Papers

We connect stochastic resetting from non-equilibrium statistical physics with ridge regularization in statistical learning. For linear gradient flow, resetting to the origin at rate $r$ produces stationary mean $(X^\top X+rI)^{-1}X^\top y$, exactly the ridge estimator with penalty $\lambda=r$. This uses the known Laplace-transform relationship between ridge regression and exponential-time averaging of gradient flow, with the exponential time now interpreted as the stationary age associated with Poisson resetting. We then extend this identity to general renewal reset laws: the exponential reset time distribution is the unique renewal law whose stationary mean reproduces scalar ridge in every eigendirection as an exact filter identity for every positive curvature, while non-exponential renewal laws generate alternative spectral filters. At the fluctuation level, we study a separate additive Ornstein-Uhlenbeck extension with constant diffusion, interpreted as a stylized SGD approximation. In this setting, the equality holds only at the level of the mean, since the reset process has a nonzero stationary covariance from accumulated OU noise and reset-timing variance, whereas deterministic ridge is a fixed estimator with the same center. Stylized experiments compare the deterministic renewal-induced filters directly and illustrate when filters induced by non-exponential reset-time laws can differ predictively from ridge. The results for the stationary mean and the induced spectral filters are established for continuous-time gradient flow with isotropic resetting on quadratic objectives; the covariance and risk formulas additionally assume additive noise with state-independent covariance.

Importance sampling (IS) consists in biasing samples from a distribution $f$ towards another distribution $g$. Concretely, given samples $X_i$ from $f$, the IS measure is $$\hat{g}_n = \frac{1}{Z_n}\sum_{i=1}^n \frac{g(X_i)}{f(X_i)} \delta_{X_i},$$ with $Z_n = \sum_{i=1}^n \frac{g(X_i)}{f(X_i)}$. The random measure $\hat{g}_n$ approximates $g$, and is used in many contexts ranging from Monte Carlo integration to Bayesian inference. We show that, in high dimension ($d \geqslant 3$), the Wasserstein cost $W_p^p(\hat{g}_n, g)$ has order $n^{-p/d}$ in expectation, i.e. $$\beta^{\mathrm{low}}_{p,d}\int gf^{-p/d}\leqslant \liminf_{n \to \infty} n^{p/d} \mathbb{E}[W_p^p(\hat{g}_n, g)] \leqslant \limsup_{n \to \infty} n^{p/d} \mathbb{E}[W_p^p(\hat{g}_n, g)] \leqslant\beta_{p,d} \int g f^{-p/d}$$ where $0<\beta^{\mathrm{low}}_{p,d}\leqslant \beta_{p,d}$ are constants depending only on $p$ and $d$, which are equal for $p=2$ and conjectured to be equal for any $p\geqslant 1$. Our results are valid for all $p\geqslant 1$ and $d\geqslant 3$. In the case where $\beta^{\mathrm{low}}_{p,d} = \beta_{p,d}$, we show that the asymptotically optimal sampling distribution $f^*$ for importance sampling is not equal to $g$ but to a tempered version of $g$, namely $f^* \propto g^{d/(p+d)}$, which is reminiscent of Zador's theorem in the domain of measure quantization.

Contact (or mixing, or more generally connectivity) matrices are a fundamental component of modelling and inference for infectious disease epidemiology. Their structure and parametrisation directly accounts for the frequency of interactions between different subpopulations of individuals, as well as having the potential to encode dynamic heterogeneity in these interactions across demographic axes, space and time. Considerable research has been devoted to the structure and estimation of (components of) these matrices to help inform outbreak control and forecast disease spread. In this paper, we review the existing literature on the data types used to construct contact matrices and the methods for incorporating uncertainties and heterogeneities into them. We also highlight remaining challenges and future directions in the use of these contact matrices for epidemiological research.

