A Framework for Hybrid Collective Inference in Distributed Sensor Networks

Andrew Nash; Dirk Pesch; Krishnendu Guha

cs.DCFeb 19, 2026

A Framework for Hybrid Collective Inference in Distributed Sensor Networks

Authors: Andrew Nash, Dirk Pesch, Krishnendu Guha

Organizations: School of Computer Science and IT, University College Cork, Ireland.

Abstract

With the ever-increasing range of applications of Internet in Things (IoT) and sensor networks, challenges are emerging in various categories of classification tasks. Applications such as vehicular networking, UAV swarm coordination and cyber-physical systems require global classification over distributed sensors, with tight constraints on communication and computation resources. There has been much research in decentralized and distributed data-exchange for communication-efficient collective inference. Likewise, there has been considerable research involving the use of cloud and edge computing paradigms for efficient task allocation. To the best of our knowledge, there has been no research on the integration of these two concepts to create a hybrid cloud and distributed approach that makes dynamic runtime communication strategy decisions. In this paper, we focus on aspects of combining distributed and hierarchical communication and classification approaches for collective inference. We derive optimal policies for agents that implement this hybrid approach, and evaluate their performance under various scenarios of the distribution of underlying data. Our analysis shows that this approach can maintain a high level of classification accuracy (comparable to that of centralised joint inference over all data), at reduced theoretical communication cost. We expect there is potential for our approach to facilitate efficient collective inference for real-world applications, including instances that involves more complex underlying data distributions.

Figures & tables

Fig. 1 : Illustrative diagram of a sample network architecture of a Low-Power Wireless Sensor Network (LPWSN) used in our proposed collective inference model

Reference	Dist. Data	Agent Based	P2P Comm.	Dynamic Comm.	Pow./Comm. Efficient	Hierarchical	Early Exit/Edge	Value of Information	Cloud/Fog Server(s)
[ 18 ]	✓	✓	✓	✓	✓			✓
[ 27 ] [ 24 ]	✓	✓	✓	✓
[ 8 ]	✓	✓	✓		✓
[ 6 ]	✓	✓	✓
[ 23 ]	✓		✓	✓	✓
[ 1 ]	✓						✓

TABLE I : Comparison of Related Works

$Y$	The global state or outcome being predicted
$N$	Number of sensing devices, or data sources
$S_{i},\;s.t.\;i\in[1,N]$	The random variable describing the data generated at sensor $i$
$E$	Used to denote a cloud/fog server where joint classification can be performed.
$C_{S_{i}S_{j}},C_{S_{i}E}$	Cost of communication between sensing devices, or a sensing device and $E$

TABLE II : Notation and Symbols used

Panel of Figure 4 — Fig. 2 : Visual representation of the three main aspects of our proposed framework in Section III-D .

Param.	Explanation
$\delta_{\mu}$	$\mu_{s_{i}\|Y=1}-\mu_{s_{i}\|Y=0}$ , the degree of separation between distribution means for the same sensor under different states
$\sigma$	The standard deviation of all distributions
$\lambda$	The policy threshold parameter (as per Sec. III-D )
$C_{S_{i}E}$	The energy expended in communicating a single observation from each sensor to the cloud/fog server (as per Sec. III-E2 )
$P_{D}$	The overall probability that the sensor will be able to directly make a prediction with confidence greater than $\lambda$ . This corresponds to the first component of our proposed policy framework.
$P_{RQ}$	A pair of probabilities ( $p_{1},p_{2}$ ). $p_{1}$ is the overall probability that the sensor will decide to make a request for $p_{2}$ ’s data in the expectation that it has low expected cost – as defined by the second component of our proposed policy. $p_{2}$ is the probability of such requests being successful.

TABLE III : Parameters varied across each experiment.

$\delta_{\mu},\sigma$	$\lambda$	$C_{S_{i}E}$	Acc. (%)	Avg. # Direct Decisions	Avg. # Successful Requests.	Avg. Cost
(1, 1.5)	0.75	1	0.119	0.0	0.0	0.0
(1, 1.5)	0.75	2	0.119	0.88	0.203	2.281
(1, 1.5)	0.75	4	0.119	0.88	0.203	3.682
(1, 1.5)	0.85	1	0.013	0.0	0.0	0.0
(1, 1.5)	0.85	2	0.013	0.986	0.073	2.814
(1, 1.5)	0.85	4	0.013	0.986	0.073	4.643

TABLE IV : Evaluation of the performance of the globally optimized baseline. Explanations of the parameters in each column are available in Table III . All metrics (other than accuracy) are the averages across all

10\,000

samples for each set of parameters. The fifth and sixth columns correspond to the average number of direct inferences, and requests from a sensor to the other, which leads to a direct inference.

