Papers

Jamming and spoofing pose significant threats to wireless and satellite navigation by disrupting radio-frequency (RF) signals and compromising availability and integrity. Robust RF interference direction finding through angle-of-arrival (AoA) estimation is therefore essential for detecting and localizing anomalous signals. Although data-driven methods perform well under line-of-sight (LoS) conditions, their performance degrades in practical environments due to non-line-of-sight (NLoS) multipath propagation. In this work, we propose a hybrid learning framework that incorporates physics-informed constraints into deep neural networks to improve the robustness of AoA estimation. A neural network is trained to estimate the azimuth and elevation of incoming signals received by a four-element antenna array, while a physics-informed loss enforces consistency between the predicted angles and inter-antenna phase differences under a plane-wave model. We further introduce a latent-space classifier to distinguish LoS from NLoS samples. Since inter-antenna phase differences under LoS propagation exhibit domain-invariant structure across environments, the physics-based loss is applied only to LoS samples, promoting physically consistent and domain-invariant representations without over-constraining the model in NLoS scenarios. In addition, domain-incremental learning (DIL) across NLoS environments with varying scatterer distributions improves cross-domain generalization. Evaluations on real-world datasets show that the proposed method reduces AoA estimation error by up to 6{\deg} in low-exemplar settings compared with DIL baselines.

We introduce a broad class of normalized scale-invariant indices (NSIIs) generated by measurable symmetric homogeneous functions and encompassing several well-known measures, including the Gini coefficient, generalized Gini indices, entropy-based measures, and variability indices. Explicit expressions are obtained for these indices under Gamma populations. Exploiting the independence between the total sum and the associated Dirichlet proportions, we derive a simple unbiased estimator based on a U-statistic. The resulting estimator is shown to be unbiased for any NSII in the proposed class when the underlying population follows a Gamma distribution. Several examples are provided to illustrate the general theory. A Monte Carlo simulation study is carried out that shows the good performance of the unbiased estimator in several scenarios of index choices. We evaluate the effectiveness of the NSIIs and their estimates in modeling a real-world dataset related to gross domestic product per capita in the Americas.

Mapping the directed flow of information between brain regions – their effective connectivity – is central to understanding brain function, yet large-scale recordings sample only a fraction of the brain at a time: sessions, animals, and laboratories cover different, partially overlapping regions, usually without a shared temporal reference. Established directed-connectivity methods (Granger causality, dynamic causal modeling, partial directed coherence, PDC) require all regions to be recorded simultaneously and with a common clock. We introduce SPIDER, a non-parametric, frequency-domain framework that recovers directed information flow from such incomplete, asynchronous recordings: it stitches local power-spectral estimates from overlapping channel subsets into a global spectral matrix and obtains frequency-resolved directed interactions by canonical spectral factorization and PDC, without temporal alignment, while nuclear-norm completion fills in never-co-observed region pairs. With consistency guarantees, we validate SPIDER on simulations, two-photon calcium imaging, and the International Brain Laboratory Neuropixels dataset, recovering directed flow among 50 areas from 43 sessions in 12 laboratories never recorded together. Beyond validation, SPIDER reveals what no single recording can: brain-wide spontaneous flow is largely recurrent, but in the theta band it forms a significant feedforward hierarchy with the hippocampal formation at its source. Applied to resting human intracranial EEG (43 patients, non-overlapping coverage), it recovers the same theta-band hierarchy across species and modality. SPIDER makes whole-brain effective-connectivity analysis tractable for multi-session, multi-animal datasets previously incompatible with directed-flow inference.