We develop dimension-reduction-free tests for the slope function in functional linear regression when the functional regressor may be endogenous or measured with error. The tests are based on a functional moment condition induced by an auxiliary functional variable and do not require estimation of the slope function, providing a functional analogue of Anderson–Rubin-type moment testing. They remain asymptotically valid under weak or even failed relevance of the auxiliary variable: such relevance affects power, not size. The trade-off is that power is confined to alternatives detectable through the moment operator, a subspace we characterize explicitly. We establish the asymptotic null distribution, consistency against detectable alternatives, and local power under drifting alternatives. We also derive the locally optimal test within a class of weighted test statistics. Feasible critical values for implementation of the tests are obtained from data. Simulations show reliable size control and competitive power, including under weak relevance. We illustrate the method using a functional regression analysis of residential electricity demand and temperature distributions in South Korea.

This paper considers how to classify the effects of interventions in causal models for outcomes and exposures observed over time. First, we demonstrate the limitations of the most common uses of potential outcomes and causal directed acyclic graphs for capturing all possible interventions in a time varying framework, particularly in problems where the key question concerns interventions to maintain or change equilibrium behaviour. Second, we adopt a system and state based approach rather than a measurement-based approach to identify the causal parameters. In particular, we discuss how assumptions about the system's equilibrium and the effects of interventions on that equilibrium can allow for more specific causal interpretations and clarify the goals of design and analysis. Third, we show how the ability to identify the the causal parameters of a time varying system depends on the selection of timepoints for measuring the system's states. We address this by proposing a novel version of the null effect, which is designed to distinguish between transient and lasting causal effects.

Localization is essential in ensemble-based data assimilation because finite ensembles produce noisy covariance estimates, causing spurious updates and excessive loss of ensemble variance. In subsurface applications, localization is usually based on spatial distance, but this criterion can be hard to justify when parameter-data relationships are controlled by flow dynamics, nonlinear operators, non-local parameters, or prior conditioning effects. This work investigates correlation-based localization as an alternative strategy in which tapering coefficients are computed from the statistical reliability of estimated model-data correlations. We interpret localization as a shrinkage problem in correlation space and propose three tapers: a generalized power-law taper motivated by mean-square-error correction, a logistic taper derived from a Bayesian spike-and-slab formulation, and a discrepancy-based taper inspired by Morozov's principle. The tapers are evaluated using synthetic reservoir data assimilation problems involving scalar and grid-based parameters, localized flow responses, non-trivial correlation patterns, and increasing model dimension. The results show that correlation-based localization can suppress spurious correlations while preserving meaningful parameter-data relationships. In several cases, the proposed power-law and logistic tapers retained more posterior ensemble variance than distance-based localization while maintaining acceptable data-match quality. The logistic taper provided the strongest variance preservation, whereas smoother tapers favored better data matches. Overall, the results indicate that correlation-based localization is a statistically motivated alternative to distance-based localization, especially when spatial distance is unavailable or misleading.

Sparse recovery in linear systems underpins applications from signal processing to high-dimensional regression. Sparse Bayesian Learning, grounded in the principle of automatic relevance determination (ARD), offers a practical Bayesian mechanism for feature sparsity via marginal likelihood optimization. Yet, its reliance on a homoscedastic noise model renders it sensitive to data contaminations such as outliers or misspecified noise, harming model fit and predictions. Instead, we propose jointly learning individual feature and sample relevancies, enabling simultaneous model and data sparsification via a single Bayesian objective. This symmetric pruning of model and data offers a natural extension that preserves conjugacy, admits closed-form updates for standard optimization procedures, and aligns with perspectives from robust regression and influence functions. Empirical results across diverse regression tasks affirm that a joint ARD approach consistently yields both sparse and robust prediction models.

Modern statistical learning theory and deep learning characterize generalization primarily in terms of continuous capacity control (e.g., norm-based regularization, margin maximization, low-rank bias). While highly successful in continuous domains, deep learning consistently fails to extrapolate exact algorithmic or discrete algebraic rules, reflecting a missing inductive bias toward algorithmic complexity minimization. We propose the Cayley-table completion as the canonical testbed for this missing bias, serving as the discrete algebraic counterpart to matrix completion. Just as matrix factorization combined with weight decay yields an implicit geometric bias toward low linear rank, recent results demonstrate that operator-valued tensor factorizations paired with a flatness prior yield an implicit algorithmic bias toward exact discrete associativity. We pose the open problem of establishing formal exact recovery bounds for Cayley-table completion, and challenge the community to generalize continuous flatness priors to autonomously discover broader discrete algorithmic axioms without combinatorial search.

