Relationships among teachers are known to influence their teaching-related perceptions. We study whether and how teachers' advising relationships (networks) are related to their perceptions of satisfaction, students, and influence over educational policies, recorded as their responses to a questionnaire (item responses). We propose a novel joint model of network and item responses (JNIRM) with correlated latent variables to understand these co-varying ties. This methodology allows the analyst to test and interpret the dependence between a network and item responses. Using JNIRM, we discover that teachers' advising relationships contribute to their perceptions of satisfaction and students more often than their perceptions of influence over educational policies. In addition, we observe that the complementarity principle applies in certain schools, where teachers tend to seek advice from those who are different from them. JNIRM shows superior parameter estimation and model fit over separately modeling the network and item responses with latent variable models.
Unraveling the co-expression of genes across studies enhances the understanding of cellular processes. Inferring gene co-expression networks from transcriptome data presents many challenges, including spurious gene correlations, sample correlations, and batch effects. To address these complexities, we introduce a robust method for high-dimensional graph inference from multiple independent studies. We base our approach on the premise that each dataset is essentially a noisy linear mixture of gene loadings that follow a multivariate $t$-distribution with a sparse precision matrix, which is shared across studies. This allows us to show that we can identify the co-expression matrix up to a scaling factor among other model parameters. Our method employs an Expectation-Maximization procedure for parameter estimation. Empirical evaluation on synthetic and gene expression data demonstrates our method's improved ability to learn the underlying graph structure compared to baseline methods.
Accurate dynamic modeling is critical for autonomous racing vehicles, especially during high-speed and agile maneuvers where precise motion prediction is essential for safety. Traditional parameter estimation methods face limitations such as reliance on initial guesses, labor-intensive fitting procedures, and complex testing setups. On the other hand, purely data-driven machine learning methods struggle to capture inherent physical constraints and typically require large datasets for optimal performance. To address these challenges, this paper introduces the Fine-Tuning Hybrid Dynamics (FTHD) method, which integrates supervised and unsupervised Physics-Informed Neural Networks (PINNs), combining physics-based modeling with data-driven techniques. FTHD fine-tunes a pre-trained Deep Dynamics Model (DDM) using a smaller training dataset, delivering superior performance compared to state-of-the-art methods such as the Deep Pacejka Model (DPM) and outperforming the original DDM. Furthermore, an Extended Kalman Filter (EKF) is embedded within FTHD (EKF-FTHD) to effectively manage noisy real-world data, ensuring accurate denoising while preserving the vehicle's essential physical characteristics. The proposed FTHD framework is validated through scaled simulations using the BayesRace Physics-based Simulator and full-scale real-world experiments from the Indy Autonomous Challenge. Results demonstrate that the hybrid approach significantly improves parameter estimation accuracy, even with reduced data, and outperforms existing models. EKF-FTHD enhances robustness by denoising real-world data while maintaining physical insights, representing a notable advancement in vehicle dynamics modeling for high-speed autonomous racing.
Scientific modeling and engineering applications rely heavily on parameter estimation methods to fit physical models and calibrate numerical simulations using real-world measurements. In the absence of analytic statistical models with tractable likelihoods, modern simulation-based inference (SBI) methods first use a numerical simulator to generate a dataset of parameters and simulated outputs. This dataset is then used to approximate the likelihood and estimate the system parameters given observation data. Several SBI methods employ machine learning emulators to accelerate data generation and parameter estimation. However, applying these approaches to high-dimensional physical systems remains challenging due to the cost and complexity of training high-dimensional emulators. This paper introduces Embed and Emulate (E&E): a new SBI method based on contrastive learning that efficiently handles high-dimensional data and complex, multimodal parameter posteriors. E&E learns a low-dimensional latent embedding of the data (i.e., a summary statistic) and a corresponding fast emulator in the latent space, eliminating the need to run expensive simulations or a high dimensional emulator during inference. We illustrate the theoretical properties of the learned latent space through a synthetic experiment and demonstrate superior performance over existing methods in a realistic, non-identifiable parameter estimation task using the high-dimensional, chaotic Lorenz 96 system.
