Papers

We propose a simple, scalable algorithm for using stochastic interpolants to sample from unnormalized densities and for fine-tuning generative models. The approach, Tilt Matching, arises from a dynamical equation relating the flow matching velocity to one targeting the same distribution tilted by a reward, implicitly solving a stochastic optimal control problem. The new velocity inherits the regularity of stochastic interpolant transports while also being the minimizer of an objective with strictly lower variance than flow matching itself. The update to the velocity field can be interpreted as the sum of all joint cumulants of the stochastic interpolant and copies of the reward, and to first order is their covariance. The algorithms do not require any access to gradients of the reward or backpropagating through trajectories of the flow or diffusion. We empirically verify that the approach is efficient and highly scalable, providing state-of-the-art results on sampling under Lennard-Jones potentials and is competitive on fine-tuning Stable Diffusion, without requiring reward multipliers. It can also be straightforwardly applied to tilting few-step flow map models.

High-quality labeled data are essential for reliable statistical inference, but are often limited by validation costs. While surrogate labels provide cost-effective alternatives, their noise can introduce non-negligible bias. To address this challenge, we propose the surrogate-powered inference (SPI) toolbox, a unified framework that leverages both the validity of high-quality labels and the abundance of surrogates to enable reliable statistical inference. SPI comprises three progressively enhanced versions. Base-SPI integrates validated labels and surrogates through augmentation to improve estimation efficiency. SPI+ incorporates regularized regression to safely handle multiple surrogates, preventing performance degradation due to error accumulation. SPI++ further optimizes efficiency under limited validation budgets through an adaptive, multiwave labeling procedure that prioritizes informative subjects for labeling. Compared to traditional methods, SPI substantially reduces the estimation error and increases the power in risk factor identification. These results demonstrate the value of SPI in improving the reproducibility. Theoretical guarantees and extensive simulation studies further illustrate the properties of our approach.

Ensemble learning is traditionally justified as a variance-reduction strategy, explaining its strong performance for unstable predictors such as decision trees. This explanation, however, does not account for ensembles constructed from intrinsically stable estimators-including smoothing splines, kernel ridge regression, Gaussian process regression, and other regularized reproducing kernel Hilbert space (RKHS) methods whose variance is already tightly controlled by regularization and spectral shrinkage. This paper develops a general weighting theory for ensemble learning that moves beyond classical variance-reduction arguments. We formalize ensembles as linear operators acting on a hypothesis space and endow the space of weighting sequences with geometric and spectral constraints. Within this framework, we derive a refined bias-variance approximation decomposition showing how non-uniform, structured weights can outperform uniform averaging by reshaping approximation geometry and redistributing spectral complexity, even when variance reduction is negligible. Our main results provide conditions under which structured weighting provably dominates uniform ensembles, and show that optimal weights arise as solutions to constrained quadratic programs. Classical averaging, stacking, and recently proposed Fibonacci-based ensembles appear as special cases of this unified theory, which further accommodates geometric, sub-exponential, and heavy-tailed weighting laws. Overall, the work establishes a principled foundation for structure-driven ensemble learning, explaining why ensembles remain effective for smooth, low-variance base learners and setting the stage for distribution-adaptive and dynamically evolving weighting schemes developed in subsequent work.

Nature rarely reveals her secrets bluntly, yet in the Fibonacci sequence she grants us a glimpse of her quiet architecture of growth, harmony, and recursive stability \citep{Koshy2001Fibonacci, Livio2002GoldenRatio}. From spiral galaxies to the unfolding of leaves, this humble sequence reflects a universal grammar of balance. In this work, we introduce Fibonacci Ensembles, a mathematically principled yet philosophically inspired framework for ensemble learning that complements and extends classical aggregation schemes such as bagging, boosting, and random forests \citep{Breiman1996Bagging, Breiman2001RandomForests, Friedman2001GBM, Zhou2012Ensemble, HastieTibshiraniFriedman2009ESL}. Two intertwined formulations unfold: (1) the use of normalized Fibonacci weights – tempered through orthogonalization and Rao–Blackwell optimization – to achieve systematic variance reduction among base learners, and (2) a second-order recursive ensemble dynamic that mirrors the Fibonacci flow itself, enriching representational depth beyond classical boosting. The resulting methodology is at once rigorous and poetic: a reminder that learning systems flourish when guided by the same intrinsic harmonies that shape the natural world. Through controlled one-dimensional regression experiments using both random Fourier feature ensembles \citep{RahimiRecht2007RFF} and polynomial ensembles, we exhibit regimes in which Fibonacci weighting matches or improves upon uniform averaging and interacts in a principled way with orthogonal Rao–Blackwellization. These findings suggest that Fibonacci ensembles form a natural and interpretable design point within the broader theory of ensemble learning.

