We introduce Blind Plug-and-Play Diffusion Models (Blind-PnPDM) as a novel framework for solving blind inverse problems where both the target image and the measurement operator are unknown. Unlike conventional methods that rely on explicit priors or separate parameter estimation, our approach performs posterior sampling by recasting the problem into an alternating Gaussian denoising scheme. We leverage two diffusion models as learned priors: one to capture the distribution of the target image and another to characterize the parameters of the measurement operator. This PnP integration of diffusion models ensures flexibility and ease of adaptation. Our experiments on blind image deblurring show that Blind-PnPDM outperforms state-of-the-art methods in terms of both quantitative metrics and visual fidelity. Our results highlight the effectiveness of treating blind inverse problems as a sequence of denoising subproblems while harnessing the expressive power of diffusion-based priors.
This work investigates a practical reconfigurable intelligent surface (RIS)-aided integrated sensing and communication (ISAC) system, where a subset of RIS elements fail to function properly and reflect incident signals randomly towards unintended directions, thereby degrading system performance. To date, no study has addressed such impairments caused by faulty RIS elements in ISAC systems. This work aims to fill the gap. First, to quantify the impact of faulty elements on ISAC performance, we derive the misspecified Cram\'er-Rao bound (MCRB) for sensing parameter estimation and signal-to-interference-and-noise ratio (SINR) for communication quality. Then, to mitigate the performance loss caused by faulty elements, we jointly design the remaining functional RIS phase shifts and transmit beamforming to minimize the MCRB, subject to the communication SINR and transmit power constraints. The resulting optimization problem is highly non-convex due to the intricate structure of the MCRB expression and constant-modulus constraint imposed on RIS. To address this, we reformulate it into a more tractable form and propose a block coordinate descent (BCD) algorithm that incorporates majorization-minimization (MM), successive convex approximation (SCA), and penalization techniques. Simulation results demonstrate that our proposed approach reduces the MCRB performance loss by 24.36% on average compared to the case where the presence of faulty elements is ignored. Furthermore, the performance gain becomes more evident as the number of faulty elements increases.
Simulation-based inference (SBI) enables cosmological parameter estimation when closed-form likelihoods or models are unavailable. However, SBI relies on machine learning for neural compression and density estimation. This requires large training datasets which are prohibitively expensive for high-quality simulations. We overcome this limitation with multifidelity transfer learning, combining less expensive, lower-fidelity simulations with a limited number of high-fidelity simulations. We demonstrate our methodology on dark matter density maps from two separate simulation suites in the hydrodynamical CAMELS Multifield Dataset. Pre-training on dark-matter-only $N$-body simulations reduces the required number of high-fidelity hydrodynamical simulations by a factor between $8$ and $15$, depending on the model complexity, posterior dimensionality, and performance metrics used. By leveraging cheaper simulations, our approach enables performant and accurate inference on high-fidelity models while substantially reducing computational costs.
Temporal networks observed continuously over time through timestamped relational events data are commonly encountered in application settings including online social media communications, financial transactions, and international relations. Temporal networks often exhibit community structure and strong dependence patterns among node pairs. This dependence can be modeled through mutual excitations, where an interaction event from a sender to a receiver node increases the possibility of future events among other node pairs. We provide statistical results for a class of models that we call dependent community Hawkes (DCH) models, which combine the stochastic block model with mutually exciting Hawkes processes for modeling both community structure and dependence among node pairs, respectively. We derive a non-asymptotic upper bound on the misclustering error of spectral clustering on the event count matrix as a function of the number of nodes and communities, time duration, and the amount of dependence in the model. Our result leverages recent results on bounding an appropriate distance between a multivariate Hawkes process count vector and a Gaussian vector, along with results from random matrix theory. We also propose a DCH model that incorporates only self and reciprocal excitation along with highly scalable parameter estimation using a Generalized Method of Moments (GMM) estimator that we demonstrate to be consistent for growing network size and time duration.
