We study grammar induction with mildly context-sensitive grammars for unsupervised discontinuous parsing. Using the probabilistic linear context-free rewriting system (LCFRS) formalism, our approach fixes the rule structure in advance and focuses on parameter learning with maximum likelihood. To reduce the computational complexity of both parsing and parameter estimation, we restrict the grammar formalism to LCFRS-2 (i.e., binary LCFRS with fan-out two) and further discard rules that require O(n^6) time to parse, reducing inference to O(n^5). We find that using a large number of nonterminals is beneficial and thus make use of tensor decomposition-based rank-space dynamic programming with an embedding-based parameterization of rule probabilities to scale up the number of nonterminals. Experiments on German and Dutch show that our approach is able to induce linguistically meaningful trees with continuous and discontinuous structures
Variance parameter estimation in linear mixed models is a challenge for many classical nonlinear optimization algorithms due to the positive-definiteness constraint of the random effects covariance matrix. We take a completely novel view on parameter estimation in linear mixed models by exploiting the intrinsic geometry of the parameter space. We formulate the problem of residual maximum likelihood estimation as an optimization problem on a Riemannian manifold. Based on the introduced formulation, we give geometric higher-order information on the problem via the Riemannian gradient and the Riemannian Hessian. Based on that, we test our approach with Riemannian optimization algorithms numerically. Our approach yields a higher quality of the variance parameter estimates compared to existing approaches.
Multi-object state estimation is a fundamental problem for robotic applications where a robot must interact with other moving objects. Typically, other objects' relevant state features are not directly observable, and must instead be inferred from observations. Particle filtering can perform such inference given approximate transition and observation models. However, these models are often unknown a priori, yielding a difficult parameter estimation problem since observations jointly carry transition and observation noise. In this work, we consider learning maximum-likelihood parameters using particle methods. Recent methods addressing this problem typically differentiate through time in a particle filter, which requires workarounds to the non-differentiable resampling step, that yield biased or high variance gradient estimates. By contrast, we exploit Fisher's identity to obtain a particle-based approximation of the score function (the gradient of the log likelihood) that yields a low variance estimate while only requiring stepwise differentiation through the transition and observation models. We apply our method to real data collected from autonomous vehicles (AVs) and show that it learns better models than existing techniques and is more stable in training, yielding an effective smoother for tracking the trajectories of vehicles around an AV.
Hawkes processes have recently risen to the forefront of tools when it comes to modeling and generating sequential events data. Multidimensional Hawkes processes model both the self and cross-excitation between different types of events and have been applied successfully in various domain such as finance, epidemiology and personalized recommendations, among others. In this work we present an adaptation of the Frank-Wolfe algorithm for learning multidimensional Hawkes processes. Experimental results show that our approach has better or on par accuracy in terms of parameter estimation than other first order methods, while enjoying a significantly faster runtime.
The geographically weighted regression (GWR) is an essential tool for estimating the spatial variation of relationships between dependent and independent variables in geographical contexts. However, GWR suffers from the problem that classical linear regressions, which compose the GWR model, are more prone to be underfitting, especially for significant volume and complex nonlinear data, causing inferior comparative performance. Nevertheless, some advanced models, such as the decision tree and the support vector machine, can learn features from complex data more effectively while they cannot provide explainable quantification for the spatial variation of localized relationships. To address the above issues, we propose a geographically gradient boosting weighted regression model, GWRBoost, that applies the localized additive model and gradient boosting optimization method to alleviate underfitting problems and retains explainable quantification capability for spatially-varying relationships between geographically located variables. Furthermore, we formulate the computation method of the Akaike information score for the proposed model to conduct the comparative analysis with the classic GWR algorithm. Simulation experiments and the empirical case study are applied to prove the efficient performance and practical value of GWRBoost. The results show that our proposed model can reduce the RMSE by 18.3% in parameter estimation accuracy and AICc by 67.3% in the goodness of fit.
We study the relationship between adversarial robustness and differential privacy in high-dimensional algorithmic statistics. We give the first black-box reduction from privacy to robustness which can produce private estimators with optimal tradeoffs among sample complexity, accuracy, and privacy for a wide range of fundamental high-dimensional parameter estimation problems, including mean and covariance estimation. We show that this reduction can be implemented in polynomial time in some important special cases. In particular, using nearly-optimal polynomial-time robust estimators for the mean and covariance of high-dimensional Gaussians which are based on the Sum-of-Squares method, we design the first polynomial-time private estimators for these problems with nearly-optimal samples-accuracy-privacy tradeoffs. Our algorithms are also robust to a nearly optimal fraction of adversarially-corrupted samples.
