The main contribution of this article is a new prior distribution over directed acyclic graphs, which gives larger weight to sparse graphs. This distribution is intended for structured Bayesian networks, where the structure is given by an ordered block model. That is, the nodes of the graph are objects which fall into categories (or blocks); the blocks have a natural ordering. The presence of a relationship between two objects is denoted by an arrow, from the object of lower category to the object of higher category. The models considered here were introduced in Kemp et al. (2004) for relational data and extended to multivariate data in Mansinghka et al. (2006). The prior over graph structures presented here has an explicit formula. The number of nodes in each layer of the graph follow a Hoppe Ewens urn model. We consider the situation where the nodes of the graph represent random variables, whose joint probability distribution factorises along the DAG. We describe Monte Carlo schemes for finding the optimal aposteriori structure given a data matrix and compare the performance with Mansinghka et al. (2006) and also with the uniform prior.

Oscillations lie at the core of many biological processes, from the cell cycle, to circadian oscillations and developmental processes. Time-keeping mechanisms are essential to enable organisms to adapt to varying conditions in environmental cycles, from day/night to seasonal. Transcriptional regulatory networks are one of the mechanisms behind these biological oscillations. However, while identifying cyclically expressed genes from time series measurements is relatively easy, determining the structure of the interaction network underpinning the oscillation is a far more challenging problem. Here, we explicitly leverage the oscillatory nature of the transcriptional signals and present a method for reconstructing network interactions tailored to this special but important class of genetic circuits. Our method is based on projecting the signal onto a set of oscillatory basis functions using a Discrete Fourier Transform. We build a Bayesian Hierarchical model within a frequency domain linear model in order to enforce sparsity and incorporate prior knowledge about the network structure. Experiments on real and simulated data show that the method can lead to substantial improvements over competing approaches if the oscillatory assumption is met, and remains competitive also in cases it is not.

Bayesian probability theory is one of the most successful frameworks to model reasoning under uncertainty. Its defining property is the interpretation of probabilities as degrees of belief in propositions about the state of the world relative to an inquiring subject. This essay examines the notion of subjectivity by drawing parallels between Lacanian theory and Bayesian probability theory, and concludes that the latter must be enriched with causal interventions to model agency. The central contribution of this work is an abstract model of the subject that accommodates causal interventions in a measure-theoretic formalisation. This formalisation is obtained through a game-theoretic Ansatz based on modelling the inside and outside of the subject as an extensive-form game with imperfect information between two players. Finally, I illustrate the expressiveness of this model with an example of causal induction.

We consider the problem of estimating undirected triangle-free graphs of high dimensional distributions. Triangle-free graphs form a rich graph family which allows arbitrary loopy structures but 3-cliques. For inferential tractability, we propose a graphical Fermat's principle to regularize the distribution family. Such principle enforces the existence of a distribution-dependent pseudo-metric such that any two nodes have a smaller distance than that of two other nodes who have a geodesic path include these two nodes. Guided by this principle, we show that a greedy strategy is able to recover the true graph. The resulting algorithm only requires a pairwise distance matrix as input and is computationally even more efficient than calculating the minimum spanning tree. We consider graph estimation problems under different settings, including discrete and nonparametric distribution families. Thorough numerical results are provided to illustrate the usefulness of the proposed method.

Factorized information criterion (FIC) is a recently developed approximation technique for the marginal log-likelihood, which provides an automatic model selection framework for a few latent variable models (LVMs) with tractable inference algorithms. This paper reconsiders FIC and fills theoretical gaps of previous FIC studies. First, we reveal the core idea of FIC that allows generalization for a broader class of LVMs, including continuous LVMs, in contrast to previous FICs, which are applicable only to binary LVMs. Second, we investigate the model selection mechanism of the generalized FIC. Our analysis provides a formal justification of FIC as a model selection criterion for LVMs and also a systematic procedure for pruning redundant latent variables that have been removed heuristically in previous studies. Third, we provide an interpretation of FIC as a variational free energy and uncover a few previously-unknown their relationships. A demonstrative study on Bayesian principal component analysis is provided and numerical experiments support our theoretical results.

