VIMs) are widely used to assign to each predictor or input variable a numerical score that represents the extent to which that predictor impacts the fitted model's response predictions across the training data. It is well known that the most common existing VIMs, namely marginal Shapley and marginal permutation-based methods, can produce unreliable results if the predictors are highly correlated, because they require extrapolation of the response at predictor values that fall far outside the training data. Conditional versions of Shapley and permutation VIMs avoid or reduce the extrapolation but can substantially deflate the importance of correlated predictors. For the related goal of visualizing the effects of each predictor when strong predictor correlation is present, accumulated local effects (ALE) plots were recently introduced and have been widely adopted. This paper presents a new VIM approach based on ALE concepts that avoids both the extrapolation and the VIM deflation problems when predictors are correlated. We contrast, both theoretically and numerically, ALE VIMs with Shapley and permutation VIMs. Our results indicate that ALE VIMs produce similar variable importance rankings as Shapley and permutation VIMs when predictor correlations are mild and more reliable rankings when correlations are strong. An additional advantage is that ALE VIMs are far less computationally expensive.

We consider the problem of ranking $n$ experts according to their abilities, based on the correctness of their answers to $d$ questions. This is modeled by the so-called crowd-sourcing model, where the answer of expert $i$ on question $k$ is modeled by a random entry, parametrized by $M_{i,k}$ which is increasing linearly with the expected quality of the answer. To enable the unambiguous ranking of the experts by ability, several assumptions on $M$ are available in the literature. We consider here the general isotonic crowd-sourcing model, where $M$ is assumed to be isotonic up to an unknown permutation $\pi^*$ of the experts - namely, $M_{\pi^{*-1}(i),k} \geq M_{\pi^{*-1}(i+1),k}$ for any $i\in [n-1], k \in [d]$. Then, ranking experts amounts to constructing an estimator of $\pi^*$. In particular, we investigate here the existence of statistically optimal and computationally efficient procedures and we describe recent results that disprove the existence of computational-statistical gaps for this problem. To provide insights on the key ideas, we start by discussing simpler and yet related sub-problems, namely sub-matrix detection and estimation. This corresponds to specific instances of the ranking problem where the matrix $M$ is constrained to be of the form $\lambda \mathbf 1\{S\times T\}$ where $S\subset [n], T\subset [d]$. This model has been extensively studied. We provide an overview of the results and proof techniques for this problem with a particular emphasis on the computational lower bounds based on low-degree polynomial methods. Then, we build upon this instrumental sub-problem to discuss existing results and algorithmic ideas for the general ranking problem.

Deep neural networks have achieved remarkable success in practice, yet a mechanistic understanding of how features evolve during training remains incomplete, especially in the large-depth limit. For ResNets under depth-$\mu$P scaling, prior work treats the layer index $\ell$ as a continuous time $t_\ell = \ell/L$, yielding SDE descriptions of the training dynamics. A key unresolved issue is that backpropagation reuses each forward weight matrix $W_\ell$ through its transpose $W_\ell^\top$, creating correlations between forward features and backward gradients whose behavior and role in feature learning remain unclear. We study this reused-weight forward–backward coupling in one-layer ResNets under depth-$\mu$P. Using conditional Gaussian representations, we explicitly separate the coupling terms induced by weight reuse from decoupled Gaussian fluctuations before taking any network limit. At initialization, we prove that the coupling is a finite-width effect and vanishes at rate $O(n^{-1})$, uniformly over depth. During training, however, SGD induces a nontrivial forward–backward correlation term that survives the infinite-width limit. The key depth effect is that, under depth-$\mu$P scaling, this surviving term is higher order in depth and its accumulated contribution over layers becomes negligible as $L\to\infty$. This depth-induced suppression motivates Neural Feature Dynamics (NFD), a forward–backward SDE system with decoupled backward weights that retains the feature-gradient covariance structure generated during training. Under nondegeneracy assumptions, we prove that the finite-network training dynamics converge to its NFD limit with an $O(L^{-1})$ depth-discretization error, while the reused-weight coupling term has a faster $O(L^{-2})$ decay. These results provide a rigorous infinite-depth limit for the feature-learning dynamics of one-layer ResNets under depth-$\mu$P.

