Cascaded High Dimensional Histograms: A Generative Approach to Density Estimation

We present tree- and list- structured density estimation methods for high dimensional binary/categorical data. Our density estimation models are high dimensional analogies to variable bin width histograms. In each leaf of the tree (or list), the density is constant, similar to the flat density within the bin of a histogram. Histograms, however, cannot easily be visualized in higher dimensions, whereas our models can. The accuracy of histograms fades as dimensions increase, whereas our models have priors that help with generalization. Our models are sparse, unlike high-dimensional histograms. We present three generative models, where the first one allows the user to specify the number of desired leaves in the tree within a Bayesian prior. The second model allows the user to specify the desired number of branches within the prior. The third model returns lists (rather than trees) and allows the user to specify the desired number of rules and the length of rules within the prior. Our results indicate that the new approaches yield a better balance between sparsity and accuracy of density estimates than other methods for this task.Comment: 27 pages, 13 figure

Metaphorisms in programming

This paper introduces the metaphorism pattern of relational specification and addresses how specification following this pattern can be refined into recursive programs. Metaphorisms express input-output relationships which preserve relevant information while at the same time some intended optimization takes place. Text processing, sorting, representation changers, etc., are examples of metaphorisms. The kind of metaphorism refinement proposed in this paper is a strategy known as change of virtual data structure. It gives sufficient conditions for such implementations to be calculated using relation algebra and illustrates the strategy with the derivation of quicksort as example.The author wishes to thank the anonymous referees for their comments and suggestions. This work is funded by ERDF - European Regional Development Fund through the COMPETE Programme (operational programme for competitiveness) and by National Funds through the FCT - Funda¸c˜ao para a Ciˆencia e a Tecnologia (Portuguese Foundation for Science and Technology) within project FCOMP-01-0124-FEDER-02053

Zero-safe net models for transactions in Linda

Abstract Zero-safe nets are a variation of Petri nets, where transactions can be suitably modeled. The idea is to distinguish between stable places (whose markings define observable states) and zero-safe places (where tokens can only be temporarily allocated, defining hidden states): Transactions must start and end in observable states. We propose an extension of the coordination language Linda, called TraLinda, where a few basic primitives for expressing transactions are introduced by means of different typing of tuples. By exploiting previous results of Busi, Gorrieri and Zavattaro on the net modeling of Linda-like languages, we define a concurrent operational semantics based on zero-safe nets for TraLinda, where the typing of tuples reflects evidently on the distinction between stable and zero-safe places

A Coordination Language for Databases

We present a coordination language for the modeling of distributed database applications. The language, baptized Klaim-DB, borrows the concepts of localities and nets of the coordination language Klaim but re-incarnates the tuple spaces of Klaim as databases. It provides high-level abstractions and primitives for the access and manipulation of structured data, with integrity and atomicity considerations. We present the formal semantics of Klaim-DB and develop a type system that avoids potential runtime errors such as certain evaluation errors and mismatches of data format in tables, which are monitored in the semantics. The use of the language is illustrated in a scenario where the sales from different branches of a chain of department stores are aggregated from their local databases. Raising the abstraction level and encapsulating integrity checks in the language primitives have benefited the modeling task considerably

Learning classifiers from linked data

The emergence of many interlinked, physically distributed, and autonomously maintained linked data sources amounts to the rapid growth of Linked Open Data (LOD) cloud, which offers unprecedented opportunities for predictive modeling and knowledge discovery from such data. However existing machine learning approaches are limited in their applicability because it is neither desirable nor feasible to gather all of the data in a centralized location for analysis due to access, memory, bandwidth, or computational restrictions. In some applications additional schema such as subclass hierarchies may be available and exploited by the learner. Furthermore, in other applications, the attributes that are relevant for specific prediction tasks are not known a priori and hence need to be discovered by the algorithm. Against this background, we present a series of approaches that attempt to address such scenarios. First, we show how to learn Relational Bayesian Classifiers (RBCs) from a single but remote data store using statistical queries, and we extend to the setting where the attributes that are relevant for prediction are not known a priori, by selectively crawling the data store for attributes of interest. Next, we introduce an algorithm for learning classifiers from a remote data store enriched with subclass hierarchies. Our algorithm encodes the constraints specified in a subclass hierarchy using latent variables in a directed graphical model, and adopts the Variational Bayesian EM approach to efficiently learn parameters. In retrospect, we observe that in learning from linked data it is often useful to represent an instance as tuples of bags of attribute values. With this inspiration, we introduce, formulate, and present solutions for a novel type of learning problem which we call distributional instance classification. Finally, building up from the foundations, we consider the problem of learning predictive models from multiple interlinked data stores. We introduce a distributed learning framework, and identify three special cases of linked data fragmentation then describe effective strategies for learning predictive models in each case. Further, we consider a novel application of a matrix reconstruction technique from the field of Computerized Tomography to approximate the statistics needed by the learning algorithm from projections using count queries, thus dramatically reducing the amount of information transmitted from the remote data sources to the learner

Cluster and Feature Modeling from Combinatorial Stochastic Processes

One of the focal points of the modern literature on Bayesian nonparametrics has been the problem of clustering, or partitioning, where each data point is modeled as being associated with one and only one of some collection of groups called clusters or partition blocks. Underlying these Bayesian nonparametric models are a set of interrelated stochastic processes, most notably the Dirichlet process and the Chinese restaurant process. In this paper we provide a formal development of an analogous problem, called feature modeling, for associating data points with arbitrary nonnegative integer numbers of groups, now called features or topics. We review the existing combinatorial stochastic process representations for the clustering problem and develop analogous representations for the feature modeling problem. These representations include the beta process and the Indian buffet process as well as new representations that provide insight into the connections between these processes. We thereby bring the same level of completeness to the treatment of Bayesian nonparametric feature modeling that has previously been achieved for Bayesian nonparametric clustering.Comment: Published in at http://dx.doi.org/10.1214/13-STS434 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org