A Unified View of Algorithms for Path Planning Using Probabilistic Inference on Factor Graphs

Even if path planning can be solved using standard techniques from dynamic programming and control, the problem can also be approached using probabilistic inference. The algorithms that emerge using the latter framework bear some appealing characteristics that qualify the probabilistic approach as a powerful alternative to the more traditional control formulations. The idea of using estimation on stochastic models to solve control problems is not new and the inference approach considered here falls under the rubric of Active Inference (AI) and Control as Inference (CAI). In this work, we look at the specific recursions that arise from various cost functions that, although they may appear similar in scope, bear noticeable differences, at least when applied to typical path planning problems. We start by posing the path planning problem on a probabilistic factor graph, and show how the various algorithms translate into specific message composition rules. We then show how this unified approach, presented both in probability space and in log space, provides a very general framework that includes the Sum-product, the Max-product, Dynamic programming and mixed Reward/Entropy criteria-based algorithms. The framework also expands algorithmic design options for smoother or sharper policy distributions, including generalized Sum/Max-product algorithm, a Smooth Dynamic programming algorithm and modified versions of the Reward/Entropy recursions. We provide a comprehensive table of recursions and a comparison through simulations, first on a synthetic small grid with a single goal with obstacles, and then on a grid extrapolated from a real-world scene with multiple goals and a semantic map.

Path Planning Using Probability Tensor Flows

Probability models have been proposed in the literature to account for "intelligent" behavior in many contexts. In this paper, probability propagation is applied to model agent's motion in potentially complex scenarios that include goals and obstacles. The backward flow provides precious background information to the agent's behavior, viz., inferences coming from the future determine the agent's actions. Probability tensors are layered in time in both directions in a manner similar to convolutional neural networks. The discussion is carried out with reference to a set of simulated grids where, despite the apparent task complexity, a solution, if feasible, is always found. The original model proposed by Attias has been extended to include non-absorbing obstacles, multiple goals and multiple agents. The emerging behaviors are very realistic and demonstrate great potentials of the application of this framework to real environments.

An Analysis of Word2Vec for the Italian Language

Word representation is fundamental in NLP tasks, because it is precisely from the coding of semantic closeness between words that it is possible to think of teaching a machine to understand text. Despite the spread of word embedding concepts, still few are the achievements in linguistic contexts other than English. In this work, analysing the semantic capacity of the Word2Vec algorithm, an embedding for the Italian language is produced. Parameter setting such as the number of epochs, the size of the context window and the number of negatively backpropagated samples is explored.

Intent Classification in Question-Answering Using LSTM Architectures

Question-answering (QA) is certainly the best known and probably also one of the most complex problem within Natural Language Processing (NLP) and artificial intelligence (AI). Since the complete solution to the problem of finding a generic answer still seems far away, the wisest thing to do is to break down the problem by solving single simpler parts. Assuming a modular approach to the problem, we confine our research to intent classification for an answer, given a question. Through the use of an LSTM network, we show how this type of classification can be approached effectively and efficiently, and how it can be properly used within a basic prototype responder.

Optimized Realization of Bayesian Networks in Reduced Normal Form using Latent Variable Model

Bayesian networks in their Factor Graph Reduced Normal Form (FGrn) are a powerful paradigm for implementing inference graphs. Unfortunately, the computational and memory costs of these networks may be considerable, even for relatively small networks, and this is one of the main reasons why these structures have often been underused in practice. In this work, through a detailed algorithmic and structural analysis, various solutions for cost reduction are proposed. An online version of the classic batch learning algorithm is also analyzed, showing very similar results (in an unsupervised context); which is essential even if multilevel structures are to be built. The solutions proposed, together with the possible online learning algorithm, are included in a C++ library that is quite efficient, especially if compared to the direct use of the well-known sum-product and Maximum Likelihood (ML) algorithms. The results are discussed with particular reference to a Latent Variable Model (LVM) structure.

3-D Hand Pose Estimation from Kinect's Point Cloud Using Appearance Matching

We present a novel appearance-based approach for pose estimation of a human hand using the point clouds provided by the low-cost Microsoft Kinect sensor. Both the free-hand case, in which the hand is isolated from the surrounding environment, and the hand-object case, in which the different types of interactions are classified, have been considered. The hand-object case is clearly the most challenging task having to deal with multiple tracks. The approach proposed here belongs to the class of partial pose estimation where the estimated pose in a frame is used for the initialization of the next one. The pose estimation is obtained by applying a modified version of the Iterative Closest Point (ICP) algorithm to synthetic models to obtain the rigid transformation that aligns each model with respect to the input data. The proposed framework uses a "pure" point cloud as provided by the Kinect sensor without any other information such as RGB values or normal vector components. For this reason, the proposed method can also be applied to data obtained from other types of depth sensor, or RGB-D camera.

Discrete Independent Component Analysis (DICA) with Belief Propagation

We apply belief propagation to a Bayesian bipartite graph composed of discrete independent hidden variables and discrete visible variables. The network is the Discrete counterpart of Independent Component Analysis (DICA) and it is manipulated in a factor graph form for inference and learning. A full set of simulations is reported for character images from the MNIST dataset. The results show that the factorial code implemented by the sources contributes to build a good generative model for the data that can be used in various inference modes.

Towards Building Deep Networks with Bayesian Factor Graphs

We propose a Multi-Layer Network based on the Bayesian framework of the Factor Graphs in Reduced Normal Form (FGrn) applied to a two-dimensional lattice. The Latent Variable Model (LVM) is the basic building block of a quadtree hierarchy built on top of a bottom layer of random variables that represent pixels of an image, a feature map, or more generally a collection of spatially distributed discrete variables. The multi-layer architecture implements a hierarchical data representation that, via belief propagation, can be used for learning and inference. Typical uses are pattern completion, correction and classification. The FGrn paradigm provides great flexibility and modularity and appears as a promising candidate for building deep networks: the system can be easily extended by introducing new and different (in cardinality and in type) variables. Prior knowledge, or supervised information, can be introduced at different scales. The FGrn paradigm provides a handy way for building all kinds of architectures by interconnecting only three types of units: Single Input Single Output (SISO) blocks, Sources and Replicators. The network is designed like a circuit diagram and the belief messages flow bidirectionally in the whole system. The learning algorithms operate only locally within each block. The framework is demonstrated in this paper in a three-layer structure applied to images extracted from a standard data set.

A Comparison of Algorithms for Learning Hidden Variables in Normal Graphs

A Bayesian factor graph reduced to normal form consists in the interconnection of diverter units (or equal constraint units) and Single-Input/Single-Output (SISO) blocks. In this framework localized adaptation rules are explicitly derived from a constrained maximum likelihood (ML) formulation and from a minimum KL-divergence criterion using KKT conditions. The learning algorithms are compared with two other updating equations based on a Viterbi-like and on a variational approximation respectively. The performance of the various algorithm is verified on synthetic data sets for various architectures. The objective of this paper is to provide the programmer with explicit algorithms for rapid deployment of Bayesian graphs in the applications.