The intelligent reflecting surface (IRS) technology has recently attracted a lot of interest in wireless communications research. An IRS consists of passive reflective elements capable of tuning the phase, amplitude, frequency and polarization of the impinging waveforms. Given such desirable properties, the wireless channel characteristics can be controlled and optimized for specific signal design and processing needs -- thus promising significant potential in radar applications. In this paper, we establish the theoretical foundations for introducing IRS into a radar system and study the potential to improve target parameter estimation. More specifically, we will investigate the deployment of IRS in cases where the line-of-sight (LOS) link is weak or blocked by obstructions. We demonstrate that the IRS can provide a virtual or non-line-of-sight (NLOS) link between the radar and target leading to an enhanced radar performance. The effectiveness of such an IRS-provided virtual link in estimating the moving target parameters is illustrated under both optimized and non-optimized IRS scenarios. Numerical simulations indicate that the IRS can enhance the target parameter estimation when the LOS link is weaker than $\sim 10^{-1}$ in relative strength in comparison with the NLOS link.
It is crucially important to estimate unknown parameters in earth system models by integrating observation and numerical simulation. For many applications in earth system sciences, an optimization method which allows parameters to temporally change is required. In the present paper, an efficient and practical method to estimate the time-varying parameters of relatively low dimensional models is presented. In the newly proposed method, called Hybrid Offline Online Parameter Estimation with Particle Filtering (HOOPE-PF), an inflation method to maintain the spread of ensemble members in a sampling-importance-resampling particle filter is improved using a non-parametric posterior probabilistic distribution of time-invariant parameters obtained by comparing simulated and observed climatology. The HOOPE-PF outperforms the original sampling-importance-resampling particle filter in synthetic experiments with toy models and a real-data experiment with a conceptual hydrological model especially when the ensemble size is small. The advantage of HOOPE-PF is that its performance is not greatly affected by the size of perturbation to be added to ensemble members to maintain their spread while it is critically important to get the optimal performance in the original particle filter. Since HOOPE-PF is the extension of the existing particle filter which has been extensively applied to many earth system models such as land, ecosystem, hydrology, and paleoclimate reconstruction, the HOOPE-PF can be applied to improve the simulation of these earth system models by considering time-varying model parameters.
In federated learning, differences in the data or objectives between the participating nodes motivate approaches to train a personalized machine learning model for each node. One such approach is weighted averaging between a locally trained model and the global model. In this theoretical work, we study weighted model averaging for arbitrary scalar mean estimation problems under minimal assumptions on the distributions. In a variant of the bias-variance trade-off, we find that there is always some positive amount of model averaging that reduces the expected squared error compared to the local model, provided only that the local model has a non-zero variance. Further, we quantify the (possibly negative) benefit of weighted model averaging as a function of the weight used and the optimal weight. Taken together, this work formalizes an approach to quantify the value of personalization in collaborative learning and provides a framework for future research to test the findings in multivariate parameter estimation and under a range of assumptions.
We propose a new \textit{quadratic programming-based} method of approximating a nonstandard density using a multivariate Gaussian density. Such nonstandard densities usually arise while developing posterior samplers for unobserved components models involving inequality constraints on the parameters. For instance, Chan et al. (2016) provided a new model of trend inflation with linear inequality constraints on the stochastic trend. We implemented the proposed quadratic programming-based method for this model and compared it to the existing approximation. We observed that the proposed method works as well as the existing approximation in terms of the final trend estimates while achieving gains in terms of sample efficiency.