For the majority of run sizes N where N <= 20, the literature reports the best D- and A-optimal designs for the main-effects model which sequentially minimizes the aliasing between main effects and interaction effects and among interaction effects. The only series of run sizes for which all the minimally aliased D- and A-optimal main-effects designs remain unknown are those with run sizes three more than a multiple of four. To address this, in our paper, we propose an algorithm to generate all non-isomorphic D- and A-optimal main-effects designs for run sizes three more than a multiple of four. We enumerate all such designs for run sizes up to 19, report the numbers of designs we obtained, and identify those that minimize the aliasing between main effects and interaction effects and among interaction effects.

Diffusion models are a class of generative models that have demonstrated remarkable success in tasks such as image generation. However, one of the bottlenecks of these models is slow sampling due to the delay before the onset of trajectory bifurcation, at which point substantial reconstruction begins. This issue degrades generation quality, especially in the early stages. Our primary objective is to mitigate bifurcation-related issues by preprocessing the training data to enhance reconstruction quality, particularly for small-scale network architectures. Specifically, we propose applying Gaussianization preprocessing to the training data to make the target distribution more closely resemble an independent Gaussian distribution, which serves as the initial density of the reconstruction process. This preprocessing step simplifies the model's task of learning the target distribution, thereby improving generation quality even in the early stages of reconstruction with small networks. The proposed method is, in principle, applicable to a broad range of generative tasks, enabling more stable and efficient sampling processes.

Modeling sparse count data, which arise across numerous scientific fields, presents significant statistical challenges. This chapter addresses these challenges in the context of infectious disease prediction, with a focus on predicting outbreaks in geographic regions that have historically reported zero cases. To this end, we present the detailed computational framework and experimental application of the Poisson Hierarchical Indian Buffet Process (PHIBP), with demonstrated success in handling sparse count data in microbiome and ecological studies. The PHIBP's architecture, grounded in the concept of absolute abundance, systematically borrows statistical strength from related regions and circumvents the known sensitivities of relative-rate methods to zero counts. Through a series of experiments on infectious disease data, we show that this principled approach provides a robust foundation for generating coherent predictive distributions and for the effective use of comparative measures such as alpha and beta diversity. The chapter's emphasis on algorithmic implementation and experimental results confirms that this unified framework delivers both accurate outbreak predictions and meaningful epidemiological insights in data-sparse settings.

Data science plays a critical role in transforming complex data into actionable insights across numerous domains. Recent developments in large language models (LLMs) have significantly automated data science workflows, but a fundamental question persists: Can these agentic AI systems truly match the performance of human data scientists who routinely leverage domain-specific knowledge? We explore this question by designing a prediction task where a crucial latent variable is hidden in relevant image data instead of tabular features. As a result, agentic AI that generates generic codes for modeling tabular data cannot perform well, while human experts could identify the important hidden variable using domain knowledge. We demonstrate this idea with a synthetic dataset for property insurance. Our experiments show that agentic AI that relies on generic analytics workflow falls short of methods that use domain-specific insights. This highlights a key limitation of the current agentic AI for data science and underscores the need for future research to develop agentic AI systems that can better recognize and incorporate domain knowledge.

Free-response observer performance studies are of great importance for accuracy evaluation and comparison in tasks related to the detection and localization of multiple targets or signals. The free-response receiver operating characteristic (FROC) curve and many similar curves based on the free-response observer performance assessment data are important tools to display the accuracy of detection under different thresholds. The true positive rate at a fixed false positive rate and summary indices such as the area under the FROC curve are also commonly used as the figures of merit in the statistical evaluation of these studies. Motivated by a free-response observer performance assessment research of a Software as a Medical Device (SaMD), we propose a unified method based on the initial-detection-and-candidate model to simultaneously estimate a smooth curve and derive confidence intervals for summary indices and the true positive rate at a fixed false positive rate. A maximum likelihood estimator is proposed and its asymptotic normality property is derived. Confidence intervals are constructed based on the asymptotic normality of our maximum likelihood estimator. Simulation studies are conducted to evaluate the finite sample performance of the proposed method. We apply the proposed method to evaluate the diagnostic performance of the SaMD for detecting pulmonary lesions.

