This paper studies the problem of distributed classification with a network of heterogeneous agents. The agents seek to jointly identify the underlying target class that best describes a sequence of observations. The problem is first abstracted to a hypothesis-testing framework, where we assume that the agents seek to agree on the hypothesis (target class) that best matches the distribution of observations. Non-Bayesian social learning theory provides a framework that solves this problem in an efficient manner by allowing the agents to sequentially communicate and update their beliefs for each hypothesis over the network. Most existing approaches assume that agents have access to exact statistical models for each hypothesis. However, in many practical applications, agents learn the likelihood models based on limited data, which induces uncertainty in the likelihood function parameters. In this work, we build upon the concept of uncertain models to incorporate the agents' uncertainty in the likelihoods by identifying a broad set of parametric distribution that allows the agents' beliefs to converge to the same result as a centralized approach. Furthermore, we empirically explore extensions to non-parametric models to provide a generalized framework of uncertain models in non-Bayesian social learning.

We propose a model-agnostic pipeline to recover graph signals from an expert system by exploiting the content addressable memory property of restricted Boltzmann machine and the representational ability of a neural network. The proposed pipeline requires the deep neural network that is trained on a downward machine learning task with clean data, data which is free from any form of corruption or incompletion. We show that denoising the representations learned by the deep neural networks is usually more effective than denoising the data itself. Although this pipeline can deal with noise in any dataset, it is particularly effective for graph-structured datasets.

We introduce factorize sum split product networks (FSPNs), a new class of probabilistic graphical models (PGMs). FSPNs are designed to overcome the drawbacks of existing PGMs in terms of estimation accuracy and inference efficiency. Specifically, Bayesian networks (BNs) have low inference speed and performance of tree structured sum product networks(SPNs) significantly degrades in presence of highly correlated variables. FSPNs absorb their advantages by adaptively modeling the joint distribution of variables according to their dependence degree, so that one can simultaneously attain the two desirable goals: high estimation accuracy and fast inference speed. We present efficient probability inference and structure learning algorithms for FSPNs, along with a theoretical analysis and extensive evaluation evidence. Our experimental results on synthetic and benchmark datasets indicate the superiority of FSPN over other PGMs.

We prove a new concentration inequality for U-statistics of order two for uniformly ergodic Markov chains. Working with bounded $\pi$-canonical kernels, we show that we can recover the convergence rate of Arcones and Gine (1993) who proved a concentration result for U-statistics of independent random variables and canonical kernels. Our proof relies on an inductive analysis where we use martingale techniques, uniform ergodicity, Nummelin splitting and Bernstein's type inequality where the spectral gap of the chain emerges. Our result allows us to conduct three applications. First, we establish a new exponential inequality for the estimation of spectra of trace class integral operators with MCMC methods. The novelty is that this result holds for kernels with positive and negative eigenvalues, which is new as far as we know. In addition, we investigate generalization performance of online algorithms working with pairwise loss functions and Markov chain samples. We provide an online-to-batch conversion result by showing how we can extract a low risk hypothesis from the sequence of hypotheses generated by any online learner. We finally give a non-asymptotic analysis of a goodness-of-fit test on the density of the invariant measure of a Markov chain. We identify the classes of alternatives over which our test based on the L2 distance has a prescribed power.

We present an approach to data fusion that combines the interpretability of structured probabilistic graphical models with the flexibility of neural networks. The proposed method, lightweight data fusion (LDF), emphasizes posterior analysis over latent variables using two types of information: primary data, which are well-characterized but with limited availability, and auxiliary data, readily available but lacking a well-characterized statistical relationship to the latent quantity of interest. The lack of a forward model for the auxiliary data precludes the use of standard data fusion approaches, while the inability to acquire latent variable observations severely limits direct application of most supervised learning methods. LDF addresses these issues by utilizing neural networks as conjugate mappings of the auxiliary data: nonlinear transformations into sufficient statistics with respect to the latent variables. This facilitates efficient inference by preserving the conjugacy properties of the primary data and leads to compact representations of the latent variable posterior distributions. We demonstrate the LDF methodology on two challenging inference problems: (1) learning electrification rates in Rwanda from satellite imagery, high-level grid infrastructure, and other sources; and (2) inferring county-level homicide rates in the USA by integrating socio-economic data using a mixture model of multiple conjugate mappings.