Panel of Figure 7 — Fig. 3 : Visualisations of basic scenarios where our framework shows trivial behaviour.

Fig. 4 : Case where one sensor is poorly separated and one well separated.

$\delta_{\mu},\sigma$	$\lambda$	$d_{S_{i}E}$	$P_{D}(S_{1})$	$P_{RQ}(S_{1})$	$E_{C}(S_{1})$
(1, 1.5)	0.75	5	0.119	(0.88, 0.203)	4.782
(1, 1.5)	0.75	10	0.119	(0.88, 0.203)	6.597
(1, 1.5)	0.75	25	0.119	(0.88, 0.203)	17.839
(1, 1.5)	0.85	5	0.013	(0.986, 0.073)	5.896
(1, 1.5)	0.85	10	0.013	(0.986, 0.073)	8.265
(1, 1.5)	0.85	25	0.013	(0.986, 0.073)	22.935

TABLE V : Evaluation of the functioning of our proposed framework on the basic case of two Gaussian sensors and a binomial hidden state over a broad range of parameters. Explanations of column headings are given in Table III

$\delta_{\mu},\lambda$ , $C_{S_{i}E}$	Acc. (%)	Avg. # Direct Decisions	Avg. # Successful Requests.	Avg. Cost	Cloud Acc.	Cloud Avg. Cost	Ind. Acc
2, 0.75, 2	0.804	1.01	0.56	1.85	0.826	4.0	0.747
2, 0.75, 4	0.805	1.01	0.55	2.73	0.827	8.0	0.748
2, 0.75, 6	0.807	1.01	0.56	3.57	0.827	12.0	0.749
2, 0.85, 2	0.808	0.57	0.6	3.07	0.828	4.0	0.749
2, 0.85, 4	0.808	0.58	0.6	4.72	0.828	8.0	0.748
2, 0.85, 6	0.806	0.57	0.6	6.39	0.829	12.0	0.748

TABLE VI : Empirical results obtained by simulating the proposed framework on randomly sampled data in the simplest case –

N=2,Y\in\{0,1\},\sigma=1.5

. All metrics (other than accuracy) are the averages across all

10\,000

samples for each set of parameters. The fifth and sixth columns correspond to the average number of direct inferences, and requests from a sensor to the other, which leads to a direct inference.

$\delta_{\mu}$ , $\lambda$ , $C_{S_{i}E}$	Acc. (%)	Avg. # Direct Decisions	Avg. # Successful Requests.	Avg. Cost	Cloud Acc.	Cloud Avg. Cost	Ind. Acc
2, 0.75, 2	0.786	1.02	0.42	1.84	0.829	4.0	0.748
2, 0.75, 4	0.805	1.01	0.56	2.73	0.827	8.0	0.748
2, 0.75, 6	0.806	1.01	0.56	3.56	0.828	12.0	0.747
2, 0.85, 2	0.78	0.58	0.32	2.8	0.828	4.0	0.747
2, 0.85, 4	0.807	0.58	0.6	4.71	0.829	8.0	0.746
2, 0.85, 6	0.806	0.58	0.6	6.37	0.826	12.0	0.746

TABLE VII : Empirical results obtained by simulating our proposed framework on randomly sampled data in the case of

N=4,Y\in\{0,1,2,3\},\sigma=1.5

. All metrics (other than accuracy) are the averages across all

10\,000

samples for each set of parameters. The fifth and sixth columns correspond to the average number of direct inferences, and requests from a sensor to the other, which leads to a direct inference.

$\delta_{\mu}$ , $\lambda$ , $C_{S_{i}E}$	Acc. (%)	Avg. # Direct Decisions	Avg. # Successful Requests.	Avg. Cost
2, 0.75, 2	0.76	1.01	0.1	1.93
2, 0.75, 4	0.793	1.01	0.49	2.84
2, 0.75, 6	0.806	1.01	0.55	3.61
2, 0.85, 2	0.777	0.58	0.17	2.78
2, 0.85, 4	0.787	0.58	0.44	4.84
2, 0.85, 6	0.8	0.57	0.54	6.56

TABLE VIII : Performance of the heuristic algorithm from Section- IV-D1 under the same conditions as the uniform sampling method in Table VII .