Across fields such as machine learning, social science, and geology, considerable attention has been given to models that factorize a nonnegative matrix into the product of two or three matrices, subject to nonnegative or row-sum-to-1 constraints. Although these models are to a large extent similar or even equivalent, they are presented under different names, and their similarity is not well known. This paper highlights similarities among five models, latent budget analysis (LBA) and latent class analysis (LCA) from social science, end-member analysis (EMA) from geology, probabilistic latent semantic analysis (PLSA) and nonnegative matrix factorization (NMF) from machine learning. We focus on the identifiability of these models. We prove that the solution of LBA, EMA, LCA, PLSA is unique if and only if the solution of NMF is unique. Consequently, existing uniqueness theorems for NMF directly apply to LBA, EMA, LCA, PLSA, and vice versa. We also provide a brief review of algorithms for the estimation of these models. We illustrate NMF on a sedimentary grain-size distribution dataset from sedimentary geology, and end the paper with a discussion of closely related model: archetypal analysis.

Designs which are minimax in the presence of model misspecifications have been constructed so as to minimize the maximum, over classes of alternate response models, of the integrated mean squared error of the predicted values. This mean squared error decomposes into a term arising solely from variation, and a bias term arising from the model errors. Here we consider the problem of designing so as to minimize the variance of the predictors, subject to a bound on the maximum (over model misspecifications) bias. We consider as well designing so as to minimize the maximum bias, subject to a bound on the variance. We show that solutions to both problems are given by the minimax designs, with appropriately chosen values of their tuning constants. Conversely, any minimax design solves each problem for an appropriate choice of the bound on the maximum bias or on the variance.

Phylogenetic trees provide a fundamental representation of evolutionary relationships, yet the combinatorial explosion of possible tree topologies renders inference computationally challenging. Classical approaches to characterizing tree space, such as the Billera-Holmes-Vogtmann (BHV) space, offer elegant geometric structure but suffer from statistical and computational limitations. An alternative perspective arises from tropical geometry, the tropical Grassmannian tropGr(2,n), introduced by Speyer and Sturmfels, which coincides with phylogenetic tree space. In this paper, we review the structure of the tropical Grassmannian and present algorithmic methods for its computational study, including procedures for sampling from the tropical Grassmannian. Our aim is to make these concepts accessible to evolutionary biologists and computational scientists, and to motivate new research directions at the interface of algebraic geometry and phylogenetic inference.

We explore the edge-flipping mechanism, a type of input perturbation, to release the directed graph under edge-local differential privacy. By using the noisy bi-degree sequence from the output graph, we construct the moment equations to estimate the unknown parameters in the $p_0$ model, which is an exponential family distribution with the bi-degree sequence as the natural sufficient statistic. We show that the resulting private estimator is asymptotically consistent and normally distributed under some conditions. In addition, we compare the performance of input and output perturbation mechanisms for releasing bi-degree sequences in terms of parameter estimation accuracy and privacy protection. Numerical studies demonstrate our theoretical findings and compare the performance of the private estimates obtained by different types of perturbation methods. We apply the proposed method to analyze the UC Irvine message network.