We introduce the Topological Stability Index (TSI), a variance-based scalar measure for persistence barcodes that quantifies the dispersion of persistence lifetimes. Unlike persistent entropy, which depends only on normalized weights, the TSI captures absolute variability and is sensitive to heterogeneous feature scales. We establish fundamental properties of the TSI, including its scaling behavior, invariance under lifetime translation and explicit update formulas under insertion and deletion of bars. We also consider a complementary first-moment-type quantity, the Topological Signal Index (TSigI), which captures the typical scale of persistence lifetimes and provides additional interpretability alongside the TSI. We further introduce a normalized version, $cv\text{TSI}$, which is scale invariant and admits an explicit algebraic relation to the Rényi entropy of order two. In particular, $cv\text{TSI}$ is an affine function of the collision probability $\sum_i p_i^2$, and therefore a monotone reparametrization of the Rényi entropy, providing a direct link between variance-based and entropy-based summaries in topological data analysis. Numerical experiments on synthetic data and stochastic time series demonstrate that the TSI captures structural variability complementary to entropy: it is relatively insensitive to deterministic trends, while responding strongly to stochastic fluctuations and variations in persistence magnitude.

Despite strong average-case performance, deep learning models often exhibit systematic errors on specific population groups, known as error slices. Identifying these groups and the root causes of their failures is critical for model debugging and bias mitigation. However, existing error Slice Discovery Methods (SDMs) typically generate explanations disconnected from the model's inference process, thus only approximating the underlying error source and may be inaccurate. We address this limitation by leveraging Concept Bottleneck Models (CBMs), whose predictions are directly dependent on human-understandable semantic concepts. Since downstream task failures in CBMs commonly arise from concept mispredictions, concept representations provide a strong candidate for error slice identification, offering fine-grained explanations directly linked to the error source. Building on this insight, we introduce CB-SLICE, a concept-based SDM that groups samples with shared concept prediction failures and identifies the keyword concepts most responsible for each slice's failure mode. Across multiple benchmarks, we show that CB-SLICE outperforms state-of-the-art methods in uncovering well-known biases while providing richer and more faithful explanations of model errors.

We introduce an Indian-buffet-type model for multi-factorial innovation in which each arriving agent may exhibit both previously observed and new features. The number of new features follows a power-law behavior, while the probability of selecting an old feature combines self-reinforcement, depending on the feature-specific popularity, with a mean-field interaction term depending on the average popularity of all observed features. The model is governed by the usual innovation parameters (mass, discount and concentration), together with two additional parameters: one controlling the strength of reinforcement against a forcing input toward zero, and one regulating the intensity of the mean-field interaction. Although the growth of the total number of distinct observed features has the same behavior as in the three-parameter Indian buffet process, the mean-field interaction mechanism produces new asymptotic regimes. For aggregate quantities, including the predictive mean, the averaged number of features per agent, the mean inclusion probability, and the mean feature popularity, the phase transition is determined by the comparison between the discount parameter and the weight of the forcing input. For feature-specific quantities, a further transition appears according to the comparison between the interaction level and a critical threshold. In particular, high interaction leads to an asymptotic synchronization of feature-specific inclusion probabilities. We establish strong laws and second-order asymptotic results, including central limit theorems in regimes where martingale fluctuations compete with deterministic or random terms. The analysis relies on novel general results for recursive stochastic dynamics, which may be useful beyond the present framework.

R. A. Fisher was one of the greatest scientists of the last century. He made many ground-breaking contributions, so many indeed that it seems almost impossible to list all of them. His revolutionary contributions to the design of experiments can mostly be traced to the early part of his academic career, and they are inextricably linked to his involvement with agricultural field experiments at Rothamsted Experiment Station. In this talk I will review Fisher's key ideas on experimental design and relate them to some of the work I am involved in, most of which directly focuses on field experiments in agriculture. Topics covered include systematic designs, row-column designs, augmented row-column designs, multi-environment trials, partially replicated designs, optimal allocation of trials to zones in sub-divided target populations of environments, and the connection of trialling systems across countries.

