Papers

We introduce a physically grounded framework for coordination in a population based on information constrained feedback in a partially observed stochastic dynamical system. Population size evolves as a continuous time birth death Markov process whose transition rates respond to a shared stochastic measurement signal correlated with the underlying population state. Individuals neither communicate directly nor optimise strategies; instead, coordination emerges from macro to micro feedback mediated by imperfect common information. We show that geometric Brownian motion arises as a limiting case of the conditional dynamics when measurement strength and population statistics satisfy suitable conditions. More generally, varying the signal to noise properties of the measurement channel produces a wider class of stochastic growth processes, including diffusive and jump like regimes, even though ensemble average growth remains exponential. In an appropriate limit the framework recovers the stochastic multiplicative growth model of Peters and Adamou, providing a physical interpretation of coordination as inference and feedback under partial observability.

Modeling non-stationary stochastic systems requires balancing the representational capacity of deep learning with the structural transparency of classical probabilistic models. Markov transition matrices provide such a framework, but traditional frequency-based estimation collapses at high resolutions due to data sparsity. We propose a hybrid approach that parameterizes the manifold of stochastic matrices through a neural network, enabling estimation of time-inhomogeneous Markov chains in sparse-data regimes, and use financial markets as a testbed to investigate the Markov state variable as a critical inductive bias. We show that conditioning on realized volatility produces a more internally consistent Markovian structure than return-based states, achieving a $5.6\%$ reduction in Chapman-Kolmogorov discrepancy and superior held-out likelihood in 9 of 10 assets. Unlike black-box sequence models, our approach generates explicit matrices amenable to direct geometric analysis, surfacing structural findings such as the universal homogenization of transition probabilities under high-volatility regimes.

We study the problem of learning Gaussian mixture models under overparameterization. Prior work has shown that while overparameterization is essential for avoiding spurious local optima and enables global recovery of the ground-truth model using the gradient-EM (expectation-maximization) algorithm, it can dramatically slow down the local rate of convergence. Under certain assumptions on the mixture weights, we show that a standard divergence measure minimized by statistical learning procedures possesses a manifold of slow growth on which the well-known Polyak stepsize reduces the loss geometrically, and design a gradient-based method that converges to minimizers at a locally linear rate. Additionally, we show that our method converges to nearly optimal solutions – up to a natural misspecification threshold – for mixtures with arbitrary weights. At a high level, the method alternates between several "short" gradient descent steps that approach the manifold and "long" Polyak steps that contract the distance to minimizers. Our results suggest that slow convergence is not an intrinsic challenge of overparameterization, but can be overcome by exploiting the favorable structure of the loss landscape.

A central aim of deep learning theory is to characterize how neural networks make predictions in the regime of simultaneously large model and training set size. Since the limits of diverging number of model parameters and dataset size do not commute it is not clear a priori what limits exist. In this work, we shed new light on these questions by studying Bayesian inference in deep non-linear MLPs in the regime where the number of training samples ($P$), the input dimension ($N_0$), the hidden layer width ($N$), and the number of hidden layers ($L$) can all be large. We build on the Neural Covariance SDE (Li et al., 2022) to analyze predictive posteriors in the regime where $LP/N\in\Theta(1)$, playing the role of an effective network depth. Our framework covers both smooth and ReLU activation functions and applies to arbitrary temperature. We find to first order in $LP/N$ a simple criterion for which data generating processes benefit from depth in the sense that larger $LP/N$ increases the Bayesian model evidence. We also give a novel derivation of a prior result from the physics literature that at least to first order in $LP/N$, the Bayesian predictive posterior is remarkably simple and is simply equivalent to that of a data-dependent kernel method.

