Circular and non-flat data distributions are prevalent across diverse domains of data science, yet their specific geometric structures often remain underutilized in machine learning frameworks. A principled approach to accounting for the underlying geometry of such data is pivotal, particularly when extending statistical models, like the pervasive Gaussian distribution. In this work, we tackle those issue by focusing on the manifold of symmetric positive definite (SPD) matrices, a key focus in information geometry. We introduce a non-isotropic wrapped Gaussian by leveraging the exponential map, we derive theoretical properties of this distribution and propose a maximum likelihood framework for parameter estimation. Furthermore, we reinterpret established classifiers on SPD through a probabilistic lens and introduce new classifiers based on the wrapped Gaussian model. Experiments on synthetic and real-world datasets demonstrate the robustness and flexibility of this geometry-aware distribution, underscoring its potential to advance manifold-based data analysis. This work lays the groundwork for extending classical machine learning and statistical methods to more complex and structured data.
This paper addresses the critical challenge of latent heterogeneity in online decision-making, where individual responses to business actions vary due to unobserved characteristics. While existing approaches in data-driven decision-making have focused on observable heterogeneity through contextual features, they fall short when heterogeneity stems from unobservable factors such as lifestyle preferences and personal experiences. We propose a novel latent heterogeneous bandit framework that explicitly models this unobserved heterogeneity in customer responses, with promotion targeting as our primary example. Our methodology introduces an innovative algorithm that simultaneously learns latent group memberships and group-specific reward functions. Through theoretical analysis and empirical validation using data from a mobile commerce platform, we establish high-probability bounds for parameter estimation, convergence rates for group classification, and comprehensive regret bounds. Notably, our theoretical analysis reveals two distinct types of regret measures: a ``strong regret'' against an oracle with perfect knowledge of customer memberships, which remains non-sub-linear due to inherent classification uncertainty, and a ``regular regret'' against an oracle aware only of deterministic components, for which our algorithm achieves a sub-linear rate that is minimax optimal in horizon length and dimension. We further demonstrate that existing bandit algorithms ignoring latent heterogeneity incur constant average regret that accumulates linearly over time. Our framework provides practitioners with new tools for decision-making under latent heterogeneity and extends to various business applications, including personalized pricing, resource allocation, and inventory management.
This paper proposes an active model-based fault and failure tolerant control scheme for a class of marine vehicles with thruster redundancy. Unlike widely used state and parameter estimation methods, where the estimation errors are utilized to generate residual, in this paper we directly apply the trajectory tracking error terms to construct residual and detect thruster fault and failure in the steady state of the tracking system. As for identification or diagnosis, this paper proposes a novel scheme through a detailed examination of the tracking error trends and the combinations of thruster configurations. Since this fault detection and identification operates within the same closed-loop of the tracking control system, control reconfiguration can be easily achieved by adjusting the weight parameter of the isolated thruster to minimize tracking errors or residual. Numerical studies with the real world vehicle model is also carried out to verify the effectiveness of the proposed method.
We provide a new online learning algorithm for tackling the Multinomial Logit Bandit (MNL-Bandit) problem. Despite the challenges posed by the combinatorial nature of the MNL model, we develop a novel Upper Confidence Bound (UCB)-based method that achieves Pareto optimality by balancing regret minimization and estimation error of the assortment revenues and the MNL parameters. We develop theoretical guarantees characterizing the tradeoff between regret and estimation error for the MNL-Bandit problem through information-theoretic bounds, and propose a modified UCB algorithm that incorporates forced exploration to improve parameter estimation accuracy while maintaining low regret. Our analysis sheds critical insights into how to optimally balance the collected revenues and the treatment estimation in dynamic assortment optimization.