The ever-increasing quality and complexity of astronomical data underscores the need for new and powerful data analysis applications. This need has led to the development of Sherpa, a modeling and fitting program in the CIAO software package that enables the analysis of multi-dimensional, multi-wavelength data. In this paper, we present an overview of Sherpa's features, which include: support for a wide variety of input and output data formats, including the new Model Descriptor List (MDL) format; a model language which permits the construction of arbitrarily complex model expressions, including ones representing instrument characteristics; a wide variety of fit statistics and methods of optimization, model comparison, and parameter estimation; multi-dimensional visualization, provided by ChIPS; and new interactive analysis capabilities provided by embedding the S-Lang interpreted scripting language. We conclude by showing example Sherpa analysis sessions.
Visual object tracking has boosted extensive intelligent applications for unmanned aerial vehicles (UAVs). However, the state-of-the-art (SOTA) enhancers for nighttime UAV tracking always neglect the uneven light distribution in low-light images, inevitably leading to excessive enhancement in scenarios with complex illumination. To address these issues, this work proposes a novel enhancer, i.e., LDEnhancer, enhancing nighttime UAV tracking with light distribution suppression. Specifically, a novel image content refinement module is developed to decompose the light distribution information and image content information in the feature space, allowing for the targeted enhancement of the image content information. Then this work designs a new light distribution generation module to capture light distribution effectively. The features with light distribution information and image content information are fed into the different parameter estimation modules, respectively, for the parameter map prediction. Finally, leveraging two parameter maps, an innovative interweave iteration adjustment is proposed for the collaborative pixel-wise adjustment of low-light images. Additionally, a challenging nighttime UAV tracking dataset with uneven light distribution, namely NAT2024-2, is constructed to provide a comprehensive evaluation, which contains 40 challenging sequences with over 74K frames in total. Experimental results on the authoritative UAV benchmarks and the proposed NAT2024-2 demonstrate that LDEnhancer outperforms other SOTA low-light enhancers for nighttime UAV tracking. Furthermore, real-world tests on a typical UAV platform with an NVIDIA Orin NX confirm the practicality and efficiency of LDEnhancer. The code is available at https://github.com/vision4robotics/LDEnhancer.
A global threshold (e.g., 0.5) is often applied to determine which bounding boxes should be included in the final results for an object detection task. A higher threshold reduces false positives but may result in missing a significant portion of true positives. A lower threshold can increase detection recall but may also result in more false positives. Because of this, using a preset global threshold (e.g., 0.5) applied to all the bounding box candidates may lead to suboptimal solutions. In this paper, we propose a Test-time Self-guided Bounding-box Propagation (TSBP) method, leveraging Earth Mover's Distance (EMD) to enhance object detection in histology images. TSBP utilizes bounding boxes with high confidence to influence those with low confidence, leveraging visual similarities between them. This propagation mechanism enables bounding boxes to be selected in a controllable, explainable, and robust manner, which surpasses the effectiveness of using simple thresholds and uncertainty calibration methods. Importantly, TSBP does not necessitate additional labeled samples for model training or parameter estimation, unlike calibration methods. We conduct experiments on gland detection and cell detection tasks in histology images. The results show that our proposed TSBP significantly improves detection outcomes when working in conjunction with state-of-the-art deep learning-based detection networks. Compared to other methods such as uncertainty calibration, TSBP yields more robust and accurate object detection predictions while using no additional labeled samples. The code is available at https://github.com/jwhgdeu/TSBP.
The mean squared error and regularized versions of it are standard loss functions in supervised machine learning. However, calculating these losses for large data sets can be computationally demanding. Modifying an approach of J. Dick and M. Feischl [Journal of Complexity 67 (2021)], we present algorithms to reduce extensive data sets to a smaller size using rank-1 lattices. Rank-1 lattices are quasi-Monte Carlo (QMC) point sets that are, if carefully chosen, well-distributed in a multidimensional unit cube. The compression strategy in the preprocessing step assigns every lattice point a pair of weights depending on the original data and responses, representing its relative importance. As a result, the compressed data makes iterative loss calculations in optimization steps much faster. We analyze the errors of our QMC data compression algorithms and the cost of the preprocessing step for functions whose Fourier coefficients decay sufficiently fast so that they lie in certain Wiener algebras or Korobov spaces. In particular, we prove that our approach can lead to arbitrary high convergence rates as long as the functions are sufficiently smooth.
