Making use of partial knowledge about hidden states in HMMs : an approach based on belief functions.

International audienceThis paper addresses the problem of parameter estimation and state prediction in Hidden Markov Models (HMMs) based on observed outputs and partial knowledge of hidden states expressed in the belief function framework. The usual HMM model is recovered when the belief functions are vacuous. Parameters are learnt using the Evidential Expectation- Maximization algorithm, a recently introduced variant of the Expectation-Maximization algorithm for maximum likelihood estimation based on uncertain data. The inference problem, i.e., finding the most probable sequence of states based on observed outputs and partial knowledge of states, is also addressed. Experimental results demonstrate that partial information about hidden states, when available, may substantially improve the estimation and prediction performances

Partially-Hidden Markov Models.

International audienceThis paper addresses the problem of Hidden Markov Models (HMM) training and inference when the training data are composed of feature vectors plus uncertain and imprecise labels. The "soft" labels represent partial knowledge about the possible states at each time step and the "softness" is encoded by belief functions. For the obtained model, called a Partially-Hidden Markov Model (PHMM), the training algorithm is based on the Evidential Expectation-Maximisation (E2M) algorithm. The usual HMM model is recovered when the belief functions are vacuous and the obtained model includes supervised, unsupervised and semi-supervised learning as special cases

Learning why things change: The Difference-Based Causality Learner

In this paper, we present the Difference-Based Causality Learner (DBCL), an algorithm for learning a class of discrete-time dynamic models that represents all causation across time by means of difference equations driving change in a system. We motivate this representation with real-world mechanical systems and prove DBCL's correctness for learning structure from time series data, an endeavour that is complicated by the existence of latent derivatives that have to be detected. We also prove that, under common assumptions for causal discovery, DBCL will identify the presence or absence of feedback loops, making the model more useful for predicting the effects of manipulating variables when the system is in equilibrium. We argue analytically and show empirically the advantages of DBCL over vector autoregression (VAR) and Granger causality models as well as modified forms of Bayesian and constraintbased structure discovery algorithms. Finally, we show that our algorithm can discover causal directions of alpha rhythms in human brains from EEG data

On the 3D point cloud for human-pose estimation

This thesis aims at investigating methodologies for estimating a human pose from a 3D point cloud that is captured by a static depth sensor. Human-pose estimation (HPE) is important for a range of applications, such as human-robot interaction, healthcare, surveillance, and so forth. Yet, HPE is challenging because of the uncertainty in sensor measurements and the complexity of human poses. In this research, we focus on addressing challenges related to two crucial components in the estimation process, namely, human-pose feature extraction and human-pose modeling. In feature extraction, the main challenge involves reducing feature ambiguity. We propose a 3D-point-cloud feature called viewpoint and shape feature histogram (VISH) to reduce feature ambiguity by capturing geometric properties of the 3D point cloud of a human. The feature extraction consists of three steps: 3D-point-cloud pre-processing, hierarchical structuring, and feature extraction. In the pre-processing step, 3D points corresponding to a human are extracted and outliers from the environment are removed to retain the 3D points of interest. This step is important because it allows us to reduce the number of 3D points by keeping only those points that correspond to the human body for further processing. In the hierarchical structuring, the pre-processed 3D point cloud is partitioned and replicated into a tree structure as nodes. Viewpoint feature histogram (VFH) and shape features are extracted from each node in the tree to provide a descriptor to represent each node. As the features are obtained based on histograms, coarse-level details are highlighted in large regions and fine-level details are highlighted in small regions. Therefore, the features from the point cloud in the tree can capture coarse level to fine level information to reduce feature ambiguity. In human-pose modeling, the main challenges involve reducing the dimensionality of human-pose space and designing appropriate factors that represent the underlying probability distributions for estimating human poses. To reduce the dimensionality, we propose a non-parametric action-mixture model (AMM). It represents high-dimensional human-pose space using low-dimensional manifolds in searching human poses. In each manifold, a probability distribution is estimated based on feature similarity. The distributions in the manifolds are then redistributed according to the stationary distribution of a Markov chain that models the frequency of human actions. After the redistribution, the manifolds are combined according to a probability distribution determined by action classification. Experiments were conducted using VISH features as input to the AMM. The results showed that the overall error and standard deviation of the AMM were reduced by about 7.9% and 7.1%, respectively, compared with a model without action classification. To design appropriate factors, we consider the AMM as a Bayesian network and propose a mapping that converts the Bayesian network to a neural network called NN-AMM. The proposed mapping consists of two steps: structure identification and parameter learning. In structure identification, we have developed a bottom-up approach to build a neural network while preserving the Bayesian-network structure. In parameter learning, we have created a part-based approach to learn synaptic weights by decomposing a neural network into parts. Based on the concept of distributed representation, the NN-AMM is further modified into a scalable neural network called NND-AMM. A neural-network-based system is then built by using VISH features to represent 3D-point-cloud input and the NND-AMM to estimate 3D human poses. The results showed that the proposed mapping can be utilized to design AMM factors automatically. The NND-AMM can provide more accurate human-pose estimates with fewer hidden neurons than both the AMM and NN-AMM can. Both the NN-AMM and NND-AMM can adapt to different types of input, showing the advantage of using neural networks to design factors