Major depressive disorder (MDD) presents challenges in diagnosis and treatment due to its complex and heterogeneous nature. Emerging evidence indicates that reward processing abnormalities may serve as a behavioral marker for MDD. To measure reward processing, patients perform computer-based behavioral tasks that involve making choices or responding to stimulants that are associated with different outcomes. Reinforcement learning (RL) models are fitted to extract parameters that measure various aspects of reward processing to characterize how patients make decisions in behavioral tasks. Recent findings suggest the inadequacy of characterizing reward learning solely based on a single RL model; instead, there may be a switching of decision-making processes between multiple strategies. An important scientific question is how the dynamics of learning strategies in decision-making affect the reward learning ability of individuals with MDD. Motivated by the probabilistic reward task (PRT) within the EMBARC study, we propose a novel RL-HMM framework for analyzing reward-based decision-making. Our model accommodates learning strategy switching between two distinct approaches under a hidden Markov model (HMM): subjects making decisions based on the RL model or opting for random choices. We account for continuous RL state space and allow time-varying transition probabilities in the HMM. We introduce a computationally efficient EM algorithm for parameter estimation and employ a nonparametric bootstrap for inference. We apply our approach to the EMBARC study to show that MDD patients are less engaged in RL compared to the healthy controls, and engagement is associated with brain activities in the negative affect circuitry during an emotional conflict task.
Dense-to-sparse gating mixture of experts (MoE) has recently become an effective alternative to a well-known sparse MoE. Rather than fixing the number of activated experts as in the latter model, which could limit the investigation of potential experts, the former model utilizes the temperature to control the softmax weight distribution and the sparsity of the MoE during training in order to stabilize the expert specialization. Nevertheless, while there are previous attempts to theoretically comprehend the sparse MoE, a comprehensive analysis of the dense-to-sparse gating MoE has remained elusive. Therefore, we aim to explore the impacts of the dense-to-sparse gate on the maximum likelihood estimation under the Gaussian MoE in this paper. We demonstrate that due to interactions between the temperature and other model parameters via some partial differential equations, the convergence rates of parameter estimations are slower than any polynomial rates, and could be as slow as $\mathcal{O}(1/\log(n))$, where $n$ denotes the sample size. To address this issue, we propose using a novel activation dense-to-sparse gate, which routes the output of a linear layer to an activation function before delivering them to the softmax function. By imposing linearly independence conditions on the activation function and its derivatives, we show that the parameter estimation rates are significantly improved to polynomial rates. Finally, we conduct a simulation study to empirically validate our theoretical results.
This paper presents a structure-preserving Bayesian approach for learning nonseparable Hamiltonian systems using stochastic dynamic models allowing for statistically-dependent, vector-valued additive and multiplicative measurement noise. The approach is comprised of three main facets. First, we derive a Gaussian filter for a statistically-dependent, vector-valued, additive and multiplicative noise model that is needed to evaluate the likelihood within the Bayesian posterior. Second, we develop a novel algorithm for cost-effective application of Bayesian system identification to high-dimensional systems. Third, we demonstrate how structure-preserving methods can be incorporated into the proposed framework, using nonseparable Hamiltonians as an illustrative system class. We assess the method's performance based on the forecasting accuracy of a model estimated from single-trajectory data. We compare the Bayesian method to a state-of-the-art machine learning method on a canonical nonseparable Hamiltonian model and a chaotic double pendulum model with small, noisy training datasets. The results show that using the Bayesian posterior as a training objective can yield upwards of 724 times improvement in Hamiltonian mean squared error using training data with up to 10% multiplicative noise compared to a standard training objective. Lastly, we demonstrate the utility of the novel algorithm for parameter estimation of a 64-dimensional model of the spatially-discretized nonlinear Schr\"odinger equation with data corrupted by up to 20% multiplicative noise.
Phosphorus removal is vital in wastewater treatment to reduce reliance on limited resources. Deep reinforcement learning (DRL) is a machine learning technique that can optimize complex and nonlinear systems, including the processes in wastewater treatment plants, by learning control policies through trial and error. However, applying DRL to chemical and biological processes is challenging due to the need for accurate simulators. This study trained six models to identify the phosphorus removal process and used them to create a simulator for the DRL environment. Although the models achieved high accuracy (>97%), uncertainty and incorrect prediction behavior limited their performance as simulators over longer horizons. Compounding errors in the models' predictions were identified as one of the causes of this problem. This approach for improving process control involves creating simulation environments for DRL algorithms, using data from supervisory control and data acquisition (SCADA) systems with a sufficient historical horizon without complex system modeling or parameter estimation.
