Factored Particles for Scalable Monitoring

Exact monitoring in dynamic Bayesian networks is intractable, so approximate algorithms are necessary. This paper presents a new family of approximate monitoring algorithms that combine the best qualities of the particle filtering and Boyen-Koller methods. Our algorithms maintain an approximate representation the belief state in the form of sets of factored particles, that correspond to samples of clusters of state variables. Empirical results show that our algorithms outperform both ordinary particle filtering and the Boyen-Koller algorithm on large systems.Comment: Appears in Proceedings of the Eighteenth Conference on Uncertainty in Artificial Intelligence (UAI2002

Distributed High Accuracy Peer-to-Peer Localization in Mobile Multipath Environments

In this paper we consider the problem of high accuracy localization of mobile nodes in a multipath-rich environment where sub-meter accuracies are required. We employ a peer to peer framework where the vehicles/nodes can get pairwise multipath-degraded ranging estimates in local neighborhoods together with a fixed number of anchor nodes. The challenge is to overcome the multipath-barrier with redundancy in order to provide the desired accuracies especially under severe multipath conditions when the fraction of received signals corrupted by multipath is dominating. We invoke a message passing analytical framework based on particle filtering and reveal its high accuracy localization promise through simulations.Comment: 5 pages, 5 figures, Accepted at IEEE Globecom 2010, Miami, F

Regression with Linear Factored Functions

Many applications that use empirically estimated functions face a curse of dimensionality, because the integrals over most function classes must be approximated by sampling. This paper introduces a novel regression-algorithm that learns linear factored functions (LFF). This class of functions has structural properties that allow to analytically solve certain integrals and to calculate point-wise products. Applications like belief propagation and reinforcement learning can exploit these properties to break the curse and speed up computation. We derive a regularized greedy optimization scheme, that learns factored basis functions during training. The novel regression algorithm performs competitively to Gaussian processes on benchmark tasks, and the learned LFF functions are with 4-9 factored basis functions on average very compact.Comment: Under review as conference paper at ECML/PKDD 201

PID control system analysis and design

With its three-term functionality offering treatment of both transient and steady-state responses, proportional-integral-derivative (PID) control provides a generic and efficient solution to realworld control problems. The wide application of PID control has stimulated and sustained research and development to "get the best out of PID", and "the search is on to find the next key technology or methodology for PID tuning". This article presents remedies for problems involving the integral and derivative terms. PID design objectives, methods, and future directions are discussed. Subsequently, a computerized, simulation-based approach is presented, together with illustrative design results for first-order, higher order, and nonlinear plants. Finally, we discuss differences between academic research and industrial practice, so as to motivate new research directions in PID control

From Least Squares to Signal Processing and Particle Filtering

De Facto, signal processing is the interpolation and extrapolation of a sequence of observations viewed as a realization of a stochastic process. Its role in applied statistics ranges from scenarios in forecasting and time series analysis, to image reconstruction, machine learning, and the degradation modeling for reliability assessment. A general solution to the problem of filtering and prediction entails some formidable mathematics. Efforts to circumvent the mathematics has resulted in the need for introducing more explicit descriptions of the underlying process. One such example, and a noteworthy one, is the Kalman Filter Model, which is a special case of state space models or what statisticians refer to as Dynamic Linear Models. Implementing the Kalman Filter Model in the era of "big and high velocity non-Gaussian data" can pose computational challenges with respect to efficiency and timeliness. Particle filtering is a way to ease such computational burdens. The purpose of this paper is to trace the historical evolution of this development from its inception to its current state, with an expository focus on two versions of the particle filter, namely, the propagate first-update next and the update first-propagate next version. By way of going beyond a pure review, this paper also makes transparent the importance and the role of a less recognized principle, namely the principle of conditionalization, in filtering and prediction based on Bayesian methods. Furthermore, the paper also articulates the philosophical underpinnings of the filtering and prediction set-up, a matter that needs to ne made explicit, and Yule's decomposition of a random variable in terms of a sequence of innovations