We investigate the issue of parameter estimation with nonuniform negative sampling for imbalanced data. We first prove that, with imbalanced data, the available information about unknown parameters is only tied to the relatively small number of positive instances, which justifies the usage of negative sampling. However, if the negative instances are subsampled to the same level of the positive cases, there is information loss. To maintain more information, we derive the asymptotic distribution of a general inverse probability weighted (IPW) estimator and obtain the optimal sampling probability that minimizes its variance. To further improve the estimation efficiency over the IPW method, we propose a likelihood-based estimator by correcting log odds for the sampled data and prove that the improved estimator has the smallest asymptotic variance among a large class of estimators. It is also more robust to pilot misspecification. We validate our approach on simulated data as well as a real click-through rate dataset with more than 0.3 trillion instances, collected over a period of a month. Both theoretical and empirical results demonstrate the effectiveness of our method.
In this study, two classes of methods including statistical and variational data assimilation algorithms will be described. In statistical methods, the model state is updated sequentially based on the previous estimate. Variational methods, on the other hand, seek an estimation in space and time by minimizing a cost function. Both of these methods require estimates of background state which is the prior information of the system and its error covariances. In terms of linear and Gaussian problems, they have the same solution. In the family of Kalman Filter algorithms, the conventional Kalman Filter (KF) and Ensemble Kalman Filter (EnKF) will be implemented. A three-dimension variational method (3D-Var) will be employed to illustrate the variational approaches. A simple case of an ordinary differential equation (ODE) is coupled to highlight the difference between these algorithms. Namely, a mass-spring system governed by a second order differential equation will be examined. We also look at the situation where a periodic external force is applied to the system. Then different data assimilation algorithms will be applied to this system. Results from the experiments will be analyzed to showcase the advantages and disadvantages of each method.
We propose a nested weighted Tchebycheff Multi-objective Bayesian optimization framework where we build a regression model selection procedure from an ensemble of models, towards better estimation of the uncertain parameters of the weighted-Tchebycheff expensive black-box multi-objective function. In existing work, a weighted Tchebycheff MOBO approach has been demonstrated which attempts to estimate the unknown utopia in formulating acquisition function, through calibration using a priori selected regression model. However, the existing MOBO model lacks flexibility in selecting the appropriate regression models given the guided sampled data and therefore, can under-fit or over-fit as the iterations of the MOBO progress, reducing the overall MOBO performance. As it is too complex to a priori guarantee a best model in general, this motivates us to consider a portfolio of different families of predictive models fitted with current training data, guided by the WTB MOBO; the best model is selected following a user-defined prediction root mean-square-error-based approach. The proposed approach is implemented in optimizing a multi-modal benchmark problem and a thin tube design under constant loading of temperature-pressure, with minimizing the risk of creep-fatigue failure and design cost. Finally, the nested weighted Tchebycheff MOBO model performance is compared with different MOBO frameworks with respect to accuracy in parameter estimation, Pareto-optimal solutions and function evaluation cost. This method is generalized enough to consider different families of predictive models in the portfolio for best model selection, where the overall design architecture allows for solving any high-dimensional (multiple functions) complex black-box problems and can be extended to any other global criterion multi-objective optimization methods where prior knowledge of utopia is required.
In this paper, we present a novel approach to compute ambiguities in thinned uniform linear arrays, i.e., sparse non-uniform linear arrays, via a mixed-integer program. Ambiguities arise when there exists a set of distinct directions-of-arrival, for which the corresponding steering matrix is rank-deficient and are associated with nonunique parameter estimation. Our approach uses Young tableaux for which a submatrix of the steering matrix has a vanishing determinant, which can be expressed through vanishing sums of unit roots. Each of these vanishing sums then corresponds to an ambiguous set of directions-of-arrival. We derive a method to enumerate such ambiguous sets using a mixed-integer program and present results on several examples.
