A “Look-Backward-and-Forward” Adaptation Strategy for Assessing Parameter Estimation Error of Human Motion Prediction Model

Graphs are commonly used in various applications such as online social networks (OSNs), E-commerce systems and social recommender systems. Random walk sampling is often used to conduct statistical estimation over such graphs. This paper develops an algorithmic framework to reduce the mean square error of such statistical estimation. Our algorithmic framework is inspired by that the mean square error can be decomposed into a sum of the bias and variance of the estimator. More specifically, we apply the bootstrapping technique to design a bias reduction algorithm. A new feature of this bias reduction algorithm is that it allows the variance to increase whenever the bias can be further reduced. The increased variance may lead to a large mean square error of the estimator. We use multiple parallel random walks to reduce this variance such that it can be reduced to arbitrarily small by deploying a sufficient number of random walks. Our algorithmic framework enables one to attain different trade-offs between the sample complexity (i.e., number of parallel random walks) and the mean square error of the statistical estimation. Also, the proposed bias reduction algorithm is generic and can be applied to optimize a large class of random walk sampling algorithms. To demonstrate the versatility of the framework, we apply it to optimize the Metropolis random walk and simple random walk sampling. Extensive experiments confirm the effectiveness and efficiency of our proposed algorithmic framework.

Introduction: Quantile regression is a valuable alternative for survival data analysis, enabling flexible evaluations of covariate effects on survival outcomes with intuitive interpretations. It offers practical computation and reliability. However, challenges arise when applying quantile regression to censored data, particularly for upper quantiles. The minimum distance approach, utilizing dual-kernel estimation and the inverse cumulative distribution function, shows promise in addressing these challenges, especially with higher-dimensional covariates. Methods: This study contrasts two methods within the realm of quantile linear regression for survival analysis: check-based modeling and the minimum distance approach. Effectiveness is assessed across various scenarios through comprehensive simulation. Results: The simulation results showed that using the quantile regression model with the minimum distance approach reduces the percentage of root mean square error in parameter estimation compared to the quantile regression models based on the check loss function. Additionally, a larger sample size and reduced censoring percentage led to decreased root mean square error in parameter estimation. Conclusion: The research highlights the benefits of using the minimum distance approach for quantile regression. It reduces errors, improves model predictions, captures patterns, and optimizes parameters even with complete data. However, this approach has limitations. The accuracy of estimated quantiles can be influenced by the choice of distance metric and weighting scheme. The assumption of independence between censoring mechanism and survival time may not hold in real-world scenarios. Additionally, dealing with large datasets can be computationally complex.

Co-efficient of variation is a unitless measure of dispersion and is very frequently used in scientific investigations. This has motivated several researchers to propose estimators and tests concerning the co-efficient of variation of normal distribution(s). While proposing a class of estimators for the co-efficient of variation of a finite population, Tripathi et al., (2002) suggested that the estimator of co-efficient of variation of a finite population can also be used as an estimator of C.V for any distribution when the sampling design is SRSWR. This has motivated us to propose 28 estimators of finite population co-efficient of variation as estimators of co-efficient of variation of one component of a bivariate normal distribution when prior information is available regarding the second component. Cramer Rao type lower bound is derived to the mean square error of these estimators. Extensive simulation is carried out to compare these estimators. The results indicate that out of these 28 estimators, eight estimators have larger relative efficiency compared to the sample co-efficient of variation. The asymptotic mean square errors of the best estimators are derived to the order of  for the benefit of users of co-efficient of variation.

In this paper, we propose a genetic algorithm based approach to determine the pose of an object in Automated Visual Inspection having three degrees of freedom. We have investigated the effect of noise at 20 dB SNR and also mismatch resulting from incorrect correspondences between the object space points and the image space points, on the estimation of pose parameters. The maximum error in translation parameters is less than 0.45 cm and rotational error is less than 0.2 degree at 20 dB SNR. The error in parameter estimation is insignificant upto 7 pairs of mismatched points out of 24 points in object space and the results skyrockets when 8 or more pairs of points are mismatched. We have compared our result with that obtained by least square technique and it shows that GA based method outperform the gradient based technique when the number of vertices of the object to be inspected is small. These results have clearly established the robustness of GA in estimating the pose of an object with small number of vertices in automated visual inspection.