We study the Lipschitz bandit problem, where a learner sequentially maximizes an unknown Lipschitz function $f$ over a domain $\mathcal{X} \subset [0,1]^d$ using noisy pointwise evaluations. Existing regret bounds are either worst-case, scaling as $\tilde{\Theta} \left ( T^{d+1/d+2}\right )$, or adaptive via the zooming dimension $d_z$, yielding $\tilde{\Theta} \left ( T^{d_z+1/d_z+2}\right )$. However, such zooming-based guarantees are only partially instance-dependent, as they depend solely on the asymptotic growth of near-optimal level sets and fail to capture finer structural properties of $f$. We provide an analysis and an algorithm that characterizes the regret through integrals of the suboptimality gap of $f$ over its level sets. This yields regret bounds that adapt to the local growth of level sets, rather than only their asymptotic behavior. As a corollary, when the set of maximizers has dimension $d^\star>0$, we obtain improved adaptive rates of order $\tilde{\mathcal{O}} \left ( T^{d_z+1 / \max(d_z,d^\star)+2}\right )$ strictly improving over classical zooming bounds in this regime. Finally, we extend our analysis to the full-information setting (Lipschitz experts) and show how some of the regularity assumptions can be relaxed.

Starting from the exact Projected Central Limit Theorem on hyperspheres, we rederive the Beta distribution for subsystem occupation probabilities and Lubkin's purity formula from elementary hyperspherical moments, quantifying the finite-size “platykurtic” suppression of tails relative to the Gaussian approximation used in standard eigenstate-thermalization and typicality treatments. Our main new result concerns the bipartite quantum mutual information $\langle I(A{:}B)\rangle$ for Haar-random pure states. We show that its full asymptotic expansion in $1/N$ admits a Bernoulli-factorized form in which every order $k \ge 1$ carries the symmetric factor $(d_A^{2k}-1)(d_B^{2k}-1)$ and all higher odd-order corrections vanish identically. Through an exact algebraic reorganization of Page's formula (conjectured in Ref.~\cite{Page1993} and subsequently proven~\cite{Foong1994, SanchezRuiz1995, Sen1996}), we establish that the leading finite-size correction separates into a dominant $\mathfrak{su}(d_A) \otimes \mathfrak{su}(d_B)$ bipartite quantum coherence contribution $(d_A^2 - 1)(d_B^2 - 1)/(2N)$ and a subtracted classical-probability (Cartan $\otimes$ Cartan) contribution $(d_A - 1)(d_B - 1)/(2N)$, and we trace this separation to the difference between diagonal and eigenvalue entropies via Schur's majorisation theorem, with the dimensional counts $(d-1)$ and $(d^2-1)$ acquiring meaning through the Cartan structure of the generalised Bloch decomposition. These results admit a single non-perturbative closed form: the exact typical mutual information factors as $\langle I(A{:}B)\rangle = (d_A^2-1)(d_B^2-1)\,\mathcal{G}(d_A,d_B,d_E)$, with $\mathcal{G}$ given by an explicit Bose–Einstein integral whose asymptotic expansion in $1/N$ reproduces the Bernoulli series.

The average bipartite quantum mutual information $\langle I(A{:}B)\rangle$ of Haar-random pure states can be expressed exactly through Page's formula in terms of digamma functions. We show that this quantity admits a single non-perturbative closed form: $\langle I(A{:}B)\rangle = (d_A^2-1)(d_B^2-1)\,\mathcal{G}(d_A,d_B,d_E)$, where $\mathcal{G}$ is given by an explicit convergent integral over a Bose–Einstein kernel. The overall factor $(d_A^2-1)(d_B^2-1)=\dim[\mathfrak{su}(d_A)]\cdot\dim[\mathfrak{su}(d_B)]$ is exact, not merely asymptotic. The asymptotic expansion of $\mathcal{G}$ in $1/N$ yields a Bernoulli-factorised series whose coefficients involve $\zeta(1{-}2k)$; this series diverges, and our integral is its exact Borel sum. The integral representation also makes $\langle I\rangle < (d_A^2{-}1)(d_B^2{-}1)/(2N)$ manifest via a scale-inversion symmetry of the kernel. Our derivation traces the mutual information's structure to an exact decomposition of Page's entropy into a diagonal (Dirichlet) contribution and a Schur-majorisation eigenvalue correction, whose assembly into the mutual information cleanly separates classical from quantum correlations.