Current transfer learning methods for high-dimensional linear regression assume feature alignment across domains, restricting their applicability to semantically matched features. In many real-world scenarios, however, distinct features in the target and source domains can play similar predictive roles, creating a form of cross-semantic similarity. To leverage this broader transferability, we propose the Cross-Semantic Transfer Learning (CSTL) framework. It captures potential relationships by comparing each target coefficient with all source coefficients through a weighted fusion penalty. The weights are derived from the derivative of the SCAD penalty, effectively approximating an ideal weighting scheme that preserves transferable signals while filtering out source-specific noise. For computational efficiency, we implement CSTL using the Alternating Direction Method of Multipliers (ADMM). Theoretically, we establish that under mild conditions, CSTL achieves the oracle estimator with overwhelming probability. Empirical results from simulations and a real-data application confirm that CSTL outperforms existing methods in both cross-semantic and partial signal similarity settings.

Predictive inference requires balancing statistical accuracy against informational complexity, yet the choice of complexity measure is usually imposed rather than derived. We treat econometric objects as predictive rules, mappings from information to reported predictive distributions, and impose three structural requirements on evaluation: locality, strict propriety, and coherence under aggregation (coarsening/refinement) of outcome categories. These axioms characterize (uniquely, up to affine transformations) the logarithmic score and induce Shannon mutual information (Kullback-Leibler divergence) as the corresponding measure of predictive complexity. The resulting entropy-regularized prediction problem admits Gibbs-form optimal rules, and we establish an essentially complete-class result for the admissible rules we study under joint risk-complexity dominance. Rational inattention emerges as the constrained dual, corresponding to frontier points with binding information capacity. The entropy penalty contributes additive curvature to the predictive criterion; in weakly identified settings, such as weak instruments in IV regression, where the unregularized objective is flat, this curvature stabilizes the predictive criterion. We derive a local quadratic (LAQ) expansion connecting entropy regularization to classical weak-identification diagnostics.

Diffusion models have become a central tool in deep generative modeling, but standard formulations rely on a single network and a single diffusion schedule to transform a simple prior, typically a standard normal distribution, into the target data distribution. As a result, the model must simultaneously represent the global structure of the distribution and its fine-scale local variations, which becomes difficult when these scales are strongly mismatched. This issue arises both in natural images, where coarse manifold-level structure and fine textures coexist, and in low-dimensional distributions with highly concentrated local structure. To address this issue, we propose Residual Prior Diffusion (RPD), a two-stage framework in which a coarse prior model first captures the large-scale structure of the data distribution, and a diffusion model is then trained to represent the residual between the prior and the target data distribution. We formulate RPD as an explicit probabilistic model with a tractable evidence lower bound, whose optimization reduces to the familiar objectives of noise prediction or velocity prediction. We further introduce auxiliary variables that leverage information from the prior model and theoretically analyze how they reduce the difficulty of the prediction problem in RPD. Experiments on synthetic datasets with fine-grained local structure show that standard diffusion models fail to capture local details, whereas RPD accurately captures fine-scale detail while preserving the large-scale structure of the distribution. On natural image generation tasks, RPD achieved generation quality that matched or exceeded that of representative diffusion-based baselines and it maintained strong performance even with a small number of inference steps.

Despite numerous attempts at mitigation since the inception of language models, hallucinations remain a persistent problem even in today's frontier LLMs. Why is this? We review existing definitions of hallucination and fold them into a single, unified definition wherein prior definitions are subsumed. We argue that hallucination can be unified by defining it as simply inaccurate (internal) world modeling, in a form where it is observable to the user. For example, stating a fact which contradicts a knowledge base OR producing a summary which contradicts the source. By varying the reference world model and conflict policy, our framework unifies prior definitions. We argue that this unified view is useful because it forces evaluations to clarify their assumed reference "world", distinguishes true hallucinations from planning or reward errors, and provides a common language for comparison across benchmarks and discussion of mitigation strategies. Building on this definition, we also connect our framework to HalluWorld, a complementary benchmark that instantiates fully specified reference world models for stress-testing model hallucinations.