Large scale structure introduces two different kinds of errors in the luminosity distance estimates from standardizable candles such as supernovae Ia (SNe) - a Poissonian scatter for each SN and a coherent component due to correlated fluctuations between different SNe. Increasing the number of SNe helps reduce the first type of error but not the second. The coherent component has been largely ignored in forecasts of dark energy parameter estimation from upcoming SN surveys. For instance it is commonly thought, based on Poissonian considerations, that peculiar motion is unimportant, even for a low redshift SN survey such as the Nearby Supernova Factory (SNfactory; z = 0.03 - 0.08), which provides a useful anchor for future high redshift surveys by determining the SN zero-point. We show that ignoring coherent peculiar motion leads to an underestimate of the zero-point error by about a factor of 2, despite the fact that SNfactory covers almost half of the sky. More generally, there are four types of fluctuations: peculiar motion, gravitational lensing, gravitational redshift and what is akin to the integrated Sachs-Wolfe effect. Peculiar motion and lensing dominates at low and high redshifts respectively. Taking into account all significant luminosity distance fluctuations due to large scale structure leads to a degradation of up to 60% in the determination of the dark energy equation of state from upcoming high redshift SN surveys, when used in conjunction with a low redshift anchor such as the SNfactory. The most relevant fluctuations are the coherent ones due to peculiar motion and the Poissonian ones due to lensing, with peculiar motion playing the dominant role. We also discuss to what extent the noise here can be viewed as a useful signal, and whether corrections can be made to reduce the degradation.
A variety of complex biological, natural and man-made systems exhibit non-Markovian dynamics that can be modeled through fractional order differential equations, yet, we lack sample comlexity aware system identification strategies. Towards this end, we propose an affine discrete-time fractional order dynamical system (FoDS) identification algorithm and provide a detailed sample complexity analysis. The algorithm effectively addresses the challenges of FoDS identification in the presence of noisy data. The proposed algorithm consists of two key steps. Firstly, it avoids solving higher-order polynomial equations, which would otherwise result in multiple potential solutions for the fractional orders. Secondly, the identification problem is reformulated as a least squares estimation, allowing us to infer the system parameters. We derive the expectation and probabilistic bounds for the FoDS parameter estimation error, assuming prior knowledge of the functions \( f \) and \( g \) in the FoDS model. The error decays at a rate of \( N = O\left( \frac{d}{\epsilon} \right) \), where \( N \) is the number of samples, \( d \) is the dimension of the state variable, and \( \epsilon \) represents the desired estimation accuracy. Simulation results demonstrate that our theoretical bounds are tight, validating the accuracy and robustness of this algorithm.
Diffusion magnetic resonance imaging (dMRI) often suffers from low spatial and angular resolution due to inherent limitations in imaging hardware and system noise, adversely affecting the accurate estimation of microstructural parameters with fine anatomical details. Deep learning-based super-resolution techniques have shown promise in enhancing dMRI resolution without increasing acquisition time. However, most existing methods are confined to either spatial or angular super-resolution, limiting their effectiveness in capturing detailed microstructural features. Furthermore, traditional pixel-wise loss functions struggle to recover intricate image details essential for high-resolution reconstruction. To address these challenges, we propose SARL-dMRI, a novel Spatial-Angular Representation Learning framework for high-fidelity, continuous super-resolution in dMRI. SARL-dMRI explores implicit neural representations and spherical harmonics to model continuous spatial and angular representations, simultaneously enhancing both spatial and angular resolution while improving microstructural parameter estimation accuracy. To further preserve image fidelity, a data-fidelity module and wavelet-based frequency loss are introduced, ensuring the super-resolved images remain consistent with the original input and retain fine details. Extensive experiments demonstrate that, compared to five other state-of-the-art methods, our method significantly enhances dMRI data resolution, improves the accuracy of microstructural parameter estimation, and provides better generalization capabilities. It maintains stable performance even under a 45$\times$ downsampling factor.
This paper discusses an approach to inertial parameter estimation for the case of cargo carrying spacecraft that is based on causal learning, i.e. learning from the responses of the spacecraft, under actuation. Different spacecraft configurations (inertial parameter sets) are simulated under different actuation profiles, in order to produce an optimised time-series clustering classifier that can be used to distinguish between them. The actuation is comprised of finite sequences of constant inputs that are applied in order, based on typical actuators available. By learning from the system's responses across multiple input sequences, and then applying measures of time-series similarity and F1-score, an optimal actuation sequence can be chosen either for one specific system configuration or for the overall set of possible configurations. This allows for both estimation of the inertial parameter set without any prior knowledge of state, as well as validation of transitions between different configurations after a deployment event. The optimisation of the actuation sequence is handled by a reinforcement learning model that uses the proximal policy optimisation (PPO) algorithm, by repeatedly trying different sequences and evaluating the impact on classifier performance according to a multi-objective metric.
