Household-travel surveys (HTSs) have long provided the empirical backbone for this work by coupling rich trip diaries with respondent characteristics such as age, gender, income, and household composition. Analyses drawing on these surveys consistently show that, after accounting for the built environment, so-ciodemographic traits still correlate with car ownership, mode choice, trip frequency, and trip-chaining behavior (Bhat and Koppelman, 1994; Lee et al., 2007; Lu and Pas, 1999; McGuckin and Murakami, 1999; Mokhtarian and Chen, 2004) In the past dozen years, the ubiquity of GPS-enabled smartphones has spawned a parallel, industry-scale source of mobility evidence in passively-generated mobile data, which includes call-detail records (CDR), location-based service (LBS) pings, connected-vehicle traces, and the like (Chen et al., 2016). These datasets dwarf HTSs in both sample size and temporal length, are refreshed continuously, and can often be licensed at a fraction of the cost of running a tailored survey. Their content, however, is almost exclusively spatial temporal; they record where and when a device was observed but remain agnostic about who was holding it. This missing dimension limits many distributional and behavioral analyses, including those that require understanding how travel patterns vary across population subgroups. Despite this blind spot, public agencies have been keen on experimenting with mobile data products (Ugurel et al., 2024). Metropolitan planning organizations (MPOs) see potential in using them to stitch origin-destination matrices (Alexander et al., 2015; Iqbal et al., 2014), site electric-vehicle chargers (Yang et al., 2017), and evaluate complete-street retrofits (Bian et al., 2023). Yet the lack of respondent attributes imposes two related hazards.

Social and collaborative platforms emit multivariate time-series traces in which early interactions--such as views, likes, or downloads--are followed, sometimes months or years later, by higher impact like citations, sales, or reviews. We formalize this setting as Lead-Lag Forecasting (LLF): given an early usage channel (the lead), predict a correlated but temporally shifted outcome channel (the lag). Despite the ubiquity of such patterns, LLF has not been treated as a unified forecasting problem within the time-series community, largely due to the absence of standardized datasets. To anchor research in LLF, here we present two high-volume benchmark datasets--arXiv (accesses citations of 2.3M papers) and GitHub (pushes/stars forks of 3M repositories)--and outline additional domains with analogous lead-lag dynamics, including Wikipedia (page-views edits), Spotify (streams concert attendance), e-commerce (click-throughs purchases), and LinkedIn profile (views messages). Our datasets provide ideal testbeds for lead-lag forecasting, by capturing long-horizon dynamics across years, spanning the full spectrum of outcomes, and avoiding sur-vivorship bias in sampling. We documented all technical details of data cura-tion and cleaning, verified the presence of lead-lag dynamics through statistical and classification tests, and benchmarked parametric and non-parametric baselines for regression. Our study establishes LLF as a novel forecasting paradigm and lays an empirical foundation for its systematic exploration in social and usage data. The success of human activities is often measured by their collective impact, ranging from music streams and movie box office revenues to product sales and social media popularity. These impact metrics typically follow heavy-tailed distributions (Clauset et al., 2009) and slow decay patterns across timescales (Candia et al., 2019), making early identification of future hits fundamentally challenging (Cheng et al., 2014; Martin et al., 2016). At the same time, digital platforms increasingly log online user interactions--searches, views, downloads, likes, and shares--that often precede these long-term dynamics. These temporal lead-lag dynamics are remarkably ubiquitous, spanning domains as diverse as science (Haque & Ginsparg, 2009), economics (Wu & Brynjolfsson, 2015), arts (Goel et al., 2010), culture (Gruhl et al., 2005), and social movements (Johnson et al., 2016). A systematic understanding of such lead-lag dynamics is not only crucial for anticipating and optimizing impact in digital ecosystems, but also essential for designing effective strategies that identify and promote emerging innovations and products.

Riesz regression has garnered attention as a tool in debiased machine learning for causal and structural parameter estimation (Chernozhukov et al., 2021). This study shows that Riesz regression is closely related to direct density-ratio estimation (DRE) in important cases, including average treat- ment effect (ATE) estimation. Specifically, the idea and objective in Riesz regression coincide with the one in least-squares importance fitting (LSIF, Kanamori et al., 2009) in direct density-ratio estimation. While Riesz regression is general in the sense that it can be applied to Riesz representer estimation in a wide class of problems, the equivalence with DRE allows us to directly import exist- ing results in specific cases, including convergence-rate analyses, the selection of loss functions via Bregman-divergence minimization, and regularization techniques for flexible models, such as neural networks. Conversely, insights about the Riesz representer in debiased machine learning broaden the applications of direct density-ratio estimation methods. This paper consolidates our prior results in Kato (2025a) and Kato (2025b).

Generative Bayesian Filtering (GBF) provides a powerful and flexible framework for performing posterior inference in complex nonlinear and non-Gaussian state-space models. Our approach extends Generative Bayesian Computation (GBC) to dynamic settings, enabling recursive posterior inference using simulation-based methods powered by deep neural networks. GBF does not require explicit density evaluations, making it particularly effective when observation or transition distributions are analytically intractable. To address parameter learning, we introduce the Generative-Gibbs sampler, which bypasses explicit density evaluation by iteratively sampling each variable from its implicit full conditional distribution. Such technique is broadly applicable and enables inference in hierarchical Bayesian models with intractable densities, including state-space models. We assess the performance of the proposed methodologies through both simulated and empirical studies, including the estimation of $α$-stable stochastic volatility models. Our findings indicate that GBF significantly outperforms existing likelihood-free approaches in accuracy and robustness when dealing with intractable state-space models.

