Papers

Epileptic seizure detection from EEG signals remains challenging due to the high dimensionality and nonlinear, potentially stochastic, dynamics of neural activity. In this work, we investigate whether features derived from topological data analysis (TDA) can improve the classification of brain states in preictal, ictal and interictal iEEG recordings from epilepsy patients using multichannel data. We analyze data from 55 patients, significantly larger than many previous studies that rely on patient-specific models. Persistence diagrams derived from iEEG signals are vectorized using several TDA representations, including Carlsson coordinates, persistence images, and template functions. To understand how topological representations interact with modern machine learning pipelines, we conduct a large-scale ablation study across multiple iEEG frequency bands, dimensionality reduction techniques, feature representations, and classifier architectures. Our experiments show that dimension-reduced topological representations achieve up to 80% balanced accuracy for three-class classification. Interestingly, classical machine learning models perform comparably to deep learning models, achieving up to 79.17% balanced accuracy, suggesting that carefully designed topological features can substantially reduce model complexity requirements. In contrast, pipelines preserving the full multichannel feature structure exhibit severe overfitting due to the high-dimensional feature space. These findings highlight the importance of structure-preserving dimensionality reduction when applying topology-based representations to multichannel neural data.

We study signal propagation at initialization in transformers through the averaged partial Jacobian norm (APJN), a measure of gradient amplification across layers. We extend APJN analysis to transformers with bidirectional attention and permutation-symmetric input token configurations by deriving recurrence relations for activation statistics and APJNs across layers. Our theory predicts how attention modifies the asymptotic behavior of the APJN at large depth and matches APJNs measured in deep vision transformers. The criticality picture known from residual networks carries over to transformers: the pre-LayerNorm architecture exhibits power-law APJN growth, whereas transformers with LayerNorm replaced by elementwise $\tanh$-like nonlinearities have stretched-exponential APJN growth, indicating that the latter are subcritical. Applied to Dynamic Tanh (DyT) and Dynamic erf (Derf) transformers, the theory explains why these architectures can be more sensitive to initialization and optimization choices and require careful tuning for stable training.

In optimization problems, some variable subsets may have a joint non-linear or non-monotonical influence on the function value. Therefore, knowledge of variable dependencies may be crucial for effective optimization, and many state-of-the-art optimizers leverage it to improve performance. However, some real-world problem instances may be the subject of noise of various origins. In such a case, variable dependencies relevant to optimization may be hard or impossible to tell using dependency checks sufficient for problems without noise, making highly effective operators, e.g., Partition Crossover (PX), useless. Therefore, we use Statistical Linkage Learning (SLL) to decompose problems with noise and propose a new SLL-dedicated mask construction algorithm. We prove that if the quality of the SLL-based decomposition is sufficiently high, the proposed clustering algorithm yields masks equivalent to PX masks for the noise-free instances. The experiments show that the optimizer using the proposed mechanisms remains equally effective despite the noise level and outperforms state-of-the-art optimizers for the problems with high noise.

Uncertainty in estimating the log-law parameters is arguably the greatest obstacle to establishing definitive conclusions regarding their numerical values and universality. This challenge is exacerbated by the limited number of studies that provide thorough uncertainty analyses of experimental data and fitting procedures, and those that do often adopt different approaches, undermining direct comparisons. The present study applies the generalised least squares (GLS) principle to the log-law velocity profile to establish a standardised, comprehensive framework for quantifying uncertainty in the log-law parameters across datasets. GLS contrasts with ordinary least squares (OLS) and weighted least squares (WLS), which do not account for correlation in errors across measured quantities, as well as with alternative heuristic methods that independently sample primitive variables. Instead, it incorporates a full covariance matrix of the residuals, propagated from the uncertainties in the primitive variables and consistent with the experimental methods employed. The study presents a systematic analysis of the response of the log-law regression model using synthetic data, emulating measurements from a hot-wire anemometer mounted on a linear traverse. This analysis serves as a predictive tool for experimental design, identifying a priori the dominant sources of uncertainty in the log-law parameters and potential mitigation strategies. The study also provides new insights into the correlation between the log-law parameters and proposes a new fitting procedure that eliminates the need to prescribe the location and extent of the log region. The open-source Python implementation of the log-law regression model is available for download on GitHub at https://github.com/ma2ferreira/gls_loglaw.git.