A convergence analysis of the angular position and velocity tracking errors and parametric estimation errors for a 2-link robot dynamics in the absence of noise exist in the literature (Slotine and Li in Applied nonlinear control. Prentice- Hall Inc, Englewood Cliffs, NJ, 1991). In this paper, we consider the effect of noise on the robot dynamics as well as on the parameter update equation. Noise in the robot dynamics arises due to errors in reading \(q,\dot{q}\), i.e., the angular positions and velocities of the robot link that are used for calculating the errors e, \(\dot{e}\) used to generate the feedback torque via the PD controller. Noise is chosen as Gaussian because it is produced as the cumulative effect of several small independent random effects like electrons moving in the motor wire and dust friction, and we know from the central limit theorem that the sum of a large number of small independent effects has a Gaussian distribution. Noise in the parametric update equation arises due to finite register effects in the digital computer. Both of these noises are modeled as white Gaussian, and the robot and parametric update dynamics have thus been modeled as nonlinear coupled stochastic differential equations. Using linearization of this coupled SDE system around the non-random components of the trajectory estimation error and parametric estimation errors, we first derive stochastic integral expressions for the random components in these errors. We then evaluate the average rate of change of the Lyapunov energy function using Ito calculus and obtain conditions on the noise amplitude so that the limiting value of this average rate of change is negative, guaranteeing asymptotic average stability of the system and parametric estimation algorithm. One of the novelties of this work is the new algorithm for parameter estimation which enables us to improve on the algorithm convergence rate as compared to previous work (Slotine and Li 1991). Finally, our stochastic algorithm is verified by performing hardware experiments with the actual PHANToM Omni robot.

Using Propensity Score Methods to Approximate Factorial Experimental Designs to Analyze the Relationship Between Two Variables and an Outcome

This study aims to accurately estimate the target’s motion parameter for constant wave (CW) radar and to reduce the computing complexity. Firstly, the echo signal of CW radar is separated into two sine signals by a novel signal transform, and the frequency of each sine signal is proportional to one of motion parameter for target; then these motion parameters are estimated by the frequency estimation algorithm which is based on chirp-z transform and Fast Fourier Transform (FFT). The statistical character of this method is analyzed and the mean square error of parameter estimation is deduced. The simulation result shows that the proposed method has a low computational cost and high performance close to Cramer-Rao lower bound (CRLB).KeywordsMotion ParameterLinear Frequency ModulationMonte Carlo ExperimentSine SignalLinear Frequency Modulation SignalThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

: Two studies were carried out to evaluate the quality of multidimensional item response theory (MIRT) model parameter estimates obtained from the computer program NOHARM. The purpose of the first study was to compute empirical estimates of the standard errors of the parameters. In addition, the parameter estimates were evaluated for bias and the effects of using different starting values and anchor items. The second study was included to compare the performance of NOHARM with the findings of an earlier simulation study which evaluated other MIRT estimation programs. Results were generally good, with fairly small standard errors for most parameter estimates and little indication of bias. Although the estimation procedure appeared to be robust under different starting values, the specific choice of items used to anchor the solution appears to have important effects on the magnitude of the estimated standard errors. The comparison of NOHARM with other programs was very favorable and supports the use of NORHARM for practical MIRT applications.

Direct investigations are required for future missions to small planetary bodies, in addition to obtain terrain maps and collecting samples from the surface. Rovers, mobile robots on surface of a planetary body, are effective in investigating into several specific points. We proposed a method of localization for navigating rovers to specific features. The proposed method measures two-way range between the rover and the mother spacecraft orbiting around the investigating planetary body using radio waves. The proposed method can be applied with reasonable accuracy on large and small planetary bodies and it can particularly be used with sub-hundred-meter-sized bodies, which conventional methods cannot be applied to. Sensitivity analysis of the proposed method is summarized in this paper, according with estimation errors in rotation parameters of the planetary body. A method of estimation is described here, which takes into account errors of rotational parameters.