The nature of the Fermi gamma-ray Galactic Center Excess (GCE) has remained a persistent mystery for over a decade. Although the excess is broadly compatible with emission expected due to dark matter annihilation, an explanation in terms of a population of unresolved astrophysical point sources e.g., millisecond pulsars, remains viable. The effort to uncover the origin of the GCE is hampered in particular by an incomplete understanding of diffuse emission of Galactic origin. This can lead to spurious features that make it difficult to robustly differentiate smooth emission, as expected for a dark matter origin, from more "clumpy" emission expected for a population of relatively bright, unresolved point sources. We use recent advancements in the field of simulation-based inference, in particular density estimation techniques using normalizing flows, in order to characterize the contribution of modeled components, including unresolved point source populations, to the GCE. Compared to traditional techniques based on the statistical distribution of photon counts, our machine learning-based method is able to utilize more of the information contained in a given model of the Galactic Center emission, and in particular can perform posterior parameter estimation while accounting for pixel-to-pixel spatial correlations in the gamma-ray map. This makes the method demonstrably more resilient to certain forms of model misspecification. On application to Fermi data, the method generically attributes a smaller fraction of the GCE flux to unresolved point sources when compared to traditional approaches. We nevertheless infer such a contribution to make up a non-negligible fraction of the GCE across all analysis variations considered, with at least $38^{+9}_{-19}\%$ of the excess attributed to unresolved point sources in our baseline analysis.
We introduce and analyze Generalized Time Domain Velocity Vector (GTVV), an extension of the previously presented acoustic multipath footprint extracted from the Ambisonic recordings. GTVV is better adapted to adverse acoustic conditions, and enables efficient parameter estimation of multiple plane wave components in the recorded multichannel mixture. Experiments on simulated data confirm the predicted theoretical advantages of these new spatio-temporal features.
We present a data-driven approach to characterizing nonidentifiability of a model's parameters and illustrate it through dynamic as well as steady kinetic models. By employing Diffusion Maps and their extensions, we discover the minimal combinations of parameters required to characterize the output behavior of a chemical system: a set of effective parameters for the model. Furthermore, we introduce and use a Conformal Autoencoder Neural Network technique, as well as a kernel-based Jointly Smooth Function technique, to disentangle the redundant parameter combinations that do not affect the output behavior from the ones that do. We discuss the interpretability of our data-driven effective parameters, and demonstrate the utility of the approach both for behavior prediction and parameter estimation. In the latter task, it becomes important to describe level sets in parameter space that are consistent with a particular output behavior. We validate our approach on a model of multisite phosphorylation, where a reduced set of effective parameters (nonlinear combinations of the physical ones) has previously been established analytically.
The high penetration of distributed renewable energy resources in power systems has changed their dynamic behavior, not only at the distribution level but also at the transmission levels. For analyses performed in this new reality of interconnected systems, a suitable equivalent model is required to represent the active dynamics of distribution systems. In this context, this paper proposes the application of a gray-box method to obtain an appropriate equivalent model for active distribution networks. From data measured at the point of common coupling, a trajectory sensitivity analysis is carried out to select the most important parameters of this equivalent model, which are then estimated by an evolutionary algorithm. The results show that the application of the sensitivity analysis can improve the quality of the parameter estimation process (since it focuses only on relevant parameters), enabling an efficient tuning of an equivalent ADN model.
Modeling biological dynamical systems is challenging due to the interdependence of different system components, some of which are not fully understood. To fill existing gaps in our ability to mechanistically model physiological systems, we propose to combine neural networks with physics-based models. Specifically, we demonstrate how we can approximate missing ordinary differential equations (ODEs) coupled with known ODEs using Bayesian filtering techniques to train the model parameters and simultaneously estimate dynamic state variables. As a study case we leverage a well-understood model for blood circulation in the human retina and replace one of its core ODEs with a neural network approximation, representing the case where we have incomplete knowledge of the physiological state dynamics. Results demonstrate that state dynamics corresponding to the missing ODEs can be approximated well using a neural network trained using a recursive Bayesian filtering approach in a fashion coupled with the known state dynamic differential equations. This demonstrates that dynamics and impact of missing state variables can be captured through joint state estimation and model parameter estimation within a recursive Bayesian state estimation (RBSE) framework. Results also indicate that this RBSE approach to training the NN parameters yields better outcomes (measurement/state estimation accuracy) than training the neural network with backpropagation through time in the same setting.