Quantitative ultrasound (QUS) analyzes the ultrasound backscattered data to find the properties of scatterers that correlate with the tissue microstructure. Statistics of the envelope of the backscattered radiofrequency (RF) data can be utilized to estimate several QUS parameters. Different distributions have been proposed to model envelope data. The homodyned K-distribution (HK distribution) is one of the most comprehensive distributions that can model ultrasound backscattered envelope data under diverse scattering conditions (varying scatterer number density and coherent scattering). The scatterer clustering parameter (alpha) and the ratio of the coherent to diffuse scattering power (k) are the parameters of this distribution that have been used extensively for tissue characterization in diagnostic ultrasound. The estimation of these two parameters (which we refer to as HK parameters) is done using optimization algorithms in which statistical features such as the envelope point-wise signalto-noise ratio (SNR), skewness, kurtosis, and the log-based moments have been utilized as input to such algorithms. The optimization methods minimize the difference between features and their theoretical value from the HK model. We propose that the true value of these statistical features is a hyperplane that covers a small portion of the feature space. In this paper, we follow two approaches to reduce the effect of sample features' error. We propose a model projection neural network based on denoising autoencoders to project the noisy features into this space based on this assumption. We also investigate if the noise distribution can be learned by the deep estimators. We compare the proposed methods with conventional methods using simulations, an experimental phantom, and data from an in vivo animal model of hepatic steatosis. A demo code are available online at http://code.sonography.ai
Adaptive backstepping control provides a feasible solution to achieve asymptotic tracking for mismatched uncertain nonlinear systems. However, input-to-state stability depends on high-gain feedback generated by nonlinear damping terms, and closed-loop exponential stability with parameter convergence involves a stringent condition named persistent excitation (PE). This paper proposes a composite learning backstepping control (CLBC) strategy based on modular backstepping and high-order tuners to compensate for the transient process of parameter estimation and achieve closed-loop exponential stability without the nonlinear damping terms and the PE condition. A novel composite learning mechanism that maximizes the staged exciting strength is designed for parameter estimation, such that parameter convergence can be achieved under a condition of interval excitation (IE) or even partial IE that is strictly weaker than PE. An extra prediction error is employed in the adaptive law to ensure the transient performance without nonlinear damping terms. The exponential stability of the closed-loop system is proved rigorously under the partial IE or IE condition. Simulations have demonstrated the effectiveness and superiority of the proposed method in both parameter estimation and control compared to state-of-the-art methods.
Room geometry inference (RGI) aims at estimating room shapes from measured room impulse responses (RIRs) and has received lots of attention for its importance in environment-aware audio rendering and virtual acoustic representation of a real venue. A lot of estimation models utilizing time difference of arrival (TDoA) or time of arrival (ToA) information in RIRs have been proposed. However, an estimation model should be able to handle more general features and complex relations between reflections to cope with various room shapes and uncertainties such as the unknown number of walls. In this study, we propose a deep neural network that can estimate various room shapes without prior assumptions on the shape or number of walls. The proposed model consists of three sub-networks: a feature extractor, parameter estimation, and evaluation networks, which extract key features from RIRs, estimate parameters, and evaluate the confidence of estimated parameters, respectively. The network is trained by about 40,000 RIRs simulated in rooms of different shapes using a single source and spherical microphone array and tested for rooms of unseen shapes and dimensions. The proposed algorithm achieves almost perfect accuracy in finding the true number of walls and shows negligible errors in room shapes.
The lack of anomaly detection methods during mechanized tunnelling can cause financial loss and deficits in drilling time. On-site excavation requires hard obstacles to be recognized prior to drilling in order to avoid damaging the tunnel boring machine and to adjust the propagation velocity. The efficiency of the structural anomaly detection can be increased with intelligent optimization techniques and machine learning. In this research, the anomaly in a simple structure is detected by comparing the experimental measurements of the structural vibrations with numerical simulations using parameter estimation methods.
The Ultra-Reliable Low-Latency Communications (URLLC) paradigm in sixth-generation (6G) systems heavily relies on precise channel modeling, especially when dealing with rare and extreme events within wireless communication channels. This paper explores a novel methodology integrating Extreme Value Theory (EVT) and Generative Adversarial Networks (GANs) to achieve the precise channel modeling in real-time. The proposed approach harnesses EVT by employing the Generalized Pareto Distribution (GPD) to model the distribution of extreme events. Subsequently, Generative Adversarial Networks (GANs) are employed to estimate the parameters of the GPD. In contrast to conventional GAN configurations that focus on estimating the overall distribution, the proposed approach involves the incorporation of an additional block within the GAN structure. This specific augmentation is designed with the explicit purpose of directly estimating the parameters of the Generalized Pareto Distribution (GPD). Through extensive simulations across different sample sizes, the proposed GAN based approach consistently demonstrates superior adaptability, surpassing Maximum Likelihood Estimation (MLE), particularly in scenarios with limited sample sizes.