Hollmann et al. (Nature 637 (2025) 319-326) recently introduced TabPFN, a transformer-based deep learning model for regression and classification on tabular data, which they claim "outperforms all previous methods on datasets with up to 10,000 samples by a wide margin, using substantially less training time." Furthermore, they have called TabPFN a "foundation model" for tabular data, as it can support "data generation, density estimation, learning reusable embeddings and fine-tuning". If these statements are well-supported, TabPFN may have the potential to supersede existing modeling approaches on a wide range of statistical tasks, mirroring a similar revolution in other areas of artificial intelligence that began with the advent of large language models. In this paper, we provide a tailored explanation of how TabPFN works for a statistics audience, by emphasizing its interpretation as approximate Bayesian inference. We also provide more evidence of TabPFN's "foundation model" capabilities: We show that an out-of-the-box application of TabPFN vastly outperforms specialized state-of-the-art methods for semi-supervised parameter estimation, prediction under covariate shift, and heterogeneous treatment effect estimation. We further show that TabPFN can outperform LASSO at sparse regression and can break a robustness-efficiency trade-off in classification. All experiments can be reproduced using the code provided at https://github.com/qinglong-tian/tabpfn_study (https://github.com/qinglong-tian/tabpfn_study).
In this paper, we theoretically investigate the effects of noisy labels in offline alignment, with a focus on the interplay between privacy and robustness against adversarial corruption. Specifically, under linear modeling assumptions, we present a unified analysis covering both reinforcement learning from human feedback (RLHF) and direct preference optimization (DPO) under different privacy-corruption scenarios, such as Local differential privacy-then-Corruption (LTC), where human preference labels are privatized before being corrupted by an adversary, and Corruption-then-Local differential privacy (CTL), where labels are corrupted before privacy protection. Our analysis leverages a reduction framework that reduces the offline alignment problem under linear modeling assumptions to parameter estimation in logistic regression. This framework allows us to establish an interesting separation result between LTC and CTL, demonstrating that LTC presents a greater challenge than CTL in offline alignment, even under linear models. As important by-products, our findings also advance the state-of-the-art theoretical results in offline alignment under privacy-only or corruption-only scenarios.
In this paper, channel estimation (CE) for uplink hybrid-field communications involving multiple Internet of Things (IoT) devices assisted by an active intelligent reflecting surface (IRS) is investigated. Firstly, to reduce the complexity of near-field (NF) channel modeling and estimation between IoT devices and active IRS, a sub-blocking strategy for active IRS is proposed. Specifically, the entire active IRS is divided into multiple smaller sub-blocks, so that IoT devices are located in the far-field (FF) region of each sub block, while also being located in the NF region of the entire active IRS. This strategy significantly simplifies the channel model and reduces the parameter estimation dimension by decoupling the high-dimensional NF channel parameter space into low dimensional FF sub channels. Subsequently, the relationship between channel approximation error and CE error with respect to the number of sub blocks is derived, and the optimal number of sub blocks is solved based on the criterion of minimizing the total error. In addition, considering that the amplification capability of active IRS requires power consumption, a closed-form expression for the optimal power allocation factor is derived. To further reduce the pilot overhead, a lightweight CE algorithm based on convolutional autoencoder (CAE) and multi-head attention mechanism, called CAEformer, is designed. The Cramer-Rao lower bound is derived to evaluate the proposed algorithm's performance. Finally, simulation results demonstrate the proposed CAEformer network significantly outperforms the conventional least square and minimum mean square error scheme in terms of estimation accuracy.
Reconfigurable intelligent surfaces (RISs) have the potential to significantly enhance the performance of integrated sensing and communication (ISAC) systems, particularly in line-of-sight (LoS) blockage scenarios. However, as larger RISs are integrated into ISAC systems, mutual coupling (MC) effects between RIS elements become more pronounced, leading to a substantial degradation in performance, especially for localization applications. In this paper, we first conduct a misspecified and standard Cram\'er-Rao bound analysis to quantify the impact of MC on localization performance, demonstrating severe degradations in accuracy, especially when MC is ignored. Building on this, we propose a novel joint user equipment localization and RIS MC parameter estimation (JLMC) method in near-field wireless systems. Our two-stage MC-aware approach outperforms classical methods that neglect MC, significantly improving localization accuracy and overall system performance. Simulation results validate the effectiveness and advantages of the proposed method in realistic scenarios.