Forecast reconciliation is considered an effective method for achieving coherence and improving forecast accuracy. However, the value of reconciled forecasts in downstream decision-making tasks has been mostly overlooked. In a multi-agent setup with heterogeneous loss functions, this oversight may lead to unfair outcomes, hence resulting in conflicts during the reconciliation process. To address this, we propose a value-oriented forecast reconciliation approach that focuses on the forecast value for individual agents. Fairness is ensured through the use of a Nash bargaining framework. Specifically, we model this problem as a cooperative bargaining game, where each agent aims to optimize their own gain while contributing to the overall reconciliation process. We then present a primal-dual algorithm for parameter estimation based on empirical risk minimization. From an application perspective, we consider an aggregated wind energy trading problem, where profits are distributed using a weighted allocation rule. We demonstrate the effectiveness of our approach through several numerical experiments, showing that it consistently results in increased profits for all agents involved.
Temporal point processes (TPPs) are stochastic process models used to characterize event sequences occurring in continuous time. Traditional statistical TPPs have a long-standing history, with numerous models proposed and successfully applied across diverse domains. In recent years, advances in deep learning have spurred the development of neural TPPs, enabling greater flexibility and expressiveness in capturing complex temporal dynamics. The emergence of large language models (LLMs) has further sparked excitement, offering new possibilities for modeling and analyzing event sequences by leveraging their rich contextual understanding. This survey presents a comprehensive review of recent research on TPPs from three perspectives: Bayesian, deep learning, and LLM approaches. We begin with a review of the fundamental concepts of TPPs, followed by an in-depth discussion of model design and parameter estimation techniques in these three frameworks. We also revisit classic application areas of TPPs to highlight their practical relevance. Finally, we outline challenges and promising directions for future research.
Parameter estimation and trajectory reconstruction for data-driven dynamical systems governed by ordinary differential equations (ODEs) are essential tasks in fields such as biology, engineering, and physics. These inverse problems -- estimating ODE parameters from observational data -- are particularly challenging when the data are noisy, sparse, and the dynamics are nonlinear. We propose the Eigen-Fourier Physics-Informed Gaussian Process (EFiGP), an algorithm that integrates Fourier transformation and eigen-decomposition into a physics-informed Gaussian Process framework. This approach eliminates the need for numerical integration, significantly enhancing computational efficiency and accuracy. Built on a principled Bayesian framework, EFiGP incorporates the ODE system through probabilistic conditioning, enforcing governing equations in the Fourier domain while truncating high-frequency terms to achieve denoising and computational savings. The use of eigen-decomposition further simplifies Gaussian Process covariance operations, enabling efficient recovery of trajectories and parameters even in dense-grid settings. We validate the practical effectiveness of EFiGP on three benchmark examples, demonstrating its potential for reliable and interpretable modeling of complex dynamical systems while addressing key challenges in trajectory recovery and computational cost.
Inverse problems can be described as limited-data problems in which the signal of interest cannot be observed directly. A physics-based forward model that relates the signal with the observations is typically needed. Unfortunately, unknown model parameters and imperfect forward models can undermine the signal recovery. Even though supervised machine learning offers promising avenues to improve the robustness of the solutions, we have to rely on model-based learning when there is no access to ground truth for the training. Here, we studied a linear inverse problem that included an unknown non-linear model parameter and utilized a Bayesian model-based learning approach that allowed signal recovery and subsequently estimation of the model parameter. This approach, called Bayesian Approximation Error approach, employed a simplified model of the physics of the problem augmented with an approximation error term that compensated for the simplification. An error subspace was spanned with the help of the eigenvectors of the approximation error covariance matrix which allowed, alongside the primary signal, simultaneous estimation of the induced error. The estimated error and signal were then used to determine the unknown model parameter. For the model parameter estimation, we tested different approaches: a conditional Gaussian regression, an iterative (model-based) optimization, and a Gaussian process that was modeled with the help of physics-informed learning. In addition, alternating optimization was used as a reference method. As an example application, we focused on the problem of reconstructing brain activity from EEG recordings under the condition that the electrical conductivity of the patient's skull was unknown in the model. Our results demonstrated clear improvements in EEG source localization accuracy and provided feasible estimates for the unknown model parameter, skull conductivity.