Mixtures of regression are a powerful class of models for regression learning with respect to a highly uncertain and heterogeneous response variable of interest. In addition to being a rich predictive model for the response given some covariates, the parameters in this model class provide useful information about the heterogeneity in the data population, which is represented by the conditional distributions for the response given the covariates associated with a number of distinct but latent subpopulations. In this paper, we investigate conditions of strong identifiability, rates of convergence for conditional density and parameter estimation, and the Bayesian posterior contraction behavior arising in finite mixture of regression models, under exact-fitted and over-fitted settings and when the number of components is unknown. This theory is applicable to common choices of link functions and families of conditional distributions employed by practitioners. We provide simulation studies and data illustrations, which shed some light on the parameter learning behavior found in several popular regression mixture models reported in the literature.
Physics-Informed Neural Networks (PINNs) have recently been proposed to solve scientific and engineering problems, where physical laws are introduced into neural networks as prior knowledge. With the embedded physical laws, PINNs enable the estimation of critical parameters, which are unobservable via physical tools, through observable variables. For example, Power Electronic Converters (PECs) are essential building blocks for the green energy transition. PINNs have been applied to estimate the capacitance, which is unobservable during PEC operations, using current and voltage, which can be observed easily during operations. The estimated capacitance facilitates self-diagnostics of PECs. Existing PINNs are often manually designed, which is time-consuming and may lead to suboptimal performance due to a large number of design choices for neural network architectures and hyperparameters. In addition, PINNs are often deployed on different physical devices, e.g., PECs, with limited and varying resources. Therefore, it requires designing different PINN models under different resource constraints, making it an even more challenging task for manual design. To contend with the challenges, we propose Automated Physics-Informed Neural Networks (AutoPINN), a framework that enables the automated design of PINNs by combining AutoML and PINNs. Specifically, we first tailor a search space that allows finding high-accuracy PINNs for PEC internal parameter estimation. We then propose a resource-aware search strategy to explore the search space to find the best PINN model under different resource constraints. We experimentally demonstrate that AutoPINN is able to find more accurate PINN models than human-designed, state-of-the-art PINN models using fewer resources.
In-home gait analysis is important for providing early diagnosis and adaptive treatments for individuals with gait disorders. Existing systems include wearables and pressure mats, but they have limited scalability. Recent studies have developed vision-based systems to enable scalable, accurate in-home gait analysis, but it faces privacy concerns due to the exposure of people's appearances. Our prior work developed footstep-induced structural vibration sensing for gait monitoring, which is device-free, wide-ranged, and perceived as more privacy-friendly. Although it has succeeded in temporal gait event extraction, it shows limited performance for spatial gait parameter estimation due to imprecise footstep localization. In particular, the localization error mainly comes from the estimation error of the wave arrival time at the vibration sensors and its error propagation to wave velocity estimations. Therefore, we present GaitVibe+, a vibration-based footstep localization method fused with temporarily installed cameras for in-home gait analysis. Our method has two stages: fusion and operating. In the fusion stage, both cameras and vibration sensors are installed to record only a few trials of the subject's footstep data, through which we characterize the uncertainty in wave arrival time and model the wave velocity profiles for the given structure. In the operating stage, we remove the camera to preserve privacy at home. The footstep localization is conducted by estimating the time difference of arrival (TDoA) over multiple vibration sensors, whose accuracy is improved through the reduced uncertainty and velocity modeling during the fusion stage. We evaluate GaitVibe+ through a real-world experiment with 50 walking trials. With only 3 trials of multi-modal fusion, our approach has an average localization error of 0.22 meters, which reduces the spatial gait parameter error from 111% to 27%.
