Learning From What You Don't Observe

arXiv.org Artificial Intelligence

The process of diagnosis involves learning about the state of a system from various observations of symptoms or findings about the system. Sophisticated Bayesian (and other) algorithms have been developed to revise and maintain beliefs about the system as observations are made. Nonetheless, diagnostic models have tended to ignore some common sense reasoning exploited by human diagnosticians; In particular, one can learn from which observations have not been made, in the spirit of conversational implicature. There are two concepts that we describe to extract information from the observations not made. First, some symptoms, if present, are more likely to be reported before others. Second, most human diagnosticians and expert systems are economical in their data-gathering, searching first where they are more likely to find symptoms present. Thus, there is a desirable bias toward reporting symptoms that are present. We develop a simple model for these concepts that can significantly improve diagnostic inference.

Integrating Probabilistic, Taxonomic and Causal Knowledge in Abductive Diagnosis

arXiv.org Artificial Intelligence

We propose an abductive diagnosis theory that integrates probabilistic, causal and taxonomic knowledge. Probabilistic knowledge allows us to select the most likely explanation; causal knowledge allows us to make reasonable independence assumptions; taxonomic knowledge allows causation to be modeled at different levels of detail, and allows observations be described in different levels of precision. Unlike most other approaches where a causal explanation is a hypothesis that one or more causative events occurred, we define an explanation of a set of observations to be an occurrence of a chain of causation events. These causation events constitute a scenario where all the observations are true. We show that the probabilities of the scenarios can be computed from the conditional probabilities of the causation events. Abductive reasoning is inherently complex even if only modest expressive power is allowed. However, our abduction algorithm is exponential only in the number of observations to be explained, and is polynomial in the size of the knowledge base. This contrasts with many other abduction procedures that are exponential in the size of the knowledge base.

Estimating the Size of a Large Network and its Communities from a Random Sample

Neural Information Processing Systems

Most real-world networks are too large to be measured or studied directly and there is substantial interest in estimating global network properties from smaller sub-samples. One of the most important global properties is the number of vertices/nodes in the network. Estimating the number of vertices in a large network is a major challenge in computer science, epidemiology, demography, and intelligence analysis. In this paper we consider a population random graph G = (V;E) from the stochastic block model (SBM) with K communities/blocks. A sample is obtained by randomly choosing a subset W and letting G(W) be the induced subgraph in G of the vertices in W. In addition to G(W), we observe the total degree of each sampled vertex and its block membership. Given this partial information, we propose an efficient PopULation Size Estimation algorithm, called PULSE, that accurately estimates the size of the whole population as well as the size of each community. To support our theoretical analysis, we perform an exhaustive set of experiments to study the effects of sample size, K, and SBM model parameters on the accuracy of the estimates. The experimental results also demonstrate that PULSE significantly outperforms a widely-used method called the network scale-up estimator in a wide variety of scenarios.

An SIR Graph Growth Model for the Epidemics of Communicable Diseases

arXiv.org Machine Learning

It is the main purpose of this paper to introduce a graph-valued stochastic process in order to model the spread of a communicable infectious disease. The major novelty of the SIR model we promote lies in the fact that the social network on which the epidemics is taking place is not specified in advance but evolves through time, accounting for the temporal evolution of the interactions involving infective individuals. Without assuming the existence of a fixed underlying network model, the stochastic process introduced describes, in a flexible and realistic manner, epidemic spread in non-uniformly mixing and possibly heterogeneous populations. It is shown how to fit such a (parametrised) model by means of Approximate Bayesian Computation methods based on graph-valued statistics. The concepts and statistical methods described in this paper are finally applied to a real epidemic dataset, related to the spread of HIV in Cuba in presence of a contact tracing system, which permits one to reconstruct partly the evolution of the graph of sexual partners diagnosed HIV positive between 1986 and 2006.

Bayesian Inference of Individualized Treatment Effects using Multi-task Gaussian Processes

Neural Information Processing Systems

Predicated on the increasing abundance of electronic health records, we investigate the problem of inferring individualized treatment effects using observational data. Stemming from the potential outcomes model, we propose a novel multi-task learning framework in which factual and counterfactual outcomes are modeled as the outputs of a function in a vector-valued reproducing kernel Hilbert space (vvRKHS). We develop a nonparametric Bayesian method for learning the treatment effects using a multi-task Gaussian process (GP) with a linear coregionalization kernel as a prior over the vvRKHS. The Bayesian approach allows us to compute individualized measures of confidence in our estimates via pointwise credible intervals, which are crucial for realizing the full potential of precision medicine. The impact of selection bias is alleviated via a risk-based empirical Bayes method for adapting the multi-task GP prior, which jointly minimizes the empirical error in factual outcomes and the uncertainty in (unobserved) counterfactual outcomes. We conduct experiments on observational datasets for an interventional social program applied to premature infants, and a left ventricular assist device applied to cardiac patients wait-listed for a heart transplant. In both experiments, we show that our method significantly outperforms the state-of-the-art.