There is a dearth of publications on the subject of spreading-aided Orthogonal Time Frequency Space (OTFS) solutions, especially for Integrated Sensing and Communication (ISAC), even though Code Division Multiple Access (CDMA) assisted multi-user OTFS (CDMA/OTFS) exhibits tangible benefits. Hence, this work characterises both the communication Bit Error Rate (BER) and sensing Root Mean Square Error (RMSE) performance of CDMA/OTFS, and contrasts them to pure OTFS. Three CDMA/OTFS configurations are considered: Delay Code Division Multiple Access OTFS (Dl-CDMA/OTFS), Doppler Code Division Multiple Access OTFS (Dp-CDMA/OTFS), and Delay Doppler Code Division Multiple Access OTFS (DD-CDMA/OTFS), which harness direct sequence spreading along the delay axis, Doppler axis, and DD domains respectively. For each configuration, the performance of Gold, Hadamard, and Zadoff-Chu sequences is investigated. The results demonstrate that Zadoff-Chu Dl-CDMA/OTFS and DD-CDMA/OTFS consistently outperform pure OTFS sensing, whilst maintaining a similar communication performance at the same throughput. The extra modulation complexity of CDMA/OTFS is similar to that of other OTFS multi-user methodologies, but the demodulation complexity of CDMA/OTFS is lower than that of some other OTFS multi-user methodologies. CDMA/OTFS sensing can also consistently outperform OTFS sensing whilst not requiring any additional complexity for target parameter estimation. Therefore, CDMA/OTFS is an appealing candidate for implementing multi-user OTFS ISAC.
Ultra-massive multiple-input and multiple-output (MIMO) systems have been seen as the key radio technology for the advancement of wireless communication systems, due to its capability to better utilize the spatial dimension of the propagation channels. Channel sounding is essential for developing accurate and realistic channel models for the massive MIMO systems. However, channel sounding with large-scale antenna systems has faced significant challenges in practice. The real antenna array based (RAA) sounder suffers from high complexity and cost, while virtual antenna array (VAA) solutions are known for its long measurement time. Notably, these issues will become more pronounced as the antenna array configuration gets larger for future radio systems. In this paper, we propose the concept of multiplicative array (MA) for channel sounding applications to achieve large antenna aperture size with reduced number of required antenna elements. The unique characteristics of the MA are exploited for wideband spatial channel sounding purposes, supported by both one-path and multi-path numerical simulations. To address the fake paths and distortion in the angle delay profile issues inherent for MA in multipath channel sounding, a novel channel parameter estimation algorithm for MA based on successive interference cancellation (SIC) principle is proposed. Both numerical simulations and experimental validation results are provided to demonstrate the effectiveness and robustness of the proposed SIC algorithm for the MA. This research contributes significantly to the channel sounding and characterization of massive MIMO systems for future applications.
We introduce a technique to enhance the reliability of gravitational wave parameter estimation results produced by machine learning. We develop two independent machine learning models based on the Vision Transformer to estimate effective spin and chirp mass from spectrograms of gravitational wave signals from binary black hole mergers. To enhance the reliability of these models, we utilize attention maps to visualize the areas our models focus on when making predictions. This approach enables demonstrating that both models perform parameter estimation based on physically meaningful information. Furthermore, by leveraging these attention maps, we demonstrate a method to quantify the impact of glitches on parameter estimation. We show that as the models focus more on glitches, the parameter estimation results become more strongly biased. This suggests that attention maps could potentially be used to distinguish between cases where the results produced by the machine learning model are reliable and cases where they are not.
