Quantitative MRI (qMRI) offers significant advantages over weighted images by providing objective parameters related to tissue properties. Deep learning-based methods have demonstrated effectiveness in estimating quantitative maps from series of weighted images. In this study, we present qMRI Diffuser, a novel approach to qMRI utilising deep generative models. Specifically, we implemented denoising diffusion probabilistic models (DDPM) for T1 quantification in the brain, framing the estimation of quantitative maps as a conditional generation task. The proposed method is compared with the residual neural network (ResNet) and the recurrent inference machine (RIM) on both phantom and in vivo data. The results indicate that our method achieves improved accuracy and precision in parameter estimation, along with superior visual performance. Moreover, our method inherently incorporates stochasticity, enabling straightforward quantification of uncertainty. Hence, the proposed method holds significant promise for quantitative MR mapping.
This paper addresses the challenge of probabilistic parameter estimation given measurement uncertainty in real-time. We provide a general formulation and apply this to pose estimation for an autonomous visual landing system. We present three probabilistic parameter estimators: a least-squares sampling approach, a linear approximation method, and a probabilistic programming estimator. To evaluate these estimators, we introduce novel closed-form expressions for measuring calibration and sharpness specifically for multivariate normal distributions. Our experimental study compares the three estimators under various noise conditions. We demonstrate that the linear approximation estimator can produce sharp and well-calibrated pose predictions significantly faster than the other methods but may yield overconfident predictions in certain scenarios. Additionally, we demonstrate that these estimators can be integrated with a Kalman filter for continuous pose estimation during a runway approach where we observe a 50\% improvement in sharpness while maintaining marginal calibration. This work contributes to the integration of data-driven computer vision models into complex safety-critical aircraft systems and provides a foundation for developing rigorous certification guidelines for such systems.
In this paper, we apply the recently developed generalized parameter estimation-based observer design technique for state-affine systems to the practically important case of linear time-varying descriptor systems with uncertain parameters. We give simulation results of benchmark examples that illustrate the performance of the proposed adaptive observer.
Many application areas rely on models that can be readily simulated but lack a closed-form likelihood, or an accurate approximation under arbitrary parameter values. Existing parameter estimation approaches in this setting are generally approximate. Recent work on using neural network models to reconstruct the mapping from the data space to the parameters from a set of synthetic parameter-data pairs suffers from the curse of dimensionality, resulting in inaccurate estimation as the data size grows. We propose a dimension-reduced approach to likelihood-free estimation which combines the ideas of reconstruction map estimation with dimension-reduction approaches based on subject-specific knowledge. We examine the properties of reconstruction map estimation with and without dimension reduction and explore the trade-off between approximation error due to information loss from reducing the data dimension and approximation error. Numerical examples show that the proposed approach compares favorably with reconstruction map estimation, approximate Bayesian computation, and synthetic likelihood estimation.
We propose a constrained generalized method of moments estimator (GMM) incorporating theoretical conditions for the unique existence of equilibrium prices for estimating conduct parameters in a log-linear model with homogeneous goods markets. First, we derive such conditions. Second, Monte Carlo simulations confirm that in a log-linear model, incorporating the conditions resolves the problems of implausibly low or negative values of conduct parameters.
This paper analyzes monostatic sensing by a user equipment (UE) for a setting in which the UE is unable to resolve multiple targets due to their interference within a single resolution bin. It is shown how sensing accuracy, in terms of both detection rate and localization accuracy, can be boosted by a reconfigurable intelligent surface (RIS), which can be advantageously used to provide signal diversity and aid in resolving the targets. Specifically, assuming prior information on the presence of a cluster of targets, a RIS beam sweep procedure is used to facilitate the high resolution sensing. We derive the Cram\'er-Rao lower bounds (CRLBs) for channel parameter estimation and sensing and an upper bound on the detection probability. The concept of coherence is defined and analyzed theoretically. Then, we propose an orthogonal matching pursuit (OMP) channel estimation algorithm combined with data association to fuse the information of the non-RIS signal and the RIS signal and perform sensing. Finally, we provide numerical results to verify the potential of RIS for improving sensor resolution, and to demonstrate that the proposed methods can realize this potential for RIS-assisted high resolution sensing.
This study introduces a new approach to addressing positive and unlabeled (PU) data through the double exponential tilting model (DETM). Traditional methods often fall short because they only apply to selected completely at random (SCAR) PU data, where the labeled positive and unlabeled positive data are assumed to be from the same distribution. In contrast, our DETM's dual structure effectively accommodates the more complex and underexplored selected at random PU data, where the labeled and unlabeled positive data can be from different distributions. We rigorously establish the theoretical foundations of DETM, including identifiability, parameter estimation, and asymptotic properties. Additionally, we move forward to statistical inference by developing a goodness-of-fit test for the SCAR condition and constructing confidence intervals for the proportion of positive instances in the target domain. We leverage an approximated Bayes classifier for classification tasks, demonstrating DETM's robust performance in prediction. Through theoretical insights and practical applications, this study highlights DETM as a comprehensive framework for addressing the challenges of PU data.