Fine-tuning is often believed to reduce uncertainty and diversity in large language models, but existing analyses overlook output length, a key confounder, and therefore fail to capture how uncertainty is distributed across an entire generation rollout. To address this, we propose Canopy Entropy ($\mathrm{CE}^\star$), a measure that views language generation from a tree perspective, where “canopy” represents the space of all possible rollouts, making $\mathrm{CE}^\star$ naturally quantify the effective size of the generation space. $\mathrm{CE}^\star$ jointly captures uncertainty in both the output length $N$ and the generated sequence $Y_{1:N}$ – indeed, we show that it equals to total Shannon entropy $H(N, Y_{1:N}\mid X)$, where $X$ denotes the prompt. This formulation yields interpretable metrics, including a length-entropy correlation term $\rho(N, r_N)$, where $r_N$ is the entropy rate, quantifying information conveyance efficiency by indicating whether longer outputs are more or less informative per token. Empirically, across tasks and model families, we find that fine-tuned models consistently exhibit stronger positive correlation $\rho(N, r_N)$, even when total entropy decreases. Furthermore, after controlling for model family, task, prompt, and output-length effects, we find that fine-tuning nearly triples the correlation strength between entropy rate and semantic diversity, suggesting that aligned models convert token uncertainty into semantic diversity more efficiently. Overall, these results demonstrate that fine-tuning does not simply reduce uncertainty, but fundamentally reorganizes it into more informative and semantically meaningful generations. Our code is available at https://github.com/WeiyiTian/canopy-entropy.

Unlearning in diffusion models aims to remove undesirable data or concepts while preserving the utility of pretrained models – two fundamentally conflicting objectives. We propose a principled constrained optimization framework that formulates unlearning as minimizing the deviation from a pretrained model, subject to explicit separation constraints from the unlearning distributions. Specifically, we formulate three constrained optimization problems based on reverse and forward KL divergences, and likelihood constraints. The first two generalize existing approaches for concept and data unlearning, while the third offers a novel and natural formulation for unlearning. Despite the nonconvexity of the KL constraints, we establish strong duality for all three problems, enabling us to explicitly characterize their optimal solutions as unlearning targets and develop primal-dual algorithms for each formulation. Experimental results demonstrate that our KL-constrained approach achieves superior retention-unlearning tradeoffs compared to weight-based baselines for concept and data unlearning, and that our likelihood-based approach matches unlearning effectiveness while better preserving retained concepts compared to baselines.

A Brain-Computer Interface (BCI) speller systems based on Event-Related Potentials (ERPs) enables users to select characters by detecting brain responses to visual stimuli, recorded through electroencephalogram (EEG). One challenge is to accurately identify target-related responses, such as the P300 component. However, existing methods tend to ignore feature selection, perform feature selection without interpretability, or require large computational effort or data manipulation. To address these limitations, we propose a novel Bayesian generative modeling framework to the binary classification of EEG responses to stimuli. Our approach employs a Probit-link Split-and-merge Gaussian Process (P-SMGP) prior to perform spatial-temporal feature selection, effectively capturing the distinctions between target and non-target ERP responses. Through both simulation studies and real EEG data analysis, our approach provides statistical interpretations on transformed ERP functions while maintaining comparable prediction accuracy with a computationally motivated design. These findings underscore the value of interpretable, stimulus-level modeling for advancing predictive and personalized BCI systems.

Epistemic uncertainty quantification (UQ) for deep neural networks (DNNs) is a requirement for safe adoption of AI in mission-critical settings. Several leading methods for UQ linearize DNNs to form Bayesian Generalized Linear Models (GLMs), where epistemic uncertainty is modeled via the predictive posterior distribution. Linearizing around the parameters of the final connected layer of a DNN is a commonly used approximation for reducing the computational burden of such GLMs, though it is often believed to come at the cost of degraded performance. In this work, we compare GLMs arising from full-network and last-layer linearization using both theoretical and empirical approaches. We first employ tools from random matrix theory to conduct a theoretical comparison; this analysis reveals no meaningful improvement in the UQ capabilities of full linearization. Coupled with a large-scale empirical evaluation across a range of modern machine learning tasks, we arrive at the following conclusion: a last-layer approximation yields comparable UQ performance while offering substantially improved computational efficiency.

