arXiv subjects

Petar M. Djuric

Publications and source records attributed to Petar M. Djuric.

17 recordsLinked to original sources

arXiv2025

Model Proficiency in Centralized Multi-Agent Systems: A Performance Study

Autonomous agents are increasingly deployed in dynamic environments where their ability to perform a given task depends on both individual and team-level proficiency. While proficiency self-assessment (PSA) has been studied for single agents, its extension to a team of agents remains underexplored. This letter addresses this gap by presenting a framework for team PSA in centralized settings. We investigate three metrics for centralized team PSA: the measurement prediction bound (MPB), the Kolmogorov-Smirnov (KS) statistic, and the Kullback-Leibler (KL) divergence. These metrics quantify the discrepancy between predicted and actual measurements. We use the KL divergence as a reference metric since it compares the true and predictive distributions, whereas the MPB and KS provide efficient indicators for in situ assessment. Simulation results in a target tracking scenario demonstrate that both MPB and KS metrics accurately capture model mismatches, align with the KL divergence reference, and enable real-time proficiency assessment.

stat.AP↗

arXiv2025

Uncertainty Quantification in Probabilistic Machine Learning Models: Theory, Methods, and Insights

Uncertainty Quantification (UQ) is essential in probabilistic machine learning models, particularly for assessing the reliability of predictions. In this paper, we present a systematic framework for estimating both epistemic and aleatoric uncertainty in probabilistic models. We focus on Gaussian Process Latent Variable Models and employ scalable Random Fourier Features-based Gaussian Processes to approximate predictive distributions efficiently. We derive a theoretical formulation for UQ, propose a Monte Carlo sampling-based estimation method, and conduct experiments to evaluate the impact of uncertainty estimation. Our results provide insights into the sources of predictive uncertainty and illustrate the effectiveness of our approach in quantifying the confidence in the predictions.

stat.ML↗

arXiv2024

On Counterfactual Interventions in Vector Autoregressive Models

Counterfactual reasoning allows us to explore hypothetical scenarios in order to explain the impacts of our decisions. However, addressing such inquires is impossible without establishing the appropriate mathematical framework. In this work, we introduce the problem of counterfactual reasoning in the context of vector autoregressive (VAR) processes. We also formulate the inference of a causal model as a joint regression task where for inference we use both data with and without interventions. After learning the model, we exploit linearity of the VAR model to make exact predictions about the effects of counterfactual interventions. Furthermore, we quantify the total causal effects of past counterfactual interventions. The source code for this project is freely available at https://github.com/KurtButler/counterfactual_interventions.

cs.LG↗

arXiv2024

Explainable Learning with Gaussian Processes

The field of explainable artificial intelligence (XAI) attempts to develop methods that provide insight into how complicated machine learning methods make predictions. Many methods of explanation have focused on the concept of feature attribution, a decomposition of the model's prediction into individual contributions corresponding to each input feature. In this work, we explore the problem of feature attribution in the context of Gaussian process regression (GPR). We take a principled approach to defining attributions under model uncertainty, extending the existing literature. We show that although GPR is a highly flexible and non-parametric approach, we can derive interpretable, closed-form expressions for the feature attributions. When using integrated gradients as an attribution method, we show that the attributions of a GPR model also follow a Gaussian process distribution, which quantifies the uncertainty in attribution arising from uncertainty in the model. We demonstrate, both through theory and experimentation, the versatility and robustness of this approach. We also show that, when applicable, the exact expressions for GPR attributions are both more accurate and less computationally expensive than the approximations currently used in practice. The source code for this project is freely available under MIT license at https://github.com/KurtButler/2024_attributions_paper.

cs.LG↗

arXiv2024

Fusion of Gaussian Processes Predictions with Monte Carlo Sampling

In science and engineering, we often work with models designed for accurate prediction of variables of interest. Recognizing that these models are approximations of reality, it becomes desirable to apply multiple models to the same data and integrate their outcomes. In this paper, we operate within the Bayesian paradigm, relying on Gaussian processes as our models. These models generate predictive probability density functions (pdfs), and the objective is to integrate them systematically, employing both linear and log-linear pooling. We introduce novel approaches for log-linear pooling, determining input-dependent weights for the predictive pdfs of the Gaussian processes. The aggregation of the pdfs is realized through Monte Carlo sampling, drawing samples of weights from their posterior. The performance of these methods, as well as those based on linear pooling, is demonstrated using a synthetic dataset.

cs.LG↗

arXiv2024

Dagma-DCE: Interpretable, Non-Parametric Differentiable Causal Discovery

We introduce Dagma-DCE, an interpretable and model-agnostic scheme for differentiable causal discovery. Current non- or over-parametric methods in differentiable causal discovery use opaque proxies of ``independence'' to justify the inclusion or exclusion of a causal relationship. We show theoretically and empirically that these proxies may be arbitrarily different than the actual causal strength. Juxtaposed to existing differentiable causal discovery algorithms, \textsc{Dagma-DCE} uses an interpretable measure of causal strength to define weighted adjacency matrices. In a number of simulated datasets, we show our method achieves state-of-the-art level performance. We additionally show that \textsc{Dagma-DCE} allows for principled thresholding and sparsity penalties by domain-experts. The code for our method is available open-source at https://github.com/DanWaxman/DAGMA-DCE, and can easily be adapted to arbitrary differentiable models.