A methodology is developed to extract $d$ invariant features $W=f(X)$ that predict a response variable $Y$ without being confounded by variables $Z$ that may influence both $X$ and $Y$. The methodology's main ingredient is the penalization of any statistical dependence between $W$ and $Z$ conditioned on $Y$, replaced by the more readily implementable plain independence between $W$ and the random variable $Z_Y = T(Z,Y)$ that solves the [Monge] Optimal Transport Barycenter Problem for $Z\mid Y$. In the Gaussian case considered in this article, the two statements are equivalent. When the true confounders $Z$ are unknown, other measurable contextual variables $S$ can be used as surrogates, a replacement that involves no relaxation in the Gaussian case if the covariance matrix $\Sigma_{ZS}$ has full range. The resulting linear feature extractor adopts a closed form in terms of the first $d$ eigenvectors of a known matrix. The procedure extends with little change to more general, non-Gaussian / non-linear cases.

Mycotoxin contamination poses a significant risk to cereal crop quality, food safety, and agricultural productivity. Accurate prediction of mycotoxin levels can support early intervention strategies and reduce economic losses. This study investigates the use of neural networks and transfer learning models to predict mycotoxin contamination in Irish oat crops as a multi-response prediction task. Our dataset comprises oat samples collected in Ireland, containing a mix of environmental, agronomic, and geographical predictors. Five modelling approaches were evaluated: a baseline multilayer perceptron (MLP), an MLP with pre-training, and three transfer learning models; TabPFN, TabNet, and FT-Transformer. Model performance was evaluated using regression (RMSE, $R^2$) and classification (AUC, F1) metrics, with results reported per toxin and on average. Additionally, permutation-based variable importance analysis was conducted to identify the most influential predictors across both prediction tasks. The transfer learning approach TabPFN provided the overall best performance, followed by the baseline MLP. Our variable importance analysis revealed that weather history patterns in the 90-day pre-harvest period were the most important predictors, alongside seed moisture content.

Recent works have proposed optimal subsampling algorithms to improve computational efficiency in large datasets and to design validation studies in the presence of measurement error. Existing approaches generally fall into two categories: (i) designs that optimize individualized sampling rules, where unit-specific probabilities are assigned and applied independently, and (ii) designs based on stratified sampling with simple random sampling within strata. Focusing on the logistic regression setting, we derive the asymptotic variances of estimators under both approaches and compare them numerically through extensive simulations and an application to data from the Vanderbilt Comprehensive Care Clinic cohort. Our results reinforce that stratified sampling is not merely an approximation to individualized sampling, showing instead that optimal stratified designs are often more efficient than optimal individualized designs through their elimination of between-stratum contributions to variance. These findings suggest that optimizing over the class of individualized sampling rules overlooks highly efficient sampling designs and highlight the often underappreciated advantages of stratified sampling.

In spectroscopic analysis, the peak-based signal-to-noise ratio (pSNR) is commonly used but suffers from limitations such as sensitivity to noise spikes and reduced effectiveness for broader peaks. We introduce the area-based signal-to-noise ratio (aSNR) as a robust alternative that integrates the signal over a defined region of interest, reducing noise variance and improving detection for various lineshapes. We used Monte Carlo simulations (n=2,000 trials per condition) to test aSNR on Gaussian, Lorentzian, and Voigt lineshapes. We found that aSNR requires significantly lower amplitudes than pSNR to achieve a 50% detection probability. Receiver operating characteristic (ROC) curves show that aSNR performs better than pSNR at low amplitudes. Our results show that aSNR works especially advantageously for broad peaks and could be extended to volume-based SNR for multidimensional spectra.

A linear functional of an object from a convex symmetric set can be optimally estimated, in a worst-case sense, by a linear functional of observations made on the object. This well-known fact is extended here to a nonlinear setting: other simple functionals of the object can be optimally estimated by functionals of the observations that share a similar simple structure. This is established for the maximum of several linear functionals and even for the $\ell$th largest among them. Proving the latter requires an unusual refinement of the analytical Hahn–Banach theorem. The existence results are accompanied by practical recipes relying on convex optimization to construct the desired functionals, thereby justifying the term of estimation algorithms.