Deep learning underpins a wide range of applications in MRI, including reconstruction, artifact removal, and segmentation. However, progress has been driven largely by public datasets focused on brain and knee imaging, shaping how models are trained and evaluated. As a result, careful studies of the reliability of these models across diverse anatomical settings remain limited. In this work, we introduce MosaicMRI, a large and diverse collection of fully sampled raw musculoskeletal (MSK) MR measurements designed for training and evaluating machine-learning–based methods. MosaicMRI is the largest open-source raw MSK MRI dataset to date, comprising 3,150 volumes and 89,830 slices, including a 3,096-volume 1.5~T core dataset and a 54-volume 0.55~T low-field set. The dataset offers substantial diversity in volume orientation (e.g., axial, sagittal), imaging contrasts (e.g., PD, T1, T2), anatomies (e.g., spine, knee, hip, ankle, and others), numbers of acquisition coils, and field strengths. Using accelerated reconstruction as a testbed, we study scaling, robustness, and data selection under realistic MSK distribution shifts. Across E2E-VarNet, U-Net, and ViT baselines, mixed-anatomy training improves over anatomy-specific training, showing that the benefit of anatomical diversity is not architecture-specific. Zero-shot experiments on the 0.55~T low-field set highlight that using more training data improves average reconstruction under field-strength shift. Controlled subset experiments further suggest that these gains come from transferable cross-anatomy structure, rather than anatomy or contrast matching alone.

We study the problem of identifying change points in high-dimensional generalized linear models, and propose an approach based on sample-weighted empirical risk minimization. Our method, Weighted ERM, encodes priors on the change points via weights assigned to each sample, to obtain weighted versions of standard estimators such as M-estimators and maximum-likelihood estimators. Under mild assumptions on the data, we obtain a precise asymptotic characterization of the performance of our method for general Gaussian designs, in the high-dimensional limit where the number of samples and covariate dimension grow proportionally. We show how this characterization can be used to efficiently construct a posterior distribution over change points. Numerical experiments on both simulated and real data illustrate the efficacy of Weighted ERM compared to existing approaches, demonstrating that sample weights constructed with weakly informative priors can yield accurate change point estimators. Our method is implemented as an open-source package, weightederm, available in Python and R.

We consider the problem of clustering nested or hierarchical data, where observations are grouped and there are both group-level and observation-level variables. In our motivating OneK1K dataset, observations consist of single-cell RNA-sequencing (scRNA-seq) data from 982 individuals (groups), totaling 1.27 million cells (observations), along with individual-specific genotype data. This type of data would enable the identification of cell types and the investigation of how genetic variations among individuals influence differences in cell-type profiles. Our goal, therefore, is to jointly cluster cells and individuals to capture the heterogeneity across both levels using cell-specific gene expressions as well as individual-specific genotypes. However, existing grouped clustering methods do not incorporate group-level variables, thereby limiting their ability to capture the heterogeneity of genotypes in our motivating application. To address this, we propose the Nested Atoms Model (NAM), a new Bayesian nonparametric approach that enables the desired two-layered clustering, accounting for both group-level and observation-level variables. To scale NAM for high-dimensional data, we develop a fast variational Bayesian inference algorithm. Simulations show that NAM outperforms existing methods that ignore group-level variables. Applied to the OneK1K dataset, NAM identifies clusters of genetically similar individuals with homogeneous cell-type profiles. The resulting cell clusters align with known immune cell types based on differential gene expression, underscoring the ability of NAM to capture nested heterogeneity and provide biologically meaningful insights.

General first-order methods (GFOM) are a flexible class of iterative algorithms which update a state vector by matrix-vector multiplications and entrywise nonlinearities. A long line of work has sought to understand the large-n dynamics of GFOM, mostly focusing on "very random" input matrices and the approximate message passing (AMP) special case of GFOM whose state is asymptotically Gaussian. Yet, it has long remained unknown how to construct iterative algorithms that retain this Gaussianity for more structured inputs, or why existing AMP algorithms can be as effective for some deterministic matrices as they are for random matrices. We analyze diagrammatic expansions of GFOM via the limiting traffic distribution of the input matrix, the collection of all limiting values of permutation-invariant polynomials in the matrix entries, to obtain the following results: 1. We calculate the traffic distribution for the first non-trivial deterministic matrices, including (minor variants of) the Walsh-Hadamard and discrete sine and cosine transform matrices. This determines the limiting dynamics of GFOM on these inputs, resolving parts of longstanding conjectures of Marinari, Parisi, and Ritort (1994). 2. We design a new AMP iteration which unifies several previous AMP variants and generalizes to new input types, whose limiting dynamics are Gaussian conditional on some latent random variables. The asymptotic dynamics hold for a large and natural class of traffic distributions (encompassing both random and deterministic input matrices) and the algorithm's analysis gives a simple combinatorial interpretation of the Onsager correction, answering questions posed recently by Wang, Zhong, and Fan (2022).

