Learning and Communications Co-Design for Remote Inference Systems: Feature Length Selection and Transmission Scheduling

In this paper, we consider a remote inference system, where a neural network is used to infer a time-varying target (e.g., robot movement), based on features (e.g., video clips) that are progressively received from a sensing node (e.g., a camera). Each feature is a temporal sequence of sensory data. The learning performance of the system is determined by (i) the timeliness and (ii) the temporal sequence length of the features, where we use Age of Information (AoI) as a metric for timeliness. While a longer feature can typically provide better learning performance, it often requires more channel resources for sending the feature. To minimize the time-averaged inference error, we study a learning and communication co-design problem that jointly optimizes feature length selection and transmission scheduling. When there is a single sensor-predictor pair and a single channel, we develop low-complexity optimal co-designs for both the cases of time-invariant and time-variant feature length. When there are multiple sensor-predictor pairs and multiple channels, the co-design problem becomes a restless multi-arm multi-action bandit problem that is PSPACE-hard. For this setting, we design a low-complexity algorithm to solve the problem. Trace-driven evaluations suggest that the proposed co-designs can significantly reduce the time-averaged inference error of remote inference systems.Comment: 41 pages, 8 figures. The manuscript has been submitted to IEEE Journal on Selected Areas in Information Theor

Partition MCMC for inference on acyclic digraphs

Acyclic digraphs are the underlying representation of Bayesian networks, a widely used class of probabilistic graphical models. Learning the underlying graph from data is a way of gaining insights about the structural properties of a domain. Structure learning forms one of the inference challenges of statistical graphical models. MCMC methods, notably structure MCMC, to sample graphs from the posterior distribution given the data are probably the only viable option for Bayesian model averaging. Score modularity and restrictions on the number of parents of each node allow the graphs to be grouped into larger collections, which can be scored as a whole to improve the chain's convergence. Current examples of algorithms taking advantage of grouping are the biased order MCMC, which acts on the alternative space of permuted triangular matrices, and non ergodic edge reversal moves. Here we propose a novel algorithm, which employs the underlying combinatorial structure of DAGs to define a new grouping. As a result convergence is improved compared to structure MCMC, while still retaining the property of producing an unbiased sample. Finally the method can be combined with edge reversal moves to improve the sampler further.Comment: Revised version. 34 pages, 16 figures. R code available at https://github.com/annlia/partitionMCM

Reconstructing a Graph from Path Traces

This paper considers the problem of inferring the structure of a network from indirect observations. Each observation (a "trace") is the unordered set of nodes which are activated along a path through the network. Since a trace does not convey information about the order of nodes within the path, there are many feasible orders for each trace observed, and thus the problem of inferring the network from traces is, in general, illposed. We propose and analyze an algorithm which inserts edges by ordering each trace into a path according to which pairs of nodes in the path co-occur most frequently in the observations. When all traces involve exactly 3 nodes, we derive necessary and sufficient conditions for the reconstruction algorithm to exactly recover the graph. Finally, for a family of random graphs, we present expressions for reconstruction error probabilities (false discoveries and missed detections)