Fig. 5 : Visualising the effect of increasing $N$ on overall cost and accuracy.

Panel of Figure 14 — Fig. 6 : Visualising the effect of increasing $\delta_{\mu}$ on overall cost and accuracy. N=4 top, N=8 bottom.

Fig. 7 : Visualisation of the effect of increasing $C_{S_{i}E}$ on overall cost and accuracy (assuming $C_{S_{i}S_{j}}=1J$ . We see cost savings over the cloud baseline increase as the cloud becomes increasingly expensive for offloads. For very low costs, we see an interesting dip in accuracy.

Fig. 8 : Visualising the effect of increasing the domain of $Y$ on overall cost and accuracy (assuming $C_{S_{i}S_{j}}=1J$ , $C_{S_{i}E}=4J$ . As expected, we see that this has increasing cost, with decreasing accuracy.

Distributed Inference

Distributed inference runs machine-learning models across multiple devices or sites to meet compute, latency, memory, privacy, and reliability needs.

See all 75 papers

Test-Time Collaborative Classification over Multi-Agent Networks
Aug 25, 2026Ping Hu, Mert Kayaalp, Ali H. SayedMulti-Agent Collaboration Classification
School of Engineering, École Polytechnique Fédérale de Lausanne (EPFL), 1015 Lausanne, Switzerland · DTI, SUPSI, Dalle Molle Institute for Artificial Intelligence (IDSIA USI-SUPSI), 6962 Lugano, Switzerland
SAGE: Training-Free Semantic Evidence Composition for Edge-Cloud Inference under Hard Uplink Budgets
Apr 21, 2026Inhyeok Choi, Hyuncheol ParkEfficient Inference Edge-Cloud Computing
School of Electrical Engineering, Korea Advanced Institute of Science and Technology (KAIST), Daejeon, South Korea
A Fundamental Limit in Decentralized Decision-Making
Sep 7, 2026Marco Carpentiero, Felice Scala, Vincenzo Matta +1Classification Distributed Inference
Department of Information and Electrical Engineering and Applied Mathematics (DIEM), University of Salerno, I-84084 Fisciano (SA), Italy · Institute of Electrical and Micro Engineering, EPFL, CH-1015 Lausanne, Switzerland

Aug 25, 2026J/K move · Enter open · S save

Test-Time Collaborative Classification over Multi-Agent Networks

Ping Hu, Mert Kayaalp, Ali H. Sayed

School of Engineering, École Polytechnique Fédérale de Lausanne (EPFL), 1015 Lausanne, Switzerland · DTI, SUPSI, Dalle Molle Institute for Artificial Intelligence (IDSIA USI-SUPSI), 6962 Lugano, Switzerland

Multi-Agent Collaboration Classification Multi-Agent Systems Multi-Agent Communication

Open paper AskPDF arXiv

The increasing heterogeneity of multi-agent systems poses significant challenges for jointly training a global model across agents. At the same time, cooperative inference between agents has long been recognized as a powerful mechanism for distributed decision making over networks. Motivated by these observations, we propose a collaboration framework for distributed binary classification over multi-agent networks, where a set of independently trained agents, potentially differing in architecture, feature space, or modality, coordinate their actions during test time to form collective predictions. This coordination is achieved by exchanging local decision statistics through a distributed learning protocol. We develop a theoretical and experimental study of this independent training and cooperative inference paradigm, and examine its performance under different communication budgets and distributed learning rules. We establish classification error guarantees under sufficient, finite-round, and finite-precision communication, together with PAC-style generalization bounds. These results capture the influence of model heterogeneity, network topology, combination policy, and communication constraints on prediction accuracy. Taken together with the experimental results, they reveal both the price of independent training and the benefit of collective prediction for the proposed distributed decision making framework with models learned from data.

Abstract

Distributed Inference

Explore similar work

Test-Time Collaborative Classification over Multi-Agent Networks

SAGE: Training-Free Semantic Evidence Composition for Edge-Cloud Inference under Hard Uplink Budgets

A Fundamental Limit in Decentralized Decision-Making