Heterogeneous network data with rich nodal information become increasingly prevalent across multidisciplinary research, yet accurately modeling complex nodal heterogeneity and simultaneously selecting influential nodal attributes remains an open challenge. This problem is central to many applications in economics and sociology, when both nodal heterogeneity and high-dimensional individual characteristics highly affect network formation. We propose a statistically grounded, unified deep neural network approach for modeling nodal heterogeneity in random networks with high-dimensional nodal attributes, namely “NetworkNet”. A key innovation of NetworkNet lies in a tailored neural architecture that explicitly parameterizes attribute-driven heterogeneity, and at the same time, embeds a scalable attribute selection mechanism. NetworkNet consistently estimates two types of latent heterogeneity functions, i.e., nodal expansiveness and popularity, while simultaneously performing data-driven attribute selection to extract influential nodal attributes. By unifying classical statistical network modeling with deep learning, NetworkNet delivers the expressive power of DNNs with methodological interpretability, algorithmic scalability, and statistical rigor with a non-asymptotic approximation error bound. Empirically, simulations demonstrate strong performance in both heterogeneity estimation and high-dimensional attribute selection. We further apply NetworkNet to a large-scale author-citation network among statisticians, revealing new insights into the dynamic evolution of research fields and scholarly impact.

We develop a novel reference prior for Gaussian hierarchical models with intrinsic conditional autoregressive (ICAR) random effects. This is particularly important in the context of objective Bayes variable selection with sample size $n$ and $k$ regressors. In this context, a previously published reference prior requires the computation of spectral decompositions of two $n$-dimensional matrices for each model under consideration. As a consequence, for variable selection the computational cost of this previous reference prior grows as $O(n^3 2^k)$. In contrast, our novel reference prior requires the computation of the spectral decomposition of one $n$-dimensional matrix that can be used for all models under consideration. Thus, the computational cost of our novel reference prior grows much slower as $O(n^3)$. Hence, computational savings can be substantial, e.g. in a problem with 10 regressors, when compared to the previously published reference prior, computations based on our novel reference prior are more than 1000 times faster. We provide a proof of the equivalence of the two priors. A simulation study shows that, while both reference priors provide equivalent variable selection results, for large sample sizes computations based on our novel prior are several orders of magnitude faster. Finally, the utility of our novel reference prior is illustrated with a spatial regression study of county-level median household income on socio-economic regressors for 3108 counties in the contiguous United States.

We study computational aspects of a key problem in robust statistics – the penalized least trimmed squares (LTS) regression problem, a robust estimator that mitigates the influence of outliers in data by capping residuals with large magnitudes. Although statistically attractive, penalized LTS is NP-hard, and existing mixed-integer optimization (MIO) formulations scale poorly due to weak relaxations and exponential worst-case complexity in the number of observations. We propose a new MIO formulation that embeds hyperplane arrangement logic into a perspective reformulation, explicitly enforcing structural properties of optimal solutions. We show that, if the number of features is fixed, the resulting branch-and-bound tree is of polynomial size in the sample size. Moreover, we develop a tailored branch-and-bound algorithm that uses first-order methods with dual bounds to solve node relaxations efficiently. Computational experiments on synthetic and real datasets demonstrate substantial improvements over existing MIO approaches: on synthetic instances with 5000 samples and 20 features, our tailored solver reaches a 1% gap in 1 minute while competing approaches fail to do so within one hour. These gains enable exact robust regression at significantly larger sample sizes in low-dimensional settings.

