Using supervised machine learning approaches to recognize human activities from on-body wearable accelerometers generally requires a large amount of labelled data. When ground truth information is not available, too expensive, time consuming or difficult to collect, one has to rely on unsupervised approaches. This paper presents a new unsupervised approach for human activity recognition from raw acceleration data measured using inertial wearable sensors. The proposed method is based upon joint segmentation of multidimensional time series using a Hidden Markov Model (HMM) in a multiple regression context. The model is learned in an unsupervised framework using the Expectation-Maximization (EM) algorithm where no activity labels are needed. The proposed method takes into account the sequential appearance of the data. It is therefore adapted for the temporal acceleration data to accurately detect the activities. It allows both segmentation and classification of the human activities. Experimental results are provided to demonstrate the efficiency of the proposed approach with respect to standard supervised and unsupervised classification approaches

The problem of human activity recognition is central for understanding and predicting the human behavior, in particular in a prospective of assistive services to humans, such as health monitoring, well being, security, etc. There is therefore a growing need to build accurate models which can take into account the variability of the human activities over time (dynamic models) rather than static ones which can have some limitations in such a dynamic context. In this paper, the problem of activity recognition is analyzed through the segmentation of the multidimensional time series of the acceleration data measured in the 3-d space using body-worn accelerometers. The proposed model for automatic temporal segmentation is a specific statistical latent process model which assumes that the observed acceleration sequence is governed by sequence of hidden (unobserved) activities. More specifically, the proposed approach is based on a specific multiple regression model incorporating a hidden discrete logistic process which governs the switching from one activity to another over time. The model is learned in an unsupervised context by maximizing the observed-data log-likelihood via a dedicated expectation-maximization (EM) algorithm. We applied it on a real-world automatic human activity recognition problem and its performance was assessed by performing comparisons with alternative approaches, including well-known supervised static classifiers and the standard hidden Markov model (HMM). The obtained results are very encouraging and show that the proposed approach is quite competitive even it works in an entirely unsupervised way and does not requires a feature extraction preprocessing step.

Model-based clustering approaches concern the paradigm of exploratory data analysis relying on the finite mixture model to automatically find a latent structure governing observed data. They are one of the most popular and successful approaches in cluster analysis. The mixture density estimation is generally performed by maximizing the observed-data log-likelihood by using the expectation-maximization (EM) algorithm. However, it is well-known that the EM algorithm initialization is crucial. In addition, the standard EM algorithm requires the number of clusters to be known a priori. Some solutions have been provided in [31, 12] for model-based clustering with Gaussian mixture models for multivariate data. In this paper we focus on model-based curve clustering approaches, when the data are curves rather than vectorial data, based on regression mixtures. We propose a new robust EM algorithm for clustering curves. We extend the model-based clustering approach presented in [31] for Gaussian mixture models, to the case of curve clustering by regression mixtures, including polynomial regression mixtures as well as spline or B-spline regressions mixtures. Our approach both handles the problem of initialization and the one of choosing the optimal number of clusters as the EM learning proceeds, rather than in a two-fold scheme. This is achieved by optimizing a penalized log-likelihood criterion. A simulation study confirms the potential benefit of the proposed algorithm in terms of robustness regarding initialization and funding the actual number of clusters.

In this paper, we propose an outlier-robust regularized kernel-based method for linear system identification. The unknown impulse response is modeled as a zero-mean Gaussian process whose covariance (kernel) is given by the recently proposed stable spline kernel, which encodes information on regularity and exponential stability. To build robustness to outliers, we model the measurement noise as realizations of independent Laplacian random variables. The identification problem is cast in a Bayesian framework, and solved by a new Markov Chain Monte Carlo (MCMC) scheme. In particular, exploiting the representation of the Laplacian random variables as scale mixtures of Gaussians, we design a Gibbs sampler which quickly converges to the target distribution. Numerical simulations show a substantial improvement in the accuracy of the estimates over state-of-the-art kernel-based methods.

We propose a probabilistic graphical model realizing a minimal encoding of real variables dependencies based on possibly incomplete observation and an empirical cumulative distribution function per variable. The target application is a large scale partially observed system, like e.g. a traffic network, where a small proportion of real valued variables are observed, and the other variables have to be predicted. Our design objective is therefore to have good scalability in a real-time setting. Instead of attempting to encode the dependencies of the system directly in the description space, we propose a way to encode them in a latent space of binary variables, reflecting a rough perception of the observable (congested/non-congested for a traffic road). The method relies in part on message passing algorithms, i.e. belief propagation, but the core of the work concerns the definition of meaningful latent variables associated to the variables of interest and their pairwise dependencies. Numerical experiments demonstrate the applicability of the method in practice.