In Bayesian analysis, the prior effective sample size (ESS) expresses the information carried by a prior distribution in units of observations, quantifying how much independent information the prospective data must provide to outweigh an informative prior elicited from a previous study. For network models such as Gaussian graphical models (GGMs), the prior ESS is not straightforward to compute. The Wishart and G-Wishart priors induce dependence among the entries of the precision matrix, and their informativeness has never been expressed in an interpretable, observation-equivalent unit. As a result, researchers eliciting an informative prior for a GGM have had no principled basis for sample size planning. In this paper, we close this gap by formalizing a pre-data ESS for GGMs under the Wishart and G-Wishart priors. We adapt five ESS estimators to the GGM setting and compute each through two aggregation schemes: a global ESS measure based on a determinant ratio, and a parameterwise version based on a Cholesky decomposition. Building on these measures, we introduce two complementary planning strategies: the Data-to-Prior Information Ratio (DPIR), which determines the sample size at which the data dominate the prior, and a GGM extension of Bayes Factor Design Analysis (BFDA), which determines the sample size required for conclusive edge-based evidence. Simulation studies show that the two procedures target complementary design goals and that the ESS estimators differ systematically in their sensitivity to network structure and geometry. We conclude by outlining extensions to other graphical models, including time-dependent variants, as well as to matrix-variate mixture priors.

This paper introduces Wittgenstein's Rule Following (WRF) data evolution, a framework in philomatics for evolving or generating a new dataset from a sequence of previously observed datasets. The method is inspired by Ludwig Wittgenstein's rule-following considerations and his notion of family resemblance in Philosophical Investigations. Unlike standard synthetic data generation, where the goal is usually to sample from or augment a fixed distribution, WRF aims to continue the implicit rule expressed by a historical sequence of datasets while preserving resemblance to the previous datasets. WRF represents each dataset by structural descriptors rather than pointwise correspondences. These descriptors summarize geometric, distributional, clustering, and, in the supervised case, label-based properties of the data. The method predicts a rule-following target by extrapolating descriptor trajectories and a family-resemblance target by averaging historical descriptors. Candidate datasets are then generated from the observed history through balanced or bounded mixture recombination, scored according to these targets, and optionally refined through differentiable optimization in descriptor space. The proposed framework allows both sample size and feature dimension to vary over time and does not assume that the next dataset is a direct transformation of the last one. Simulations on synthetic and image datasets show that WRF can generate meaningful continuations of evolving datasets in both unsupervised and supervised settings.

We propose Markov Chain from Human Feedback (MCHF), an elementary approach for aligning generative models from pairwise human preferences. Unlike Reinforcement Learning from Human Feedback (RLHF), which reduces comparisons to a scalar reward, and Nash Learning from Human Feedback (NLHF), which preserves pairwise utilities through a KL-regularized minimax optimization, MCHF uses pairwise preferences directly to define a transition mechanism over model outputs. Given a pairwise utility $U(x,y)$, which quantifies human preference for $y$ over $x$, and a reference probability distribution $\mu_{\mathsf{ref}}$, we define a Markov kernel $\mathsf{P}(x, dy)\propto \exp(U(x,y))\mu_{\mathsf{ref}}(dy)$, and take the Markov chain starting from $\mu_{\mathsf{ref}}$ as an iterative alignment procedure. We show that MCHF converges geometrically fast to the stationary distribution, with a convergence rate governed by the seminorm $\|U\|_\oplus=\inf_{g,f\in L^\infty(\mu_{\mathsf{ref}})}\|U-g\oplus f\|_\infty$, which quantifies the non-transitive structure of the pairwise utility. We further show that a mirror-descent algorithm for NLHF satisfies an analogous structure-adaptive convergence guarantee. Finally, through a perturbation analysis, we prove that when $\|U\|_\oplus$ is small, MCHF and NLHF agree up to first order around an RLHF solution, which yields a unified view of reward-based, game-theoretic, and Markovian approaches to alignment. In particular, for two natural algorithms that converge to the MCHF/NLHF equilibria, we show that the first step of MCHF and NLHF recovers the RLHF solution based on the column-sum reward $\hat{f}(y)=\int \mu_{\mathsf{ref}}(dx) U(x, y)$, and starting from the second iteration, both algorithms incorporate the same linear functional of the residual $U-(-\hat f)\oplus \hat f$, which captures the non-transitive structure of the pairwise utility $U$.