Several performance measures are used to evaluate binary and multiclass classification tasks. But individual observations may often have distinct weights, and none of these measures are sensitive to such varying weights. We propose a new weighted Pearson-Matthews Correlation Coefficient (MCC) for binary classification as well as weighted versions of related multiclass measures. The weighted MCC varies between $-1$ and $1$. But crucially, the weighted MCC values are higher for classifiers that perform better on highly weighted observations, and hence is able to distinguish them from classifiers that have a similar overall performance and ones that perform better on the lowly weighted observations. Furthermore, we prove that the weighted measures are robust with respect to the choice of weights in a precise manner: if the weights are changed by at most $\epsilon$, the value of the weighted measure changes at most by a factor of $\epsilon$ in the binary case and by a factor of $\epsilon^2$ in the multiclass case. Our computations demonstrate that the weighted measures clearly identify classifiers that perform better on higher weighted observations, while the unweighted measures remain completely indifferent to the choices of weights.

Understanding the processes that influence groundwater levels is crucial for forecasting and responding to hazards such as groundwater droughts. Mixed models, which combine a fixed mean, expressed using independent predictors, with autocorrelated random errors, are used for inference, forecasting and filling in missing values in groundwater level time series. Estimating parameters of mixed models using maximum likelihood has high computational complexity. For large datasets, this leads to restrictive simplifying assumptions such as fixing certain free parameters in practical implementations. In this paper, we propose a method to jointly estimate all parameters of mixed models using the Whittle likelihood, a frequency-domain quasi-likelihood. Our method is robust to missing and non-Gaussian data and can handle much larger data sizes. We demonstrate the utility of our method both in a simulation study and with real-world data, comparing against maximum likelihood and an alternative two-stage approach that estimates fixed and random effect parameters separately.

We study the problem of subgroup discovery for survival analysis, where the goal is to find an interpretable subset of the data on which a Cox model is highly accurate. Our work is the first to study this particular subgroup problem, for which we make several contributions. Subgroup discovery methods generally require a "quality function" in order to sift through and select the most advantageous subgroups. We first examine why existing natural choices for quality functions are insufficient to solve the subgroup discovery problem for the Cox model. To address the shortcomings of existing metrics, we introduce two technical innovations: the *expected prediction entropy (EPE)*, a novel metric for evaluating survival models which predict a hazard function; and the *conditional rank statistics (CRS)*, a statistical object which quantifies the deviation of an individual point to the distribution of survival times in an existing subgroup. We study the EPE and CRS theoretically and show that they can solve many of the problems with existing metrics. We introduce a total of eight algorithms for the Cox subgroup discovery problem. The main algorithm is able to take advantage of both the EPE and the CRS, allowing us to give theoretical correctness results for this algorithm in a well-specified setting. We evaluate all of the proposed methods empirically on both synthetic and real data. The experiments confirm our theory, showing that our contributions allow for the recovery of a ground-truth subgroup in well-specified cases, as well as leading to better model fit compared to naively fitting the Cox model to the whole dataset in practical settings. Lastly, we conduct a case study on jet engine simulation data from NASA. The discovered subgroups uncover known nonlinearities/homogeneity in the data, and which suggest design choices which have been mirrored in practice.

Algorithmic lending has transformed the consumer credit landscape, with machine learning models commonly facilitating underwriting decisions. To comply with fair lending laws, these algorithms exclude legally protected characteristics, such as race and gender. Yet algorithmic underwriting can still inadvertently favor certain groups, prompting concerns about whether lending algorithms exhibit discriminatory behavior. Using proprietary loan-level data from a major U.S. fintech platform, we audit lending decisions across approximately 80,000 personal loans. We find that loans made to men and Black borrowers yielded lower profits than loans to other groups, suggesting that men and Black borrowers benefited from relatively favorable pricing. We trace these disparities to miscalibration in the platform's underwriting model, which overestimates risk for women and underestimates risk for Black borrowers. We then show that one could correct this miscalibration – and the corresponding disparities – by including race and gender in underwriting models, illustrating a tension between competing notions of fairness.