Automatic modulation recognition (AMR) is a promising technology for intelligent communication receivers to detect signal modulation schemes. Recently, the emerging deep learning (DL) research has facilitated high-performance DL-AMR approaches. However, most DL-AMR models only focus on recognition accuracy, leading to huge model sizes and high computational complexity, while some lightweight and low-complexity models struggle to meet the accuracy requirements. This letter proposes an efficient DL-AMR model based on phase parameter estimation and transformation, with convolutional neural network (CNN) and gated recurrent unit (GRU) as the feature extraction layers, which can achieve high recognition accuracy equivalent to the existing state-of-the-art models but reduces more than a third of the volume of their parameters. Meanwhile, our model is more competitive in training time and test time than the benchmark models with similar recognition accuracy. Moreover, we further propose to compress our model by pruning, which maintains the recognition accuracy higher than 90% while has less than 1/8 of the number of parameters comparing with state-of-the-art models.
With significant advances in deep learning, many computer vision applications have reached the inflection point. However, these deep learning models need large amount of labeled data for model training and optimum parameter estimation. Limited labeled data for model training results in over-fitting and impacts their generalization performance. However, the collection and annotation of large amount of data is a very time consuming and expensive operation. Further, due to privacy and security concerns, the large amount of labeled data could not be collected for certain applications such as those involving medical field. Self-training, Co-training, and Self-ensemble methods are three types of semi-supervised learning methods that can be used to exploit unlabeled data. In this paper, we propose self-ensemble based deep learning model that along with limited labeled data, harness unlabeled data for improving the generalization performance. We evaluated the proposed self-ensemble based deep-learning model for soft-biometric gender and age classification. Experimental evaluation on CelebA and VISOB datasets suggest gender classification accuracy of 94.46% and 81.00%, respectively, using only 1000 labeled samples and remaining 199k samples as unlabeled samples for CelebA dataset and similarly,1000 labeled samples with remaining 107k samples as unlabeled samples for VISOB dataset. Comparative evaluation suggest that there is $5.74\%$ and $8.47\%$ improvement in the accuracy of the self-ensemble model when compared with supervised model trained on the entire CelebA and VISOB dataset, respectively. We also evaluated the proposed learning method for age-group prediction on Adience dataset and it outperformed the baseline supervised deep-learning learning model with a better exact accuracy of 55.55 $\pm$ 4.28 which is 3.92% more than the baseline.
Watershed models such as the Soil and Water Assessment Tool (SWAT) consist of high-dimensional physical and empirical parameters. These parameters need to be accurately calibrated for models to produce reliable predictions for streamflow, evapotranspiration, snow water equivalent, and nutrient loading. Existing parameter estimation methods are time-consuming, inefficient, and computationally intensive, with reduced accuracy when estimating high-dimensional parameters. In this paper, we present a fast, accurate, and reliable methodology to calibrate the SWAT model (i.e., 21 parameters) using deep learning (DL). We develop DL-enabled inverse models based on convolutional neural networks to ingest streamflow data and estimate the SWAT model parameters. Hyperparameter tuning is performed to identify the optimal neural network architecture and the nine next best candidates. We use ensemble SWAT simulations to train, validate, and test the above DL models. We estimated the actual parameters of the SWAT model using observational data. We test and validate the proposed DL methodology on the American River Watershed, located in the Pacific Northwest-based Yakima River basin. Our results show that the DL models-based calibration is better than traditional parameter estimation methods, such as generalized likelihood uncertainty estimation (GLUE). The behavioral parameter sets estimated by DL have narrower ranges than GLUE and produce values within the sampling range even under high relative observational errors. This narrow range of parameters shows the reliability of the proposed workflow to estimate sensitive parameters accurately even under noise. Due to its fast and reasonably accurate estimations of process parameters, the proposed DL workflow is attractive for calibrating integrated hydrologic models for large spatial-scale applications.