Contextual bandit algorithms have transformed modern experimentation by enabling real-time adaptation for personalized treatment. Yet these advantages create challenges for statistical inference due to adaptivity. We study inference with contextual-bandit data without assuming a well-specified outcome model. In this setting, we show a previously overlooked issue: standard algorithms such as LinUCB may fail to stabilize under misspecified working models, leading to non-Gaussian estimator behavior and invalid inference. This issue is practically important, as misspecified working models – such as approximations of complex dynamical systems – are often employed by online agents in real-world adaptive experiments to balance reward, computational tractability, and robustness. We develop an inverse-probability-weighted Z-estimation framework for a broad class of marginal moment targets, including projection parameters, structural parameters with noisy contexts, and off-policy values. We identify a stability condition tailored to this framework, scaled inverse-propensity convergence, under which the IPW-Z estimator is consistent and asymptotically normal with a consistent sandwich variance estimator. We further establish sufficient conditions for scaled inverse-propensity convergence for several policy classes, including multi-armed bandit algorithms and smooth contextual allocation policies. Simulations and a HeartSteps V1 real-data-calibrated application show reliable coverage and competitive performance across multiple targets. Overall, our results highlight the importance of stability-aware adaptive design for valid post-experiment inference.

We prove an explicit spectral-gap lower bound for the lazy swap chain on binary matrices with prescribed row and column sums. This chain is a standard sampler for fixed-margin null models in ecology, statistics, and network analysis. Kannan, Tetali, and Vempala (KTV) conjectured that it mixes rapidly for all feasible margins \citep{kannan1997simple}. We show that for every feasible set of margins on an $m\times n$ binary matrix, the lazy swap chain has spectral gap at least $$\binom{m}{2}^{-1}\binom{n}{2}^{-1}.$$ The bound is tight in the worst case. Thus, our result proves this KTV conjecture in a stronger quantitative form. The same spectral-gap bound also verifies the Mihail–Vazirani conjecture for fixed-margin 0/1-matrix polytopes. The proof gives a new route to fixed-margin sampling that avoids stability assumptions and canonical-path constructions. We compare the swap chain with a two-row heat-bath chain and use a local-to-global spectral reduction to reduce the analysis from arbitrary $m\times n$ matrices to a three-row problem. The remaining three-row inequality is then proved by separating the scalar column-count sector from the non-scalar Johnson harmonic sectors. The proof itself was generated by ChatGPT 5.5 Pro. The author's role was to pose the problem, guide the search direction, evaluate the AI-generated arguments, rewrite the proof, and take responsibility for the final form and validity of the result. The full proof of the main theorem has been formalized in Lean, and the accompanying formalization is available at the anonymous repository https://github.com/guanyangwang/ktv-swap-lean.

This paper presents a robust Expectation-Maximization framework for covariance estimation in Scale-Invariant Random Vector (SIRV) models with missing data under ignorable missingness mechanisms. By adopting an inverse-gamma prior on the scale variables, the resulting observation model leads to a complex multivariate Student-t distribution and allows closed-form E-step and M-step updates. The proposed algorithm incorporates numerical robustness techniques such as computation reuse for common observation patterns, regularized matrix inversions, and explicit enforcement of Hermitian positive semidefinite structure. Experiments on synthetic data and Sentinel-1 interferograms show effective missing value reconstruction and denoising performance under both MCAR and MNAR scenarios.

We revisit the problem of approximating a bivariate distribution with finite support by another such distribution which is totally positive of order two (TP2). Approximation is meant in a maximum likelihood sense.

This paper extends the approximate Bayesian estimation framework for Stochastic Volatility in Mean (SVM) models to accommodate heavy-tailed distributions from the Scale Mixture of Normals (SMN) family. To overcome the computational challenges arising from these models, we propose a numerically stable estimation procedure that exploits special functions to eliminate the need for direct numerical integration. Furthermore, the implementation incorporates parallel computing strategies that substantially reduce computational costs. Simulation studies and empirical applications demonstrate that the proposed approach delivers accurate inference while achieving computational times that are approximately an order of magnitude smaller than those required by conventional Markov chain Monte Carlo (MCMC) methods.

