Gene silencing via small interfering RNA (siRNA) represents a transformative tool in cancer therapy, offering specificity and reduced off-target effects compared to conventional treatments. A crucial step in siRNA-based therapies is endosomal escape, the release of siRNA from endosomes into the cytoplasm. Quantifying endosomal escape is challenging due to the dynamic nature of the process and limitations in imaging and analytical techniques. Traditional methods often rely on fluorescence intensity measurements or manual image processing, which are time-intensive and fail to capture continuous dynamics. This paper presents a novel computational framework that integrates automated image processing to analyze time-lapse fluorescent microscopy data of endosomal escape, hierarchical Bayesian inference, and stochastic simulations. Our method employs image segmentation techniques such as binary masks, Gaussian filters, and multichannel color quantification to extract precise spatial and temporal data from microscopy images. Using a hierarchical Bayesian approach, we estimate the parameters of a compartmental model that describes endosomal escape dynamics, accounting for variability over time. These parameters inform a Gillespie stochastic simulation algorithm, ensuring realistic simulations of siRNA release events over time. Our framework provides a scalable and reproducible method for quantifying endosomal escape. The model captures uncertainty and variability in parameter estimation, and endosomal escape dynamics. Additionally, synthetic data generation allows researchers to validate experimental findings and explore alternative conditions without extensive laboratory work. This integrated approach not only improves the accuracy of endosomal escape quantification but also provides predictive insights for optimizing siRNA delivery systems and advancing gene therapy research.
Model misspecification analysis strategies, such as anomaly detection, model validation, and model comparison are a key component of scientific model development. Over the last few years, there has been a rapid rise in the use of simulation-based inference (SBI) techniques for Bayesian parameter estimation, applied to increasingly complex forward models. To move towards fully simulation-based analysis pipelines, however, there is an urgent need for a comprehensive simulation-based framework for model misspecification analysis. In this work, we provide a solid and flexible foundation for a wide range of model discrepancy analysis tasks, using distortion-driven model misspecification tests. From a theoretical perspective, we introduce the statistical framework built around performing many hypothesis tests for distortions of the simulation model. We also make explicit analytic connections to classical techniques: anomaly detection, model validation, and goodness-of-fit residual analysis. Furthermore, we introduce an efficient self-calibrating training algorithm that is useful for practitioners. We demonstrate the performance of the framework in multiple scenarios, making the connection to classical results where they are valid. Finally, we show how to conduct such a distortion-driven model misspecification test for real gravitational wave data, specifically on the event GW150914.
We introduce GenAI4UQ, a software package for inverse uncertainty quantification in model calibration, parameter estimation, and ensemble forecasting in scientific applications. GenAI4UQ leverages a generative artificial intelligence (AI) based conditional modeling framework to address the limitations of traditional inverse modeling techniques, such as Markov Chain Monte Carlo methods. By replacing computationally intensive iterative processes with a direct, learned mapping, GenAI4UQ enables efficient calibration of model input parameters and generation of output predictions directly from observations. The software's design allows for rapid ensemble forecasting with robust uncertainty quantification, while maintaining high computational and storage efficiency. GenAI4UQ simplifies the model training process through built-in auto-tuning of hyperparameters, making it accessible to users with varying levels of expertise. Its conditional generative framework ensures versatility, enabling applicability across a wide range of scientific domains. At its core, GenAI4UQ transforms the paradigm of inverse modeling by providing a fast, reliable, and user-friendly solution. It empowers researchers and practitioners to quickly estimate parameter distributions and generate model predictions for new observations, facilitating efficient decision-making and advancing the state of uncertainty quantification in computational modeling. (The code and data are available at https://github.com/patrickfan/GenAI4UQ).
This work studies the problem of jointly estimating unknown parameters from Kronecker-structured multidimensional signals, which arises in applications like intelligent reflecting surface (IRS)-aided channel estimation. Exploiting the Kronecker structure, we decompose the estimation problem into smaller, independent subproblems across each dimension. Each subproblem is posed as a sparse recovery problem using basis expansion and solved using a novel off-grid sparse Bayesian learning (SBL)-based algorithm. Additionally, we derive probabilistic error bounds for the decomposition, quantify its denoising effect, and provide convergence analysis for off-grid SBL. Our simulations show that applying the algorithm to IRS-aided channel estimation improves accuracy and runtime compared to state-of-the-art methods through the low-complexity and denoising benefits of the decomposition step and the high-resolution estimation capabilities of off-grid SBL.
