On Approximate Nonlinear Gaussian Message Passing On Factor Graphs

Factor graphs have recently gained increasing attention as a unified framework for representing and constructing algorithms for signal processing, estimation, and control. One capability that does not seem to be well explored within the factor graph tool kit is the ability to handle deterministic nonlinear transformations, such as those occurring in nonlinear filtering and smoothing problems, using tabulated message passing rules. In this contribution, we provide general forward (filtering) and backward (smoothing) approximate Gaussian message passing rules for deterministic nonlinear transformation nodes in arbitrary factor graphs fulfilling a Markov property, based on numerical quadrature procedures for the forward pass and a Rauch-Tung-Striebel-type approximation of the backward pass. These message passing rules can be employed for deriving many algorithms for solving nonlinear problems using factor graphs, as is illustrated by the proposition of a nonlinear modified Bryson-Frazier (MBF) smoother based on the presented message passing rules

Model-Predictive Control with New NUV Priors

Normals with unknown variance (NUV) can represent many useful priors including $L_p$ norms and other sparsifying priors, and they blend well with linear-Gaussian models and Gaussian message passing algorithms. In this paper, we elaborate on recently proposed discretizing NUV priors, and we propose new NUV representations of half-space constraints and box constraints. We then demonstrate the use of such NUV representations with exemplary applications in model predictive control, with a variety of constraints on the input, the output, or the internal stateof the controlled system. In such applications, the computations boil down to iterations of Kalman-type forward-backward recursions, with a complexity (per iteration) that is linear in the planning horizon. In consequence, this approach can handle long planning horizons, which distinguishes it from the prior art. For nonconvex constraints, this approach has no claim to optimality, but it is empirically very effective

A factor graph description of deep temporal active inference

Active inference is a corollary of the Free Energy Principle that prescribes how self-organizing biological agents interact with their environment. The study of active inference processes relies on the definition of a generative probabilistic model and a description of how a free energy functional is minimized by neuronal message passing under thatmodel. This paper presents a tutorial introduction to specifying active inference processes by Forney-style factor graphs (FFG). The FFG framework provides both an insightful representation of the probabilistic model and a biologically plausible inference scheme that, in principle, can be automatically executed in a computer simulation. As an illustrative example, we present an FFG for a deep temporal active inference process. The graph clearly shows how policy selection by expected free energy minimization results from free energy minimization per se, in an appropriate generative policy model

Simulating Active Inference Processes by Message Passing

The free energy principle (FEP) offers a variational calculus-based description for how biological agents persevere through interactions with their environment. Active inference (AI) is a corollary of the FEP, which states that biological agents act to fulfill prior beliefs about preferred future observations (target priors). Purposeful behavior then results from variational free energy minimization with respect to a generative model of the environment with included target priors. However, manual derivations for free energy minimizing algorithms on custom dynamic models can become tedious and error-prone. While probabilistic programming (PP) techniques enable automatic derivation of inference algorithms on free-form models, full automation of AI requires specialized tools for inference on dynamic models, together with the description of an experimental protocol that governs the interaction between the agent and its simulated environment. The contributions of the present paper are two-fold. Firstly, we illustrate how AI can be automated with the use of ForneyLab, a recent PP toolbox that specializes in variational inference on flexibly definable dynamic models. More specifically, we describe AI agents in a dynamic environment as probabilistic state space models (SSM) and perform inference for perception and control in these agents by message passing on a factor graph representation of the SSM. Secondly, we propose a formal experimental protocol for simulated AI. We exemplify how this protocol leads to goal-directed behavior for flexibly definable AI agents in two classical RL examples, namely the Bayesian thermostat and the mountain car parking problems

Factor Graphs for Quantum Probabilities

A factor-graph representation of quantum-mechanical probabilities (involving any number of measurements) is proposed. Unlike standard statistical models, the proposed representation uses auxiliary variables (state variables) that are not random variables. All joint probability distributions are marginals of some complex-valued function $q$, and it is demonstrated how the basic concepts of quantum mechanics relate to factorizations and marginals of $q$.Comment: To appear in IEEE Transactions on Information Theory, 201

Autonomous Swarm Navigation

Robotic swarm systems attract increasing attention in a wide variety of applications, where a multitude of self-organized robotic entities collectively accomplish sensing or exploration tasks. Compared to a single robot, a swarm system offers advantages in terms of exploration speed, robustness against single point of failures, and collective observations of spatio-temporal processes. Autonomous swarm navigation, including swarm self-localization, the localization of external sources, and swarm control, is essential for the success of an autonomous swarm application. However, as a newly emerging technology, a thorough study of autonomous swarm navigation is still missing. In this thesis, we systematically study swarm navigation systems, particularly emphasizing on their collective performance. The general theory of swarm navigation as well as an in-depth study on a specific swarm navigation system proposed for future Mars exploration missions are covered. Concerning swarm localization, a decentralized algorithm is proposed, which achieves a near-optimal performance with low complexity for a dense swarm network. Regarding swarm control, a position-aware swarm control concept is proposed. The swarm is aware of not only the position estimates and the estimation uncertainties of itself and the sources, but also the potential motions to enrich position information. As a result, the swarm actively adapts its formation to improve localization performance, without losing track of other objectives, such as goal approaching and collision avoidance. The autonomous swarm navigation concept described in this thesis is verified for a specific Mars swarm exploration system. More importantly, this concept is generally adaptable to an extensive range of swarm applications