Gaussian Processes (GPs) are a powerful tool for Bayesian time-series modeling, yet their cubic computational cost remains a severe barrier for application to long, high-cadence datasets in astronomy. While specialized scalable solvers like Celerite elegantly reduce this scaling to linear time, repeatedly evaluating the exact likelihood during iterative Bayesian sampling is a bottleneck for developing more complex models, like hierarchical or additive models in which Celerite is only one component. To make this inference computationally tractable, we introduce a generative surrogate framework. By utilizing a Variational Autoencoder (VAE) to learn a compressed representation of the Celerite prior, we map highly correlated stochastic dependencies into a low-dimensional, isotropic manifold. This transition completely bypasses exact covariance operations, shifting the computational burden to a rapid neural network forward pass. Through an extensive simulation study, we show that the generative surrogate accurately reproduces the structural fidelity of exact physical kernels like Celerite. Finally, we demonstrate embedding our VAE approximation into an additive model that combines Celerite and a hidden Markov model (HMM) for stellar flare detection in time series data of stars. We evaluate the joint VAE+HMM architecture against the exact Celerite+HMM framework on empirical astrophysical time series and demonstrate that the proposed methodology achieves significant reductions in computational time, enabling the rigorous, large-scale characterization of stellar flares across massive data archives.

We introduce OASIS, a simulation-based inference framework for scientific settings where observations are distorted by measurement error, selection effects, and other survey-specific transformations. In many real applications, simulators generate latent, noiseless quantities, while the data are observed only after passing through a complex observational pipeline. Standard simulation-based inference methods often ignore this distinction, comparing observations to idealized simulator outputs or relying on low-dimensional summaries that can miss important structure. OASIS addresses this mismatch by explicitly embedding the observation model into the simulator and performing inference directly at the level of observed-data distributions. The method constructs a pseudo-posterior by reweighting prior samples according to a maximum mean discrepancy (MMD) loss between the empirical distributions of the observed data and forward-simulated observations, thereby avoiding both handcrafted summaries and learned neural surrogates. We provide theoretical guarantees for Monte Carlo consistency, convergence of the empirical pseudo-posterior to its population counterpart, and posterior concentration on the MMD-identified parameter set, with consistency for the true parameter under correct specification and identifiability. In controlled errors-in-variables regression experiments, OASIS delivers robust parameter recovery and well-calibrated uncertainty under heterogeneous and non-Gaussian measurement noise. We then demonstrate the method on a realistic cosmological application involving galaxy cluster observations across multiple wavelengths, in which latent physical properties are linked to observables through nonlinear scaling relations, heteroscedastic errors, selection functions, and incomplete coverage.

Empirical conclusions can depend on how researchers model dependence when constructing standard errors. We develop contrast-local validity, which asks whether a covariance restriction is accurate for the particular coefficient or weighted contrast being reported, even when the restriction is globally misspecified. The method tests target-specific covariance contamination, compares numerically certified structured corrections with an unrestricted benchmark, and adapts inference to the economic target. In a separate growing-block benchmark, valid structure achieves an optimal faster rate for estimating the target variance, while any globally misspecified covariance approximation must fail for some contrast. In a Fama–French calibration where validity is imposed, the feasible selector preserves nominal coverage and reduces variance-estimation root mean squared error by 39 percent. A publicly available FHFA house-price application illustrates target-specific verdicts across regional exposures. Detectability and coverage-risk analyses show when non-rejection is informative and when unrestricted inference should remain primary.

