Residual Weighted Learning for Estimating Individualized Treatment Rules

Personalized medicine has received increasing attention among statisticians, computer scientists, and clinical practitioners. A major component of personalized medicine is the estimation of individualized treatment rules (ITRs). Recently, Zhao et al. (2012) proposed outcome weighted learning (OWL) to construct ITRs that directly optimize the clinical outcome. Although OWL opens the door to introducing machine learning techniques to optimal treatment regimes, it still has some problems in performance. In this article, we propose a general framework, called Residual Weighted Learning (RWL), to improve finite sample performance. Unlike OWL which weights misclassification errors by clinical outcomes, RWL weights these errors by residuals of the outcome from a regression fit on clinical covariates excluding treatment assignment. We utilize the smoothed ramp loss function in RWL, and provide a difference of convex (d.c.) algorithm to solve the corresponding non-convex optimization problem. By estimating residuals with linear models or generalized linear models, RWL can effectively deal with different types of outcomes, such as continuous, binary and count outcomes. We also propose variable selection methods for linear and nonlinear rules, respectively, to further improve the performance. We show that the resulting estimator of the treatment rule is consistent. We further obtain a rate of convergence for the difference between the expected outcome using the estimated ITR and that of the optimal treatment rule. The performance of the proposed RWL methods is illustrated in simulation studies and in an analysis of cystic fibrosis clinical trial data.Comment: 48 pages, 3 figure

Towards Understanding Reasoning Complexity in Practice

Although the computational complexity of the logic underlying the standard OWL 2 for the Web Ontology Language (OWL) appears discouraging for real applications, several contributions have shown that reasoning with OWL ontologies is feasible in practice. It turns out that reasoning in practice is often far less complex than is suggested by the established theoretical complexity bound, which reflects the worstcase scenario. State-of-the reasoners like FACT++, HERMIT, PELLET and RACER have demonstrated that, even with fairly expressive fragments of OWL 2, acceptable performances can be achieved. However, it is still not well understood why reasoning is feasible in practice and it is rather unclear how to study this problem. In this paper, we suggest first steps that in our opinion could lead to a better understanding of practical complexity. We also provide and discuss some initial empirical results with HERMIT on prominent ontologie

Reasoning in the OWL 2 Full Ontology Language using First-Order Automated Theorem Proving

OWL 2 has been standardized by the World Wide Web Consortium (W3C) as a family of ontology languages for the Semantic Web. The most expressive of these languages is OWL 2 Full, but to date no reasoner has been implemented for this language. Consistency and entailment checking are known to be undecidable for OWL 2 Full. We have translated a large fragment of the OWL 2 Full semantics into first-order logic, and used automated theorem proving systems to do reasoning based on this theory. The results are promising, and indicate that this approach can be applied in practice for effective OWL reasoning, beyond the capabilities of current Semantic Web reasoners. This is an extended version of a paper with the same title that has been published at CADE 2011, LNAI 6803, pp. 446-460. The extended version provides appendices with additional resources that were used in the reported evaluation

Tunable Hybridization at Mid Zone and Anomalous Bloch-Zener Oscillations in Optical Waveguide Ladders

We have studied the optical oscillation and tunneling of light waves in optical waveguide ladders formed by two coupled planar optical waveguide arrays. For the band structure, a mid-zone gap is formed due to band hybridization and its wavenumber position can be tuned throughout the whole Brillouin zone, which is different from the Bragg gap. By imposing a gradient in the propagation constant in each array, Bloch-Zener oscillation (BZO) is realized with Zener tunneling between the bands occurring at mid zone, which is contrary to the common BZO with tunneling at the center or edge of the Brillouin zone. The occurrence of BZO is demonstrated by using the field-evolution analysis. The tunable hybridization at mid zone enhances the tunability of BZO in the optical waveguide ladders. This work is of general and fundamental importance in understanding the coherent phenomena in lattice structures.Comment: Submitted to Optics Letter

Analyzing Consistency of Behavioral REST Web Service Interfaces

REST web services can offer complex operations that do more than just simply creating, retrieving, updating and deleting information from a database. We have proposed an approach to design the interfaces of behavioral REST web services by defining a resource and a behavioral model using UML. In this paper we discuss the consistency between the resource and behavioral models that represent service states using state invariants. The state invariants are defined as predicates over resources and describe what are the valid state configurations of a behavioral model. If a state invariant is unsatisfiable then there is no valid state configuration containing the state and there is no service that can implement the service interface. We also show how we can use reasoning tools to determine the consistency between these design models.Comment: In Proceedings WWV 2012, arXiv:1210.578