Recently, significant improvements in rate-distortion performance of image compression have been achieved with deep-learning techniques. A key factor in this success is the use of additional bits to predict an approximation of the latent vector, which is the output of the encoder, through another neural network. Then, only the difference between the prediction and the latent vector is coded into the bitstream, along with its estimated probability distribution. We introduce a new predictive structure consisting of the auxiliary coarse network and the main network, inspired by neural video compression. The auxiliary coarse network encodes the auxiliary information and predicts the approximation of the original image as multi-scale features. The main network encodes the residual between the predicted feature from the auxiliary coarse network and the feature of the original image. To further leverage our new structure, we propose Auxiliary info-guided Feature Prediction (AFP) module that uses global correlation to predict more accurate predicted features. Moreover, we present Context Junction module that refines the auxiliary feature from AFP module and produces the residuals between the refined features and the original image features. Finally, we introduce Auxiliary info-guided Parameter Estimation (APE) module, which predicts the approximation of the latent vector and estimates the probability distribution of these residuals. We demonstrate the effectiveness of the proposed modules by various ablation studies. Under extensive experiments, our model outperforms other neural image compression models and achieves a 19.49\% higher rate-distortion performance than VVC on Tecnick dataset.
The standard contextual bandit framework assumes fully observable and actionable contexts. In this work, we consider a new bandit setting with partially observable, correlated contexts and linear payoffs, motivated by the applications in finance where decision making is based on market information that typically displays temporal correlation and is not fully observed. We make the following contributions marrying ideas from statistical signal processing with bandits: (i) We propose an algorithmic pipeline named EMKF-Bandit, which integrates system identification, filtering, and classic contextual bandit algorithms into an iterative method alternating between latent parameter estimation and decision making. (ii) We analyze EMKF-Bandit when we select Thompson sampling as the bandit algorithm and show that it incurs a sub-linear regret under conditions on filtering. (iii) We conduct numerical simulations that demonstrate the benefits and practical applicability of the proposed pipeline.
Homodyned K-distribution (HK-distribution) parameter estimation in quantitative ultrasound (QUS) has been recently addressed using Bayesian Neural Networks (BNNs). BNNs have been shown to significantly reduce computational time in speckle statistics-based QUS without compromising accuracy and precision. Additionally, they provide estimates of feature uncertainty, which can guide the clinician's trust in the reported feature value. The total predictive uncertainty in Bayesian modeling can be decomposed into epistemic (uncertainty over the model parameters) and aleatoric (uncertainty inherent in the data) components. By decomposing the predictive uncertainty, we can gain insights into the factors contributing to the total uncertainty. In this study, we propose a method to compute epistemic and aleatoric uncertainties for HK-distribution parameters ($\alpha$ and $k$) estimated by a BNN, in both simulation and experimental data. In addition, we investigate the relationship between the prediction error and both uncertainties, shedding light on the interplay between these uncertainties and HK parameters errors.
Mixed multinomial logits are discrete mixtures introduced several decades ago to model the probability of choosing an attribute from $p$ possible candidates, in heterogeneous populations. The model has recently attracted attention in the AI literature, under the name softmax mixtures, where it is routinely used in the final layer of a neural network to map a large number $p$ of vectors in $\mathbb{R}^L$ to a probability vector. Despite its wide applicability and empirical success, statistically optimal estimators of the mixture parameters, obtained via algorithms whose running time scales polynomially in $L$, are not known. This paper provides a solution to this problem for contemporary applications, such as large language models, in which the mixture has a large number $p$ of support points, and the size $N$ of the sample observed from the mixture is also large. Our proposed estimator combines two classical estimators, obtained respectively via a method of moments (MoM) and the expectation-minimization (EM) algorithm. Although both estimator types have been studied, from a theoretical perspective, for Gaussian mixtures, no similar results exist for softmax mixtures for either procedure. We develop a new MoM parameter estimator based on latent moment estimation that is tailored to our model, and provide the first theoretical analysis for a MoM-based procedure in softmax mixtures. Although consistent, MoM for softmax mixtures can exhibit poor numerical performance, as observed other mixture models. Nevertheless, as MoM is provably in a neighborhood of the target, it can be used as warm start for any iterative algorithm. We study in detail the EM algorithm, and provide its first theoretical analysis for softmax mixtures. Our final proposal for parameter estimation is the EM algorithm with a MoM warm start.