We propose CerT-MCMC, a framework that equips learned-transport Markov chain Monte Carlo with automatic, rigorous convergence certificates. A normalising flow maps a Gaussian reference to an approximation of the target posterior; the same flow then serves as both the independence Metropolis-Hastings proposal and the basis for a computable spectral-gap bound. We develop two complementary certificates. The covering certificate bounds the weight-ratio oscillation over the full proposal support via finite-sample covering arguments, yielding full-support spectral-gap bounds when a conservative gradient bound is available; its correction term scales as O(n^{-1/D}), making it rapidly weak and eventually vacuous as dimension increases. We prove a matching Omega(n^{-1/D}) lower bound, establishing that this barrier is intrinsic to pointwise Lipschitz certification. The quantile-core certificate restricts attention to a high-probability residual core on which the oscillation is controlled by one-dimensional empirical quantiles, with a finite-sample probability slack of O(n^{-1/2}), independent of the ambient dimension. On synthetic targets (D=2-20), structural-engineering posteriors (D=6,8), real-data logistic regression on the Heart Disease data set (D=13), and synthetic Bayesian logistic regression (D=20), the quantile-core certificate delivers non-vacuous spectral-gap bounds where the covering certificate is vacuous, and its spectral-gap proxy tracks empirical effective sample sizes within 7%. A negative control experiment confirms that the certificate discriminates flow quality by a factor exceeding 10x, whereas acceptance rates differ by only 1.15x. To our knowledge, the dual-certificate framework is the first to provide automatic, dimension-aware convergence certificates for learned-transport MCMC, distinguishing genuine transport failure from proof-technique limitations.

Forecasting agricultural commodity prices in emerging economies is difficult due to high volatility, frequent supply disruptions, and strong cultural influences on demand. This study introduces the Kalimati Vegetable Price Index (KVPI), a new inverse-volatility weighted composite index that aggregates 135 daily wholesale commodities from Kathmandu over ten years (2013-2023). By creating a stable macro-level signal, the KVPI reduces the noise inherent in modelling individual crops. A rich set of 64 causally valid features was developed, including festival lead-lag effects, rolling statistics, and calendar variables. Fourteen forecasting models spanning statistical, tree-based, deep learning, hybrid, and transformer architectures were rigorously evaluated across short (7-day), medium (14- and 30-day), and long-term (90-day) horizons. Tree-based ensembles proved notably robust, while classical statistical models and complex transformers struggled with the noisy dataset. The proposed Momentum-Corrected Online Stacking Ensemble achieved the strongest performance, yielding a Root Mean Square Error (RMSE) of 1.771, an exceptionally low Mean Absolute Percentage Error (MAPE) of 0.68%, and explaining 84.5% of the variance (R-squared = 0.845) at the 90-day horizon. This open-source pipeline provides policymakers and supply chain actors in Nepal and similar markets with a practical, reliable tool for anticipating price movements and strengthening food security.

Topic models are often used as dimension-reduction tools before regression, with estimated document-level topic shares treated as observed covariates. This plug-in workflow creates two inferential difficulties: valid inference requires a regular first-stage-to-second-stage expansion that propagates topic-estimation uncertainty, and, at fixed document length, a document's topic mixture cannot be consistently recovered from its own words even when the population topic matrix is known. Corrected spectral moment methods for latent Dirichlet allocation (LDA) offer a starting point: when the total Dirichlet concentration is known, low-order word moments can be corrected to yield operators diagonal in the latent topic basis. We extend this to downstream regression. Under a finite LDA model with response residuals orthogonal to the low-order token moments used for identification, response-weighted word moments admit the same correction, and the resulting supervised operator identifies the regression coefficient $\beta$ directly, without estimating document-level topic shares. The main obstacle is that the correction depends on the unknown total concentration $\alpha_0$. We show that, for $k\ge3$ topics and under a generic finite-probe condition, $\alpha_0$ is identified by commutativity: at the true value a family of corrected word-moment operators commute, whereas away from it they generically do not. This yields a feasible estimator and lets uncertainty in $\hat\alpha_0$ propagate into inference for $\beta$. The estimator is asymptotically linear as the number of documents grows with fixed document length, with sandwich standard errors from document-level moment contributions. Simulations show near-nominal coverage where plug-in topic-share regressions can undercover, and an application to top economics journals illustrates contrast inference for latent topic effects.

Agentic LLMs must continuously decide whether newly extracted facts should be added, merged with existing memories, or ignored, yet prior work has focused more on retrieval and storage than on principled write-side control. We frame memory evolution as a novelty-detection problem and propose SAGE, a Spherical Adaptive Gate for memory Evolution that scores candidate facts with a von Mises-Fisher-based density estimator over memory embeddings and routes them with an adaptive threshold that tracks memory-store geometry. SAGE resolves clearly novel facts as ADD, clearly redundant facts as NOOP, and sends only uncertain cases to an LLM merge step, reducing expensive write-time reasoning. On LoCoMo, SAGE achieves the best average token-F1 against Mem0 on all seven open-weight backbone comparisons, while on GPT-4o-mini it reduces add-phase API cost by 3.4$\times$ and add-phase latency by 2.5$\times$ with only a small average judge-score gap. As a drop-in binary gate for A-Mem, SAGE skips roughly 16-18% of LLM calls across five models with minimal quality change on open-weight backbones. These results suggest that novelty-aware write control is a practical lever for improving both memory quality and system efficiency in long-term agentic memory. The source code for our approach is accessible at https://github.com/swang1024/SAGE.

