Detecting Complex Dependencies in Categorical Data

Locating and evaluating relationships among values in multiple streams of data is a di cult and important task. Consider the data owing from monitors in an intensive care unit. Readings from various subsets of the monitors are indicative and predictive of certain aspects of the patient's state. We present an algorithm that facilitates discovery and assessment of the strength of such predictive relationships called Multi-stream Dependency Detection (msdd). We use heuristic search to guide our exploration of the space of potentially interesting dependencies to uncover those that are signi cant. We begin by reviewing the dependency detection technique described in [3], and extend it to the multiple stream case, describing in detail our heuristic search over the space of possible dependencies. Quantitative evidence for the utility of our approach is provided through a series of experiments with arti cially-generated data. In addition, we present results from the application of our algorithm to two real problem domains: feature-based classi cation and prediction of pathologies in a simulated shipping network. 1. Dependency Detection A dependency is an unexpectedly frequent or infrequent co-occurrence of events over time. Our goal is to nd dependencies between tokens contained in multiple streams. A stream is sequence of values produced over time, and a token is one of the nite set of values that a stream can produce. Dependencies across multiple streams may take many forms: perhaps token a in stream 1 predicts token b in stream 2, or perhaps token a in stream 1 and token c in stream 2 predict token b in stream 2. In general, if stream j contains tj distinct tokens, there are [ Qn j=1 tj + 1] 2 possible dependencies between two items. The dependency detection technique in [3] uses contingency tables to assess the signi cance of dependencies in a single stream of data. Let (tp; ts; ) denote a dependency. Each dependency rule states that when the precursor token, tp, occurs at time step i in the stream, the successor token, ts, will occur at time step i + in the stream with some probability. When this probability is high, the dependency is strong. Consider the stream acbabaccbaabacbbacba. Of all 19 pairs of tokens at lag 1 (e.g. ac, cb, ba, : : : ) 7 pairs have b as the precursor; 6 of those have a as the successor, and one has something other than a (denoted a), as the successor. The following contingency table represents this information: Table(b,a,1) = a a total