Every day, billions of mobile network events (i.e. CDRs) are generated by cellular phone operator companies. Latent in this data are inspiring insights about human actions and behaviors, the discovery of which is important because context-aware applications and services hold the key to user-driven, intelligent services, which can enhance our everyday lives such as social and economic development, urban planning, and health prevention. The major challenge in this area is that interpreting such a big stream of data requires a deep understanding of mobile network events' context through available background knowledge. This article addresses the issues in context awareness given heterogeneous and uncertain data of mobile network events missing reliable information on the context of this activity. The contribution of this research is a model from a combination of logical and statistical reasoning standpoints for enabling human activity inference in qualitative terms from open geographical data that aimed at improving the quality of human behaviors recognition tasks from CDRs. We use open geographical data, Openstreetmap (OSM), as a proxy for predicting the content of human activity in the area. The user study performed in Trento shows that predicted human activities (top level) match the survey data with around 93% overall accuracy. The extensive validation for predicting a more specific economic type of human activity performed in Barcelona, by employing credit card transaction data. The analysis identifies that appropriately normalized data on points of interest (POI) is a good proxy for predicting human economical activities, with 84% accuracy on average. So the model is proven to be efficient for predicting the context of human activity, when its total level could be efficiently observed from cell phone data records, missing contextual information however.

In theory, Bayesian nonparametric (BNP) models are well suited to streaming data scenarios due to their ability to adapt model complexity with the observed data. Unfortunately, such benefits have not been fully realized in practice; existing inference algorithms are either not applicable to streaming applications or not extensible to BNP models. For the special case of Dirichlet processes, streaming inference has been considered. However, there is growing interest in more flexible BNP models building on the class of normalized random measures (NRMs). We work within this general framework and present a streaming variational inference algorithm for NRM mixture models. Our algorithm is based on assumed density filtering (ADF), leading straightforwardly to expectation propagation (EP) for large-scale batch inference as well. We demonstrate the efficacy of the algorithm on clustering documents in large, streaming text corpora.

We consider two connected aspects of maximum likelihood estimation of the parameter for high-dimensional discrete graphical models: the existence of the maximum likelihood estimate (mle) and its computation. When the data is sparse, there are many zeros in the contingency table and the maximum likelihood estimate of the parameter may not exist. Fienberg and Rinaldo (2012) have shown that the mle does not exists iff the data vector belongs to a face of the so-called marginal cone spanned by the rows of the design matrix of the model. Identifying these faces in high-dimension is challenging. In this paper, we take a local approach : we show that one such face, albeit possibly not the smallest one, can be identified by looking at a collection of marginal graphical models generated by induced subgraphs $G_i,i=1,\ldots,k$ of $G$. This is our first contribution. Our second contribution concerns the composite maximum likelihood estimate. When the dimension of the problem is large, estimating the parameters of a given graphical model through maximum likelihood is challenging, if not impossible. The traditional approach to this problem has been local with the use of composite likelihood based on local conditional likelihoods. A more recent development is to have the components of the composite likelihood be marginal likelihoods centred around each $v$. We first show that the estimates obtained by consensus through local conditional and marginal likelihoods are identical. We then study the asymptotic properties of the composite maximum likelihood estimate when both the dimension of the model and the sample size $N$ go to infinity.

In data science and machine learning, hierarchical parametric models, such as mixture models, are often used. They contain two kinds of variables: observable variables, which represent the parts of the data that can be directly measured, and latent variables, which represent the underlying processes that generate the data. Although there has been an increase in research on the estimation accuracy for observable variables, the theoretical analysis of estimating latent variables has not been thoroughly investigated. In a previous study, we determined the accuracy of a Bayes estimation for the joint probability of the latent variables in a dataset, and we proved that the Bayes method is asymptotically more accurate than the maximum-likelihood method. However, the accuracy of the Bayes estimation for a single latent variable remains unknown. In the present paper, we derive the asymptotic expansions of the error functions, which are defined by the Kullback-Leibler divergence, for two types of single-variable estimations when the statistical regularity is satisfied. Our results indicate that the accuracies of the Bayes and maximum-likelihood methods are asymptotically equivalent and clarify that the Bayes method is only advantageous for multivariable estimations.

We study the problem of topic modeling in corpora whose documents are organized in a multi-level hierarchy. We explore a parametric approach to this problem, assuming that the number of topics is known or can be estimated by cross-validation. The models we consider can be viewed as special (finite-dimensional) instances of hierarchical Dirichlet processes (HDPs). For these models we show that there exists a simple variational approximation for probabilistic inference. The approximation relies on a previously unexploited inequality that handles the conditional dependence between Dirichlet latent variables in adjacent levels of the model's hierarchy. We compare our approach to existing implementations of nonparametric HDPs. On several benchmarks we find that our approach is faster than Gibbs sampling and able to learn more predictive models than existing variational methods. Finally, we demonstrate the large-scale viability of our approach on two newly available corpora from researchers in computer security---one with 350,000 documents and over 6,000 internal subcategories, the other with a five-level deep hierarchy.