Bayesian multidimensional scaling (BMDS) embeds $n$ objects in a low-dimensional space to approximately preserve an observed dissimilarity matrix. Compared to classic MDS, BMDS is more robust to model misspecification and supports posterior uncertainty quantification and joint estimation within hierarchical models. However, standard BMDS inference is computationally prohibitive, requiring $O(n^2)$ operations per MCMC iteration to evaluate the likelihood. We propose Barnes–Hut BMDS (BH-BMDS), which uses a tree-based approximation to the likelihood and a Gibbs sampler that leverages this structure, remaining compatible with hierarchical extensions. BH-BMDS reduces computational complexity to $O(n \log n)$ while preserving the geometric fidelity of the embedding. We further establish consistency for the stationary measure of BH-BMDS, proving that it concentrates around the true latent configuration even as the total error of the surrogate likelihood diverges. Notably, this consistency holds in the infinite-dimensional limit. We evaluate the approximation on datasets with diverse structure, including air traffic networks, arXiv abstracts, MNIST images and neural activity recordings from mouse models of tau pathology. Across all settings, BH-BMDS closely matches BMDS while achieving substantial computational gains, with approximately 10-fold speedups at $n=1{,}000$ and 70-fold speedups at $n=10{,}000$. These gains increase with $n$, demonstrating strong empirical scalability.

Subsampling-based Markov chain Monte Carlo (MCMC) algorithms aim to accelerate Bayesian inference by evaluating the likelihood using only a subset of the data at each iteration. However, in many standard tall-data applications, individual likelihood contributions are inexpensive to evaluate and the resulting reductions in actual computing time are often substantially smaller than the nominal reduction in data size due to computational overhead. We study a different computational regime arising in frequency-domain inference for continuous-time processes observed at equally spaced discrete time points. This gives rise to aliasing, whereby each contribution to the Whittle likelihood requires summation over shifted frequency components, unlike standard discrete-time spectral settings where spectral evaluations do not require such summation. We demonstrate that this structure makes subsampling MCMC, a subsampling-based MCMC approach that estimates the log-likelihood using data subsampling and efficient control variates, particularly effective for reducing computational cost. We illustrate the approach for Bayesian frequency-domain inference in discretely observed continuous-time autoregressive moving average models driven by finite second-moment Lévy processes.

This study introduces SEGOMOE, a Bayesian optimization tool for optimizing complex, computationally expensive systems, especially in aeronautics. It efficiently handles mixed design variables (continuous, discrete, categorical, hierarchical) using adaptive Gaussian process models. SEGOMOE combines expert models to address nonlinearities in objectives and constraints, leveraging the open-source Surrogate Modeling Toolbox (SMT). The tool supports multi-fidelity data and solves both single- and multi-objective problems, including hidden constraints and high-dimensional decomposition. Validated through benchmarks and real-world aeronautical applications, SEGOMOE proves to be robust and versatile for tackling multidisciplinary challenges.

Each year the American Statistical Association (ASA) hosts the Annual Data Challenge Expo, which tasks participants with analyzing a given dataset and presenting their work at the Joint Statistical Meeting (JSM). The 2025 Data Challenge Expo tasked participants with analyzing over 35 years of commercial flight data from the United States Bureau of Transportation Statistics (BTS). These data provide extensive geographic coverage and operational details for the U.S. domestic aviation market. For millions of past flights, there is information about the flight's date, origin, destination, carrier, plane, departure, and arrival. In this article, we present our analysis for the 2025 JSM Data Challenge Expo. We chose to explore patterns in the daily scheduling of departures and arrivals across airlines, airports, and time. In doing so, we observed distinct scheduling “waves”, or periodic structures at major airline hubs as well as large Federal Aviation Administration (FAA) hubs. In the remainder of this article, we detail the process of visualizing periodicity in flight scheduling as well as quantifying it through the calculation of Shannon entropy. An additional element to the 2025 Data Challenge Expo is the incorporation of a second dataset, to be decided by the participants. We detail the use of a BTS dataset with passenger enplanement (boarding) information to determine Federal Aviation Administration (FAA) hub classification (as opposed to airline-specific hubs). Furthermore, we discuss results from this visual and quantitative analysis, highlighting noticeable differences in the scheduling periodicity and entropy across airports, for the “big four” or four largest carriers, in U.S. aviation: American Airlines, Delta Air Lines, United Airlines, and Southwest Airlines.

