Are you going to the party: depends, who else is coming? [Learning hidden group dynamics via conditional latent tree models]

Scalable probabilistic modeling and prediction in high dimensional multivariate time-series is a challenging problem, particularly for systems with hidden sources of dependence and/or homogeneity. Examples of such problems include dynamic social networks with co-evolving nodes and edges and dynamic student learning in online courses. Here, we address these problems through the discovery of hierarchical latent groups. We introduce a family of Conditional Latent Tree Models (CLTM), in which tree-structured latent variables incorporate the unknown groups. The latent tree itself is conditioned on observed covariates such as seasonality, historical activity, and node attributes. We propose a statistically efficient framework for learning both the hierarchical tree structure and the parameters of the CLTM. We demonstrate competitive performance in multiple real world datasets from different domains. These include a dataset on students' attempts at answering questions in a psychology MOOC, Twitter users participating in an emergency management discussion and interacting with one another, and windsurfers interacting on a beach in Southern California. In addition, our modeling framework provides valuable and interpretable information about the hidden group structures and their effect on the evolution of the time series

The IBMAP approach for Markov networks structure learning

In this work we consider the problem of learning the structure of Markov networks from data. We present an approach for tackling this problem called IBMAP, together with an efficient instantiation of the approach: the IBMAP-HC algorithm, designed for avoiding important limitations of existing independence-based algorithms. These algorithms proceed by performing statistical independence tests on data, trusting completely the outcome of each test. In practice tests may be incorrect, resulting in potential cascading errors and the consequent reduction in the quality of the structures learned. IBMAP contemplates this uncertainty in the outcome of the tests through a probabilistic maximum-a-posteriori approach. The approach is instantiated in the IBMAP-HC algorithm, a structure selection strategy that performs a polynomial heuristic local search in the space of possible structures. We present an extensive empirical evaluation on synthetic and real data, showing that our algorithm outperforms significantly the current independence-based algorithms, in terms of data efficiency and quality of learned structures, with equivalent computational complexities. We also show the performance of IBMAP-HC in a real-world application of knowledge discovery: EDAs, which are evolutionary algorithms that use structure learning on each generation for modeling the distribution of populations. The experiments show that when IBMAP-HC is used to learn the structure, EDAs improve the convergence to the optimum

Towards generalization of semi-supervised place classification over generalized Voronoi graph

With the progress of human-robot interaction (HRI), the ability of a robot to perform high-level tasks in complex environments is fast becoming an essential requirement. To this end, it is desirable for a robot to understand the environment at both geometric and semantic levels. Therefore in recent years, research towards place classification has been gaining in popularity. After the era of heuristic and rule-based approaches, supervised learning algorithms have been extensively used for this purpose, showing satisfactory performance levels. However, most of those approaches have only been trained and tested in the same environments and thus impede a generalized solution. In this paper, we have proposed a semi-supervised place classification over a generalized Voronoi graph (SPCoGVG) which is a semi-supervised learning framework comprised of three techniques: support vector machine (SVM), conditional random field (CRF) and generalized Voronoi graph (GVG), in order to improve the generalizability. The inherent problem of training CRF with partially labeled data has been solved using a novel parameter estimation algorithm. The effectiveness of the proposed algorithm is validated through extensive analysis of data collected in international university environments. © 2013 Elsevier B.V. All rights reserved

Minimization over the l1-ball using an active-set non-monotone projected gradient

The l1-ball is a nicely structured feasible set that is widely used in many fields (e.g., machine learning, statistics and signal analysis) to enforce some sparsity in the model solutions. In this paper, we devise an active-set strategy for efficiently dealing with minimization problems over the l1-ball and embed it into a tailored algorithmic scheme that makes use of a non-monotone first-order approach to explore the given subspace at each iteration. We prove global convergence to stationary points. Finally, we report numerical experiments, on two different classes of instances, showing the effectiveness of the algorithm

Group Lasso estimation of high-dimensional covariance matrices

In this paper, we consider the Group Lasso estimator of the covariance matrix of a stochastic process corrupted by an additive noise. We propose to estimate the covariance matrix in a high-dimensional setting under the assumption that the process has a sparse representation in a large dictionary of basis functions. Using a matrix regression model, we propose a new methodology for high-dimensional covariance matrix estimation based on empirical contrast regularization by a group Lasso penalty. Using such a penalty, the method selects a sparse set of basis functions in the dictionary used to approximate the process, leading to an approximation of the covariance matrix into a low dimensional space. Consistency of the estimator is studied in Frobenius and operator norms and an application to sparse PCA is proposed

Efficient comparison of independence structures of log-linear models

Log-linear models are a family of probability distributions which capture a variety of relationships between variables, including context-specific independencies. There are a number of approaches for automatic learning of their independence structures from data, although to date, no efficient method exists for evaluating these approaches directly in terms of the structures of the models. The only known methods evaluate these approaches indirectly through the complete model produced, that includes not only the structure but also the model parameters, introducing potential distortions in the comparison. This work presents such a method, that is, a measure for the direct comparison of the independence structures of log-linear models, inspired by the Hamming distance comparison method used in undirected graphical models. The measure presented can be efficiently computed in terms of the number of variables of the domain, and is proven to be a distance metric

A survey on independence-based Markov networks learning

This work reports the most relevant technical aspects in the problem of learning the \emph{Markov network structure} from data. Such problem has become increasingly important in machine learning, and many other application fields of machine learning. Markov networks, together with Bayesian networks, are probabilistic graphical models, a widely used formalism for handling probability distributions in intelligent systems. Learning graphical models from data have been extensively applied for the case of Bayesian networks, but for Markov networks learning it is not tractable in practice. However, this situation is changing with time, given the exponential growth of computers capacity, the plethora of available digital data, and the researching on new learning technologies. This work stresses on a technology called independence-based learning, which allows the learning of the independence structure of those networks from data in an efficient and sound manner, whenever the dataset is sufficiently large, and data is a representative sampling of the target distribution. In the analysis of such technology, this work surveys the current state-of-the-art algorithms for learning Markov networks structure, discussing its current limitations, and proposing a series of open problems where future works may produce some advances in the area in terms of quality and efficiency. The paper concludes by opening a discussion about how to develop a general formalism for improving the quality of the structures learned, when data is scarce.Comment: 35 pages, 1 figur