In this paper, we investigate 3-D localization and frequency synchronization with multiple reconfigurable intelligent surfaces (RISs) in the presence of carrier frequency offset (CFO) for a stationary user equipment (UE). In line with the 6G goals of sustainability and efficiency, we focus on a frugal communication scenario with minimal spatial and spectral resources (i.e., narrowband single-input single-ouput system), considering both the presence and blockage of the line-of-sight (LoS) path between the base station (BS) and the UE. We design a generalized likelihood ratio test (GLRT)-based LoS detector, channel parameter estimation and localization algorithms, with varying complexity. To verify the efficiency of our estimators, we compare the root mean-squared error (RMSE) to the Cram\'er- Rao bound (CRB) of the unknown parameters. We also evaluate the sensitivity of our algorithms to the presence of uncontrolled multi-path components (MPC) and various levels of CFO. Simulation results showcase the effectiveness of the proposed algorithms under minimal hardware and spectral requirements, and a wide range of operating conditions, thereby confirming the viability of RIS-aided frugal localization in 6G scenarios.
This work presents the development of an online parameter estimation algorithm for the identification of resonating modes in a linear system of arbitrary order. The method employs a short-time Fourier transform of the input and output signals and uses a recursive least square (RLS) algorithm to detect resonant frequencies and damping factors of the resonant modes.
In recent years, dynamic parameterization of acoustic environments has garnered attention in audio processing. This focus includes room volume and reverberation time (RT60), which define local acoustics independent of sound source and receiver orientation. Previous studies show that purely attention-based models can achieve advanced results in room parameter estimation. However, their success relies on supervised pretrainings that require a large amount of labeled true values for room parameters and complex training pipelines. In light of this, we propose a novel Self-Supervised Blind Room Parameter Estimation (SS-BRPE) system. This system combines a purely attention-based model with self-supervised learning to estimate room acoustic parameters, from single-channel noisy speech signals. By utilizing unlabeled audio data for pretraining, the proposed system significantly reduces dependencies on costly labeled datasets. Our model also incorporates dynamic feature augmentation during fine-tuning to enhance adaptability and generalizability. Experimental results demonstrate that the SS-BRPE system not only achieves more superior performance in estimating room parameters than state-of-the-art (SOTA) methods but also effectively maintains high accuracy under conditions with limited labeled data. Code available at https://github.com/bjut-chunxiwang/SS-BRPE.
In this paper, we propose a novel and efficient parameter estimator based on $k$-Nearest Neighbor ($k$NN) and data generation method for the Lognormal-Rician turbulence channel. The Kolmogorov-Smirnov (KS) goodness-of-fit statistical tools are employed to investigate the validity of $k$NN approximation under different channel conditions and it is shown that the choice of $k$ plays a significant role in the approximation accuracy. We present several numerical results to illustrate that solving the constructed objective function can provide a reasonable estimate for the actual values. The accuracy of the proposed estimator is investigated in terms of the mean square error. The simulation results show that increasing the number of generation samples by two orders of magnitude does not lead to a significant improvement in estimation performance when solving the optimization problem by the gradient descent algorithm. However, the estimation performance under the genetic algorithm (GA) approximates to that of the saddlepoint approximation and expectation-maximization estimators. Therefore, combined with the GA, we demonstrate that the proposed estimator achieves the best tradeoff between the computation complexity and the accuracy.