Measurement-based quantum computation (MBQC) is a framework for quantum information processing in which a computational task is carried out through one-qubit measurements on a highly entangled resource state. Due to the indeterminacy of the outcomes of a quantum measurement, the random outcomes of these operations, if not corrected, yield a variational quantum channel family. Traditionally, this randomness is corrected through classical processing in order to ensure deterministic unitary computations. Recently, variational measurement-based quantum computation (VMBQC) has been introduced to exploit this measurement-induced randomness to gain an advantage in generative modeling. A limitation of this approach is that the corresponding channel model has twice as many parameters compared to the unitary model, scaling as $N \times D$, where $N$ is the number of logical qubits (width) and $D$ is the depth of the VMBQC model. This can often make optimization more difficult and may lead to poorly trainable models. In this paper, we present a restricted VMBQC model that extends the unitary setting to a channel-based one using only a single additional trainable parameter. We show, both numerically and algebraically, that this minimal extension is sufficient to generate probability distributions that cannot be learned by the corresponding unitary model.

High-dimensional inference methods often rely on coefficient sparsity, an assumption that can be restrictive when signals are dense but individually weak. In such settings, valid inference may still be possible if the covariates exhibit sparse conditional dependence. Motivated by this observation, we propose Neighborhood-Localized Nested Regression (NLNR), a framework for coordinatewise inference in high-dimensional linear models with potentially dense coefficients. The central idea is to localize inference for a target coefficient to a low-dimensional working regression determined by a Sparse Conditional Neighborhood (SCN) of the target covariate. Specifically, for a given covariate, we estimate its SCN through nodewise $\ell_1$-penalized regression and then fit a regression using only the target covariate and its estimated neighborhood. Under suitable regularity conditions, we establish consistency and asymptotic normality of the resulting estimator. Building on this inferential reduction principle, we further develop a thresholding-based screening procedure with theoretical guarantees and a boosting variant that augments the working model with additional response-relevant covariates to improve finite-sample performance. Extensive simulations and an application to the CCLE dataset demonstrate favorable empirical performance.

Artificial intelligence (AI) is moving increasingly beyond prediction to support decisions in complex, uncertain, and dynamic environments. This shift creates a natural intersection with operations research and management science (OR/MS), which has long provided methodological foundations for sequential decision making under uncertainty. At the same time, deep learning advances, including feedforward neural networks, recurrent architectures, transformers, large language models (LLMs), and deep reinforcement learning, have expanded data-driven modeling for large-scale decisions. This tutorial presents an OR/MS-centered perspective on deep learning for sequential decision making under uncertainty, bridging neural architectures and OR/MS approaches to decision making. Its premise: deep learning complements optimization rather than replacing it. Deep learning brings adaptability and scalable approximation, whereas OR/MS provides the mathematical rigor to represent constraints, recourse, uncertainty, and decision quality. The tutorial reviews key decision making foundations, connects them to the major neural architectures in modern AI, and organizes the field around three central themes: predict-then-optimize and decision-aware learning, learning-based decision generation under constraints for continuous and discrete problems with temporal coupling, and deep reinforcement learning for sequential and combinatorial decision making. Impact spans supply chains, service systems, healthcare and epidemic response, agriculture, energy, environmental sustainability, and autonomous operations. This tutorial frames these developments as part of a shift from predictive AI toward decision-capable AI, highlighting OR/MS's role in shaping the next generation of integrated learning–optimization systems.

As generative models enable rapid creation of high-fidelity images, societal concerns about misinformation and authenticity have intensified. A promising remedy is multi-bit image watermarking, which embeds a multi-bit message into an image so that a verifier can later detect whether the image is generated by someone and further identify the source by decoding the embedded message. Existing approaches often fall short in capacity, resilience to common image distortions, and theoretical justification. To address these limitations, we propose ADD (Add, Dot, Decode), a multi-bit image watermarking method with two stages: learning a watermark to be linearly combined with the multi-bit message and added to the image, and decoding through inner products between the watermarked image and the learned watermark. On the standard MS-COCO benchmark, we demonstrate that for the challenging task of 48-bit watermarking, ADD achieves 100% decoding accuracy, with performance dropping by at most 2% under a wide range of image distortions, substantially smaller than the 14% average drop of state-of-the-art methods. In addition, ADD achieves substantial computational gains, with 2-fold faster embedding and 7.4-fold faster decoding than the fastest existing method. We further provide a theoretical analysis explaining why the learned watermark and the corresponding decoding rule are effective.