cs.LG↗

arXiv2021

Networks of UAVs of Low-Complexity for Time-Critical Localization

Future networks of unmanned aerial vehicles (UAVs) will be tasked to carry out ever-increasing complex operations that are time-critical and that require accurate localization performance (e.g., tracking the state of a malicious user). Since there is the need to preserve low UAV complexity while tackling the challenging goals of missions in effective ways, one key aspect is the UAV intelligence (UAV-I). The UAV's intelligence includes the UAV's capability to process information and to make decisions, e.g., to decide where to sense and whether to delegate some tasks to other network entities. In this paper, we provide an overview of possible solutions for the design of UAVs of low complexity, showing some of the needs of the UAVs for running efficient localization operations, performed either as a team or individually. Further, we focus on different network configurations, which possibly include assistance with edge computing. We also discuss open problems and future perspectives for these settings.

cs.NI↗

arXiv2021

Near-field Tracking with Large Antenna Arrays: Fundamental Limits and Practical Algorithms

Applications towards 6G have brought a huge interest towards arrays with a high number of antennas and operating within the millimeter and sub-THz bandwidths for joint communication and localization. With such large arrays, the plane wave approximation is often not accurate because the system may operate in the near-field propagation region (Fresnel region) where the electromagnetic field wavefront is spherical. In this case, the curvature of arrival (CoA) is a measure of the spherical wavefront that can be used to infer the source position using only a single large array. In this paper, we study a near-field tracking problem for inferring the state (i.e., the position and velocity) of a moving source with an ad-hoc observation model that accounts for the phase profile of a large receiving array. For this tracking problem, we derive the posterior Cramér-Rao Lower Bound (P-CRLB) and show the effects when the source moves inside and outside the Fresnel region. We provide insights on how the loss of positioning information outside Fresnel comes from an increase of the ranging error rather than from inaccuracies of angular estimation. Then, we investigate the performance of different Bayesian tracking algorithms in the presence of model mismatches and abrupt trajectory changes. Our results demonstrate the feasibility and high accuracy for most of the tracking approaches without the need of wideband signals and of any synchronization scheme. signals and of any synchronization scheme.

cs.IT↗

arXiv2020

Particle Filtering Under General Regime Switching

In this paper, we consider a new framework for particle filtering under model uncertainty that operates beyond the scope of Markovian switching systems. Specifically, we develop a novel particle filtering algorithm that applies to general regime switching systems, where the model index is augmented as an unknown time-varying parameter in the system. The proposed approach does not require the use of multiple filters and can maintain a diverse set of particles for each considered model through appropriate choice of the particle filtering proposal distribution. The flexibility of the proposed approach allows for long-term dependencies between the models, which enables its use to a wider variety of real-world applications. We validate the method on a synthetic data experiment and show that it outperforms state-of-the-art multiple model particle filtering approaches that require the use of multiple filters.

stat.CO↗

arXiv2020

Reinforcement Learning for UAV Autonomous Navigation, Mapping and Target Detection

In this paper, we study a joint detection, mapping and navigation problem for a single unmanned aerial vehicle (UAV) equipped with a low complexity radar and flying in an unknown environment. The goal is to optimize its trajectory with the purpose of maximizing the mapping accuracy and, at the same time, to avoid areas where measurements might not be sufficiently informative from the perspective of a target detection. This problem is formulated as a Markov decision process (MDP) where the UAV is an agent that runs either a state estimator for target detection and for environment mapping, and a reinforcement learning (RL) algorithm to infer its own policy of navigation (i.e., the control law). Numerical results show the feasibility of the proposed idea, highlighting the UAV's capability of autonomously exploring areas with high probability of target detection while reconstructing the surrounding environment.

cs.RO↗

arXiv2020

Dynamic Radar Network of UAVs: A Joint Navigation and Tracking Approach

Nowadays there is a growing research interest on the possibility of enriching small flying robots with autonomous sensing and online navigation capabilities. This will enable a large number of applications spanning from remote surveillance to logistics, smarter cities and emergency aid in hazardous environments. In this context, an emerging problem is to track unauthorized small unmanned aerial vehicles (UAVs) hiding behind buildings or concealing in large UAV networks. In contrast with current solutions mainly based on static and on-ground radars, this paper proposes the idea of a dynamic radar network of UAVs for real-time and high-accuracy tracking of malicious targets. To this end, we describe a solution for real-time navigation of UAVs to track a dynamic target using heterogeneously sensed information. Such information is shared by the UAVs with their neighbors via multi-hops, allowing tracking the target by a local Bayesian estimator running at each agent. Since not all the paths are equal in terms of information gathering point-of-view, the UAVs plan their own trajectory by minimizing the posterior covariance matrix of the target state under UAV kinematic and anti-collision constraints. Our results show how a dynamic network of radars attains better localization results compared to a fixed configuration and how the on-board sensor technology impacts the accuracy in tracking a target with different radar cross sections, especially in non line-of-sight (NLOS) situations.