Reliable integration and operation of renewable distributed energy resources requires accurate distribution grid models. However, obtaining precise models is often prohibitively expensive, given their large scale and the ongoing nature of grid operations. To address this challenge, considerable efforts have been devoted to harnessing abundant consumption data for automatic model inference. The primary result of the paper is that, while the impedance of a line or a network can be estimated without synchronized phase angle measurements in a consistent way, the admittance cannot. Furthermore, a detailed statistical analysis is presented, quantifying the expected estimation errors of four prevalent admittance estimation methods. Such errors constitute fundamental model inference limitations that cannot be resolved with more data. These findings are empirically validated using synthetic data and real measurements from the town of Walenstadt, Switzerland, confirming the theory. The results contribute to our understanding of grid estimation limitations and uncertainties, offering guidance for both practitioners and researchers in the pursuit of more reliable and cost-effective solutions.
Extended ambiguity performance (EAP), which includes all grating lobes and side peaks, indicates the maximum detectable region without undesired peaks for target parameter estimation and is critical to radar sensor design. Driven by EAP requirements of bi-static sensing, we propose design criteria for orthogonal frequency division multiplexing (OFDM) reference signal (RS) patterns. The design not only improves EAP in both time delay and Doppler shift domains under different types of sensing algorithms, but also reduces resource overhead for integrated communication and sensing. With minimal modifications of post-FFT processing for current RS patterns, guard interval is extended beyond conventional cyclic prefix (CP), while maintaining inter-symbol-interference-(ISI)-free delay estimation. For standard-resolution sensing algorithms, a staggering offset of a linear slope that is relatively prime to the RS comb size is suggested. As for super-resolution sensing algorithms, necessary and sufficient conditions of comb RS staggering offsets, plus new patterns synthesized therefrom, are derived for the corresponding achievable EAP. Furthermore, we generalize the RS pattern design criterion for super-resolution sensing algorithms to irregular forms, which minimizes number of resource elements (REs) for associated algorithms to eliminate all side peaks. Starting from staggered comb pattern in current positioning RS, our generalized design eventually removes any regular form for ultimate flexibility. Overall, the proposed techniques are promising to extend the ISI- and ambiguity-free range of distance and speed estimates for radar sensing.
We consider the problem of efficiently simulating stochastic models of chemical kinetics. The Gillespie Stochastic Simulation algorithm (SSA) is often used to simulate these models, however, in many scenarios of interest, the computational cost quickly becomes prohibitive. This is further exasperated in the Bayesian inference context when estimating parameters of chemical models, as the intractability of the likelihood requires multiple simulations of the underlying system. To deal with issues of computational complexity in this paper, we propose a novel hybrid $\tau$-leap algorithm for simulating well-mixed chemical systems. In particular, the algorithm uses $\tau$-leap when appropriate (high population densities), and SSA when necessary (low population densities, when discrete effects become non-negligible). In the intermediate regime, a combination of the two methods, which leverages the properties of the underlying Poisson formulation, is employed. As illustrated through a number of numerical experiments the hybrid $\tau$ offers significant computational savings when compared to SSA without however sacrificing the overall accuracy. This feature is particularly welcomed in the Bayesian inference context, as it allows for parameter estimation of stochastic chemical kinetics at reduced computational cost.
In the software industry, two software engineering development best practices coexist: open-source and closed-source software. The former has a shared code that anyone can contribute, whereas the latter has a proprietary code that only the owner can access. Software reliability is crucial in the industry when a new product or update is released. Applying meta-heuristic optimization algorithms for closed-source software reliability prediction has produced significant and accurate results. Now, open-source software dominates the landscape of cloud-based systems. Therefore, providing results on open-source software reliability - as a quality indicator - would greatly help solve the open-source software reliability growth-modelling problem. The reliability is predicted by estimating the parameters of the software reliability models. As software reliability models are inherently nonlinear, traditional approaches make estimating the appropriate parameters difficult and ineffective. Consequently, software reliability models necessitate a high-quality parameter estimation technique. These objectives dictate the exploration of potential applications of meta-heuristic swarm intelligence optimization algorithms for optimizing the parameter estimation of nonhomogeneous Poisson process-based open-source software reliability modelling. The optimization algorithms are firefly, social spider, artificial bee colony, grey wolf, particle swarm, moth flame, and whale. The applicability and performance evaluation of the optimization modelling approach is demonstrated through two real open-source software reliability datasets. The results are promising.