This paper addresses the challenging problem of parameter estimation in bilinear systems under colored noise. A novel approach, termed B-PF-RLS, is proposed, combining a particle filter (PF) with a recursive least squares (RLS) estimator. The B-PF-RLS algorithm tackles the complexities arising from system nonlinearities and colored noise by effectively estimating unknown system states using the particle filter, which are then integrated into the RLS parameter estimation process. Furthermore, the paper introduces an enhanced particle filter that eliminates the need for explicit knowledge of the measurement noise variance, enhancing the method's practicality for real-world applications. Numerical examples demonstrate the B-PF-RLS algorithm's superior performance in accurately estimating both system parameters and states, even under uncertain noise conditions. This work offers a robust and effective solution for system identification in various engineering applications involving bilinear models subject to complex noise environments.
IntrinsicTimescales.jl is a Julia package to perform estimation of intrinsic neural timescales (INTs). INTs are defined as the time window in which prior information from an ongoing stimulus can affect the processing of newly arriving information. INTs are estimated either from the autocorrelation function (ACF) or the power spectral density (PSD) of time-series data. In addition to the model-free estimates of INTs, IntrinsicTimescales.jl offers implementations of novel techniques of timescale estimation via performing parameter estimation of an Ornstein-Uhlenbeck process with adaptive approximate Bayesian computation (aABC) and automatic differentiation variational inference (ADVI).
Mixture of Experts (MoE) models constitute a widely utilized class of ensemble learning approaches in statistics and machine learning, known for their flexibility and computational efficiency. They have become integral components in numerous state-of-the-art deep neural network architectures, particularly for analyzing heterogeneous data across diverse domains. Despite their practical success, the theoretical understanding of model selection, especially concerning the optimal number of mixture components or experts, remains limited and poses significant challenges. These challenges primarily stem from the inclusion of covariates in both the Gaussian gating functions and expert networks, which introduces intrinsic interactions governed by partial differential equations with respect to their parameters. In this paper, we revisit the concept of dendrograms of mixing measures and introduce a novel extension to Gaussian-gated Gaussian MoE models that enables consistent estimation of the true number of mixture components and achieves the pointwise optimal convergence rate for parameter estimation in overfitted scenarios. Notably, this approach circumvents the need to train and compare a range of models with varying numbers of components, thereby alleviating the computational burden, particularly in high-dimensional or deep neural network settings. Experimental results on synthetic data demonstrate the effectiveness of the proposed method in accurately recovering the number of experts. It outperforms common criteria such as the Akaike information criterion, the Bayesian information criterion, and the integrated completed likelihood, while achieving optimal convergence rates for parameter estimation and accurately approximating the regression function.
Structural identifiability -- the theoretical ability to uniquely recover model parameters from ideal, noise-free data -- is a prerequisite for reliable parameter estimation in epidemic modeling. Despite its importance, structural identifiability analysis remains underutilized in the infectious disease modeling literature. In this tutorial, we present a practical and reproducible workflow for conducting structural identifiability analysis of ordinary differential equation models using the Julia package StructuralIdentifiability.jl. We apply the tool to a range of epidemic models, including SEIR variants with asymptomatic and pre-symptomatic transmission, vector-borne systems, and models incorporating hospitalization and disease-induced mortality. We compare results from StructuralIdentifiability.jl with those obtained using DAISY, a widely used differential algebra tool, and highlight cases where the Julia package succeeds in analyzing models that DAISY cannot handle. In particular, StructuralIdentifiability.jl efficiently handles high-dimensional systems and provides symbolic checks for assumptions often overlooked in other methods. Our findings underscore how identifiability depends on model structure, the availability of initial conditions, and the choice of observed states. All code and diagrams are publicly available, making this tutorial a valuable reference for researchers and educators working with dynamic disease models.