We show that replacing the standard MSE denoising loss in diffusion models with a nonlinear transformation induced by an f-divergence yields a simple robust training surrogate that empirically improves performance under data contamination, with small additional computational overhead. The theoretical foundation rests on a local divergence construction: under the Gaussian reverse-kernel structure of DDPM, each per-step likelihood ratio follows a lognormal distribution parameterized by a scalar mismatch, so the conditional f-divergence at each step reduces to a one-dimensional function of the denoising error. Summing these local divergences yields a training objective that unifies diffusion training as divergence induced weighted denoising, where the derivative of the induced divergence acts as a residual-space influence weight that controls the contribution of each sample. Bounded-influence divergences (Hellinger, negative exponential) suppress large error samples, with Hellinger yielding an explicit exponential weight, connecting the framework to robust M-estimation. Empirically, on CIFAR-10 under 30% contamination, NED reduces FID from 93.0 (KL) to 77.5, while also outperforming standard robust losses such as Huber and clipped MSE.

In open-ended generation, LLMs frequently fall into the "likelihood trap", characterized by repetitive degeneration and vocabulary dullness, resulting in a discrepancy between machine-generated and human-written text. While post-hoc tail truncation (e.g., Top-p, Min-p) avoids sampling from the unreliable tail, it can misalign generation with human lexical preferences by over-sampling from the uncalibrated head; fixed scalar repetition penalties, in turn, ignore how the scale of the logit distribution varies across inference steps, which can disrupt semantic coherence. To address both shortcomings, we propose Variance-Calibrated Modulation (VCM), a training-free pre-decoding intervention. VCM directly reshapes the probability distribution prior to truncation via two dynamic mechanisms: (1) Contextual Searchlight via PMI, which naturally suppresses global stopwords and elevates context-evoked tokens, and (2) Adaptive Self-Debiasing, which utilizes real-time logit standard deviation to provide scale-invariant penalization. In experiments across open-ended generation, factual QA, and mathematical reasoning, we show that VCM consistently mitigates the likelihood trap. With negligible computational overhead, VCM integrates with existing decoding strategies, improving diversity and coherence and, particularly at higher decoding temperatures, reasoning accuracy. Our code is publicly available on GitHub: https://github.com/AetherDing/VCM

Sparse signal discovery is a fundamental problem in large-scale inference, where the goal is to identify a small number of active signals hidden among a large collection of null effects. Despite the prevalence of dependence in modern applications, relatively little is known about how much dependence can be exploited for efficient sparse signal recovery from a Bayes-risk perspective. In this paper, we develop a Bayesian Step-Down (BSD) procedure for sparse signal discovery under arbitrary known covariance dependence. BSD adopts a posterior-guided model-pursuit strategy that sequentially accumulates evidence for competing sparse signal configurations while explicitly incorporating the data's covariance structure. To assess its effectiveness, we introduce a Bayes Oracle for a class of sparse one-factor dependence models and compare BSD with the Oracle, the recently proposed MRD-GBS procedure of Ghosh and Chakrabarti (2026), the original MRD procedure of Cohen et al. (2009), and the Benjamini-Hochberg method. Our simulation studies reveal a striking phenomenon: across a broad range of dimensions, sparsity levels, and dependence structures, BSD exhibits near-oracle behavior and is often virtually indistinguishable from the Bayes Oracle in terms of Bayes risk and support recovery performance. Remarkably, a similarly close agreement is observed between BSD and MRD-GBS despite their fundamentally different Bayesian and frequentist foundations. These findings provide new insight into the attainable Bayes-risk frontier for sparse signal discovery under dependence and suggest that BSD may serve as a useful benchmark when exact Oracle calculations are unavailable. Finally, we show that BSD admits a residual representation, thereby yielding admissibility under arbitrary covariance dependence and substantial computational simplifications.