Complex structures often emerge from initially homogeneous or weakly correlated states. We address the apparent tension between this ordering and entropy growth through a unified framework combining semi-microscopic phase-space dynamics, transport geometry, information theory, and coarse-grained effective modeling. The key point is that entropy depends on the level of description: a coarse-grained spatial field may become more ordered as structure forms, even while the full phase-space description becomes more complex through shell crossing, multistreaming, and the activation of velocity degrees of freedom. Using a Lagrangian–Eulerian transport map, we show how density amplification is governed by the Jacobian of the deformation and how anisotropic collapse arises from the eigenvalues of a hierarchy of deformation tensors. Long-range interaction or information flow is encoded in the displacement field, so that nonlocality enters directly through transport. We connect this geometric description to a maximum-entropy Gaussian baseline and show how nonlinear transport and nonlocal coupling generate scale coupling, higher-order correlations, and non-Gaussianity. We then formulate a Landau–Ginzburg description in which the growth of seed anisotropies is interpreted as the activation of lower effective free-energy branches, providing a coarse-grained realization of self-organization. Applied to generated cosmological fields, this framework indicates that the nonlocal tidal level becomes relevant already at moderate overdensity. Although cosmological structure formation is the main realization considered here, the framework is intended more broadly as a mesoscopic language for systems in which transport, anisotropy, nonlocality, and self-organization are central.

Quantifying the similarity of two or more datasets has widespread applications in statistics and machine learning. The method choice is, however, difficult due to the abundance of proposed methods and the lack of neutral comparison studies, especially for categorical data. Here, the most promising methods are compared concerning their ability to detect certain differences between datasets and their resource consumption. The results show that the edge count tests perform well when comparing two datasets (i.e., the two-sample case). For certain scenarios, the constrained minimum (CM) distance performs even better. For categorical data consisting of variables with five categories each, the best method depends on the type of difference between the distributions, with either the CM distance and certain graph-based tests performing best, or the classifier-based tests (C2ST). This tendency is even clearer for multiple datasets. Overall, the Friedman-Rafsky test can be recommended for two samples as a compromise of high performance, acceptable resource consumption, and computational error occurrences. For the multi-sample case, the Multi-Sample Mahalanobis Cross-Match (MMCM) test can be recommended due to its comparably good performance and low resource consumption.

We propose a novel procedure for estimating and conducting inference on average marginal effects in partially linear instrumental regressions using Reproducing Kernel Hilbert Space methods. Our procedure relies on a single regularization parameter. We obtain the consistency and asymptotic normality of our estimator. Since the variance of the limiting distribution has a complex analytical form, we propose a Bayesian bootstrap method to conduct inference and establish its validity. Our procedure is easy to implement and exhibits good finite-sample performance in simulations. Three empirical applications illustrate its implementation on real data, showing that it yields economically meaningful results.

A new class of time-dependent Dirichlet priors is introduced as a generalisation of the Wright-Fisher diffusion, allowing discontinuities in the trajectories, as well as non-Markovian memory. This class is obtained as a simple stochastic time-change (subordination), interpreted as a hyper-prior assigned to the operational time-clock of a Wright-Fisher diffusion. Explicit representations and exact sampling algorithms are obtained for prior and posterior distributions of the process and of its clock, given partially exchangeable data sampled at discrete time-points. Computability and conjugacy rely on a novel class of discrete dual processes, generalising existing results on duality and computable filters.

To better align theories of paradigm shifting discoveries and empirics identifying them, we pro-pose a novel measure that incorporates a discovery impact, novelty, and tendency to break with the past into a single, coherent measure. Calibration using the National Inventor Hall of Fame data reveals that impact, novelty, and disruptiveness are strict complements meaning, for example, that greater impact cannot substitute for moderate novelty. We illustrate the workings of the measure using data on USPTO patents from 1982 to 2015.

We consider multivariate extreme value statistics for independent but nonidentically distributed random vectors. In particular, the data may have varying tail copulas and also heteroscedastic marginal distributions. Assuming smoothly changing tail copulas, we propose a nonparametric estimator for the integrated tail copula and establish its asymptotic behavior. Notably, the heteroscedastic marginals do not affect the limiting processes. We use the main result for the integrated tail copula to test for a constant tail copula across all observations. Finally, a simulation study shows the good finite-sample behavior of our limit theorems as well as high power of the test.