Ray antenna array (RAA) is a novel multi-antenna architecture comprising massive low-cost antenna elements and a few radio-frequency (RF) chains. The antenna elements are arranged in a novel ray-like structure, where each ray corresponds to a simple uniform linear array (sULA) with deliberately designed orientation and all its antenna elements are directly connected. By further designing a ray selection network (RSN), appropriate sULAs are selected to connect to the RF chains for further baseband processing. RAA has three appealing advantages: (i) dramatically reduced hardware cost since no phase shifters are needed; (ii) enhanced beamforming gain as antenna elements with higher directivity can be used; (iii) uniform angular resolution across all signal directions. Such benefits make RAA especially appealing for integrated sensing and communication (ISAC), particularly for low-altitude unmanned aerial vehicle (UAV) swarm ISAC, where high-mobility aerial targets may easily move away from the boresight of conventional antenna arrays, causing severe communication and sensing performance degradation. Therefore, this paper studies RAA-based ISAC for low-altitude UAV swarm systems. First, we establish an input-output mathematical model for RAA-based UAV ISAC and rigorously show that RAA achieves uniform angular resolution for all directions. Besides, we design the RAA orientation and RSN. Furthermore, RAA-based ISAC with orthogonal frequency division multiplexing (OFDM) for UAV swarm is studied, and efficient algorithm is proposed for sensing target parameter estimation. Extensive simulation results demonstrate the significant performance improvement by RAA system over the conventional antenna arrays, in terms of sensing angular resolution and communication spectral efficiency, highlighting the great potential of the novel RAA system to meet the growing demands of low-altitude UAV ISAC.
Bi-static sensing is an attractive configuration for integrated sensing and communications (ISAC) systems; however, clock asynchronism between widely separated transmitters and receivers introduces time-varying time offsets (TO) and phase offsets (PO), posing significant challenges. This paper introduces a signal-subspace-based framework that estimates decoupled angles, delays, and complex gain sequences (CGS)-- the target-reflected signals -- for multiple dynamic target paths. The proposed framework begins with a novel TO alignment algorithm, leveraging signal subspace or covariance, to mitigate TO variations across temporal snapshots, enabling coherent delay-domain analysis. Subsequently, subspace-based methods are developed to compensate for TO residuals and to perform joint angle-delay estimation. Finally, leveraging the high resolution in the joint angle-delay domain, the framework compensates for the PO and estimates the CGS for each target. The framework can be applied to both single-antenna and multi-antenna systems. Extensive simulations and experiments using commercial Wi-Fi devices demonstrate that the proposed framework significantly surpasses existing solutions in parameter estimation accuracy and delay resolution. Notably, it uniquely achieves a super-resolution in the delay domain, with a probability-of-resolution curve tightly approaching that in synchronized systems.
In many scientific and industrial applications, we are given a handful of instances (a 'small ensemble') of a spatially distributed quantity (a 'field') but would like to acquire many more. For example, a large ensemble of global temperature sensitivity fields from a climate model can help farmers, insurers, and governments plan appropriately. When acquiring more data is prohibitively expensive -- as is the case with climate models -- statistical emulation offers an efficient alternative for simulating synthetic yet realistic fields. However, parameter inference using maximum likelihood estimation (MLE) is computationally prohibitive, especially for large, non-stationary fields. Thus, many recent works train neural networks to estimate parameters given spatial fields as input, sidestepping MLE completely. In this work we focus on a popular class of parametric, spatially autoregressive (SAR) models. We make a simple yet impactful observation; because the SAR parameters can be arranged on a regular grid, both inputs (spatial fields) and outputs (model parameters) can be viewed as images. Using this insight, we demonstrate that image-to-image (I2I) networks enable faster and more accurate parameter estimation for a class of non-stationary SAR models with unprecedented complexity.
The monopulse technique is characterized by its high accuracy in angle estimation and simplicity in engineering implementation. However, in the complex electromagnetic environment, the presence of the mainlobe jamming (MLJ) greatly degrades the accuracy of angle estimation. Conventional methods of jamming suppression often lead to significant deviations in monopulse ratio while suppressing MLJ. Additionally, the monopulse technique based on traditional radar cannot jointly estimate the target's range. In this paper, the four-channel adaptive beamforming (ABF) algorithm is proposed, which adds a delta-delta channel based on conventional sum-difference-difference three-channel to suppress a single MLJ. Moreover, considering the suppression of multiple MLJs and sidelobe jammings (SLJs), the row-column ABF algorithm is proposed. This algorithm utilizes more spatial degrees of freedom (DOFs) to suppress multiple jammings by the row-column adaptive beamforming at the subarray level. The key ideal of both algorithms is to suppress MLJ with null along one spatial direction while keeping the sum and difference beampatterns undistorted along another spatial direction. Therefore, the monopulse ratio remains undistorted while suppressing the MLJ, ensuring the accuracy of monopulse parameter estimation. Furthermore, by utilizing the additional degrees of freedom (DOFs) in the range domain provided by the multiple-input multiple-output space-time coding array (MIMO-STCA) radar, joint angle-range estimation can be achieved through the monopulse technique. Simulation results highlight the effectiveness of the proposed methods in suppressing multiple MLJs and enhancing the accuracy of monopulse parameter estimation, as verified by the low root mean square error (RMSE) in the parameter estimation results.