Motivated by a high-dimensional regression problem in spatial multimodal omics (SMO), we propose a Bayesian framework for local spatial feature selection, where a random domain partition prior is introduced to divide the spatial domain into several contiguous clusters with flexible shapes and an unknown number of clusters, conditional on which a local feature selection prior is imposed within each cluster. The notion of "feature" is general and may include both covariates and functional bases, allowing the framework to perform both local variable selection and local basis selection, the latter being essential for adaptively approximating spatially varying functions with localized characteristics. We derive coupled hyperparameter conditions linking domain partition and local feature selection priors, under which the consistency theory and posterior contraction rates of both the domain partition and feature selection are established. We develop an efficient informed reversible jump Markov chain Monte Carlo algorithm to address the computational challenges encountered in joint posterior sampling of domain partitions and selected features. Simulation studies demonstrate the effectiveness of the proposed model and algorithm, highlighting its advantages over existing methods. The application of our model to an SMO dataset reveals biologically meaningful spatial patterns within breast cancer tissue.

We study high-dimensional inference problems with tensor-structured data and establish conditions under which their free energy can be approximated by that of a Gaussian comparison model. Our framework applies to models with independent observations and mismatch between the data-generating distribution and the statistical model. The results extend prior work beyond matrix settings and accommodate scaling regimes where the model parameters depend on the dimension. A key technical contribution is the use of generic chaining to control remainder terms arising from likelihood expansions over tensor-structured parameter spaces. As an application, we establish free energy universality for binary hypergraph models under the minimal assumption of diverging average degree, showing that their asymptotic behavior coincides with that of a Gaussian tensor model, even under model mismatch.

Inferring continuous probability paths from sparse snapshots is a fundamental challenge in domains like single-cell biology, where high-fidelity data acquisition is often destructive and constrained by prohibitive sequencing costs. This motivates the need for active learning strategies to strategically select optimal measurement times. However, designing active learning policies for this setting remains an open problem: the target objects reside on the infinite dimensional Wasserstein space where standard Euclidean metrics are ill-defined, and current interpolation methods lack epistemic uncertainty quantification. We introduce a framework which extends active experimentation to the space of measures. By leveraging Linearized Optimal Transport (LOT), we map distributional snapshots into a tangent space amenable to Gaussian Process modeling, allowing us to construct a tractable probabilistic surrogate for the underlying probability path. This yields an acquisition policy that iteratively selects measurement times to minimize uncertainty. Empirical results demonstrate that our strategy outperforms uncertainty-agnostic baselines on both synthetic and real-world datasets.

Computational cardiovascular flow models are highly sensitive to prescribed inlet velocity profiles. While imaging-derived velocity fields provide physiologically realistic information, they can introduce increased preprocessing complexity, imaging noise, and computational burden. Simplified analytical formulations are computationally efficient but may not fully capture subject-specific flow characteristics. In this study, we present an uncertainty-aware framework that combines two-dimensional phase-contrast magnetic resonance imaging (2D PC-MRI) with mechanistic velocity-profile formulations to generate subject-specific pulmonary artery velocity representations. Imaging-derived radial velocity distributions were constructed from main pulmonary artery (MPA) PC-MRI data in canine and swine subjects using elliptical radial binning and normalization. Power-law and Womersley velocity-profile formulations were fitted within a Bayesian inference framework while accounting for uncertainty associated with imaging measurements and model representation. The two formulations were compared using regional and global weighted root mean square error (wRMSE) metrics. Both models demonstrated close agreement with the imaging-derived velocity profiles across subjects. Although the Womersley formulation provided greater flexibility near the vessel wall, it did not result in statistically significant improvements in fitting performance compared with the simpler power-law model. The proposed framework provides low-dimensional, physiologically interpretable, and uncertainty-aware velocity-profile representations that may serve as computationally efficient alternatives for subject-specific cardiovascular flow modeling.

