Abstract. We propose a simple approach to combining first-order logic and probabilistic graphical models in a single representation. A Markov logic network (MLN) is a first-order knowledge base with a weight attached to each formula (or clause). Together with a set of constants representing objects in the domain, it specifies a ground Markov network containing one feature for each possible grounding of a first-order formula in the KB, with the corresponding weight. Inference in MLNs is performed by MCMC over the minimal subset of the ground network required for answering the query. Weights are efficiently learned from relational databases by iteratively optimizing a pseudo-likelihood measure. Optionally, additional clauses are learned using inductive logic programming techniques. Experiments with a real-world database and knowledge base in a university domain illustrate the promise of this approach.

Markov logic networks (MLNs) combine logic and probability by attaching weights to first-order clauses, and viewing these as templates for features of Markov networks. In this paper we develop an algorithm for learning the structure of MLNs from relational databases, combining ideas from inductive logic programming (ILP) and feature induction in Markov networks. The algorithm performs a beam or shortestfirst search of the space of clauses, guided by a weighted pseudo-likelihood measure. This requires computing the optimal weights for each candidate structure, but we show how this can be done efficiently. The algorithm can be used to learn an MLN from scratch, or to refine an existing knowledge base. We have applied it in two real-world domains, and found that it outperforms using off-the-shelf ILP systems to learn the MLN structure, as well as pure ILP, purely probabilistic and purely knowledge-based approaches. 1.

We show how a conceptually simple search operator called Optimal Reinsertion can be applied to learning Bayesian Network structure from data. On each step we pick a node called the target. We delete all arcs entering or exiting the target. We then find, subject to some constraints, the globally optimal combination of in-arcs and out-arcs with which to reinsert it. The heart of the paper is a new algorithm called ORSearch which allows each optimal reinsertion step to be computed efficiently on large datasets. Our empirical results compare Optimal Reinsertion against a highly tuned implementation of multi-restart hill climbing. The results typically show one to two orders of magnitude speed-up on a variety of datasets. They usually show better final results, both in terms of BDEU score and in modeling of future data drawn from the same distribution. 1. Bayesian Network Structure Search Given a dataset of R records and m categorical attributes, how can we find a Bayesian network structure that provides a good model of the data? Happily, the formulation of this question into a well-defined optimization problem is now fairly well understood (Heckerman et al., 1995; Cooper & Herskovits, 1992). However, finding the optimal solution is an NP-complete problem (Chickering, 1996a). The computational issues in performing heuristic search in this space are also severe, even taking into account the numerous ingenious and effective innovations in recent years (e.g.

statistics for creating the global Bayes Net. This paper addresses three questions. Is it useful to attempt to learn a Bayesian network structure with hundreds of thousands of nodes? How should such structure search proceed practically? The third question arises out of our approach to the second: how can Frequent Sets (Agrawal et al., 1993), which are extremely popular in the area of descriptive data mining, be turned into a probabilistic model? Large sparse datasets with hundreds of thousands of records and attributes appear in social networks, warehousing, supermarket transactions and web logs. The complexity of structural search made learning of factored probabilistic models on such datasets unfeasible. We propose to use Frequent Sets to significantly speed up the structural search. Unlike previous approaches, we not only cache n-way sufficient statistics, but also exploit their local structure. We also present an empirical evaluation of our algorithm applied to several massive datasets.

Identifying residue coupling relationships within a protein family can provide important insights into the family’s evolutionary record, and has significant applications in analyzing and optimizing sequence-structure-function relationships. We present the first algorithm to infer an undirected graphical model representing residue coupling in protein families. Such a model, which we call a residue coupling network, serves as a compact description of the joint amino acid distribution, focused on the independences among residues. This stands in contrast to current methods, which manipulate dense representations of co-variation and are focused on assessing dependence, which can conflate direct and indirect relationships. Our probabilistic model provides a sound basis for predictive (will this newly designed protein be folded and functional?), diagnostic (why is this protein not stable or functional?), and abductive reasoning (what if I attempt to graft features of one protein family onto another?). Further, our algorithm can readily incorporate, as priors, hypotheses regarding possible underlying mechanistic/energetic explanations for coupling. The resulting approach constitutes a powerful and discriminatory mechanism to identify residue coupling from protein sequences and structures. Analysis results on the G-protein coupled receptor (GPCR) and PDZ domain families demonstrate the ability of our approach to effectively uncover and exploit models of residue coupling.