We propose a new gradient-free method for infinite-dimensional optimization in Hilbert spaces that requires only the computation of directional derivatives. Though functional optimization is often solved through finite-dimensional gradient descent over a parametrization, such as neural networks, we instead propose to leverage the functional nature of the optimization problem to enable provable guarantees. However, infinite-dimensional gradients are often hard to compute in practice, rendering naïve functional gradient descent intractable. To overcome this limitation, our framework leverages only directional derivatives and a pre-basis for the Hilbert space, i.e., a linearly independent set whose span is dense. This resolves the tractability issue, as pre-bases are much more accessible than full orthonormal bases or reproducing kernels – which may not even exist – and individual directional derivatives can be computed using automatic differentiation. We showcase the use of our method to solve partial differential equations à la physics-informed neural networks (PINNs), where it effectively enables provable convergence.

We study the problem of learning a low-degree spherical polynomial of degree $\ell_0 = \Theta(1) \ge 1$ defined on the unit sphere in $\RR^d$ by training an over-parameterized two-layer neural network (NN) with channel attention in this paper. Our main result is the significantly improved sample complexity for learning such low-degree polynomials. We show that, for any regression risk $\eps \in (0,1)$, a carefully designed two-layer NN with channel attention and finite width trained by the vanilla gradient descent (GD) requires the lowest sample complexity of $n \asymp \Theta(d^{\ell_0}/\eps)$ with high probability, in contrast with the representative sample complexity $\Theta\pth{d^{\ell_0} \max\set{\eps^{-2},\log d}}$, where $n$ is the training data size. Moreover, such sample complexity is not improvable since the trained network renders a sharp rate of the nonparametric regression risk of the order $\Theta(d^{\ell_0}/{n})$ with high probability. On the other hand, the minimax optimal rate for the regression risk with a kernel of rank $\Theta(d^{\ell_0})$ is $\Theta(d^{\ell_0}/{n})$, so that the rate of the nonparametric regression risk of the network trained by GD is minimax optimal. Training the two-layer NN with channel attention proceeds in two stages: (1) a provable learnable channel selection algorithm, as a learnable harmonic-degree selection process, identifies the ground truth channel number in the target function, $\ell_0$, from $L \ge \ell_0$ channels in the first-layer activation; (2) the second layer is trained by standard GD using the selected channels. To the best of our knowledge, this is the first time a minimax optimal risk bound is obtained by training an over-parameterized but finite-width neural network with feature learning capability to learn low-degree spherical polynomials.

Analyzing causality in multivariate systems involves establishing how information is generated, distributed and combined. Traditional causal discovery frameworks are capable of multivariate reasoning but their intrinsic pairwise graph topology restricts them to do so only indirectly by integrating multivariate information across pairwise edges. Higher-order information theory provides direct tools that can explicitly model higher-order interactions. In particular, Partial Information Decomposition (PID) allows the decomposition of the information that a set of sources provides about a target into redundant, unique, and synergistic components. Yet the mathematical connection between such higher-order information-theoretic measures and causal structure remains undeveloped. Here we establish the first theoretical correspondence between PID components and causal structure in both Bayesian networks and hypergraphs. We first show that in Bayesian networks unique information precisely characterizes direct causal neighbors, while synergy identifies collider relationships. This establishes a localist causal discovery paradigm in which the structure surrounding each variable can be recovered from its immediate informational footprint, eliminating the need for global search over graph space. Extending these results to more expressive causal representation, we prove that PID signatures in Bayesian hypergraphs differentiate parents, children, co-heads, and co-tails, revealing a novel collider effect unique to multi-tail hyperedges. Our results position PID as a rigorous, model-agnostic foundation for inferring both pairwise and higher-order causal structure, and introduce a fundamentally local information-theoretic viewpoint on causal discovery.