Statistical models are often structurally unidentifiable, because different sets of parameters can lead to equal model outcomes. To be useful for prediction and parameter inference from data, stochastic population models need to be identifiable, this meaning that model parameters can be uniquely inferred from a large number of model observations. In particular, precise estimation of feeding rates in consumer-resource dynamics is crucial, because consumer-resource processes are central in determining biomass transport across ecosystems. Model parameters are usually estimated at stationarity, because in that case model analyses are often easier. In this contribution we analyze the problem of parameter redundancy in a multi-resource consumer-resource model, showing that model indentifiability depends on whether the dynamics have reached stationarity or not. To be precise, we: (i) Calculate the steady-state and out-of-equilibrium probability distributions of predator's abundances analytically using generating functions, which allow us to unveil parameter redundancy and carry out proper maximum likelihood estimation. (ii) Conduct \emph{in silico} experiments by tracking the abundance of consumers that are either searching for or handling prey, data then used for maximum likelihood parameter estimation. (iii) Show that, when model observations are recorded out of equilibrium, feeding parameters are truly identifiable, whereas if sampling is done solely at stationarity, only ratios of rates can be inferred from data (i.e., parameters are redundant). We discuss the implications of our results when inferring parameters of general dynamical models.
In this paper, we examine the parameter estimation performance of three well-known sinusoidal models for speech and audio. The first one is the standard Sinusoidal Model (SM), which is based on the Fast Fourier Transform (FFT). The second is the Exponentially Damped Sinusoidal Model (EDSM) which has been proposed in the last decade, and utilizes a subspace method for parameter estimation, and finally the extended adaptive Quasi-Harmonic Model (eaQHM), which has been recently proposed for AM-FM decomposition, and estimates the signal parameters using Least Squares on a set of basis function that are adaptive to the local characteristics of the signal. The parameter estimation of each model is briefly described and its performance is compared to the others in terms of signal reconstruction accuracy versus window size on a variety of synthetic signals and versus the number of sinusoids on real signals. The latter include highly non stationary signals, such as singing voices and guitar solos. The advantages and disadvantages of each model are presented via synthetic signals and then the application on real signals is discussed. Conclusively, eaQHM outperforms EDS in medium-to-large window size analysis, whereas EDSM yields higher reconstruction values for smaller analysis window sizes. Thus, a future research direction appears to be the merge of adaptivity of the eaQHM and parameter estimation robustness of the EDSM in a new paradigm for high-quality analysis and resynthesis of general audio signals.
As indoor applications grow in diversity, wireless sensing, vital in areas like localization and activity recognition, is attracting renewed interest. Indoor wireless sensing relies on signal processing, particularly channel state information (CSI) based signal parameter estimation. Nonetheless, regarding reflected signals induced by dynamic human targets, no satisfactory algorithm yet exists for estimating the acceleration of dynamic path length change (DPLC), which is crucial for various sensing tasks in this context. Hence, this paper proposes DP-AcE, a CSI-based DPLC acceleration estimation algorithm. We first model the relationship between the phase difference of adjacent CSI measurements and the DPLC's acceleration. Unlike existing works assuming constant velocity, DP-AcE considers both velocity and acceleration, yielding a more accurate and objective representation. Using this relationship, an algorithm combining scaling with Fourier transform is proposed to realize acceleration estimation. We evaluate DP-AcE via the acceleration estimation and acceleration-based fall detection with the collected CSI. Experimental results reveal that, using distance as the metric, DP-AcE achieves a median acceleration estimation percentage error of 4.38%. Furthermore, in multi-target scenarios, the fall detection achieves an average true positive rate of 89.56% and a false positive rate of 11.78%, demonstrating its importance in enhancing indoor wireless sensing capabilities.