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.
We prove convergence guarantees for generalized low-rank matrix sensing -- i.e., where matrix sensing where the observations may be passed through some nonlinear link function. We focus on local convergence of the optimal estimator, ignoring questions of optimization. In particular, assuming the minimizer of the empirical loss $\theta^0$ is in a constant size ball around the true parameters $\theta^*$, we prove that $d(\theta^0,\theta^*)=\tilde{O}(\sqrt{dk^2/n})$. Our analysis relies on tools from Riemannian geometry to handle the rotational symmetry in the parameter space.
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.
In this project, we propose to explore the Kalman filter's performance for estimating asset prices. We begin by introducing a stochastic mean-reverting processes, the Ornstein-Uhlenbeck (OU) model. After this we discuss the Kalman filter in detail, and its application with this model. After a demonstration of the Kalman filter on a simulated OU process and a discussion of maximum likelihood estimation (MLE) for estimating model parameters, we apply the Kalman filter with the OU process and trailing parameter estimation to real stock market data. We finish by proposing a simple day-trading algorithm using the Kalman filter with the OU process and backtest its performance using Apple's stock price. We then move to the Heston model, a combination of Geometric Brownian Motion and the OU process. Maximum likelihood estimation is commonly used for Heston model parameter estimation, which results in very complex forms. Here we propose an alternative but easier way of parameter estimation, called the method of moments (MOM). After the derivation of these estimators, we again apply this method to real stock data to assess its performance.
Dynamic metasurface antennas (DMAs) represent a novel transceiver array architecture for extremely large-scale (XL) communications, offering the advantages of reduced power consumption and lower hardware costs compared to conventional arrays. This paper focuses on near-field channel estimation for XL-DMAs. We begin by analyzing the near-field characteristics of uniform planar arrays (UPAs) and introducing the Oblong Approx. model. This model decouples elevation-azimuth (EL-AZ) parameters for XL-DMAs, providing an effective means to characterize the near-field effect. It offers simpler mathematical expressions than the second-order Taylor expansion model, all while maintaining negligible model errors for oblong-shaped arrays. Building on the Oblong Approx. model, we propose an EL-AZ-decoupled estimation framework that involves near- and far-field parameter estimation for AZ/EL and EL/AZ directions, respectively. The former is formulated as a distributed compressive sensing problem, addressed using the proposed off-grid distributed orthogonal least squares algorithm, while the latter involves a straightforward parallelizable search. Crucially, we illustrate the viability of decoupled EL-AZ estimation for near-field UPAs, exhibiting commendable performance and linear complexity correlated with the number of metasurface elements. Moreover, we design an measurement matrix optimization method with the Lorentzian constraint on DMAs and highlight the estimation performance degradation resulting from this constraint.
Intelligent reflecting surface (IRS) has the potential to enhance sensing performance, due to its capability of reshaping the echo signals. Different from the existing literature, which has commonly focused on IRS beamforming optimization, in this paper, we pay special attention to designing effective signal processing approaches to extract sensing information from IRS-reshaped echo signals. To this end, we investigate an IRS-assisted non-line-of-sight (NLOS) target detection and multi-parameter estimation problem in orthogonal frequency division multiplexing (OFDM) systems. To address this problem, we first propose a novel detection and direction estimation framework, including a low-overhead hierarchical codebook that allows the IRS to generate three-dimensional beams with adjustable beam direction and width, a delay spectrum peak-based beam training scheme for detection and direction estimation, and a beam refinement scheme for further enhancing the accuracy of the direction estimation. Then, we propose a target range and velocity estimation scheme by extracting the delay-Doppler information from the IRS-reshaped echo signals. Numerical results demonstrate that the proposed schemes can achieve 99.7% target detection rate, a 10^{-3}-rad level direction estimation accuracy, and a 10^{-6}-m/10^{-5}-m/s level range/velocity estimation accuracy.
We propose a novel method for blind bistatic radar parameter estimation (RPE), which enables integrated sensing and communications (ISAC) by allowing passive (receive) base stations (BSs) to extract radar parameters (ranges and velocities of targets), without requiring knowledge of the information sent by an active (transmit) BS to its users. The contributed method is formulated with basis on the covariance of received signals, and under a generalized doubly-dispersive channel model compatible with most of the waveforms typically considered for ISAC, such as orthogonal frequency division multiplexing (OFDM), orthogonal time frequency space (OTFS) and affine frequency division multiplexing (AFDM). The original non-convex problem, which includes an $\ell_0$-norm regularization term in order to mitigate clutter, is solved not by relaxation to an $\ell_1$-norm, but by introducing an arbitrarily-tight approximation then relaxed via fractional programming (FP). Simulation results show that the performance of the proposed method approaches that of an ideal system with perfect knowledge of the transmit signal covariance with an increasing number of transmit frames.