Testing high-dimensional quantile regression coefficients is crucial, as tail quantiles often reveal more than the mean in many practical applications. Nevertheless, the sparsity pattern of the alternative hypothesis is typically unknown in practice, posing a major challenge. To address this, we propose an adaptive test that remains powerful across both sparse and dense alternatives.We first establish the asymptotic independence between the max-type test statistic proposed by \citet{tang2022conditional} and the sum-type test statistic introduced by \citet{chen2024hypothesis}. Building on this result, we propose a Cauchy combination test that effectively integrates the strengths of both statistics and achieves robust performance across a wide range of sparsity levels. Simulation studies and real data applications demonstrate that our proposed procedure outperforms existing methods in terms of both size control and power.

Federated Learning (FL) enables collaborative training on decentralized data. Differential privacy (DP) is crucial for FL, but current private methods often rely on unrealistic assumptions (e.g., bounded gradients or heterogeneity), hindering practical application. Existing works that relax these assumptions typically neglect practical FL features, including multiple local updates and partial client participation. We introduce Fed-$\alpha$-NormEC, the first differentially private FL framework providing provable convergence and DP guarantees under standard assumptions while fully supporting these practical features. Fed-$\alpha$-NormE integrates local updates (full and incremental gradient steps), separate server and client stepsizes, and, crucially, partial client participation, which is essential for real-world deployment and vital for privacy amplification. Our theoretical guarantees are corroborated by experiments on private deep learning tasks.

We present two main contributions to the expected star discrepancy theory. First, we derive a sharper expected upper bound for jittered sampling, improving the leading constants and logarithmic terms compared to the state-of-the-art [Doerr, 2022]. Second, we prove the strong partition principle for star discrepancy, showing that any equal-measure stratified sampling yields a strictly smaller expected discrepancy than simple random sampling, thereby resolving an open question in [Kiderlen and Pausinger, 2022]. Numerical simulations confirm our theoretical advances and illustrate the superiority of stratified sampling in low to moderate dimensions.

The nondecimated or translation-invariant wavelet transform (NDWT) is a central tool in classical multiscale signal analysis, valued for its stability, redundancy, and shift invariance. This paper develops two complementary quantum formulations of the NDWT that embed these classical properties coherently into quantum computation. The first formulation is based on the epsilon-decimated interpretation of the NDWT and realizes all circularly shifted wavelet transforms simultaneously by promoting the shift index to a quantum register and applying controlled circular shifts followed by a wavelet analysis unitary. The resulting construction yields an explicit, fully unitary quantum representation of redundant wavelet coefficients and supports coherent postprocessing, including quantum shrinkage via ancilla-driven completely positive trace preserving maps. The second formulation is based on the Hadamard test and uses diagonal phase operators to probe scale-shift wavelet structure through interference, providing direct access to shift-invariant energy scalograms and multiscale spectra without explicit coefficient reconstruction. Together, these two approaches demonstrate that redundancy and translation invariance can be exploited rather than avoided in the quantum setting. Applications to denoising, feature extraction, and spectral scaling illustrate how quantum NDWTs provide a flexible and physically meaningful foundation for multiscale quantum signal processing.

Being infinite dimensional, non-parametric information geometry has long faced an "intractability barrier" due to the fact that the Fisher-Rao metric is now a functional incurring difficulties in defining its inverse. This paper introduces a novel framework to resolve the intractability with an Orthogonal Decomposition of the Tangent Space ($T_fM = S \oplus S^{\perp}$), where $S$ represents an observable covariate subspace. Through the decomposition, we derive the Covariate Fisher Information Matrix (cFIM), denoted as ${\bf G}_f$, which is a finite-dimensional and computable representative of information extractable from the manifold's geometry. Significantly, by proving the Trace Theorem: $H_G(f) = \text{Tr}({\bf G}_f)$, we establish a rigorous foundation for the G-entropy previously introduced by us, thereby identifying it as a fundamental geometric invariant representing the total explainable statistical information captured by the probability distribution associated with a model. Furthermore, we establish a link between ${\bf G}_f$ and the second derivative (i.e. the curvature) of the KL-divergence, leading to the notion of Covariate Cramér-Rao Lower Bound(CRLB). We demonstrate that ${\bf G}_f$ is congruent to the Efficient Fisher Information Matrix, thereby providing fundamental limits of variance for semi-parametric estimators. Finally, we apply our geometric framework to the Manifold Hypothesis, lifting the latter from a heuristic assumption into a testable condition of rank-deficiency within the cFIM. By defining the Information Capture Ratio, we provide a rigorous method for estimating intrinsic dimensionality in high-dimensional data. In short, our work bridges the gap between abstract information geometry and the demand of explainable AI, by providing a tractable path for assessing the statistical coverage and the efficiency of non-parametric models.