Background: Mathematical models based on ordinary differential equations (ODEs) are essential tools across various scientific disciplines, including biology, ecology, and healthcare informatics. They are used to simulate complex dynamic systems and inform decision-making. In this paper, we introduce BayesianFitForecast, an R toolbox specifically developed to streamline Bayesian parameter estimation and forecasting in ODE models, making it particularly relevant to health informatics and public health decision-making. The toolbox is available at https://github.com/gchowell/BayesianFitForecast/. Results: This toolbox enables automatic generation of Stan files, allowing users to configure models, define priors, and analyze results with minimal programming expertise. To demonstrate the versatility and robustness of BayesianFitForecast, we apply it to the analysis of the 1918 influenza pandemic in San Francisco, comparing Poisson and negative binomial error structures within the SEIR model. We also test it by fitting multiple time series of state variables using simulated data. BayesianFitForecast provides robust tools for evaluating model performance, including convergence diagnostics, posterior distributions, credible intervals, and performance metrics. Conclusion: By improving the accessibility of advanced Bayesian methods, this toolbox significantly broadens the application of Bayesian inference methods to dynamical systems critical for healthcare and epidemiological forecasting. A tutorial video demonstrating the toolbox's functionality is available at https://youtu.be/jnxMjz3V3n8.
Large Language Models (LLMs) are highly resource-intensive to fine-tune due to their enormous size. While low-rank adaptation is a prominent parameter-efficient fine-tuning approach, it suffers from sensitivity to hyperparameter choices, leading to instability in model performance on fine-tuning downstream tasks. This paper highlights the importance of effective parameterization in low-rank fine-tuning to reduce estimator variance and enhance the stability of final model outputs. We propose MonteCLoRA, an efficient fine-tuning technique, employing Monte Carlo estimation to learn an unbiased posterior estimation of low-rank parameters with low expected variance, which stabilizes fine-tuned LLMs with only O(1) additional parameters. MonteCLoRA shows significant improvements in accuracy and robustness, achieving up to 3.8% higher accuracy and 8.6% greater robustness than existing efficient fine-tuning methods on natural language understanding tasks with pre-trained RoBERTa-base. Furthermore, in generative tasks with pre-trained LLaMA-1-7B, MonteCLoRA demonstrates robust zero-shot performance with 50% lower variance than the contemporary efficient fine-tuning methods. The theoretical and empirical results presented in the paper underscore how parameterization and hyperpriors balance exploration-exploitation in the low-rank parametric space, therefore leading to more optimal and robust parameter estimation during efficient fine-tuning.
The analysis of neural power spectra plays a crucial role in understanding brain function and dysfunction. While recent efforts have led to the development of methods for decomposing spectral data, challenges remain in performing statistical analysis and group-level comparisons. Here, we introduce Bayesian Spectral Decomposition (BSD), a Bayesian framework for analysing neural spectral power. BSD allows for the specification, inversion, comparison, and analysis of parametric models of neural spectra, addressing limitations of existing methods. We first establish the face validity of BSD on simulated data and show how it outperforms an established method (\fooof{}) for peak detection on artificial spectral data. We then demonstrate the efficacy of BSD on a group-level study of EEG spectra in 204 healthy subjects from the LEMON dataset. Our results not only highlight the effectiveness of BSD in model selection and parameter estimation, but also illustrate how BSD enables straightforward group-level regression of the effect of continuous covariates such as age. By using Bayesian inference techniques, BSD provides a robust framework for studying neural spectral data and their relationship to brain function and dysfunction.
Recent advancements in machine learning have transformed the discovery of physical laws, moving from manual derivation to data-driven methods that simultaneously learn both the structure and parameters of governing equations. This shift introduces new challenges regarding the validity of the discovered equations, particularly concerning their uniqueness and, hence, identifiability. While the issue of non-uniqueness has been well-studied in the context of parameter estimation, it remains underexplored for algorithms that recover both structure and parameters simultaneously. Early studies have primarily focused on idealized scenarios with perfect, noise-free data. In contrast, this paper investigates how noise influences the uniqueness and identifiability of physical laws governed by partial differential equations (PDEs). We develop a comprehensive mathematical framework to analyze the uniqueness of PDEs in the presence of noise and introduce new algorithms that account for noise, providing thresholds to assess uniqueness and identifying situations where excessive noise hinders reliable conclusions. Numerical experiments demonstrate the effectiveness of these algorithms in detecting uniqueness despite the presence of noise.