We propose ScoreMatchingRiesz, a family of Riesz representer estimators based on score matching. The Riesz representer is a key nuisance component in debiased machine learning, enabling $\sqrt{n}$-consistent and asymptotically efficient estimation of causal and structural targets via Neyman-orthogonal scores. We formulate Riesz representer estimation as a score estimation problem. This perspective stabilizes representer estimation by allowing us to leverage denoising score matching and telescoping density ratio estimation. We also introduce the policy path, a parameter that captures how policy effects evolve under continuous treatments. We show that the policy path can be estimated via score matching by smoothly connecting average marginal effect (AME) and average policy effect (APE) estimation, which improves the interpretability of policy effects.

The nonparametric regression model with normal errors has been extensively studied, both from the frequentist and Bayesian viewpoint. A central result in Bayesian nonparametrics is that under assumptions on the prior, the data-generating distribution (assuming a true frequentist model) and a semi-metric $\rho(.,.)$ on the space of regression functions that satisfy the so called testing condition, the posterior contracts around the true distribution with respect to $\rho(.,.)$, and the rate of contraction can be estimated. In the regression setting, the semi-metric $\rho(.,.)$ is often taken to be the Hellinger distance or the empirical $L^2$ norm (i.e., the $L^2$ norm with respect to the empirical distribution of the design) in the present regression context. However, extending contraction rates to the “integrated" $L^2$ norm usually requires more work, and has previously been done for instance under sufficient smoothness or boundedness assumptions, which may not necessarily hold. In this work we show that, for classes of priors based on random basis expansions or Gaussian processes with RKHS of Sobolev type and in the random design setting, such $L^2$ posterior contraction rates can be obtained under substantially weaker assumptions than those currently used in the literature. Importantly we do not require a known a priori upper bound on its supremum norm or that its smoothness is larger than $d/2$, where $d$ is the dimension of the covariates. Our proof crucially relies on an application of the matrix Bernstein concentration inequality to empirical inner product matrices, which require explicit upper bounds on the basis functions at hand that we prove in several cases of interest. In particular we obtain upper bounds on the supremum norm of Mercer eigenfunctions of several reproducing kernels (including several Matérn kernels) which are of independent interest.

In Aarab (2020), I examine U.S. stock return predictability across economic regimes and document evidence of time-varying expected returns across market states in the long run. The analysis introduces a state-switching specification in which the market state is proxied by the slope of the yield curve, and proposes an Aligned Economic Index built from the popular predictors of Welch and Goyal (2008) (augmented with bond and equity premium measures). The Aligned Economic Index under the state-switching model exhibits statistically and economically meaningful in-sample ($R^2 = 5.9\%$) and out-of-sample ($R^2_{\text{oos}} = 4.12\%$) predictive power across both recessions and expansions, while outperforming a range of widely used predictors. In this work, I examine the added value for professional practitioners by computing the economic gains for a mean-variance investor and find substantial added benefit of using the new index under the state switching model across all market states. The Aligned Economic Index can thus be implemented on a consistent real-time basis. These findings are crucial for both academics and practitioners as expansions are much longer-lived than recessions. Finally, I extend the empirical exercises by incorporating data through September 2020 and document sizable gains from using the Aligned Economic Index, relative to more traditional approaches, during the COVID-19 market turbulence.

A growing empirical literature suggests that equity-premium predictability is state dependent, with much of the forecasting power concentrated around recessionary periods (Henkel et al., 2011; Dangl and Halling, 2012; Devpura et al., 2018). I study U.S. stock return predictability across economic regimes and document strong evidence of time-varying expected returns across both expansionary and contractionary states. I contribute in two ways. First, I introduce a state-switching predictive regression in which the market state is defined in real time using the slope of the yield curve. Relative to the standard one-state predictive regression, the state-switching specification increases both in-sample and out-of-sample performance for the set of popular predictors considered by Welch and Goyal (2008), improving the out-of-sample performance of most predictors in economically meaningful ways. Second, I propose a new aggregate predictor, the Aligned Economic Index, constructed via partial least squares (PLS). Under the state-switching model, the Aligned Economic Index exhibits statistically and economically significant predictive power in sample and out of sample, and it outperforms widely used benchmark predictors and alternative predictor-combination methods.