A novel nonparametric method to impute missing values in compositional data is developed. The method is based on the $k$–$NN$ algorithm, utilizes the Jensen-Shannon divergence and employs the Fréchet mean to allow for more flexibility in the estimation process. As an extra feature, the hyper-parameters can be self-adaptive according to the pattern of missing values. Unlike restrictive parametric models, the proposed method makes no assumption about the structure of the data and, most importantly, it is applicable even when compositional data contain zero values. Through simulation studies using real data, it is shown that the proposed algorithm outperforms competing algorithms at various settings, not only in terms of accuracy but also in terms of computational efficiency.

The scaling limit where both the size of the training set $P$ and the width $N$ of a deep neural network grow at the same rate, the so-called proportional-width regime, has been intensely studied for shallow, single-hidden-layer networks. However, extending these non-perturbative results from shallow architectures to deep non-linear networks has proven very challenging. Here we present an effective approximate approach to predict the generalization performance of Bayesian multi-layer perceptrons (MLPs) of fixed depth $L$ on arbitrary high-dimensional data. We propose an equivalent Wishart Ansatz to capture the dominant stochastic fluctuations of the hierarchical empirical kernels of MLPs. This allows us to perform a large deviation analysis for the partition function of MLPs in the proportional limit, expressed in terms of a renormalized NNGP kernel. In this description, even strong representation learning in the proportional limit is encoded in at most $L$ scalar order parameters, determined self-consistently. Extending the approach to convolutional architectures (CNNs), we identify a hierarchical local kernel renormalization mechanism, which allows to quantify more complex data-dependent transformations of the large-width kernel in CNNs due to finite-width effects. We test our effective theory against sampling experiments from the Bayesian posterior of finite deep neural networks with depths $L \sim O(10)$ and $P\sim O(10^3)$ on classic benchmark datasets, finding overall very good agreement together with two distinct types of systematic deviations.

Recent work in random matrix theory (RMT) has developed the notion of deterministic equivalents: typically linear surrogate models that approximate the spectral behavior of large nonlinear random matrices, such as nonlinear feature maps in neural networks (NNs). Such equivalents make theoretical predictions tractable by reducing a complex model to a simpler one with properties that fall under the umbrella of classical RMT tools. However, this leaves open the question of whether this idealized linear equivalence remains meaningful for classification of high-dimensional nonlinearly separable data. Motivated by this, we consider the conjugate kernel (CK), which is the nonlinear feature map of a one-layer feedforward NN, under a canonical nonlinearly separable dataset for the XOR problem; and we use the study of informative outlier eigenvalues in the CK and whether their corresponding eigenvectors asymptotically align with XOR labels as a proxy for nonlinear learnability. We develop a robust quadratic equivalent of the CK matrix that enables a precise analysis of emergent informative spikes, as one modifies various knobs common in ML practice: sample complexity, signal-to-noise ratio (SNR), nonlinear activation choice, and pretrained features. We identify regimes in which these knobs move the CK beyond the linear equivalent and produce BBP-type transitions to label-aligned outlier eigenspaces. Our analysis helps bring deterministic-equivalence tools from RMT to bear on problems of practical relevance in ML.

We study contextual bandits in the stochastic i.i.d.\ setting, where a learner observes contexts drawn from an unknown distribution, selects actions from a finite set $A$, and aims to identify an approximately optimal policy from a given class based on bandit feedback. Motivated by bandit multiclass classification with zero-one rewards, we focus on the \emph{$s$-sparse} setting in which, for every context, the reward vector has $L_1$-norm at most $s \ll |A|$. Our main result is the design of algorithms that, with high probability, output an $\epsilon$-optimal policy compared to policy class $\Pi$ using $\tilde{O} ((s/\epsilon^2 + |A|/\epsilon)\log |\Pi|/\delta)$ samples. We extend this bound to general Natarajan classes and complement it with a matching lower bound (up to logarithmic factors), thereby closing a substantial gap left by prior work (Erez et al., 2024, 2025), which incurred an additional $\Theta(|A|^9)$ dependence. We obtain these results via two complementary approaches. First, we analyze contextual bandits through the lens of contextual decision making with structured observations, designing an exploration-by-optimization algorithm whose sample complexity is governed by the decision-estimation coefficient (DEC; Foster et al., 2021, 2022). We show that, with $s$-sparse rewards, the induced model class admits a sharp DEC bound that scales with $s$ and directly yields the optimal rate. Since this approach is largely information-theoretic and involves solving complex min-max optimization problems, we also develop a second, more specialized algorithmic method based on a low-variance exploration technique. This approach leads to concrete, tractable algorithms and naturally extends to contextual combinatorial semi-bandits, leading to improved sample complexity guarantees for bandit multiclass list classification.