We propose a new treatment of nonlinear regression with serially correlated disturbances that incorporates autoregressive moving average structures into feedforward neural networks. The resulting model provides an alternative to modeling temporal dependence using lagged variables. In simulations, the proposed method accurately recovers regression functions of varying complexity and the underlying error dynamics across a range of time-series lengths and signal-to-noise ratios. Finite-sample properties and out-of-sample predictive performances are shown to be robust to model misspecification induced by omitted lagged variables and incorrect specification of the error dynamics. Cloud cover is an important factor in climate projections. In an empirical study of cloud cover prediction for a grid of locations within and around the Mediterranean Sea, our proposed model yields more accurate predictions than existing methods, including long short-term memory networks. Serially correlated disturbances in place of lagged variables improve predictive accuracy across a range of land and ocean environments. Improvements over linear models with serially correlated disturbances are particularly pronounced in mountain areas, consistent with the presence of stronger nonlinear effects in cloud formation in such regions.

In the study of survival endpoints, the size of the sample is crucial. The calculation of the sample size for survival endpoints was first proposed and presented by Freedman based on the logrank statistic. Later, many statisticians gradually introduced multiple factors such as dropout rate and delayed onset, proposed various estimation methods including the lrstat method, and developed corresponding statistical programs. However, the application of professional statistical functions is relatively complex. Based on this, this paper has developed a corresponding visual web application on the basis of the R package lrstat and powerSurvEpi, and tested its functions and program accordingly. The test results are basically consistent with the case, proving the effectiveness of the application.

Attention mechanisms have demonstrated remarkable empirical success in identifying relevant information from large collections of tokens, yet the theoretical principles underlying this behavior remain poorly understood. We study a stylized softmax-attention model in which a query vector is learned by stochastic gradient ascent from a collection of informative and nuisance tokens. Exploiting the symmetry of the model, we derive a population objective and characterize the limiting ordinary differential equation governing the learning dynamics. Using tools from stochastic approximation and dynamical systems theory, we establish a rigorous connection between the stochastic learning algorithm and its deterministic limit. Our main result shows that, under suitable high-dimensional scaling assumptions and standard step-size conditions, the learned query converges almost surely to the one-dimensional signal subspace spanned by the latent informative direction. Equivalently, the query asymptotically recovers the latent signal up to the intrinsic sign ambiguity. These results provide a rigorous theoretical foundation for understanding attention mechanisms as signal extraction procedures in high-dimensional noisy environments and offer a dynamical-systems perspective on how attention discovers relevant information in the presence of substantial noise.

Penalization is a widely used approach to model selection with roots in information theory and Bayesian inference. We study a model selection problem involving non-nested candidate models for which penalization is counterproductive. We propose a Maximum Likelihood Criterion for this non-nested setting that selects the candidate model with the highest maximum likelihood. This criterion does not take into consideration the number of parameters of a candidate model. It is well-suited for situations where all candidate models are regarded as equal with no preference for models having fewer parameters. We establish the consistency of this criterion and compare its performance with that of existing penalization-based criteria.

Structure-agnostic (SA) models introduced by Balakrishnan et al. (2026) aim to reflect the general lack of knowledge of structural assumptions on data-generating laws such as smoothness or sparsity in practice. Roughly speaking, SA models restrict the observed-data generating law to be in some rn-neighborhood of (black-box machine learning) estimates, treated as given and fixed, where rn encodes the convergence rates of the estimates to the truth. Under SA models, Balakrishnan et al. (2026) show that the popular Double Machine Learning (DML) estimators for three functionals, the quadratic functional in the Gaussian sequence model, the quadratic density integral functional and the expected conditional covariance, are minimax. However, minimax estimators may be inadmissible. In this paper, we show that, for the first two of the three functionals, the DML estimator is asymptotically inadmissible under the SA model. In particular, we show that these two functionals fall into a class of functionals, which we refer to as the monotone bias class. For this class, we exhibit second-order (U-statistic) estimators, which asymptotically dominate DML estimators, under the SA model. These second-order estimators are empirical higher-order influence function (HOIF) estimators introduced in Liu et al. (2017). Furthermore, the empirical HOIF estimator, like the DML estimator, is minimax for the third functional (the expected conditional covariance), although neither asymptotically dominates the other.