We present a purely deep neural network-based approach for estimating long memory parameters of time series models that incorporate the phenomenon of long-range dependence. Parameters, such as the Hurst exponent, are critical in characterizing the long-range dependence, roughness, and self-similarity of stochastic processes. The accurate and fast estimation of these parameters holds significant importance across various scientific disciplines, including finance, physics, and engineering. We harnessed efficient process generators to provide high-quality synthetic training data, enabling the training of scale-invariant 1D Convolutional Neural Networks (CNNs) and Long Short-Term Memory (LSTM) models. Our neural models outperform conventional statistical methods, even those augmented with neural networks. The precision, speed, consistency, and robustness of our estimators are demonstrated through experiments involving fractional Brownian motion (fBm), the Autoregressive Fractionally Integrated Moving Average (ARFIMA) process, and the fractional Ornstein-Uhlenbeck (fOU) process. We believe that our work will inspire further research in the field of stochastic process modeling and parameter estimation using deep learning techniques.
The accurate modelling of structural dynamics is crucial across numerous engineering applications, such as Structural Health Monitoring (SHM), seismic analysis, and vibration control. Often, these models originate from physics-based principles and can be derived from corresponding governing equations, often of differential equation form. However, complex system characteristics, such as nonlinearities and energy dissipation mechanisms, often imply that such models are approximative and often imprecise. This challenge is further compounded in SHM, where sensor data is often sparse, making it difficult to fully observe the system's states. To address these issues, this paper explores the use of Physics-Informed Neural Networks (PINNs), a class of physics-enhanced machine learning (PEML) techniques, for the identification and estimation of dynamical systems. PINNs offer a unique advantage by embedding known physical laws directly into the neural network's loss function, allowing for simple embedding of complex phenomena, even in the presence of uncertainties. This study specifically investigates three key applications of PINNs: state estimation in systems with sparse sensing, joint state-parameter estimation, when both system response and parameters are unknown, and parameter estimation within a Bayesian framework to quantify uncertainties. The results demonstrate that PINNs deliver an efficient tool across all aforementioned tasks, even in presence of modelling errors. However, these errors tend to have a more significant impact on parameter estimation, as the optimization process must reconcile discrepancies between the prescribed model and the true system behavior. Despite these challenges, PINNs show promise in dynamical system modeling, offering a robust approach to handling uncertainties.
Extracting physical dynamical system parameters from recorded observations is key in natural science. Current methods for automatic parameter estimation from video train supervised deep networks on large datasets. Such datasets require labels, which are difficult to acquire. While some unsupervised techniques--which depend on frame prediction--exist, they suffer from long training times, initialization instabilities, only consider motion-based dynamical systems, and are evaluated mainly on synthetic data. In this work, we propose an unsupervised method to estimate the physical parameters of known, continuous governing equations from single videos suitable for different dynamical systems beyond motion and robust to initialization. Moreover, we remove the need for frame prediction by implementing a KL-divergence-based loss function in the latent space, which avoids convergence to trivial solutions and reduces model size and compute. We first evaluate our model on synthetic data, as commonly done. After which, we take the field closer to reality by recording Delfys75: our own real-world dataset of 75 videos for five different types of dynamical systems to evaluate our method and others. Our method compares favorably to others. %, yet, and real-world video datasets and demonstrate improved parameter estimation accuracy compared to existing methods. Code and data are available online:https://github.com/Alejandro-neuro/Learning_physics_from_video.
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.
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.
Gene expression prediction plays a vital role in transcriptome-wide association studies (TWAS), which seek to establish associations between tissue gene expression and complex traits. Traditional models rely on genetic variants in close genomic proximity to the gene of interest to predict the genetic component of gene expression. In this study, we propose a novel approach incorporating distal genetic variants acting through gene regulatory networks (GRNs) into gene expression prediction models, in line with the omnigenic model of complex trait inheritance. Using causal and coexpression GRNs reconstructed from genomic and transcriptomic data and modeling the data as a Bayesian network jointly over genetic variants and genes, inference of gene expression from observed genotypic data is achieved through a two-step process. Initially, the expression level of each gene in the network is predicted using its local genetic variants. The residuals, calculated as the differences between the observed and predicted expression levels, are then modeled using the genotype information of parent and/or grandparent nodes in the GRN. The final predicted expression level of the gene is obtained by summing the predictions from the local variants model and the residual model, effectively incorporating both local and distal genetic influences. Using various regularized regression techniques for parameter estimation, we found that GRN-based gene expression prediction outperformed the traditional local-variant approach on simulated data from the DREAM5 Systems Genetics Challenge and real data from the Geuvadis study and an eQTL mapping study in yeast. This study provides important insights into the challenge of gene expression prediction for TWAS. It reaffirms the importance of GRNs for understanding the genetic effects on gene expression and complex traits more generally.