We present a new benchmarking study comparing a boundary-constrained Ehrenpreis--Palamodov Gaussian Process (B-EPGP) surrogate with a classical finite element method combined with Crank--Nicolson time stepping (CN-FEM) for solving the two-dimensional wave equation with homogeneous Dirichlet boundary conditions. The B-EPGP construction leverages exponential-polynomial bases derived from the characteristic variety to enforce the PDE and boundary conditions exactly and employs penalized least squares to estimate the coefficients. To ensure fairness across paradigms, we introduce a degrees-of-freedom (DoF) matching protocol. Under matched DoF, B-EPGP consistently attains lower space-time $L^2$-error and maximum-in-time $L^{2}$-error in space than CN-FEM, improving accuracy by roughly two orders of magnitude.

Time series forecasting is essential across domains from finance to supply chain management. This paper introduces ForecastGAN, a novel decomposition based adversarial framework addressing limitations in existing approaches for multi-horizon predictions. Although transformer models excel in long-term forecasting, they often underperform in short-term scenarios and typically ignore categorical features. ForecastGAN operates through three integrated modules: a Decomposition Module that extracts seasonality and trend components; a Model Selection Module that identifies optimal neural network configurations based on forecasting horizon; and an Adversarial Training Module that enhances prediction robustness through Conditional Generative Adversarial Network training. Unlike conventional approaches, ForecastGAN effectively integrates both numerical and categorical features. We validate our framework on eleven benchmark multivariate time series datasets that span various forecasting horizons. The results show that ForecastGAN consistently outperforms state-of-the-art transformer models for short-term forecasting while remaining competitive for long-term horizons. This research establishes a more generalizable approach to time series forecasting that adapts to specific contexts while maintaining strong performance across diverse data characteristics without extensive hyperparameter tuning.

Bayesian experimental design (BED) provides a principled framework for optimizing data collection, but existing approaches do not apply to crucial real-world settings such as dynamical systems with partial observability, where only noisy and incomplete observations are available. These systems are naturally modeled as state-space models (SSMs), where latent states mediate the link between parameters and data, making the likelihood -- and thus information-theoretic objectives like the expected information gain (EIG) -- intractable. In addition, the dynamical nature of the system requires online algorithms that update posterior distributions and select designs sequentially in a computationally efficient manner. We address these challenges by deriving new estimators of the EIG and its gradient that explicitly marginalize latent states, enabling scalable stochastic optimization in nonlinear SSMs. Our approach leverages nested particle filters (NPFs) for efficient online inference with convergence guarantees. Applications to realistic models, such as the susceptible-infected-recovered (SIR) and a moving source location task, show that our framework successfully handles both partial observability and online computation.

In fact, low-rank approximations are a central tool in data analysis, being equivalent to linear dimensionality reductions techniques, with PCA and the truncated SVD as the workhorse approaches [60, 59, 45]. However, due to the sheer number of possible such decompositions, the information provided is hardly interpretable. This motivated researchers to introduce more constrained low-rank approximations. Among them, nonnegative matrix factorization (NMF) focuses on nonnegative input matrices X and imposes the factors, W and H, to be nonnegative entry-wise. Nonnegativity is motivated by physical constraints, such as nonnegative sources and activations in hyperspectral imaging [9], chemometrics [15] and audio source separation [52], and by probabilistic modeling, such as topic modeling [39, 3] and unmixing of independent distributions [38]. Moreover, NMF leads to an easily-interpretable and part-based representation of the data [39]. See also [13, 19, 25] and the references therein.

Conformal prediction has emerged as a powerful framework for constructing distribution-free prediction sets with guaranteed coverage assuming only the exchangeability assumption. However, this assumption is often violated in online environments where data distributions evolve over time. Several recent approaches have been proposed to address this limitation, but, typically, they slowly adapt to distribution shifts because they update predictions only in a forward manner, that is, they generate a prediction for a newly observed data point while previously computed predictions are not updated. In this paper, we propose a novel online conformal inference method with retrospective adjustment, which is designed to achieve faster adaptation to distributional shifts. Our method leverages regression approaches with efficient leave-one-out update formulas to retroactively adjust past predictions when new data arrive, thereby aligning the entire set of predictions with the most recent data distribution. Through extensive numerical studies performed on both synthetic and real-world data sets, we show that the proposed approach achieves faster coverage recalibration and improved statistical efficiency compared to existing online conformal prediction methods.

We introduce a density-power weighted variant for the Stein operator, called the $γ$-Stein operator. This is a novel class of operators derived from the $γ$-divergence, designed to build robust inference methods for unnormalized probability models. The operator's construction (weighting by the model density raised to a positive power $γ$ inherently down-weights the influence of outliers, providing a principled mechanism for robustness. Applying this operator yields a robust generalization of score matching that retains the crucial property of being independent of the model's normalizing constant. We extend this framework to develop two key applications: the $γ$-kernelized Stein discrepancy for robust goodness-of-fit testing, and $γ$-Stein variational gradient descent for robust Bayesian posterior approximation. Empirical results on contaminated Gaussian and quartic potential models show our methods significantly outperform standard baselines in both robustness and statistical efficiency.