Structure learning algorithms that learn the graph of a Bayesian network from observational data often do so by assuming the data correctly reflect the true distribution of the variables. However, this assumption does not hold in the presence of measurement error, which can lead to spurious edges. This is one of the reasons why the synthetic performance of these algorithms often overestimates real-world performance. This paper describes an algorithm that can be added as an additional learning phase at the end of any structure learning algorithm, and serves as a correction learning phase that removes potential false positive edges. The results show that the proposed correction algorithm successfully improves the graphical score of four well-established structure learning algorithms spanning different classes of learning in the presence of measurement error.

This paper presents how the hybrid combination of behavior trees and the neuroscientific principle of active inference can be used for action planning and execution for reactive robot behaviors in dynamic environments. We show how complex robotic tasks can be formulated as a free-energy minimisation problem, and how state estimation and symbolic decision making are handled within the same framework. The general behavior is specified offline through behavior trees, where the leaf nodes represent desired states, not actions as in classical behavior trees. The decision of which action to execute to reach a state is left to the online active inference routine, in order to resolve unexpected contingencies. This hybrid combination improves the robustness of plans specified through behavior trees, while allowing to cope with the curse of dimensionality in active inference. The properties of the proposed algorithm are analysed in terms of robustness and convergence, and the theoretical results are validated using a mobile manipulator in a retail environment.

Background: The methods with which prediction models are usually developed mean that neither the parameters nor the predictions should be interpreted causally. For many applications this is perfectly acceptable. However, when prediction models are used to support decision making, there is often a need for predicting outcomes under hypothetical interventions. Aims: We aimed to identify and compare published methods for developing and validating prediction models that enable risk estimation of outcomes under hypothetical interventions, utilizing causal inference. We aimed to identify the main methodological approaches, their underlying assumptions, targeted estimands, and possible sources of bias. Finally, we aimed to highlight unresolved methodological challenges. Methods: We systematically reviewed literature published by December 2019, considering papers in the health domain that used causal considerations to enable prediction models to be used to evaluate predictions under hypothetical interventions. We included both methodology development studies and applied studies. Results: We identified 4919 papers through database searches and a further 115 papers through manual searches. Of these, 87 papers were retained for full text screening, of which 12 were selected for inclusion. We found papers from both the statistical and the machine learning literature. Most of the identified methods for causal inference from observational data were based on marginal structural models and g-estimation.

This study presents a methodology to quantify vulnerability of cyber attacks and their impacts based on probabilistic graphical models for intelligent transportation systems under connected and autonomous vehicles framework. Cyber attack vulnerabilities from various types and their impacts are calculated for intelligent signals and cooperative adaptive cruise control (CACC) applications based on the selected performance measures. Numerical examples are given that show impact of vulnerabilities in terms of average intersection queue lengths, number of stops, average speed, and delays. At a signalized network with and without redundant systems, vulnerability can increase average queues and delays by $3\%$ and $15\%$ and $4\%$ and $17\%$, respectively. For CACC application, impact levels reach to $50\%$ delay difference on average when low amount of speed information is perturbed. When significantly different speed characteristics are inserted by an attacker, delay difference increases beyond $100\%$ of normal traffic conditions.

Most recently developed approaches to cooperative multi-agent reinforcement learning in the \emph{centralized training with decentralized execution} setting involve estimating a centralized, joint value function. In this paper, we demonstrate that, despite its various theoretical shortcomings, Independent PPO (IPPO), a form of independent learning in which each agent simply estimates its local value function, can perform just as well as or better than state-of-the-art joint learning approaches on popular multi-agent benchmark suite SMAC with little hyperparameter tuning. We also compare IPPO to several variants; the results suggest that IPPO's strong performance may be due to its robustness to some forms of environment non-stationarity.