In federated language modeling, $K$ nodes each hold $n$ samples but cannot pool data or exchange full-precision gradients or weights. We study the minimax rate at which a conditional distribution over $V$ tokens can be estimated when each node may upload at most $B$ bits per query in a public probe set. In federated probe-logit distillation (FPLD), each node transmits a scalar-quantized logit vector on the probe set, and an aggregator distills a global parametric student. Prior work (Dubey and Huo, 2026) establishes a high-probability KL rate $O(d/(Kn) + \rho\sqrt{V \log V / m} + K^{-1} \cdot 2^{-2B/V})$ plus optimization slack, with the bandwidth term in its trace-sharpened form. Whether this bandwidth-term rate is tight, and how the upper bound generalizes to heterogeneous per-node bandwidths, are left open. We close both gaps. First, the dithered FPLD construction has a matching single-round lower bound $\Omega(K^{-1} \cdot 2^{-2B/V})$ under non-degeneracy, pinning the bandwidth-axis rate at $\Theta(K^{-1} \cdot 2^{-2B/V})$. $T$-round sequential refinement with nested/scaled residual quantizers achieves $O(K^{-1} \cdot 2^{-2TB/V})$; vanilla FPLD's $T$-independent bandwidth term is suboptimal for every $T > 1$. Second, we establish a heterogeneous-bandwidth upper bound for per-node budgets $B_i$, paired with a closed-form optimal allocation $B_i^* = B_{\mathrm{tot}}/K + (V/2) \log_2(w_i / \bar{w}_g)$, a log-tilted water-filling rule that is the per-node analogue of reverse water-filling for distortion-rate optimization. A plug-in adaptive variant estimates the weights from a short warm-up phase and attains $1 + O(\sqrt{\log(K/\delta)/(m T_0)})$ relative suboptimality. Synthetic n-gram simulations confirm that empirical KL is bracketed by the upper and lower bounds and that the optimal allocation strictly dominates uniform and inverse-weighted baselines under heterogeneous clipping.

In data centers, tasks are dispatched to various servers to evenly distribute the workload. When a data center considers implementing a new scheduling algorithm, it typically conducts an A/B test prior to deployment to assess the real-world impact of this new method. However, a straightforward A/B test might be interfered with so-called “Markovian” interference. We utilized the Differences-in-Q estimator, as developed by Farias et al. (2022), and introduced mixed Differences-in-Q estimators grounded in Little's Law. We show that our A/B testing methods significantly reduce bias and variance when testing various scheduling policies. Extensive simulations were conducted under scenarios like non-stationary arrival rates, heterogeneous service rates, and communication delays. These simulations highlight the robustness and efficacy of our A/B testing approach.

In hierarchical forecasting, the process of forecast reconciliation transforms a set of "base" or "raw" forecasts, which do not satisfy the hierarchical aggregation constraints in the real data, into a set of "coherent" forecasts, which do satisfy those constraints. The academic literature provides ample simulation evidence and real-world examples demonstrating the value of forecast reconciliation in improving forecasts of hierarchical time series. This improvement is attributed to the imposition of aggregation constraints. However, this evidence is derived from base forecasts, each generated using a distinct information set, usually the univariate information set corresponding to each time series. Since reconciliation algorithms combine forecasts, it is difficult to determine the extent to which the improvement is due to the imposition of constraints versus the combination of information carried by different forecasts. In this paper, we demonstrate that when base forecasts are based on different information sets and historical data are available, there is scope for improving these forecasts by combining the information that each one carries, even when they are already coherent. We propose a new method, called the information combination (IComb) method, which combines the information content of forecasts during the reconciliation process. The method is regression-based and can be implemented using existing penalised regression packages. We provide simulation evidence to illustrate the role of information sets, as distinct from the role of aggregation constraints, in forecasting hierarchical time series. Finally, we apply our method to datasets previously used in the literature and demonstrate that it achieves superior results compared to traditional approaches.

