Inference of Temporally Varying Bayesian Networks

When analysing gene expression time series data an often overlooked but crucial aspect of the model is that the regulatory network structure may change over time. Whilst some approaches have addressed this problem previously in the literature, many are not well suited to the sequential nature of the data. Here we present a method that allows us to infer regulatory network structures that may vary between time points, utilising a set of hidden states that describe the network structure at a given time point. To model the distribution of the hidden states we have applied the Hierarchical Dirichlet Process Hideen Markov Model, a nonparametric extension of the traditional Hidden Markov Model, that does not require us to fix the number of hidden states in advance. We apply our method to exisiting microarray expression data as well as demonstrating is efficacy on simulated test data

Feature discovery and visualization of robot mission data using convolutional autoencoders and Bayesian nonparametric topic models

The gap between our ability to collect interesting data and our ability to analyze these data is growing at an unprecedented rate. Recent algorithmic attempts to fill this gap have employed unsupervised tools to discover structure in data. Some of the most successful approaches have used probabilistic models to uncover latent thematic structure in discrete data. Despite the success of these models on textual data, they have not generalized as well to image data, in part because of the spatial and temporal structure that may exist in an image stream. We introduce a novel unsupervised machine learning framework that incorporates the ability of convolutional autoencoders to discover features from images that directly encode spatial information, within a Bayesian nonparametric topic model that discovers meaningful latent patterns within discrete data. By using this hybrid framework, we overcome the fundamental dependency of traditional topic models on rigidly hand-coded data representations, while simultaneously encoding spatial dependency in our topics without adding model complexity. We apply this model to the motivating application of high-level scene understanding and mission summarization for exploratory marine robots. Our experiments on a seafloor dataset collected by a marine robot show that the proposed hybrid framework outperforms current state-of-the-art approaches on the task of unsupervised seafloor terrain characterization.Comment: 8 page

A nonparametric Bayesian approach toward robot learning by demonstration

In the past years, many authors have considered application of machine learning methodologies to effect robot learning by demonstration. Gaussian mixture regression (GMR) is one of the most successful methodologies used for this purpose. A major limitation of GMR models concerns automatic selection of the proper number of model states, i.e., the number of model component densities. Existing methods, including likelihood- or entropy-based criteria, usually tend to yield noisy model size estimates while imposing heavy computational requirements. Recently, Dirichlet process (infinite) mixture models have emerged in the cornerstone of nonparametric Bayesian statistics as promising candidates for clustering applications where the number of clusters is unknown a priori. Under this motivation, to resolve the aforementioned issues of GMR-based methods for robot learning by demonstration, in this paper we introduce a nonparametric Bayesian formulation for the GMR model, the Dirichlet process GMR model. We derive an efficient variational Bayesian inference algorithm for the proposed model, and we experimentally investigate its efficacy as a robot learning by demonstration methodology, considering a number of demanding robot learning by demonstration scenarios

Supervised learning on graphs of spatio-temporal similarity in satellite image sequences

High resolution satellite image sequences are multidimensional signals composed of spatio-temporal patterns associated to numerous and various phenomena. Bayesian methods have been previously proposed in (Heas and Datcu, 2005) to code the information contained in satellite image sequences in a graph representation using Bayesian methods. Based on such a representation, this paper further presents a supervised learning methodology of semantics associated to spatio-temporal patterns occurring in satellite image sequences. It enables the recognition and the probabilistic retrieval of similar events. Indeed, graphs are attached to statistical models for spatio-temporal processes, which at their turn describe physical changes in the observed scene. Therefore, we adjust a parametric model evaluating similarity types between graph patterns in order to represent user-specific semantics attached to spatio-temporal phenomena. The learning step is performed by the incremental definition of similarity types via user-provided spatio-temporal pattern examples attached to positive or/and negative semantics. From these examples, probabilities are inferred using a Bayesian network and a Dirichlet model. This enables to links user interest to a specific similarity model between graph patterns. According to the current state of learning, semantic posterior probabilities are updated for all possible graph patterns so that similar spatio-temporal phenomena can be recognized and retrieved from the image sequence. Few experiments performed on a multi-spectral SPOT image sequence illustrate the proposed spatio-temporal recognition method

Dirichlet Bayesian Network Scores and the Maximum Relative Entropy Principle

A classic approach for learning Bayesian networks from data is to identify a maximum a posteriori (MAP) network structure. In the case of discrete Bayesian networks, MAP networks are selected by maximising one of several possible Bayesian Dirichlet (BD) scores; the most famous is the Bayesian Dirichlet equivalent uniform (BDeu) score from Heckerman et al (1995). The key properties of BDeu arise from its uniform prior over the parameters of each local distribution in the network, which makes structure learning computationally efficient; it does not require the elicitation of prior knowledge from experts; and it satisfies score equivalence. In this paper we will review the derivation and the properties of BD scores, and of BDeu in particular, and we will link them to the corresponding entropy estimates to study them from an information theoretic perspective. To this end, we will work in the context of the foundational work of Giffin and Caticha (2007), who showed that Bayesian inference can be framed as a particular case of the maximum relative entropy principle. We will use this connection to show that BDeu should not be used for structure learning from sparse data, since it violates the maximum relative entropy principle; and that it is also problematic from a more classic Bayesian model selection perspective, because it produces Bayes factors that are sensitive to the value of its only hyperparameter. Using a large simulation study, we found in our previous work (Scutari, 2016) that the Bayesian Dirichlet sparse (BDs) score seems to provide better accuracy in structure learning; in this paper we further show that BDs does not suffer from the issues above, and we recommend to use it for sparse data instead of BDeu. Finally, will show that these issues are in fact different aspects of the same problem and a consequence of the distributional assumptions of the prior.Comment: 20 pages, 4 figures; extended version submitted to Behaviormetrik

Bayesian modeling of networks in complex business intelligence problems

Complex network data problems are increasingly common in many fields of application. Our motivation is drawn from strategic marketing studies monitoring customer choices of specific products, along with co-subscription networks encoding multiple purchasing behavior. Data are available for several agencies within the same insurance company, and our goal is to efficiently exploit co-subscription networks to inform targeted advertising of cross-sell strategies to currently mono-product customers. We address this goal by developing a Bayesian hierarchical model, which clusters agencies according to common mono-product customer choices and co-subscription networks. Within each cluster, we efficiently model customer behavior via a cluster-dependent mixture of latent eigenmodels. This formulation provides key information on mono-product customer choices and multiple purchasing behavior within each cluster, informing targeted cross-sell strategies. We develop simple algorithms for tractable inference, and assess performance in simulations and an application to business intelligence