cs.IT↗

arXiv2019

Joint Indoor Localization and Navigation of UAVs for Network Formation Control

In this paper, we propose a joint indoor localization and navigation algorithm to enable a swarm of unmanned aerial vehicles (UAVs) to deploy in a specific spatial formation in indoor environments. In the envisioned scenario, we consider a static user acting as a central unit whose main task is to acquire all the UAV measurements carrying position-dependent information and to estimate the UAV positions when there is no existing infrastructure for positioning. Subsequently, the user exploits the estimated positions as inputs for the navigation control with the aim of deploying the UAVs in a desired formation in space (formation shaping). The user plans the trajectory of each UAV in real time, guaranteeing a safe navigation in the presence of obstacles. The proposed algorithm guides the UAVs to their desired final locations with good accuracy.

eess.SP↗

arXiv2019

Dynamic Radar Networks of UAVs

In the incoming years, the low-aerial space will be crowded by unmanned aerial vehicles (UAVs), which will be providing different services. In this expected context, an emerging problem is to detect and track unauthorized or malicious mini/micro UAVs. In contrast to current solutions mainly based on fixed terrestrial radars, this article will put forth the idea of a dynamic radar network (DRN) composed of UAVs able to smartly adapt their formation-navigation control to best track malicious UAVs in real-time, with high accuracy, and in a distributed fashion. To this end, some technological solutions and the main methods for target detection and tracking will be described. Further, an optimized navigation scheme will be developed according to an information-seeking approach. Some examples of simulation results and future directions of work will be finally presented highlighting the advantages of dynamic and reconfigurable networks over static ones.

eess.SP↗

arXiv2019

Non-Centralized Navigation for Source Localization by Cooperative UAVs

In this paper, we propose a distributed solution to the navigation of a population of unmanned aerial vehicles (UAVs) to best localize a static source. The network is considered heterogeneous with UAVs equipped with received signal strength (RSS) sensors from which it is possible to estimate the distance from the source and/or the direction of arrival through ad-hoc rotations. This diversity in gathering and processing RSS measurements mitigates the loss of localization accuracy due to the adoption of low-complexity sensors. The UAVs plan their trajectories on-the-fly and in a distributed fashion. The collected data are disseminated through the network via multi-hops, therefore being subject to latency. Since not all the paths are equal in terms of information gathering rewards, the motion planning is formulated as a minimization of the uncertainty of the source position under UAV kinematic and anti-collision constraints and performed by 3D non-linear programming. The proposed analysis takes into account non-line-of-sight (NLOS) channel conditions as well as measurement age caused by the latency constraints in communication.

eess.SP↗

arXiv2012

Communications with decode-and-forward relays in mesh networks

We consider mesh networks composed of groups of relaying nodes which operate in decode-and-forward mode, where each node from a group relays information to all the nodes in the next group. We study these networks in two setups, one where the nodes have complete channel state information from the nodes that transmit to them, and another when they only have the statistics of the channel. We derive recursive expressions for the probabilities of errors of the nodes and present several implementations of detectors used in these networks. We compare the mesh networks with multihop networks, the latter being formed by a set of parallel sections of multiple relaying nodes. We demonstrate with numerous simulations that there are significant improvements in performance of mesh over multihop networks in various scenarios.

cs.IT↗

arXiv2012

Likelihood Consensus and Its Application to Distributed Particle Filtering

We consider distributed state estimation in a wireless sensor network without a fusion center. Each sensor performs a global estimation task---based on the past and current measurements of all sensors---using only local processing and local communications with its neighbors. In this estimation task, the joint (all-sensors) likelihood function (JLF) plays a central role as it epitomizes the measurements of all sensors. We propose a distributed method for computing, at each sensor, an approximation of the JLF by means of consensus algorithms. This "likelihood consensus" method is applicable if the local likelihood functions of the various sensors (viewed as conditional probability density functions of the local measurements) belong to the exponential family of distributions. We then use the likelihood consensus method to implement a distributed particle filter and a distributed Gaussian particle filter. Each sensor runs a local particle filter, or a local Gaussian particle filter, that computes a global state estimate. The weight update in each local (Gaussian) particle filter employs the JLF, which is obtained through the likelihood consensus scheme. For the distributed Gaussian particle filter, the number of particles can be significantly reduced by means of an additional consensus scheme. Simulation results are presented to assess the performance of the proposed distributed particle filters for a multiple target tracking problem.

stat.AP↗

arXiv2011

Likelihood Consensus-Based Distributed Particle Filtering with Distributed Proposal Density Adaptation

We present a consensus-based distributed particle filter (PF) for wireless sensor networks. Each sensor runs a local PF to compute a global state estimate that takes into account the measurements of all sensors. The local PFs use the joint (all-sensors) likelihood function, which is calculated in a distributed way by a novel generalization of the likelihood consensus scheme. A performance improvement (or a reduction of the required number of particles) is achieved by a novel distributed, consensus-based method for adapting the proposal densities of the local PFs. The performance of the proposed distributed PF is demonstrated for a target tracking problem.

stat.AP↗