Meta-analyses of observational studies often show substantial between-study heterogeneity, limiting the interpretability of pooled estimates. Meta-regression can be used to explore heterogeneity, but it is often underpowered to handle multiple effect modifiers. We propose a novel framework that integrates large language models (LLMs) with deep metric learning to infer study-level similarity prior to meta-analysis. Study-level clinical and methodological characteristics were processed by an LLM to generate study triplets (anchor, similar, dissimilar). These triplets were constructed by treating each study as an anchor and comparing it with pairs of other studies to identify, in each instance, the study most similar to the anchor. Then, the triplets were used into an embedding model trained with triplet loss; a deep learning approach that learns an embedding space where clinically and methodologically similar studies are clustered together. We apply our framework to a meta-analysis dataset of 58 observational studies comparing cognitive outcomes between preterm- and term-born children. Subsequently, we fit meta-analysis models within the identified study clusters and compare the results with those of the overall analysis. Results suggested three clusters two of which retained considerable between-study heterogeneity. The remaining cluster comprised the most homogeneous group of studies and exhibited a more extreme pooled effect estimate together with a narrower prediction interval compared with the overall analysis. This work presents a novel approach for exploring heterogeneity in meta-analysis by incorporating study characteristics prior to model fitting. By transforming study information into a similarity space, the framework identifies coherent subgroups and supports more precise inference in heterogeneous real-world evidence.

While parameter-efficient fine-tuning methods like low-rank adaptation (LoRA) are standard for large language models, principled estimation of epistemic uncertainty remains challenging. Recent results in the LoRA regime suggest that discrete multi-mode approaches such as deep ensembles offer little benefit over single-mode methods. This contradicts broader observations in deep learning, where ensembling independent optima typically improves generalization, and linking these modes through continuous low-loss valleys further enhances Bayesian model averaging (BMA). Whether such structure exists in the LoRA space and whether it yields functional diversity missed by local or discrete methods has not been studied. We introduce LoRA-Curve, a segmented Bézier curve parameterization in the LoRA space, with two variants: a free configuration that jointly optimizes all control points, and an anchored configuration that connects independently fine-tuned LoRA optima. We prove pathwise continuity and Lipschitz regularity of the loss along the curve and empirically show, across reasoning and classification benchmarks with Qwen2.5 7B, that linear interpolation encounters loss barriers, while our anchored multi-segment curves connect independent optima through continuous low-loss valleys. Combined with flat-minima perturbations and a Jensen-Shannon divergence regularizer, LoRA-Curve yields measurably higher mutual information of the predictive distribution without sacrificing performance, and links continuous parameter-space traversal to functional diversity.

We study offline change-point estimation for time series data exhibiting nonlinear serial dependence. To address this problem, we propose a copula-based Markov chain model with Weibull marginal distributions, which is suitable for modeling nonnegative data such as event times and volatility measures. Nonlinear dependence is incorporated through the Clayton and Joe copulas, allowing the model to capture asymmetric lower-tail and upper-tail dependence structures, respectively. We derive the corresponding likelihood function and estimate the change point and model parameters using maximum likelihood estimation implemented through the Newton–Raphson algorithm. Confidence intervals are constructed via a parametric bootstrap Monte Carlo procedure. Extensive numerical studies are conducted to evaluate the finite-sample performance and robustness of the proposed method under different dependence structures and copula misspecification scenarios. The results demonstrate that the proposed estimators perform well in terms of RMSE and relative error, particularly for the estimation of the change point. An empirical application to the VIX index during the COVID-19 pandemic further illustrates the practical usefulness of the proposed approach in detecting structural changes in both the marginal distributions and serial dependence structure.