Best-of-$N$ sampling is widely used to construct pairwise preference data: $N$ candidates are drawn from a base distribution, and the best is paired with a rejected response. Despite its widespread use, what Bradley–Terry (BT) reward learning extracts from such data, and how to choose $N$ and the base distribution, remain unclear. We specialize a recent analysis of preference data via its induced conditional distribution to Best-of-$N$. For independent-reference variants, we derive closed-form reward targets as explicit functions of $N$ and the base distribution, and show that they preserve the latent reward ranking. For the practical Best-vs-Random and Best-vs-Worst variants, chosen and rejected responses are coupled through the same candidate set, so exact BT representability generally fails; nevertheless, bounded-class minimizers approach the reference targets as $N$ grows. Although margin and connectivity are known to govern sample efficiency in pairwise preference learning, Best-of-$N$ couples them through $N$ in opposing directions: larger $N$ widens pairwise margins but reduces connectivity. This trade-off yields two design principles: use larger $N$ when preference labels are the bottleneck, smaller $N$ when generation is the bottleneck; and shape the base distribution to place mass between the responses whose comparison matters most at test time. Experiments on synthetic and real preference data support the predicted dependence on sample size and base-distribution shape.

This paper develops a regression framework for analyzing integrated conditional distribution and quantile functions. The proposed method, termed rectified linear unit (ReLU) regression, projects the ReLU-transformed outcome onto covariates and admits a closed-form estimator. Its population regression function is the best linear approximation to the integrated conditional distribution function of the outcome, and the corresponding convex conjugate, obtained via the Legendre-Fenchel transform, approximates the integrated conditional quantile function. Both the regression and its conjugate require only mild distributional assumptions and accommodate non-continuous outcomes. We establish the asymptotic distribution of the estimator and develop inference for the conjugate functional via the delta method for Hadamard directionally differentiable maps. Building on these results, we establish identification and inference for average quantile treatment effects over arbitrary subintervals of probability levels. This broadens the set of distributional parameters available to empirical work.

School gun violence in the United States is a complex phenomenon spanning social, epidemiological, demographic, and political dimensions. It remains unclear where incidents are unusually concentrated nationally after accounting for the distribution and characteristics of schools. Using a newly linked case-control dataset comprising 959 gun-violence incidents at public K-12 schools in the contiguous United States during 2000-2024, we develop a semiparametric kernel-regression framework combining school-level predictors with spatial and continuously evolving spatio-temporal residual structure. Fisher-weighted orthogonalisation defines how predictor-aligned variation is allocated between fixed and smooth components, while repeated control sampling and Monte Carlo reassignment support stable mapping and local exceedance assessment. The models identify stable school-level associations, including substantially higher adjusted odds for larger, middle, and high schools, while revealing residual structure beyond the background distribution of schools. Elevated residual odds become concentrated in a broad central-eastern corridor from the mid-2010s onward, with the strongest evidence in recent years. The analysis offers both statistical and application-specific insights. Statistically, it shows how covariate-adjusted residual surfaces can characterise local departures in case-control processes evolving over space and time. For the application, it provides epidemiological clues identifying regions in which broader social, policy, and environmental conditions may warrant targeted investigation.

High-throughput sequencing technologies have enabled the collection of large-scale longitudinal -omics data, providing new opportunities for studying co-expression networks among molecular nodes such as genes and proteins. However, the high dimensionality and temporal dependence inherent in such data require specialized statistical methods. We propose a novel approach to infer dynamic co-expression networks among features over time (DCENt), where each node (feature) is modeled with a mixed-effects model, and dependencies among nodes are captured through correlated random effects. We develop two innovative penalized algorithms which harness the state of the art of threshold covariance estimators to estimate the random-effects covariance structure. Simulation studies show improved performance over existing approaches in terms of both mean square error and mean absolute error. We further apply the methods to data from the CARDIA study to investigate how the protein co-expression networks evolve over time as well as the association between protein trajectory patterns.