Diffusion-based models on continuous spaces have seen substantial recent progress through the mathematical framework of gradient flows, leveraging the Wasserstein-2 (${W}_2$) metric via the Jordan-Kinderlehrer-Otto (JKO) scheme. Despite the increasing popularity of diffusion models on discrete spaces using continuous-time Markov chains, a parallel theoretical framework based on gradient flows has remained elusive due to intrinsic challenges in translating the ${W}_2$ distance directly into these settings. In this work, we propose the first computational approach addressing these challenges, leveraging an appropriate metric $W_K$ on the simplex of probability distributions, which enables us to interpret widely used discrete diffusion paths, such as the discrete heat equation, as gradient flows of specific free-energy functionals. Through this theoretical insight, we introduce a novel methodology for learning diffusion dynamics over discrete spaces, which recovers the underlying functional directly by leveraging first-order optimality conditions for the JKO scheme. The resulting method optimizes a simple quadratic loss, trains extremely fast, does not require individual sample trajectories, and only needs a numerical preprocessing computing $W_K$-geodesics. We validate our method through extensive numerical experiments on synthetic data, showing that we can recover the underlying functional for a variety of graph classes.

Conformal selection (CS) uses calibration data to identify test inputs whose unobserved outcomes are likely to satisfy a pre-specified minimal quality requirement, while controlling the false discovery rate (FDR). Existing methods fix the target FDR level before observing data, which prevents the user from adapting the balance between number of selected test inputs and FDR to downstream needs and constraints based on the available data. For example, in genomics or neuroimaging, researchers often inspect the distribution of test statistics, and decide how aggressively to pursue candidates based on observed evidence strength and available follow-up resources. To address this limitation, we introduce post-hoc CS (PH-CS), which generates a path of candidate selection sets, each paired with a data-driven false discovery proportion (FDP) estimate. PH-CS lets the user select any operating point on this path by maximizing a user-specified utility, arbitrarily balancing selection size and FDR. Building on conformal e-variables and the e-Benjamini-Hochberg (e-BH) procedure, PH-CS is proved to provide a finite-sample post-hoc reliability guarantee whereby the ratio between estimated FDP level and true FDP is, on average, upper bounded by 1, so that the average estimated FDP is, to first order, a valid upper bound on the true FDR. PH-CS is extended to control quality defined in terms of a general risk. Experiments on synthetic and real-world datasets demonstrate that, unlike CS, PH-CS can consistently satisfy user-imposed utility constraints while producing reliable FDP estimates and maintaining competitive FDR control.

We study the problem of modeling high-dimensional tensor-valued time series under a Tucker decomposition-based factor model while permitting the presence of multiple structural change points. Such data call for a method that (i) handles high dimensionality and complex dependence while achieving consistency in multiple change points and further, (ii) addresses a unique challenge posed by the multi-dimensional array setting, of identifying the modes associated with each change while the shifts in different modes interact with one another. To this end, we propose a change point detection procedure utilizing the low-rank structure of the data for statistical and computational efficiency. In addition, we formalize the $\textit{mode-identifiability}$ of each change and propose an algorithm for detecting the modes at which the data undergo a mode-identifiable shift. We establish the consistency of both change point detection and mode-identification methods under a weak moment condition, and demonstrate their good performance on simulated datasets where, in particular, it is shown that the mode-identification step can improve the post-segmentation estimation of the mode-wise loading space. We also analyze the datasets on New York City taxi usage and Fama–French portfolio returns using the proposed suite of methods.

Feature importance methods using unrestricted permutations are flawed due to extrapolation errors; such errors appear in all non-trivial variable importance approaches. We propose three new approaches: conditional model reliance and Knockoffs with Gaussian transformation, and restricted ALE plot designs. Theoretical and numerical results show our strategies reduce/eliminate extrapolation.