In this paper, we introduce the concept of partially-connected Receiving Reconfigurable Intelligent Surfaces (R-RISs), which refers to metasurfaces designed to efficiently sense electromagnetic waveforms impinging on them, and perform localization of the users emitting them. The presented R-RIS hardware architecture comprises subarrays of meta-atoms, with each of them incorporating a waveguide assigned to direct the waveforms reaching its meta-atoms to a reception Radio-Frequency (RF) chain, enabling signal/channel parameter estimation. We particularly focus on the scenarios where the user is located in the far-field of all the R-RIS subarrays, and present a three-Dimensional (3D) localization method which is based on narrowband signaling and Angle of Arrival (AoA) estimates of the impinging signals at each single-receive-RF R-RIS subarray. For the AoA estimation, which relies on spatially sampled versions of the received signals via each subarray's phase configuration of meta-atoms, we devise an off-grid atomic norm minimization approach, which is followed by subspace-based root MUltiple SIgnal Classification (MUSIC). The AoA estimates are finally combined via a least-squared line intersection method to obtain the position coordinates of a user emitting synchronized localization pilots. Our derived theoretical Cram\'er Rao Lower Bounds (CRLBs) on the estimation parameters, which are compared with extensive computer simulation results of our localization approach, verify the effectiveness of the proposed R-RIS-empowered 3D localization system, which is showcased to offer cm-level positioning accuracy. Our comprehensive performance evaluations also demonstrate the impact of various system parameters on the localization performance, namely the training overhead and the distance between the R-RIS and the user, as well as the spacing among the R-RIS's subarrays and its partitioning patterns.
Temporal exponential random graph models (TERGM) are powerful statistical models that can be used to infer the temporal pattern of edge formation and elimination in complex networks (e.g., social networks). TERGMs can also be used in a generative capacity to predict longitudinal time series data in these evolving graphs. However, parameter estimation within this framework fails to capture many real-world properties of social networks, including: triadic relationships, small world characteristics, and social learning theories which could be used to constrain the probabilistic estimation of dyadic covariates. Here, we propose triadic temporal exponential random graph models (TTERGM) to fill this void, which includes these hierarchical network relationships within the graph model. We represent social network learning theory as an additional probability distribution that optimizes Markov chains in the graph vector space. The new parameters are then approximated via Monte Carlo maximum likelihood estimation. We show that our TTERGM model achieves improved fidelity and more accurate predictions compared to several benchmark methods on GitHub network data.
Parametric estimation of stochastic differential equations (SDEs) has been a subject of intense studies already for several decades. The Heston model for instance is driven by two coupled SDEs and is often used in financial mathematics for the dynamics of the asset prices and their volatility. Calibrating it to real data would be very useful in many practical scenarios. It is very challenging however, since the volatility is not directly observable. In this paper, a complete estimation procedure of the Heston model without and with jumps in the asset prices is presented. Bayesian regression combined with the particle filtering method is used as the estimation framework. Within the framework, we propose a novel approach to handle jumps in order to neutralise their negative impact on the estimates of the key parameters of the model. An improvement of the sampling in the particle filtering method is discussed as well. Our analysis is supported by numerical simulations of the Heston model to investigate the performance of the estimators. And a practical follow-along recipe is given to allow for finding adequate estimates from any given data.
This is a brief tutorial on the least square estimation technique that is straightforward yet effective for parameter estimation. The tutorial is focused on the linear LSEs instead of nonlinear versions, since most nonlinear LSEs can be approximated non-trivially using its linear counterparts. Linear LSEs can also provide insight into the study of the nonlinear techniques, e.g., Gauss-Newton method and Lavenberg-Marquardt method etc. Linear LSEs are computationally efficient for most occasions, so they are widely applied in practice. In this tutorial, both the original batch least square estimation and its recursive variants are reviewed comprehensively with detailed mathematical derivations.
In this paper, a constructive and systematic strategy with more apparent degrees of freedom to achieve the accurate estimation of unknown parameters via a control perspective is proposed. By adding a virtual control in the final equation of the gradient dynamics, the Gradient Estimator (GE) and Memory Regressor and Extension (MRE) approaches are extended. The solution of the virtual control law is identified by the P&I approach. The P&I approach is based on the choice of an appropriate implicit manifold and the generation of a suitable passive output and a related storage function. This facilitates the virtual control law being obtained in a way that the parametric error converges asymptotically to zero. Because the above ideas connect with the P&I approach and GE, the developed methodology is labeled the passivity and immersion-based modified gradient estimator (MGE). The proposed P&I-based modified gradient estimator is extended via the MRE approach. This modification provides improved transient response and fast convergence. Based on certain PE and non-PE examples, a comparative analysis is carried out to show the efficacy of the proposed approaches.