We make modifications to the unscented Kalman filter (UKF) which bestow almost complete practical identifiability upon a lumped-parameter cardiovascular model with 10 parameters and 4 output observables - a highly non-linear, stiff problem of clinical significance. The modifications overcome the challenging problems of rank deficiency when applying the UKF to parameter estimation. Rank deficiency usually means only a small subset of parameters can be estimated. Traditionally, pragmatic compromises are made, such as selecting an optimal subset of parameters for estimation and fixing non-influential parameters. Kalman filters are typically used for dynamical state tracking, to facilitate the control u at every time step. However, for the purpose of parameter estimation, this constraint no longer applies. Our modification has transformed the utility of UKF for the parameter estimation purpose, including minimally influential parameters, with excellent robustness (i.e., under severe noise corruption, challenging patho-physiology, and no prior knowledge of parameter distributions). The modified UKF algorithm is robust in recovering almost all parameters to over 98% accuracy, over 90% of the time, with a challenging target data set of 50, 10-parameter samples. We compare this to the original implementation of the UKF algorithm for parameter estimation and demonstrate a significant improvement.

Forecasting conflict-related fatalities remains a central challenge in political science and policy analysis due to the sparse, bursty, and highly non-stationary nature of violence data. We introduce DynAttn, an interpretable dynamic-attention forecasting framework for high-dimensional spatio-temporal count processes. DynAttn combines rolling-window estimation, shared elastic-net feature gating, a compact weight-tied self-attention encoder, and a zero-inflated negative binomial (ZINB) likelihood. This architecture produces calibrated multi-horizon forecasts of expected casualties and exceedance probabilities, while retaining transparent diagnostics through feature gates, ablation analysis, and elasticity measures. We evaluate DynAttn using global country-level and high-resolution PRIO-grid-level conflict data from the VIEWS forecasting system, benchmarking it against established statistical and machine-learning approaches, including DynENet, LSTM, Prophet, PatchTST, and the official VIEWS baseline. Across forecast horizons from one to twelve months, DynAttn consistently achieves substantially higher predictive accuracy, with particularly large gains in sparse grid-level settings where competing models often become unstable or degrade sharply. Beyond predictive performance, DynAttn enables structured interpretation of regional conflict dynamics. In our application, cross-regional analyses show that short-run conflict persistence and spatial diffusion form the core predictive backbone, while climate stress acts either as a conditional amplifier or a primary driver depending on the conflict theater.

We study the directions of axial symmetry of multivariate distributions and relate the measure or cardinality of this set to spherical symmetry. Under Carleman's condition, two independent random projections identify all true axes of symmetry in \(\RR^2\) almost surely. We propose a level-set estimator of the symmetry axes and prove its Hausdorff consistency, in arbitrary dimension, for the zero set of the population criterion based on finitely many projections. Together with planar identification, this gives a consistent estimation of the true axes of symmetry in dimension two.