This research explores the reliability of deep learning, specifically Long Short-Term Memory (LSTM) networks, for estimating the Hurst parameter in fractional stochastic processes. The study focuses on three types of processes: fractional Brownian motion (fBm), fractional Ornstein-Uhlenbeck (fOU) process, and linear fractional stable motions (lfsm). The work involves a fast generation of extensive datasets for fBm and fOU to train the LSTM network on a large volume of data in a feasible time. The study analyses the accuracy of the LSTM network's Hurst parameter estimation regarding various performance measures like RMSE, MAE, MRE, and quantiles of the absolute and relative errors. It finds that LSTM outperforms the traditional statistical methods in the case of fBm and fOU processes; however, it has limited accuracy on lfsm processes. The research also delves into the implications of training length and valuation sequence length on the LSTM's performance. The methodology is applied by estimating the Hurst parameter in Li-ion battery degradation data and obtaining confidence bounds for the estimation. The study concludes that while deep learning methods show promise in parameter estimation of fractional processes, their effectiveness is contingent on the process type and the quality of training data.
Surround-view system (SVS) is widely used in the Advanced Driver Assistance System (ADAS). SVS uses four fisheye lenses to monitor real-time scenes around the vehicle. However, accurate intrinsic and extrinsic parameter estimation is required for the proper functioning of the system. At present, the intrinsic calibration can be pipeline by utilizing checkerboard algorithm, while extrinsic calibration is still immature. Therefore, we proposed a specific calibration pipeline to estimate extrinsic parameters robustly. This scheme takes a driving sequence of four cameras as input. It firstly utilizes lane line to roughly estimate each camera pose. Considering the environmental condition differences in each camera, we separately select strategies from two methods to accurately estimate the extrinsic parameters. To achieve accurate estimates for both front and rear camera, we proposed a method that mutually iterating line detection and pose estimation. As for bilateral camera, we iteratively adjust the camera pose and position by minimizing texture and edge error between ground projections of adjacent cameras. After estimating the extrinsic parameters, the surround-view image can be synthesized by homography-based transformation. The proposed pipeline can robustly estimate the four SVS camera extrinsic parameters in real driving environments. In addition, to evaluate the proposed scheme, we build a surround-view fisheye dataset, which contains 40 videos with 32,000 frames, acquired from different real traffic scenarios. All the frames in each video are manually labeled with lane annotation, with its GT extrinsic parameters. Moreover, this surround-view dataset could be used by other researchers to evaluate their performance. The dataset will be available soon.
Existing online continuous-time parameter estimation laws provide exact (asymptotic/exponential or finite/fixed time) identification of dynamical linear/nonlinear systems parameters only if the external perturbations are equaled to zero or independent with the regressor of the system. However, in real systems the disturbances are almost always non-vanishing and dependent with the regressor. In the presence of perturbations with such properties the above-mentioned identification approaches ensure only boundedness of a parameter estimation error. The main goal of this study is to close this gap and develop a novel online continuous-time parameter estimator, which guarantees exact asymptotic identification of unknown parameters of linear systems in the presence of unknown but bounded perturbations and has relaxed convergence conditions. To achieve the aforementioned goal, it is proposed to augment the deeply investigated Dynamic Regressor Extension and Mixing (DREM) procedure with the novel Instrumental Variables (IV) based extension scheme with averaging. Such an approach allows one to obtain a set of scalar regression equations with asymptotically vanishing perturbation if the initial disturbance that affects the plant is bounded and independent not with the system regressor, but with the instrumental variable. It is rigorously proved that a gradient estimation law designed on the basis of such scalar regressions ensures online unbiased asymptotic identification of the parameters of the perturbed linear systems if some weak independence and excitation assumptions are met. Theoretical results are illustrated and supported with adequate numerical simulations.
This paper proposes a multi-day needs-based model for activity and travel demand analysis. The model captures the multi-day dynamics in activity generation, which enables the modeling of activities with increased flexibility in time and space (e.g., e-commerce and remote working). As an enhancement to activity-based models, the proposed model captures the underlying decision-making process of activity generation by accounting for psychological needs as the drivers of activities. The level of need satisfaction is modeled as a psychological inventory, whose utility is optimized via decisions on activity participation, location, and duration. The utility includes both the benefit in the inventory gained and the cost in time, monetary expense as well as maintenance of safety stock. The model includes two sub-models, a Deterministic Model that optimizes the utility of the inventory, and an Empirical Model that accounts for heterogeneity and stochasticity. Numerical experiments are conducted to demonstrate model scalability. A maximum likelihood estimator is proposed, the properties of the log-likelihood function are examined and the recovery of true parameters is tested. This research contributes to the literature on transportation demand models in the following three aspects. First, it is arguably better grounded in psychological theory than traditional models and allows the generation of activity patterns to be policy-sensitive (while avoiding the need for ad hoc utility definitions). Second, it contributes to the development of needs-based models with a non-myopic approach to model multi-day activity patterns. Third, it proposes a tractable model formulation via problem reformulation and computational enhancements, which allows for maximum likelihood parameter estimation.