This work introduces a novel and efficient Bayesian federated learning algorithm, namely, the Federated Averaging stochastic Hamiltonian Monte Carlo (FA-HMC), for parameter estimation and uncertainty quantification. We establish rigorous convergence guarantees of FA-HMC on non-iid distributed data sets, under the strong convexity and Hessian smoothness assumptions. Our analysis investigates the effects of parameter space dimension, noise on gradients and momentum, and the frequency of communication (between the central node and local nodes) on the convergence and communication costs of FA-HMC. Beyond that, we establish the tightness of our analysis by showing that the convergence rate cannot be improved even for continuous FA-HMC process. Moreover, extensive empirical studies demonstrate that FA-HMC outperforms the existing Federated Averaging-Langevin Monte Carlo (FA-LD) algorithm.
Cognitive diagnosis has been developed for decades as an effective measurement tool to evaluate human cognitive status such as ability level and knowledge mastery. It has been applied to a wide range of fields including education, sport, psychological diagnosis, etc. By providing better awareness of cognitive status, it can serve as the basis for personalized services such as well-designed medical treatment, teaching strategy and vocational training. This paper aims to provide a survey of current models for cognitive diagnosis, with more attention on new developments using machine learning-based methods. By comparing the model structures, parameter estimation algorithms, model evaluation methods and applications, we provide a relatively comprehensive review of the recent trends in cognitive diagnosis models. Further, we discuss future directions that are worthy of exploration. In addition, we release two Python libraries: EduData for easy access to some relevant public datasets we have collected, and EduCDM that implements popular CDMs to facilitate both applications and research purposes.
This letter proposes a new method for joint state and parameter estimation in uncertain dynamical systems. We exploit the partial errors-in-variables (PEIV) principle and formulate a regression problem in the sense of weighted total least squares, where the uncertainty in the parameter prior is explicitly considered. Based thereon, the PEIV regression can be solved iteratively through the Kalman smoothing and the regularized least squares for estimating the state and the parameter, respectively. The simulations demonstrate improved accuracy of the proposed method compared to existing approaches, including the joint maximum a posterior-maximum likelihood, the expectation maximisation, and the augmented state extended Kalman smoother.
Quantum effects like entanglement and coherent amplification can be used to drastically enhance the accuracy of quantum parameter estimation beyond classical limits. However, challenges such as decoherence and time-dependent errors hinder Heisenberg-limited amplification. We introduce Quantum Signal-Processing Phase Estimation algorithms that are robust against these challenges and achieve optimal performance as dictated by the Cram\'{e}r-Rao bound. These algorithms use quantum signal transformation to decouple interdependent phase parameters into largely orthogonal ones, ensuring that time-dependent errors in one do not compromise the accuracy of learning the other. Combining provably optimal classical estimation with near-optimal quantum circuit design, our approach achieves a standard deviation accuracy of $10^{-4}$ radians for estimating unwanted swap angles in superconducting two-qubit experiments, using low-depth ($<10$) circuits. This represents up to two orders of magnitude improvement over existing methods. Theoretically and numerically, we demonstrate the optimality of our algorithm against time-dependent phase errors, observing that the variance of the time-sensitive parameter $\varphi$ scales faster than the asymptotic Heisenberg scaling in the small-depth regime. Our results are rigorously validated against the quantum Fisher information, confirming our protocol's ability to achieve unmatched precision for two-qubit gate learning.
Many dynamical systems are subjected to stochastic influences, such as random excitations, noise, and unmodeled behavior. Tracking the system's state and parameters based on a physical model is a common task for which filtering algorithms, such as Kalman filters and their non-linear extensions, are typically used. However, many of these filters use assumptions on the transition probabilities or the covariance model, which can lead to inaccuracies in non-linear systems. We will show the application of a stochastic coupling filter that can approximate arbitrary transition densities under non-Gaussian noise. The filter is based on transport maps, which couple the approximation densities to a user-chosen reference density, allowing for straightforward sampling and evaluation of probabilities.
In this paper we consider calibration of hydraulic models for district heating systems based on operational data. We extend previous theoretical work on the topic to handle real-world complications, namely unknown valve characteristics and hysteresis. We generate two datasets in the Smart Water Infrastructure laboratory in Aalborg, Denmark, on which we evaluate the proposed procedure. In the first data set the system is controlled in such a way to excite all operational modes in terms of combinations of valve set-points. Here the best performing model predicted volume flow rates within roughly 5 and 10 \% deviation from the mean volume flow rate for the consumer with the highest and lowest mean volume flow rates respectively. This performance was met in the majority of the operational region. In the second data set, the system was controlled in order to mimic real load curves. The model trained on this data set performed similarly well when evaluated on data in the operational range represented in the training data. However, the model performance deteriorated when evaluated on data which was not represented in the training data.