Long questionnaires increase the response burden for patients and healthcare workers. In the treatment of Parkinson's disease, the MDS-UPDRS questionnaire to track disease progression may be underutilized due to time requirements. While reduced item sets have been studied using Fisher information from Item Response Theory (IRT) models, optimal selection methods remain unclear. We compared three methods for selecting an optimal subset of items, with the aim of minimizing the uncertainty in the estimates of the disease severity: Ranking by the Fisher information, coordinate descent local search to directly minimize estimate uncertainty, and adaptive selection. Whereas item ranking based on the expected Fisher information outperformed random choice of items, we saw further gains with the coordinate descent algorithm that directly minimizes the uncertainty of the disease severity estimate. An adaptive algorithm gave an additional slight gain compared to the coordinate descent method. However, the performance of the adaptive method is a best-case limit as we assume that we find the optimal set for the true latent trait scores. For a 5-item subset, the ranked Fisher information method reduced the expected standard deviation by 14 percent compared to random item selection. The corresponding reductions for coordinate descent and adaptive selection were 26 percent and 34 percent respectively. More sophisticated selection methods substantially improved estimate accuracy for small item sets, with diminishing returns for larger subsets. Because item parameters are retained from the full test, reduced item sets measure the same latent construct as the original test. The choice of method entails a trade-off between methodological complexity and precision.

We analyze two widely used local attribution methods, Local Shapley Values and LIME, which aim to quantify the contribution of a feature value $x_i$ to a specific prediction $f(x_1, \dots, x_p)$. Despite their widespread use, we identify fundamental limitations in their ability to reliably detect locally important features, even under ideal conditions with exact computations and independent features. We argue that a sound local attribution method should not assign importance to features that neither influence the model output (e.g., features with zero coefficients in a linear model) nor exhibit statistical dependence with functionality-relevant features. We demonstrate that both Local SV and LIME violate this fundamental principle. To address this, we propose R-LOCO (Regional Leave Out COvariates), which bridges the gap between local and global explanations and provides more accurate attributions. R-LOCO segments the input space into regions with similar feature importance characteristics. It then applies global attribution methods within these regions, deriving an instance's feature contributions from its regional membership. This approach delivers more faithful local attributions while avoiding local explanation instability and preserving instance-specific detail often lost in global methods.

Changes in input distribution can induce shifts in the average predictions of machine learning models. Such prediction shifts may impact downstream business outcomes (e.g. a bank's loan approval rate), so understanding their causes can be crucial. We propose \ours{}: a Shapley value method for attributing prediction shifts to changes in the conditional probabilities of interpretable subgroups of data, where these subgroups are defined by the structure of decision trees. We initially apply this method to single decision trees, providing exact explanations based on conditional probability changes at split nodes. Next, we extend it to tree ensembles by selecting the most explanatory tree and accounting for residual effects. Finally, we propose a model-agnostic variant using surrogate trees grown with a novel objective function, allowing application to models like neural networks. While exact computation can be intensive, approximation techniques enable practical application. We show that \ours{} provides simple, faithful, and near-complete explanations of prediction shifts across model classes, aiding model monitoring in dynamic environments.

We present an explicit deterministic transformation of a fixed number of i.i.d. uniform random variables with exact Beta$(a,1-a)$ law for $0<a<1$, using only elementary operations (an “extended one-liner”, see \cite{devroye1996oneline}). As corollaries, the families Beta$(a,b)$ with $\min(a,b)<1$, Gamma$(c)$ with $c<1$, and Dirichlet$(\alpha_1,\dots,\alpha_d)$ with $0<\alpha_i<1$, for fixed $d$, also have extended one-\liners.

There is rising interest in using Machine Learning (ML) model predictions as outcomes in causal analysis. However, these methods have faced challenges in finding the true treatment effects. It is also challenging to make choices about which prediction models to choose, since we are interested not only in the accuracy of the prediction but in its ability to produce the correct causal effect in the analysis. In this paper I propose a decomposition of the prediction into between-unit prediction ($\eta_\mu$), within-unit-across-time prediction ($\eta_\epsilon$), and counterfactual-treatment-effect prediction ($\eta_T$). I show that the counterfactual-treatment-effect component is the one that determines whether the model recovers the true treatment effect, but only the first two components can be estimated from non-experimental data. I argue that within-unit-across-time prediction accuracy ($\eta_\epsilon$) is a structurally better proxy for the counterfactual-treatment-effect component ($\eta_T$) than overall prediction accuracy, and propose a metric to estimate it from panel data with at least two time periods. This metric serves as a diagnostic and model-selection tool for choosing ML models for causal analysis. Under the stronger assumption that $\eta_T \approx \eta_\epsilon$, it also enables constructing an approximately unbiased estimate of the treatment effect. I develop the theoretical framework and illustrate it with simulations of synthetic data.