Learning Partially Observable Deterministic Action Models

We present exact algorithms for identifying deterministic-actions effects and preconditions in dynamic partially observable domains. They apply when one does not know the action model(the way actions affect the world) of a domain and must learn it from partial observations over time. Such scenarios are common in real world applications. They are challenging for AI tasks because traditional domain structures that underly tractability (e.g., conditional independence) fail there (e.g., world features become correlated). Our work departs from traditional assumptions about partial observations and action models. In particular, it focuses on problems in which actions are deterministic of simple logical structure and observation models have all features observed with some frequency. We yield tractable algorithms for the modified problem for such domains. Our algorithms take sequences of partial observations over time as input, and output deterministic action models that could have lead to those observations. The algorithms output all or one of those models (depending on our choice), and are exact in that no model is misclassified given the observations. Our algorithms take polynomial time in the number of time steps and state features for some traditional action classes examined in the AI-planning literature, e.g., STRIPS actions. In contrast, traditional approaches for HMMs and Reinforcement Learning are inexact and exponentially intractable for such domains. Our experiments verify the theoretical tractability guarantees, and show that we identify action models exactly. Several applications in planning, autonomous exploration, and adventure-game playing already use these results. They are also promising for probabilistic settings, partially observable reinforcement learning, and diagnosis

Deep Variational Reinforcement Learning for POMDPs

Many real-world sequential decision making problems are partially observable by nature, and the environment model is typically unknown. Consequently, there is great need for reinforcement learning methods that can tackle such problems given only a stream of incomplete and noisy observations. In this paper, we propose deep variational reinforcement learning (DVRL), which introduces an inductive bias that allows an agent to learn a generative model of the environment and perform inference in that model to effectively aggregate the available information. We develop an n-step approximation to the evidence lower bound (ELBO), allowing the model to be trained jointly with the policy. This ensures that the latent state representation is suitable for the control task. In experiments on Mountain Hike and flickering Atari we show that our method outperforms previous approaches relying on recurrent neural networks to encode the past

Probabilistic Receiver Architecture Combining BP, MF, and EP for Multi-Signal Detection

Receiver algorithms which combine belief propagation (BP) with the mean field (MF) approximation are well-suited for inference of both continuous and discrete random variables. In wireless scenarios involving detection of multiple signals, the standard construction of the combined BP-MF framework includes the equalization or multi-user detection functions within the MF subgraph. In this paper, we show that the MF approximation is not particularly effective for multi-signal detection. We develop a new factor graph construction for application of the BP-MF framework to problems involving the detection of multiple signals. We then develop a low-complexity variant to the proposed construction in which Gaussian BP is applied to the equalization factors. In this case, the factor graph of the joint probability distribution is divided into three subgraphs: (i) a MF subgraph comprised of the observation factors and channel estimation, (ii) a Gaussian BP subgraph which is applied to multi-signal detection, and (iii) a discrete BP subgraph which is applied to demodulation and decoding. Expectation propagation is used to approximate discrete distributions with a Gaussian distribution and links the discrete BP and Gaussian BP subgraphs. The result is a probabilistic receiver architecture with strong theoretical justification which can be applied to multi-signal detection.Comment: 30 pages, 9 figure

Continuous-Time Gaussian Process Motion Planning via Probabilistic Inference

We introduce a novel formulation of motion planning, for continuous-time trajectories, as probabilistic inference. We first show how smooth continuous-time trajectories can be represented by a small number of states using sparse Gaussian process (GP) models. We next develop an efficient gradient-based optimization algorithm that exploits this sparsity and GP interpolation. We call this algorithm the Gaussian Process Motion Planner (GPMP). We then detail how motion planning problems can be formulated as probabilistic inference on a factor graph. This forms the basis for GPMP2, a very efficient algorithm that combines GP representations of trajectories with fast, structure-exploiting inference via numerical optimization. Finally, we extend GPMP2 to an incremental algorithm, iGPMP2, that can efficiently replan when conditions change. We benchmark our algorithms against several sampling-based and trajectory optimization-based motion planning algorithms on planning problems in multiple environments. Our evaluation reveals that GPMP2 is several times faster than previous algorithms while retaining robustness. We also benchmark iGPMP2 on replanning problems, and show that it can find successful solutions in a fraction of the time required by GPMP2 to replan from scratch.Comment: The International Journal of Robotics Research (IJRR), 2018, Volume 37, Issue 1

Gibbs Sampling in Factorized Continuous-Time Markov Processes

A central task in many applications is reasoning about processes that change over continuous time. Continuous-Time Bayesian Networks is a general compact representation language for multi-component continuous-time processes. However, exact inference in such processes is exponential in the number of components, and thus infeasible for most models of interest. Here we develop a novel Gibbs sampling procedure for multi-component processes. This procedure iteratively samples a trajectory for one of the components given the remaining ones. We show how to perform exact sampling that adapts to the natural time scale of the sampled process. Moreover, we show that this sampling procedure naturally exploits the structure of the network to reduce the computational cost of each step. This procedure is the first that can provide asymptotically unbiased approximation in such processes.Comment: Appears in Proceedings of the Twenty-Fourth Conference on Uncertainty in Artificial Intelligence (UAI2008