With data growing in scale and complexity, traditional linear dimension reduction techniques are becoming inadequate in some settings. Manifold fitting offers an important alternative by capturing low-dimensional latent geometric structures within high-dimensional spaces. This capability allows it to support downstream analysis in complex data settings. In this review, we explore the development and applications of manifold fitting. First, we introduce the basic concepts of manifold fitting and distinguish it from related techniques such as manifold embedding and denoising. We review the development of manifold fitting with three distinct stages: early nonparametric statistical methods, insights from mathematical analysis, and contemporary practical statistical approaches. Furthermore, we present diverse applications of manifold fitting, particularly in neural networks and bioinformatics, which illustrate its utility in complex data scenarios. Despite considerable progress, manifold fitting remains a fertile area for research. Many theoretical and practical questions remain unanswered, and ongoing investigations will further clarify its role in modern data science as a geometric tool for a wide range of data analysis challenges.

Principled regression for stochastic processes is a long-standing challenge with deep connections to scientific inverse problems. We introduce Flow Annealing Posterior Sampling (FLAPS), to our knowledge the first function-space posterior sampling framework that unifies stochastic-process regression and PDE inverse problems. Built on pretrained function-space flow-matching priors, FLAPS enables likelihood-guided posterior inference from sparse and noisy observations, supports variable query discretizations, and avoids explicit prior-density evaluation. Its Langevin correction uses a low-rank covariance preconditioner to exploit dominant function-space correlations across discretizations. Across Gaussian and non-Gaussian stochastic-process regression benchmarks and diverse PDE inverse problems, FLAPS produces coherent posterior samples with well-calibrated uncertainty quantification, significantly outperforming existing functional regression baselines and achieving competitive or better noisy PDE inverse performance than diffusion-based posterior samplers while reducing test-time sampling cost.

Conformal selection aims to identify test candidates whose unknown responses fall in a target region while controlling the false discovery rate. Existing methods often inherit prediction-oriented nonconformity scores, such as residual or clipped residual scores, from conformal prediction. We argue that the natural score for selection is instead the target-membership probability. This score directly addresses the binary event being selected, and any monotone transform of it gives the Neyman–Pearson oracle ranking at a fixed null selection level. This distinction is irrelevant for mean-monotone targets, where conventional scores induce essentially the same ranking, but becomes important for interval-valued, variance-driven, multimodal, or multi-condition targets, where prediction-oriented scores can be misaligned with selection power. We study membership-score-based conformal selection and isolate one conformal calibration route, Null-Calibrated Conformal Selection (NCCS), which ranks test scores against confirmed non-target calibration examples. Under null exchangeability, NCCS yields finite-sample valid null p-values, which can be combined with BY under arbitrary dependence or with BH under standard positive-dependence conditions. Experiments support the score principle: membership scores match conventional scores on mean-monotone targets, substantially improve over mean-score selection on variance-driven targets, and, when calibrated by NCCS, trade power for finite-sample null validity in rare-target regimes where direct empirical-FDP thresholding can be anti-conservative.

Adam is one of the most widely implemented and influential modern optimizers. Why is it effective across different optimization problems in practice? This question arguably lies at the center of the optimization community over the last decade and has motivated a substantial body of work aimed at understanding its convergence behavior. However, existing studies have mainly focused on the convergence rate of Adam in smooth nonconvex optimization, which unfortunately does not adequately capture practical settings, since many real-world problems are nonsmooth, such as those arising in training neural networks. Thus, these studies cannot fully explain the popularity and empirical success of Adam. Recently, an insightful and powerful framework called Online-to-Nonconvex Conversion has opened a new way to analyze Adam for nonsmooth nonconvex optimization. Unfortunately, prior works along this line share two common limitations. First, all of them ignore the important bias-correction term in the original Adam algorithm. Second and more importantly, many of them require extra operations that are not used in Adam, such as a clipping step. Therefore, the convergence guarantee for the original Adam method still remains unclear. In this work, we present the first finite-time analysis for the classical form of Adam, i.e., with the bias-correction step and without further algorithmic modifications, and prove that a randomly scaled learning rate ensures a convergence rate of $1/T^{\frac{2}{13}}$ for nonsmooth nonconvex optimization. Moreover, our result provably applies to the modern heavy-tailed noise regime, which is closer to practice. Interestingly, our theory is established under the parameter choice $\beta_1=\beta_2$, aligning with the recent empirical studies.