Extreme-mass-ratio inspiral (EMRI) signals pose significant challenges in gravitational wave (GW) astronomy owing to their low-frequency nature and highly complex waveforms, which occupy a high-dimensional parameter space with numerous variables. Given their extended inspiral timescales and low signal-to-noise ratios, EMRI signals warrant prolonged observation periods. Parameter estimation becomes particularly challenging due to non-local parameter degeneracies, arising from multiple local maxima, as well as flat regions and ridges inherent in the likelihood function. These factors lead to exceptionally high time complexity for parameter analysis while employing traditional matched filtering and random sampling methods. To address these challenges, the present study applies machine learning to Bayesian posterior estimation of EMRI signals, leveraging the recently developed flow matching technique based on ODE neural networks. Our approach demonstrates computational efficiency several orders of magnitude faster than the traditional Markov Chain Monte Carlo (MCMC) methods, while preserving the unbiasedness of parameter estimation. We show that machine learning technology has the potential to efficiently handle the vast parameter space, involving up to seventeen parameters, associated with EMRI signals. Furthermore, to our knowledge, this is the first instance of applying machine learning, specifically the Continuous Normalizing Flows (CNFs), to EMRI signal analysis. Our findings highlight the promising potential of machine learning in EMRI waveform analysis, offering new perspectives for the advancement of space-based GW detection and GW astronomy.
The weak form is a ubiquitous, well-studied, and widely-utilized mathematical tool in modern computational and applied mathematics. In this work we provide a survey of both the history and recent developments for several fields in which the weak form can play a critical role. In particular, we highlight several recent advances in weak form versions of equation learning, parameter estimation, and coarse graining, which offer surprising noise robustness, accuracy, and computational efficiency. We note that this manuscript is a companion piece to our October 2024 SIAM News article of the same name. Here we provide more detailed explanations of mathematical developments as well as a more complete list of references. Lastly, we note that the software with which to reproduce the results in this manuscript is also available on our group's GitHub website https://github.com/MathBioCU .
Hyperspectral imaging (HSI) is emerging as a promising novel imaging modality with various potential surgical applications. Currently available cameras, however, suffer from poor integration into the clinical workflow because they require the lights to be switched off, or the camera to be manually recalibrated as soon as lighting conditions change. Given this critical bottleneck, the contribution of this paper is threefold: (1) We demonstrate that dynamically changing lighting conditions in the operating room dramatically affect the performance of HSI applications, namely physiological parameter estimation, and surgical scene segmentation. (2) We propose a novel learning-based approach to automatically recalibrating hyperspectral images during surgery and show that it is sufficiently accurate to replace the tedious process of white reference-based recalibration. (3) Based on a total of 742 HSI cubes from a phantom, porcine models, and rats we show that our recalibration method not only outperforms previously proposed methods, but also generalizes across species, lighting conditions, and image processing tasks. Due to its simple workflow integration as well as high accuracy, speed, and generalization capabilities, our method could evolve as a central component in clinical surgical HSI.
The exponential growth in data sizes and storage costs has brought considerable challenges to the data science community, requiring solutions to run learning methods on such data. While machine learning has scaled to achieve predictive accuracy in big data settings, statistical inference and uncertainty quantification tools are still lagging. Priority scientific fields collect vast data to understand phenomena typically studied with statistical methods like regression. In this setting, regression parameter estimation can benefit from efficient computational procedures, but the main challenge lies in computing error process parameters with complex covariance structures. Identifying and estimating these structures is essential for inference and often used for uncertainty quantification in machine learning with Gaussian Processes. However, estimating these structures becomes burdensome as data scales, requiring approximations that compromise the reliability of outputs. These approximations are even more unreliable when complexities like long-range dependencies or missing data are present. This work defines and proves the statistical properties of the Generalized Method of Wavelet Moments with Exogenous variables (GMWMX), a highly scalable, stable, and statistically valid method for estimating and delivering inference for linear models using stochastic processes in the presence of data complexities like latent dependence structures and missing data. Applied examples from Earth Sciences and extensive simulations highlight the advantages of the GMWMX.