Estimating excursion set confidence regions seeks to identify regions where a function may exceed some threshold with a given confidence level. This paper focuses on estimating such confidence regions in cases where the function has random inputs and a functional output that is returned all at once. We develop a surrogate-based approach for estimating the confidence region, combining principal component analysis and Gaussian process regression. An active learning strategy is also introduced, based on a max-min criterion that selects new samples which are likely to reduce the uncertainty in the confidence region. This strategy leverages efficient sampling of the Gaussian process through a Karhunen-Loève expansion. The proposed approach is applied to estimate the confidence regions of three case studies: a synthetic function, the surface pressure coefficient distribution of a hypersonic vehicle, and the glide-back trajectory of a reusable launcher first stage. The method demonstrates efficiency in accurately estimating the confidence region while reducing sources of modeling uncertainties. It is benchmarked against reference methods from the literature. Relevant metrics for assessing the confidence region estimation performance are discussed.

A common challenge in data analysis is uncovering relationships between predictors and responses in problems involving large numbers of both. When the number of predictors and responses is limited, visual approaches are particularly effective. We present an R package, pandemonium, designed to explore such problems by combining cluster analysis with linked visualisations. Clustering is performed in one set of variables to identify regions with similar patterns in that space. The resulting clusters are simultaneously visualised in both spaces using linked views based on non-linear dimension reduction and animated tours. We introduce the package through two examples that illustrate different types of linked spaces. In the first example, we consider how a set of input variables is mapped to latent activations in a neural network regression model, to identify input combinations that result in similar activation patterns. In the second example, we analyse a complex multivariable mathematical model arising in physics to investigate how structure in the predictor space relates to the responses.

In randomized trials involving multiple treatments, bivariate survival outcomes present significant analytical challenges for making decisions. This paper addresses the problem of deriving optimal individualized treatment rules to maximize the joint survival probability beyond fixed time points $(t_1, t_2)$ through deep neural networks, while accounting for right censoring. We propose a novel approach that models treatment rules via stochastic policies, coupling marginal accelerated failure time models via link function to capture bivariate dependence. To enhance robustness and effectiveness of decision making, we introduce an adaptive prediction-powered method that leverages auxiliary predictions from machine learning models.

The mean squared displacement (MSD) of particles or probes is commonly estimated from microscopy videos using particle tracking approaches, which rely on tuning parameters manually, and are often unstable over the entire lag time range, especially in dense or low-contrast situations. In this work, we propose model-free ab initio uncertainty quantification (MF-AIUQ), a model-free method for scattering analysis of microscopy video based on a probabilistic framework, which estimates MSD without isolating particles and linking their trajectories. Based on the relationship between the intermediate scattering function (ISF) and the MSD derived from the cumulant theorem, MF-AIUQ estimates the MSD values by the marginal maximum likelihood estimator. To reduce the computational cost, the likelihood function is approximated by a subset of Fourier-transformed intensities. These intensities are equally spaced at the logarithmic values of Fourier basis functions and lag time points. We found that the ISF is smooth in this logarithmic input space, and the information of the ISF can be captured by this subset of inputs. We examine the method through simulation studies covering several representative stochastic processes and three experimental systems: a Newtonian fluid for evaluating performance in optically dense and bright-field settings, a gelation system with an evolving MSD shape, and snail mucin, a viscoelastic biopolymer, for modulus estimation. Across these studies, MF-AIUQ provides smooth and stable MSD estimates over the full lag time range and serves as a useful complementary approach in settings where particle tracking is unreliable or a parametric model of MSD is unavailable or unverifiable.

Task-based assessment of image quality (IQ) is critically important for the design and optimization of medical imaging systems. Ideal observers, including the Bayesian Ideal Observer (IO) and the ideal linear observer, i.e., the Hotelling observer (HO), provide objective figures of merit (FOMs) that quantify system performance on signal detection tasks. However, the application of ideal observers to high-dimensional image data is often computationally intractable. Channel mechanisms provide an effective framework for dimensionality reduction that can facilitate the computation of ideal observers. This work presents a conjugate gradient (CG)-based method to construct efficient channels for approximating the IO and HO performance.