This article examines various methods of constructingmultidimensional probabilistic forecasts of electricity prices. Building on the Multiple Split (MS) method, it incorporates forecast averaging across estimation windows of different lengths and compares its performance with that of other, well-established methods. The research demonstrates that the ensemble representation of the price distribution is particularly useful in battery energy storage system (BESS) management. It enables the direct construction of probabilistic forecasts of daily profits. These forecasts can be used to determine optimal charging and discharging hours, as well as to support risk management decisions. The methods are evaluated using data from the German and Spanish day-ahead electricity markets from 2021-2024. The results indicate that theMS method with averaging (MS-ave) generally outperforms the other considered approaches in terms of Prediction Interval Coverage Probability (PICP), the Continuous Ranked Probability Score (CRPS) and the Energy Score (ES). Moreover, it is superior in supporting BESS trading strategies, particularly in case of non-zero operational costs.

This paper investigates convergence properties of regularized Nyström subsampling applied to the unsupervised domain adaptation problem under covariate shift. We focus on the low-smoothness (misspecified) case where the target function lies outside the reproducing kernel Hilbert space. By combining Tikhonov regularization with Nyström projection onto a subsampled subspace, we obtain upper bounds on the excess risk that hold with high probability and are expressed in terms of the source condition, the effective dimension, and the sample sizes. We further extend the analysis to the setting where the Radon-Nikodym derivative between the target and source marginal distributions is unknown and must be approximated, and we identify the minimal additional sample sizes required to maintain the same convergence rate as in the oracle case.

The integration of multiple thematic data layers into a single composite map, known as the cartographic synthesis problem, is typically addressed through expert-driven weighting schemes. This study presents a multi-objective formulation of cartographic synthesis grounded in spatial autocorrelation structure. We develop a bi-objective evolutionary framework, GIS-moGA, that estimates layer weights by simultaneously maximizing global spatial structure, measured by Global Moran's I, and minimizing local spatial heterogeneity, measured by the variance of Local Indicators of Spatial Association (LISA). Because naive evaluation of spatial relationships requires O(N^2) operations, direct computation becomes impractical for larger datasets. We address this challenge by exploiting the 97.7% sparsity of queen contiguity matrices, reducing effective complexity to O(N k) and enabling scalable municipal-level analysis. The framework is evaluated on a high-dimensional spatial epidemiology dataset with N = 523 units from Araraquara, Brazil. A 64-scenario experimental design is used to examine evolutionary behavior across parameter settings. Results show that higher mutation rates are important for maintaining population diversity and preventing premature convergence in spatially autocorrelated fitness landscapes, where crossover operators can disrupt geographically coherent structures. Compared with expert-derived Analytic Hierarchy Process baselines, the resulting Pareto fronts show substantial hypervolume gains and significant improvements in spatial coherence (p < 0.001, Cliff's delta = 0.87). These findings provide a systematic and scalable framework for data-driven geographic multi-criteria decision analysis.

Diffusion models are typically sampled independently, even when the downstream objective is to obtain a diverse set of candidates. We introduce a variance-weighted batch distribution that favours collections of samples with large empirical spread after a prescribed linear feature map. The target is specified explicitly, and the sampler is derived as the corresponding Doob $h$-transform of independent diffusion dynamics. The resulting correction has a compact form: an interaction term that repels posterior denoised means, together with a curvature term that moves particles to the region of higher feature variance. This yields an interacting-particle sampler with a transparent probabilistic target rather than a heuristic repulsive drift.