In many domains, data now arrives faster than we are able to mine it. To avoid wasting this data, we must switch from the traditional "one-shot" data mining approach to systems that are able to mine continuous, high-volume, open-ended data streams as they arrive. In this extended abstract we identify some desiderata for such systems, and outline our framework for realizing them. A key property of our approach is that it minimizes the time required to build a model on a stream, while guaranteeing (as long as the data is i.i.d.) that the model learned is e#ectively indistinguishable from the one that would be obtained using infinite data. Using this framework, we have successfully adapted several learning algorithms to massive data streams, including decision tree induction, Bayesian network learning, k-means clustering, and the EM algorithm for mixtures of Gaussians. These algorithms are able to process on the order of billions of examples per day using o#-the-shelf hardware. Building on this, we are currently developing software primitives for scaling arbitrary learning algorithms to massive data streams with minimal e#ort.

For many real world problems we must perform classification under widely varying amounts of computational resources. For example, if asked to classify an instance taken from a bursty stream, we may have from milliseconds to minutes to return a class prediction. For such problems an anytime algorithm may be especially useful. In this work we show how we can convert the ubiquitous nearest neighbor classifier into an anytime algorithm that can produce an instant classification, or if given the luxury of additional time, can utilize the extra time to increase classification accuracy. We demonstrate the utility of our approach with a comprehensive set of experiments on data from diverse domains.

Graphical models are usually learned without regard to the cost of doing inference with them. As a result, even if a good model is learned, it may perform poorly at prediction, because it requires approximate inference. We propose an alternative: learning models with a score function that directly penalizes the cost of inference. Specifically, we learn arithmetic circuits with a penalty on the number of edges in the circuit (in which the cost of inference is linear). Our algorithm is equivalent to learning a Bayesian network with context-specific independence by greedily splitting conditional distributions, at each step scoring the candidates by compiling the resulting network into an arithmetic circuit, and using its size as the penalty. We show how this can be done efficiently, without compiling a circuit from scratch for each candidate. Experiments on several real-world domains show that our algorithm is able to learn tractable models with very large treewidth, and yields more accurate predictions than a standard context-specific Bayesian network learner, in far less time.

There is a large and growing mismatch between the size of the relational data sets available for mining and the amount of data our relational learning systems can process. In particular, most relational learning systems can operate on data sets containing thousands to tens of thousands of objects, while many real-world data sets grow at a rate of millions of objects a day. In this paper we explore the challenges that prevent relational learning systems from operating on massive data sets, and develop a learning system that overcomes some of them. Our system uses sampling, is efficient with disk accesses, and is able to learn from an order of magnitude more relational data than existing algorithms. We evaluate our system by using it to mine a collection of massive Web crawls, each containing millions of pages.

Improvements in data collection and the birth of online communities made it possible to obtain very large social networks (graphs). Several communities have been involved in modeling and analyzing these graphs. Usage of graphical models, such as Bayesian Networks (BN), to analyze massive data has become increasingly popular, due to their scalability and robustness to noise. In the literature BNs are primarily used for compact representation of joint distributions and to perform inference, i.e. answer queries about the data. In this work we learn Bayes Nets using the previously proposed SBNS algorithm [14]. We look at the learned networks for the purpose of analyzing the graph structure itself. We also point out a few improvements over the SBNS algorithm. The usefulness of Bayes Net structures to understand social networks is an open area. We discuss possible interpretations using a small subgraph of the Medline publications and hope to provoke some discussion and interest in further analysis.