Electrochemical hybrid battery models have major potential to enable advanced physics-based control, diagnostic, and prognostic features for next-generation lithium-ion battery management systems. This is due to the physical significance of the electrochemical model, which is complemented by a machine learning model that compensates for output prediction errors caused by system uncertainties. While hybrid models have demonstrated robust output prediction performance under large system uncertainties, they are highly susceptible to the influence of uncertainties during parameter identification, which can compromise the physical significance of the model. To address this challenge, we present a parameter estimation framework that explicitly considers system uncertainties through a discrepancy function. The approach also incorporates a downsampling procedure to address the computational barriers associated with large time-series data sets, as are typical in the battery domain. The framework was validated in simulation, yielding several mean parameter estimation errors that were one order of magnitude smaller than those of the conventional least squares approach. While developed for the high-uncertainty, electrochemical hybrid modeling context, the estimation framework is applicable to all models and is presented in a generalized form.
In this letter, we investigate the transmission of a complex-valued parameter vector from a transmitter to an intended receiver, considering both the presence and absence of an eavesdropper. The direct links from the transmitter to both the intended receiver and the eavesdropper are assumed to be blocked, and communications occur solely through cascaded channels facilitated by a beyond-diagonal reconfigurable intelligent surface (BD-RIS). While previous research has considered this system under conventional (diagonal) RIS assistance, we extend the setup to incorporate BD-RIS and quantify the resulting improvement in estimation performance at the intended receiver. This performance is measured by the trace of the Fisher information matrix (FIM), or equivalently, the average Fisher information, while simultaneously limiting the estimation capability of the eavesdropper. We propose solutions and algorithms for optimizing the BD-RIS response matrix and demonstrate their effectiveness. Numerical results reveal that the BD-RIS provides a significant enhancement in estimation quality compared to conventional diagonal RIS architectures.
Estimating physical parameters from data is a crucial application of machine learning (ML) in the physical sciences. However, systematic uncertainties, such as detector miscalibration, induce data distribution distortions that can erode statistical precision. In both high-energy physics (HEP) and broader ML contexts, achieving uncertainty-aware parameter estimation under these domain shifts remains an open problem. In this work, we address this challenge of uncertainty-aware parameter estimation for a broad set of tasks critical for HEP. We introduce a novel approach based on Contrastive Normalizing Flows (CNFs), which achieves top performance on the HiggsML Uncertainty Challenge dataset. Building on the insight that a binary classifier can approximate the model parameter likelihood ratio, we address the practical limitations of expressivity and the high cost of simulating high-dimensional parameter grids by embedding data and parameters in a learned CNF mapping. This mapping yields a tunable contrastive distribution that enables robust classification under shifted data distributions. Through a combination of theoretical analysis and empirical evaluations, we demonstrate that CNFs, when coupled with a classifier and established frequentist techniques, provide principled parameter estimation and uncertainty quantification through classification that is robust to data distribution distortions.
The recovery of block-sparse signals with unknown structural patterns remains a fundamental challenge in structured sparse signal reconstruction. By proposing a variance transformation framework, this paper unifies existing pattern-based block sparse Bayesian learning methods, and introduces a novel space power prior based on undirected graph models to adaptively capture the unknown patterns of block-sparse signals. By combining the EM algorithm with high-order equation root-solving, we develop a new structured sparse Bayesian learning method, SPP-SBL, which effectively addresses the open problem of space coupling parameter estimation in pattern-based methods. We further demonstrate that learning the relative values of space coupling parameters is key to capturing unknown block-sparse patterns and improving recovery accuracy. Experiments validate that SPP-SBL successfully recovers various challenging structured sparse signals (e.g., chain-structured signals and multi-pattern sparse signals) and real-world multi-modal structured sparse signals (images, audio), showing significant advantages in recovery accuracy across multiple metrics.