Solving inverse problems, such as parameter estimation and optimal control, is a vital part of science. Many experiments repeatedly collect data and rely on machine learning algorithms to quickly infer solutions to the associated inverse problems. We find that state-of-the-art training techniques are not well-suited to many problems that involve physical processes. The highly nonlinear behavior, common in physical processes, results in strongly varying gradients that lead first-order optimizers like SGD or Adam to compute suboptimal optimization directions. We propose a novel hybrid training approach that combines higher-order optimization methods with machine learning techniques. We take updates from a scale-invariant inverse problem solver and embed them into the gradient-descent-based learning pipeline, replacing the regular gradient of the physical process. We demonstrate the capabilities of our method on a variety of canonical physical systems, showing that it yields significant improvements on a wide range of optimization and learning problems.
In this paper we extend the analysis of an agent-based model for adaptive trading, called asynchronous stochastic price pump (ASPP) introduced by Perepelitsa and Timofeyev (2019), to the model with heterogeneous distribution of psychological parameters of speculative optimism and pessimism across the population of traders. We show that the new model has a range of qualitatively different dynamics when the correlation between those factors ranges from low negative to large positive values. A statistical parameter estimation suggests a heterogeneous ASPP with negative correlation as a model of price variations of Bitcoin.
A plethora of prediction models of SARS-CoV-2 pandemic were proposed in the past. Prediction performances not only depend on the structure and features of the model, but also on its parametrization. Official databases are often biased due to lag in reporting of cases, changing testing policy or incompleteness of data. Moreover, model parametrization is time-dependent e.g. due to changing age-structures, new emerging virus variants, non-pharmaceutical interventions and ongoing vaccination programs. To cover these aspects, we develop a principled approach to parametrize SIR-type epidemiologic models of different complexities by embedding the model structure as a hidden layer into a general Input-Output Non-Linear Dynamical System (IO-NLDS). Non-explicitly modelled impacts on the system are imposed as inputs of the system. Observable data are coupled to hidden states of the model by appropriate data models considering possible biases of the data. We estimate model parameters including their time-dependence by a Bayesian knowledge synthesis process considering parameter ranges derived from external studies as prior information. We applied this approach on a SIR-type model and data of Germany and Saxony demonstrating good prediction performances. By our approach, we can estimate and compare for example the relative effectiveness of non-pharmaceutical interventions and can provide scenarios of the future course of the epidemic under specified conditions. Our method of parameter estimation can be translated to other data sets, i.e. other countries and other SIR-type models even for other disease contexts.
We consider a general class of regression models with normally distributed covariates, and the associated nonconvex problem of fitting these models from data. We develop a general recipe for analyzing the convergence of iterative algorithms for this task from a random initialization. In particular, provided each iteration can be written as the solution to a convex optimization problem satisfying some natural conditions, we leverage Gaussian comparison theorems to derive a deterministic sequence that provides sharp upper and lower bounds on the error of the algorithm with sample-splitting. Crucially, this deterministic sequence accurately captures both the convergence rate of the algorithm and the eventual error floor in the finite-sample regime, and is distinct from the commonly used "population" sequence that results from taking the infinite-sample limit. We apply our general framework to derive several concrete consequences for parameter estimation in popular statistical models including phase retrieval and mixtures of regressions. Provided the sample size scales near-linearly in the dimension, we show sharp global convergence rates for both higher-order algorithms based on alternating updates and first-order algorithms based on subgradient descent. These corollaries, in turn, yield multiple consequences, including: (a) Proof that higher-order algorithms can converge significantly faster than their first-order counterparts (and sometimes super-linearly), even if the two share the same population update and (b) Intricacies in super-linear convergence behavior for higher-order algorithms, which can be nonstandard (e.g., with exponent 3/2) and sensitive to the noise level in the problem. We complement these results with extensive numerical experiments, which show excellent agreement with our theoretical predictions.