Singular learning theory characterizes Bayesian models with non-identifiable parameterizations through two central quantities: the real log canonical threshold (RLCT), which governs marginal likelihood asymptotics, and the singular fluctuation, which determines second-order generalization behavior and the complexity term in WAIC. While the geometric meaning of the RLCT is well understood, the interpretation of singular fluctuation has remained comparatively opaque. We show that singular fluctuation admits a precise thermodynamic interpretation. Under a tempered (Gibbs) posterior, it is exactly the curvature of the Bayesian free energy with respect to inverse temperature; equivalently, the variance of the log-likelihood observable. In this sense, singular fluctuation is the statistical analogue of specific heat. This identity clarifies why singular fluctuation controls the equation of state relating training and generalization error and explains the success of WAIC in singular models: WAIC estimates a fluctuation coefficient rather than a parameter dimension. Across Gaussian mixture models and reduced-rank regression, we demonstrate that singular fluctuation behaves as a thermodynamic response coefficient. As temperature decreases, posterior reorganization suppresses fluctuation directions that affect predictive performance, and model-specific geometric observables track the decay of singular fluctuation. Rather than introducing new asymptotic expansions, this work unifies existing variance identities, equation-of-state results, and WAIC complexity corrections under a single free-energy curvature framework.

The use of descriptive statistics in pilot testing procedures requires objective, standard diagnostic tools that are feasible for small sample sizes. While current psychometric practices report item-level statistics, they often report these raw descriptives separately rather than consolidating both mean and standard deviation into a single diagnostic tool to directly measure item quality. By leveraging the analytical properties of Cohen's d, this article repurposes its use in scale development as a standardized item deviation index. This measures the extent of an item's raw deviation relative to its scale midpoint while accounting for its own uncertainty. Analytical properties such as boundedness, scale invariance, and bias are explored to further understand how the index values behave, which will aid future efforts to establish empirical thresholds that characterize redundancy among formative indicators and consistency among reflective indicators.

Sensitivity analysis informs causal inference by assessing the sensitivity of conclusions to departures from assumptions. The consistency assumption states that there are no hidden versions of treatment and that the outcome arising naturally equals the outcome arising from intervention. When reasoning about the possibility of consistency violations, it can be helpful to distinguish between covariates and versions of treatment. In the context of surgery, for example, genomic variables are covariates and the skill of a particular surgeon is a version of treatment. There may be hidden versions of treatment, and this paper addresses that concern with a new kind of sensitivity analysis. Whereas many methods for sensitivity analysis are focused on confounding by unmeasured covariates, the methodology of this paper is focused on confounding by hidden versions of treatment. In this paper, new mathematical notation is introduced to support the novel method, and example applications are described.

Applying well-established statistical methods effectively to LLM evals requires consideration of model correlations and prediction noises. Leading evals often ignore data noise, have low statistical power, or make unnecessary trade-offs. We define and measure three types of noise: 1) prediction noise from generating different answers on a given question, 2) data noise from sampling questions, and 3) their combined total noise following the law of total variance. To emphasize relative comparisons and gain statistical power, we propose all-pairs comparison, which applies paired comparison to all pairs of LLMs and measures all the noise components based on millions of question-level predictions across many evals and settings, revealing clear trends. First, most evals exhibit a characteristic and highly predictable total noise level across all model pairs. Second, paired prediction noise typically exceeds paired data noise, which means reducing prediction noise by averaging can significantly increase statistical power. By measuring all the noises together, we can assess eval results in context and make better empirical decisions.

The data processing inequality is an information-theoretic principle stating that the information content of a signal cannot be increased by processing the observations. In particular, it suggests that there is no benefit in enhancing the signal or encoding it before addressing a classification problem. This assertion can be proven to be true for the case of the optimal Bayes classifier. However, in practice, it is common to perform "low-level" tasks before "high-level" downstream tasks despite the overwhelming capabilities of modern deep neural networks. In this paper, we aim to understand when and why low-level processing can be beneficial for classification. We present a comprehensive theoretical study of a binary classification setup, where we consider a classifier that is tightly connected to the optimal Bayes classifier and converges to it as the number of training samples increases. We prove that for any finite number of training samples, there exists a pre-classification processing that improves the classification accuracy. We also explore the effect of class separation, training set size, and class balance on the relative gain from this procedure. We support our theory with an empirical investigation of the theoretical setup. Finally, we conduct an empirical study where we investigate the effect of denoising and encoding on the performance of practical deep classifiers on benchmark datasets. Specifically, we vary the size and class distribution of the training set, and the noise level, and demonstrate trends that are consistent with our theoretical results.