Modeling structure in complex networks using Bayesian non-parametrics makes it possible to specify flexible model structures and infer the adequate model complexity from the observed data. This paper provides a gentle introduction to non-parametric Bayesian modeling of complex networks: Using an infinite mixture model as running example we go through the steps of deriving the model as an infinite limit of a finite parametric model, inferring the model parameters by Markov chain Monte Carlo, and checking the model's fit and predictive performance. We explain how advanced non-parametric models for complex networks can be derived and point out relevant literature.

In this work we address the problem of approximating high-dimensional data with a low-dimensional representation. We make the following contributions. We propose an inverse regression method which exchanges the roles of input and response, such that the low-dimensional variable becomes the regressor, and which is tractable. We introduce a mixture of locally-linear probabilistic mapping model that starts with estimating the parameters of inverse regression, and follows with inferring closed-form solutions for the forward parameters of the high-dimensional regression problem of interest. Moreover, we introduce a partially-latent paradigm, such that the vector-valued response variable is composed of both observed and latent entries, thus being able to deal with data contaminated by experimental artifacts that cannot be explained with noise models. The proposed probabilistic formulation could be viewed as a latent-variable augmentation of regression. We devise expectation-maximization (EM) procedures based on a data augmentation strategy which facilitates the maximum-likelihood search over the model parameters. We propose two augmentation schemes and we describe in detail the associated EM inference procedures that may well be viewed as generalizations of a number of EM regression, dimension reduction, and factor analysis algorithms. The proposed framework is validated with both synthetic and real data. We provide experimental evidence that our method outperforms several existing regression techniques.

We propose SPARFA-Trace, a new machine learning-based framework for time-varying learning and content analytics for education applications. We develop a novel message passing-based, blind, approximate Kalman filter for sparse factor analysis (SPARFA), that jointly (i) traces learner concept knowledge over time, (ii) analyzes learner concept knowledge state transitions (induced by interacting with learning resources, such as textbook sections, lecture videos, etc, or the forgetting effect), and (iii) estimates the content organization and intrinsic difficulty of the assessment questions. These quantities are estimated solely from binary-valued (correct/incorrect) graded learner response data and a summary of the specific actions each learner performs (e.g., answering a question or studying a learning resource) at each time instance. Experimental results on two online course datasets demonstrate that SPARFA-Trace is capable of tracing each learner's concept knowledge evolution over time, as well as analyzing the quality and content organization of learning resources, the question-concept associations, and the question intrinsic difficulties. Moreover, we show that SPARFA-Trace achieves comparable or better performance in predicting unobserved learner responses than existing collaborative filtering and knowledge tracing approaches for personalized education.

Bayesian model-based reinforcement learning is a formally elegant approach to learning optimal behaviour under model uncertainty, trading off exploration and exploitation in an ideal way. Unfortunately, finding the resulting Bayes-optimal policies is notoriously taxing, since the search space becomes enormous. In this paper we introduce a tractable, sample-based method for approximate Bayes-optimal planning which exploits Monte-Carlo tree search. Our approach outperformed prior Bayesian model-based RL algorithms by a significant margin on several well-known benchmark problems -- because it avoids expensive applications of Bayes rule within the search tree by lazily sampling models from the current beliefs. We illustrate the advantages of our approach by showing it working in an infinite state space domain which is qualitatively out of reach of almost all previous work in Bayesian exploration.

We propose a new framework for single-channel source separation that lies between the fully supervised and unsupervised setting. Instead of supervision, we provide input features for each source signal and use convex methods to estimate the correlations between these features and the unobserved signal decomposition. We analyze the case of $\ell_2$ loss theoretically and show that recovery of the signal components depends only on cross-correlation between features for different signals, not on correlations between features for the same signal. Contextually supervised source separation is a natural fit for domains with large amounts of data but no explicit supervision; our motivating application is energy disaggregation of hourly smart meter data (the separation of whole-home power signals into different energy uses). Here we apply contextual supervision to disaggregate the energy usage of thousands homes over four years, a significantly larger scale than previously published efforts, and demonstrate on synthetic data that our method outperforms the unsupervised approach.