We study true self-avoiding walk (TSAW) as a mechanism for improving empirical integral estimation via Markov chain Monte Carlo (MCMC). We consider finite-state adaptive sampling dynamics associated with an irreducible Markov kernel $P$ on a finite set, with stationary distribution $\pi$, in which the transition probabilities are penalized according to empirical overuse. Our main result is that the empirical occupation counts $L_t(i)$ and transition counts $N_t(i,j)$ of the resulting TSAW-based walk satisfy \[ L_t(i)-t\pi_i = O(\sqrt{\log t}) \quad\text{and}\quad N_t(i,j)-t\pi_iP_{ij}=O(\sqrt{\log t}) \qquad\text{almost surely} \] for every state $i$ and every edge $(i,j)$ with $P_{ij}>0$. Consequently, for every bounded function $f:V\to\mathbb R$, the error of our integral estimator converges as \[ \left|\frac1t\sum_{s=0}^{t-1} f(X_s)-\sum_{i\in V}\pi_i f(i)\right| = O\left(\frac{\sqrt{\log t}}{t}\right) \qquad\text{almost surely}. \] These results show that, in contrast with the usual $t^{-1/2}$ error scaling for empirical averages under standard random-walk-based methods, TSAW-based estimator yields empirical integral errors of order $O(\sqrt{\log t}/t)$ almost surely, thereby achieving a substantially sharper dependence on the sample size $t$.

This paper introduces software implemented in the mets R-package for calculating non-parametric and regression estimates of Restricted Mean Survival Time (RMST) and Restricted Mean Time Lost (RMTL), including RMTL due to specific causes. A unique feature is the ability to compute the non-parametric estimates of RMST and RMTL, as well as their standard errors, for all time horizons simultaneously. Regression modeling in mets is based on Inverse Probability of Censoring Weighting (IPCW) methods. The package implements different versions of IPCW adjusted estimating equations. A critical technical contribution is the provision of influence functions for all models, which enables the computation of standard errors and allows the estimates to be used as building blocks for more complex statistics, such as the while-alive estimate in recurrent events settings. To expand capabilities in causal inference, the mets package also implements methods for standardization estimates (G-computation) and the estimation of Average Treatment Effects (ATE) for both RMST and RMTL in the competing risks setting. Importantly, the computations scale linearly with the number of observations, making the software efficient for use with large datasets.

Simulation-based inference (SBI) has become an increasingly important framework for parameter estimation in models for which simulation is feasible, including cases where likelihood evaluation is unavailable or costly. While recent work has introduced benchmark frameworks to compare likelihood-free methods, these studies often do not account for structural features such as heavy-tails or discreteness. In this article, we investigate how the performance of likelihood-free inference methods depends on these structural properties. We consider four approaches: MLE, NBE, EOT and AW–NBE and evaluate them using simulations. This study highlights the importance of carefully selecting evaluation tools in the presence of extremes and discrete data.

We present improved bounds for estimating discrete probability distributions under the $\ell_\infty$ norm. These include minimax bounds in expectation and high-probability tail bounds. We resolve some of the open questions posed in Kontorovich and Painsky (JMLR, 2025) – including a fully empirical version of the tightest risk bound they presented and identifying the form of the worst-case extremal distribution. Encouraging empirical results are reported as well.

Learning to reach arbitrary goals from sparse feedback requires agents to infer a rich notion of reachability across state–goal pairs. Goal-conditioned reinforcement learning (GCRL) tackles this challenge by learning policies that generalize across goals, but this generalization becomes increasingly difficult as the underlying dynamics become high-dimensional, hybrid, or contact-dependent. To address this issue, physics-informed GCRL (Pi-GCRL) introduces optimal-control-inspired inductive biases into goal-conditioned value learning. While Pi-GCRL methods have proven effective in navigation and object-free goal-reaching domains, their reliability in contact-rich tasks remains unclear, where contact interactions induce hybrid dynamics, mode-dependent controllability, and nonsmooth value landscapes. In this work, we show that these structural properties can cause existing Pi-GCRL methods to degrade when applied naively to contact-rich manipulation. Motivated by this analysis, we introduce contact-aware and hierarchical formulations that apply physics-informed inductive biases selectively across the manipulation problem. Our results provide a principled step toward extending Pi-GCRL to contact-rich manipulation.

We provide analysis for the posterior distribution and expectation of $(p_1, p_2)$ where $Y|p_1,p_2 \sim \hbox{Binomial}(n, p_1 p_2)$ and $ (p_1, p_2)$ is uniformly distributed on the unit square $[0,1]^2$. We exhibit interesting expressions in terms of a truncated Beta distribution, a finite mixture of Beta distributions and harmonic numbers, and derive a simple large sample size $n$ approximation for the posterior expectations $\mathbb{E}(p_i|y)$ as well as for the normalization constant in the posterior joint density.