We introduce a novel projection depth for data lying in a general Hilbert space, called the regularized projection depth, with a focus on functional data. By regularizing projection directions, the proposed depth does not suffer from the degeneracy issue that may arise when the classical projection depth is naively defined on an infinite-dimensional space. Compared to existing functional depth notions, the regularized projection depth has several advantages: (i) it requires no moment assumptions on the underlying distribution, (ii) it satisfies many desirable depth properties including invariance, monotonicity, and vanishing at infinity, (iii) its sample version uniformly converges under mild conditions, and (iv) it generates a highly robust median. Furthermore, the proposed depth is statistically useful as it (v) does not produce ties in the induced ranks and (vi) effectively detects shape outlying functions. This paper focuses mainly on the theoretical properties of the regularized projection depth.

In the realm of diverse high-dimensional data, images play a significant role across various processes of manufacturing systems where efficient image anomaly detection has emerged as a core technology of utmost importance. However, when applied to textured defect images, conventional anomaly detection methods have limitations including non-negligible misidentification, low robustness, and excessive reliance on large-scale and structured datasets. This paper proposes a texture basis integrated smooth decomposition (TBSD) approach, which is targeted at efficient anomaly detection in textured images with smooth backgrounds and sparse anomalies. Mathematical formulation of quasi-periodicity and its theoretical properties are investigated for image texture estimation. TBSD method consists of two principal processes: the first process learns the texture basis functions to effectively extract quasi-periodic texture patterns; the subsequent anomaly detection process utilizes that texture basis as prior knowledge to prevent texture misidentification and capture potential anomalies with high accuracy.The proposed method surpasses benchmarks with less misidentification, smaller training dataset requirement, and superior anomaly detection performance on both simulation and real-world datasets.

Behavioral risk factors, i.e., smoking, poor nutrition, alcohol misuse, and physical inactivity (SNAP), are leading contributors to chronic diseases and healthcare costs worldwide. Their prevalence is shaped %not only by demographic characteristics %but and also by contextual ones such as socioeconomic and occupational environments. In this study, we leverage data from the Italian health and behavioral surveillance system PASSI to model SNAP behaviors through a Bayesian framework that integrates textual information on occupations. We use Structural Topic Modeling (STM) to cluster free-text job descriptions into latent occupational groups, which inform mixture weights in a multivariate ordered probit model. Covariate effects are allowed to vary across occupational clusters and evolve over time. To enhance interpretability and variable selection, we impose non-local spike-and-slab priors on regression coefficients. Finally, an online learning algorithm based on sequential Monte Carlo enables efficient updating as new data become available. This dynamic, scalable, and interpretable approach permits observing how occupational contexts modulate the impact of socio-demographic factors on health behaviors, providing valuable insights for targeted public health interventions.

Precisely estimating out-of-sample upper quantiles is very important in risk assessment and in engineering practice for structural design to prevent a greater disaster. For this purpose, the generalized extreme value (GEV) distribution has been broadly used. To estimate the parameters of GEV distribution, the maximum likelihood estimation (MLE) and L-moment estimation (LME) methods have been primarily employed. For a better estimation using the MLE, several studies considered the generalized MLE (penalized likelihood or Bayesian) methods to cooperate with a penalty function or prior information for parameters. However, a generalized LME method for the same purpose has not been developed yet in the literature. We thus propose the generalized method of L-moment estimation (GLME) to cooperate with a penalty function or prior information. The proposed estimation is based on the generalized L-moment distance and a multivariate normal likelihood approximation. Because the L-moment estimator is more efficient and robust for small samples than the MLE, we reasonably expect the advantages of LME to continue to hold for GLME. The proposed method is applied to the stationary and nonstationary GEV models with two novel (data-adaptive) penalty functions to correct the bias of LME. A simulation study indicates that the biases of LME are considerably corrected by the GLME with slight increases in the standard error. Applications to US flood damage data and maximum rainfall at Phliu Agromet in Thailand illustrate the usefulness of the proposed method. This study may promote further work on penalized or Bayesian inferences based on L-moments.