We derive a new closed-form variance-adaptive confidence sequence (CS) for estimating the average conditional mean of a sequence of bounded random variables. Empirically, it yields the tightest closed-form CS we have found for tracking time-varying means, across sample sizes up to $\approx 10^6$. When the observations happen to have the same conditional mean, our CS is asymptotically tighter than the recent closed-form CS of Waudby-Smith and Ramdas [38]. It also has other desirable properties: it is centered at the unweighted sample mean and has limiting width (multiplied by $\sqrt{t/\log t}$) independent of the significance level. We extend our results to provide a CS with the same properties for random matrices with bounded eigenvalues.

In prevalent cohort studies with delayed entry, time-to-event outcomes are often subject to left truncation where only subjects that have not experienced the event at study entry are included, leading to selection bias. Existing methods for handling left truncation mostly rely on the (quasi-)independence assumption or the weaker conditional (quasi-)independence assumption which assumes that conditional on observed covariates, the left truncation time and the event time are independent on the observed region. In practice, however, our analysis of the Honolulu Asia Aging Study (HAAS) suggests that the conditional quasi-independence assumption may fail because measured covariates often serve only as imperfect proxies for the underlying mechanisms, such as latent health status, that induce dependence between truncation and event times. To address this gap, we propose a proximal weighting identification framework that admits the dependence-inducing factors may not be fully observed. We then construct an estimator based on the framework and study its asymptotic properties. We examine the finite sample performance of the proposed estimator by comprehensive simulations, and apply it to analyzing the cognitive impairment-free survival probabilities using data from the Honolulu Asia Aging Study.

Attribution modelling lies at the heart of marketing effectiveness, yet most existing approaches depend on user-level path data, which are increasingly inaccessible due to privacy regulations and platform restrictions. This paper introduces a Causal-Driven Attribution (CDA) framework that infers channel influence using only aggregated impression-level data, avoiding any reliance on user identifiers or click-path tracking. CDA integrates temporal causal discovery (using PCMCI) with causal effect estimation via a Structural Causal Model to recover directional channel relationships and quantify their contributions to conversions. Using large-scale synthetic data designed to replicate real marketing dynamics, we show that CDA achieves an average relative RMSE of 9.50% when given the true causal graph, and 24.23% when using the predicted graph, demonstrating strong accuracy under correct structure and meaningful signal recovery even under structural uncertainty. CDA captures cross-channel interdependencies while providing interpretable, privacy-preserving attribution insights, offering a scalable and future-proof alternative to traditional path-based models.

Kolmogorov complexity of a finite binary word reflects both algorithmic structure and the empirical distribution of symbols appearing in the word. Words with symbol frequencies far from one half have smaller combinatorial richness and therefore appear less complex under the standard definition. In this paper an entropy-normalized complexity measure is introduced that divides the Kolmogorov complexity of a word by the empirical entropy of its observed distribution of zeros and ones. This adjustment isolates intrinsic descriptive complexity from the purely combinatorial effect of symbol imbalance. For Martin Löf random sequences under constructive exchangeable measures, the adjusted complexity grows linearly and converges to one. A pathological construction shows that regularity of the underlying measure is essential. The proposed framework connects Kolmogorov complexity, empirical entropy, and randomness in a natural manner and suggests applications in randomness testing and in the analysis of structured binary data.

The stable unit treatment value (SUTVA) is a crucial assumption in the Difference-in-Differences (DiD) research design. It rules out hidden versions of treatment and any sort of interference and spillover effects across units. Even if this is a strong assumption, it has not received much attention from DiD practitioners and, in many cases, it is not even explicitly stated as an assumption, especially the no-interference assumption. In this technical note, we investigate what the DiD estimand identifies in the presence of unknown interference. We show that the DiD estimand identifies a contrast of causal effects, but it is not informative on any of these causal effects separately, without invoking further assumptions. Then, we explore different sets of assumptions under which the DiD estimand becomes informative about specific causal effects. We illustrate these results by revisiting the seminal paper on minimum wages and employment by Card and Krueger (1994).