Neural Radiance Fields (NeRF) have achieved photorealistic novel views synthesis; however, the requirement of accurate camera poses limits its application. Despite analysis-by-synthesis extensions for jointly learning neural 3D representations and registering camera frames exist, they are susceptible to suboptimal solutions if poorly initialized. We propose L2G-NeRF, a Local-to-Global registration method for bundle-adjusting Neural Radiance Fields: first, a pixel-wise flexible alignment, followed by a frame-wise constrained parametric alignment. Pixel-wise local alignment is learned in an unsupervised way via a deep network which optimizes photometric reconstruction errors. Frame-wise global alignment is performed using differentiable parameter estimation solvers on the pixel-wise correspondences to find a global transformation. Experiments on synthetic and real-world data show that our method outperforms the current state-of-the-art in terms of high-fidelity reconstruction and resolving large camera pose misalignment. Our module is an easy-to-use plugin that can be applied to NeRF variants and other neural field applications. The Code and supplementary materials are available at https://rover-xingyu.github.io/L2G-NeRF/.
Using hydraulic models in control design in district heating networks can increase pumping efficiency and reduce sensitivity to hydraulic bottlenecks. These models are usually white-box, as they are obtained based on full knowledge of the district heating network and its parameters. This type of model is time-consuming to obtain, and might differ from the actual behavior of the system. In this paper, a method is proposed to obtain a grey-box hydraulic model for tree-shaped district heating systems: hydraulic parameters are estimated based on pressure measurements in only two locations. While previous works only estimate parameters related to pressure losses in pipes, this work also includes customers valves in the grey-box model structure, an important inclusion for control-oriented applications. Finally, a numerical example illustrates the proposed method on a small district heating network, showing its ability to obtain an accurate model on the basis of noisy measurements.
Parameter estimation in statistics and system identification relies on data that may contain sensitive information. To protect this sensitive information, the notion of \emph{differential privacy} (DP) has been proposed, which enforces confidentiality by introducing randomization in the estimates. Standard algorithms for differentially private estimation are based on adding an appropriate amount of noise to the output of a traditional point estimation method. This leads to an accuracy-privacy trade off, as adding more noise reduces the accuracy while increasing privacy. In this paper, we propose a new Unified Bayes Private Point (UBaPP) approach to Bayes point estimation of the unknown parameters of a data generating mechanism under a DP constraint, that achieves a better accuracy-privacy trade off than traditional approaches. We verify the performance of our approach on a simple numerical example.
Diffusion magnetic resonance imaging is sensitive to the microstructural properties of brain tissue. However, estimating clinically and scientifically relevant microstructural properties from the measured signals remains a highly challenging inverse problem that machine learning may help solve. This study investigated if recently developed rotationally invariant spherical convolutional neural networks can improve microstructural parameter estimation. We trained a spherical convolutional neural network to predict the ground-truth parameter values from efficiently simulated noisy data and applied the trained network to imaging data acquired in a clinical setting to generate microstructural parameter maps. Our network performed better than the spherical mean technique and multi-layer perceptron, achieving higher prediction accuracy than the spherical mean technique with less rotational variance than the multi-layer perceptron. Although we focused on a constrained two-compartment model of neuronal tissue, the network and training pipeline are generalizable and can be used to estimate the parameters of any Gaussian compartment model. To highlight this, we also trained the network to predict the parameters of a three-compartment model that enables the estimation of apparent neural soma density using tensor-valued diffusion encoding.
Accurate understanding of electromagnetic propagation properties in real environments is necessary for efficient design and deployment of cellular systems. In this paper, we show a method to estimate high-resolution channel parameters with a massive antenna array in real network deployments. An antenna array mounted on a vehicle is used to receive downlink long-term evolution (LTE) reference signals from neighboring base stations (BS) with mutual interference. Delay and angular information of multipath components is estimated with a novel inter-cell interference cancellation algorithm and an extension of the RIMAX algorithm. The estimated high-resolution channel parameters are consistent with the movement pattern of the vehicle and the geometry of the environment and allow for refined channel modeling and precise cellular positioning.
We propose a moving horizon estimation scheme for joint state and parameter estimation for nonlinear uncertain discrete-time systems. We establish robust exponential convergence of the combined estimation error subject to process disturbances and measurement noise. We employ a joint incremental input/output-to-state stability ($\delta$-IOSS) Lyapunov function to characterize nonlinear detectability for the states and (constant) parameters of the system. Sufficient conditions for the construction of a joint $\delta$-IOSS Lyapunov function are provided for a special class of nonlinear systems using a persistence of excitation condition. The theoretical results are illustrated by a numerical example.