Goodness-of-fit testing is often criticized for its lack of practical relevance: since ``all models are wrong'', the null hypothesis that the data conform to our model is ultimately always rejected as sample size grows. Despite this, probabilistic models are still used extensively, raising the more pertinent question of whether the model is \emph{good enough} for the task at hand. This question can be formalized as a robust goodness-of-fit testing problem by asking whether the data were generated from a distribution that is a mild perturbation of the model. In this paper, we show that existing kernel goodness-of-fit tests are not robust under common notions of robustness including both qualitative and quantitative robustness. We further show that robustification techniques using tilted kernels, while effective in the parameter estimation literature, are not sufficient to ensure both types of robustness in the testing setting. To address this, we propose the first robust kernel goodness-of-fit test, which resolves this open problem by using kernel Stein discrepancy (KSD) balls. This framework encompasses many well-known perturbation models, such as Huber's contamination and density-band models.
While fiducial inference was widely considered a big blunder by R.A. Fisher, the goal he initially set --`inferring the uncertainty of model parameters on the basis of observations' -- has been continually pursued by many statisticians. To this end, we develop a new statistical inference method called extended Fiducial inference (EFI). The new method achieves the goal of fiducial inference by leveraging advanced statistical computing techniques while remaining scalable for big data. EFI involves jointly imputing random errors realized in observations using stochastic gradient Markov chain Monte Carlo and estimating the inverse function using a sparse deep neural network (DNN). The consistency of the sparse DNN estimator ensures that the uncertainty embedded in observations is properly propagated to model parameters through the estimated inverse function, thereby validating downstream statistical inference. Compared to frequentist and Bayesian methods, EFI offers significant advantages in parameter estimation and hypothesis testing. Specifically, EFI provides higher fidelity in parameter estimation, especially when outliers are present in the observations; and eliminates the need for theoretical reference distributions in hypothesis testing, thereby automating the statistical inference process. EFI also provides an innovative framework for semi-supervised learning.
Linear causal models are important tools for modeling causal dependencies and yet in practice, only a subset of the variables can be observed. In this paper, we examine the parameter identifiability of these models by investigating whether the edge coefficients can be recovered given the causal structure and partially observed data. Our setting is more general than that of prior research - we allow all variables, including both observed and latent ones, to be flexibly related, and we consider the coefficients of all edges, whereas most existing works focus only on the edges between observed variables. Theoretically, we identify three types of indeterminacy for the parameters in partially observed linear causal models. We then provide graphical conditions that are sufficient for all parameters to be identifiable and show that some of them are provably necessary. Methodologically, we propose a novel likelihood-based parameter estimation method that addresses the variance indeterminacy of latent variables in a specific way and can asymptotically recover the underlying parameters up to trivial indeterminacy. Empirical studies on both synthetic and real-world datasets validate our identifiability theory and the effectiveness of the proposed method in the finite-sample regime. Code: https://github.com/dongxinshuai/scm-identify.
This paper presents an integrated perspective on robustness in regression. Specifically, we examine the relationship between traditional outlier-resistant robust estimation and robust optimization, which focuses on parameter estimation resistant to imaginary dataset-perturbations. While both are commonly regarded as robust methods, these concepts demonstrate a bias-variance trade-off, indicating that they follow roughly converse strategies.
Recent methods in modeling spatial extreme events have focused on utilizing parametric max-stable processes and their underlying dependence structure. In this work, we provide a unified approach for analyzing spatial extremes with little available data by estimating the distribution of model parameters or the spatial dependence directly. By employing recent developments in generative neural networks we predict a full sample-based distribution, allowing for direct assessment of uncertainty regarding model parameters or other parameter dependent functionals. We validate our method by fitting several simulated max-stable processes, showing a high accuracy of the approach, regarding parameter estimation, as well as uncertainty quantification. Additional robustness checks highlight the generalization and extrapolation capabilities of the model, while an application to precipitation extremes across Western Germany demonstrates the usability of our approach in real-world scenarios.