Diffusion on graphs is ubiquitous with numerous high-impact applications, ranging from the study of residential segregation in socioeconomics and activation cascading in neuroscience, to the modeling of disease contagion in epidemiology and malware spreading in cybersecurity. In these applications, complete diffusion histories play an essential role in terms of identifying dynamical patterns, reflecting on precaution actions, and forecasting intervention effects. Despite their importance, complete diffusion histories are rarely available and are highly challenging to reconstruct due to ill-posedness, explosive search space, and scarcity of training data. To date, few methods exist for diffusion history reconstruction. They are exclusively based on the maximum likelihood estimation (MLE) formulation and require to know true diffusion parameters. In this paper, we study an even harder problem, namely reconstructing Diffusion history from A single SnapsHot (DASH), where we seek to reconstruct the history from only the final snapshot without knowing true diffusion parameters. We start with theoretical analyses that reveal a fundamental limitation of the MLE formulation. We prove: (a) estimation error of diffusion parameters is unavoidable due to NP-hardness of diffusion parameter estimation, and (b) the MLE formulation is sensitive to estimation error of diffusion parameters. To overcome the inherent limitation of the MLE formulation, we propose a novel barycenter formulation: finding the barycenter of the posterior distribution of histories, which is provably stable against the estimation error of diffusion parameters. We further develop an effective solver named DIffusion hiTting Times with Optimal proposal (DITTO) by reducing the problem to estimating posterior expected hitting times via the Metropolis-Hastings Markov chain Monte Carlo method (M-H MCMC) and employing an unsupervised graph neural network to learn an optimal proposal to accelerate the convergence of M-H MCMC. We conduct extensive experiments to demonstrate the efficacy of the proposed method. Our code is available at https://github.com/q-rz/KDD23-DITTO. The appendix can be found at https://arxiv.org/abs/2306.00488.

Sinusoidal speech coders have been widely studied for low bit rate coding around 4 kbit/s. However, the estimation error of the sinusoidal model parameters would seriously degrade the speech quality. In general, the estimation errors are caused by the effects of various types of speech signal or background noise. In this paper we propose a sinusoidal speech coder with robust parameter determination methods. They consist of spectro-temporal autocorrelation method for robust pitch determination, frequency shifting method for robust voicing level measurement, and residual-spectrum magnitude coding method for spectral magnitude compensation. From the experimental results, we can find the robustnesses of the proposed techniques. In addition, informal listening test of the synthesized speech confirms the effectiveness of the incorporated schemes.

We discuss the effect of imperfect knowledge of the transmission channel on the performance of multicarrier-OFDM and DMT -systems. The limited accuracy in the identification of the transmission channel is caused either by errors in the estimate of the channel or by variations in the channel due to motion of the transmitter, the receiver, and/or the reflectors. We develop a model to analyze the impact of these errors and derive analytic expressions for the signal-to-interference ratio (SIR) and the probability of error as a function of the initial SNR and the mean square error in channel estimation. We compare these results to those obtained assuming Gaussian errors and show that in both cases, the performance of multicarrier systems degrades when the normalized mean square error in channel estimation is greater than 10/sup -3/ (-30 dB). Finally, we extend these concepts to errors due to variations in the transmission channel.

Optimal linear minimum mean square error (MMSE) transceiver design techniques are proposed for Bayesian learning (BL)-based sparse parameter vector estimation in a multiple-input multiple-output (MIMO) wireless sensor network (WSN). Our proposed transceiver designs rely on majorization theory and hyperparameter estimates obtained from the BL module for minimizing the mean square error (MSE) of parameter estimation at the fusion center (FC). The linear transceiver design framework is initially proposed for the general scenario with arbitrary SNR sensor observations, followed by a special case with high-SNR sensor observations scenario. Our analysis also incorporates the channel correlation. The MMSE channel estimates are determined for the sensors (SNs), followed by a robust transceiver design procedure that is resilient to the channel state information (CSI) uncertainty arising due to the channel estimation error, an aberration that is unavoidable in practical implementations. Our simulation results demonstrate the improved performance of the proposed BL framework and optimal MMSE transceiver design in sparse parameter estimation relyingon realistic imperfect channel estimates over the benchmarks.

This paper describes the creation of a tracking system represented by a wheeled robot following a target (for example, a human). An artificial neural network (ANN) is used in the control loop of the robot to determine the range and bearing of the target, which are the tracking parameters. The main focus of the work is to develop a computer model of ANN capable of calculating near-optimal estimates of tracking parameters. In this case, the root mean square error (RMSE) of tracking parameter estimates is used as the criterion of efficiency of ANN operation. As a result, for the best ANN model the RMSE for the range was 0.009 m, and for the bearing was 1.006 degrees.

An improved technique for bounding the mean-square error of signal parameter estimates is presented. The resulting bounds are independent of the bias and stronger than previously known bounds.