In the near-field region of an extremely large-scale multiple-input multiple-output (XL MIMO) system, channel reconstruction is typically addressed through sparse parameter estimation based on compressed sensing (CS) algorithms after converting the received pilot signals into the transformed domain. However, the exhaustive search on the codebook in CS algorithms consumes significant computational resources and running time, particularly when a large number of antennas are equipped at the base station (BS). To overcome this challenge, we propose a novel scheme to replace the high-cost exhaustive search procedure. We visualize the sparse channel matrix in the transformed domain as a channel image and design the channel keypoint detection network (CKNet) to locate the user and scatterers in high speed. Subsequently, we use a small-scale newtonized orthogonal matching pursuit (NOMP) based refiner to further enhance the precision. Our method is applicable to both the Cartesian domain and the Polar domain. Additionally, to deal with scenarios with a flexible number of propagation paths, we further design FlexibleCKNet to predict both locations and confidence scores. Our experimental results validate that the CKNet and FlexibleCKNet-empowered channel reconstruction scheme can significantly reduce the computational complexity while maintaining high accuracy in both user and scatterer localization and channel reconstruction tasks.
This paper presents a novel approach to enhance sensing capabilities in UAV-enabled MIMO-OFDM ISAC systems by leveraging UAV mobility as a mono-static radar. By integrating uniform planar arrays (UPAs) and modeling the UAV dynamics in $SE(3)$, we address key challenges such as 3D space sensing and trajectory design. We propose a target tracking scheme using extended Kalman filtering (EKF) in $SE(3)$, along with trajectory optimization based on the conditional Posterior Cramer-Rao bound (CPCRB). Numerical results demonstrate the effectiveness of the proposed trajectory design in enhancing performance of target tracking and physical parameter estimation in UAV-enabled MIMO-OFDM ISAC systems.
Gaussian processes (GPs) are flexible, probabilistic, non-parametric models widely employed in various fields such as spatial statistics and machine learning. A drawback of Gaussian processes is their computational cost having $\mathcal{O}(N^3)$ time and $\mathcal{O}(N^2)$ memory complexity which makes them prohibitive for large data sets. Numerous approximation techniques have been proposed to address this limitation. In this work, we systematically compare the accuracy of different Gaussian process approximations concerning likelihood evaluation, parameter estimation, and prediction taking into account the computational time required to perform these tasks. In other words, we analyze the trade-off between accuracy and runtime on multiple simulated and large-scale real-world data sets. We find that Vecchia approximations consistently emerge as the most accurate in almost all experiments.
The covariance matrix is a foundation in numerous statistical and machine-learning applications such as Principle Component Analysis, Correlation Heatmap, etc. However, missing values within datasets present a formidable obstacle to accurately estimating this matrix. While imputation methods offer one avenue for addressing this challenge, they often entail a trade-off between computational efficiency and estimation accuracy. Consequently, attention has shifted towards direct parameter estimation, given its precision and reduced computational burden. In this paper, we propose Direct Parameter Estimation for Randomly Missing Data with Categorical Features (DPERC), an efficient approach for direct parameter estimation tailored to mixed data that contains missing values within continuous features. Our method is motivated by leveraging information from categorical features, which can significantly enhance covariance matrix estimation for continuous features. Our approach effectively harnesses the information embedded within mixed data structures. Through comprehensive evaluations of diverse datasets, we demonstrate the competitive performance of DPERC compared to various contemporary techniques. In addition, we also show by experiments that DPERC is a valuable tool for visualizing the correlation heatmap.
We present a novel framework combining Deep Operator Networks (DeepONets) with Physics-Informed Neural Networks (PINNs) to solve partial differential equations (PDEs) and estimate their unknown parameters. By integrating data-driven learning with physical constraints, our method achieves robust and accurate solutions across diverse scenarios. Bayesian training is implemented through variational inference, allowing for comprehensive uncertainty quantification for both aleatoric and epistemic uncertainties. This ensures reliable predictions and parameter estimates even in noisy conditions or when some of the physical equations governing the problem are missing. The framework demonstrates its efficacy in solving forward and inverse problems, including the 1D unsteady heat equation and 2D reaction-diffusion equations, as well as regression tasks with sparse, noisy observations. This approach provides a computationally efficient and generalizable method for addressing uncertainty quantification in PDE surrogate modeling.