On the Behavior of the Homogeneous Self-Dual Model for Conic Convex Optimization

There is a natural norm associated with a starting point of the homogeneous self-dual (HSD) embedding model for conic convex optimization. In this norm two measures of the HSD model’s behavior are precisely controlled independent of the problem instance: (i) the sizes of ε-optimal solutions, and (ii) the maximum distance of ε-optimal solutions to the boundary of the cone of the HSD variables. This norm is also useful in developing a stopping-rule theory for HSD-based interior-point methods such as SeDuMi. Under mild assumptions, we show that a standard stopping rule implicitly involves the sum of the sizes of the ε-optimal primal and dual solutions, as well as the size of the initial primal and dual infeasibility residuals. This theory suggests possible criteria for developing starting points for the homogeneous self-dual model that might improve the resulting solution time in practice

Model-Based Troubleshooting of Digital Systems

This thesis describes a methodology, a representation, and an implemented program for troubleshooting digital circuit boards at roughly the level of expertise one might expect in a human novice. Existing methods for model-based troubleshooting have not scaled up to deal with complex circuits, in part because traditional circuit models do not explicitly represent aspects of the device that troubleshooters would consider important. For complex devices the model of the target device should be constructed with the goal of troubleshooting explicitly in mind. Given that methodology, the principal contributions of the thesis are ways of representing complex circuits to help make troubleshooting feasible. Temporally coarse behavior descriptions are a particularly powerful simplification. Instantiating this idea for the circuit domain produces a vocabulary for describing digital signals. The vocabulary has a level of temporal detail sufficient to make useful predictions abut the response of the circuit while it remains coarse enough to make those predictions computationally tractable. Other contributions are principles for using these representations. Although not embodied in a program, these principles are sufficiently concrete that models can be constructed manually from existing circuit descriptions such as schematics, part specifications, and state diagrams. One such principle is that if there are components with particularly likely failure modes or failure modes in which their behavior is drastically simplified, this knowledge should be incorporated into the model. Further contributions include the solution of technical problems resulting from the use of explicit temporal representations and design descriptions with tangled hierarchies.

Using Analogy to Acquire Commonsense Knowledge from Human Contributors

The goal of the work reported here is to capture the commonsense knowledge of non-expert human contributors. Achieving this goal will enable more intelligent human-computer interfaces and pave the way for computers to reason about our world. In the domain of natural language processing, it will provide the world knowledge much needed for semantic processing of natural language. To acquire knowledge from contributors not trained in knowledge engineering, I take the following four steps: (i) develop a knowledge representation (KR) model for simple assertions in natural language, (ii) introduce cumulative analogy, a class of nearest-neighbor based analogical reasoning algorithms over this representation, (iii) argue that cumulative analogy is well suited for knowledge acquisition (KA) based on a theoretical analysis of effectiveness of KA with this approach, and (iv) test the KR model and the effectiveness of the cumulative analogy algorithms empirically. To investigate effectiveness of cumulative analogy for KA empirically, Learner, an open source system for KA by cumulative analogy has been implemented, deployed, and evaluated. (The site "1001 Questions," is available at http://teach-computers.org/learner.html). Learner acquires assertion-level knowledge by constructing shallow semantic analogies between a KA topic and its nearest neighbors and posing these analogies as natural language questions to human contributors. Suppose, for example, that based on the knowledge about "newspapers" already present in the knowledge base, Learner judges "newspaper" to be similar to "book" and "magazine." Further suppose that assertions "books contain information" and "magazines contain information" are also already in the knowledge base. Then Learner will use cumulative analogy from the similar topics to ask humans whether "newspapers contain information." Because similarity between topics is computed based on what is already known about them, Learner exhibits bootstrapping behavior --- the quality of its questions improves as it gathers more knowledge. By summing evidence for and against posing any given question, Learner also exhibits noise tolerance, limiting the effect of incorrect similarities. The KA power of shallow semantic analogy from nearest neighbors is one of the main findings of this thesis. I perform an analysis of commonsense knowledge collected by another research effort that did not rely on analogical reasoning and demonstrate that indeed there is sufficient amount of correlation in the knowledge base to motivate using cumulative analogy from nearest neighbors as a KA method. Empirically, evaluating the percentages of questions answered affirmatively, negatively and judged to be nonsensical in the cumulative analogy case compares favorably with the baseline, no-similarity case that relies on random objects rather than nearest neighbors. Of the questions generated by cumulative analogy, contributors answered 45% affirmatively, 28% negatively and marked 13% as nonsensical; in the control, no-similarity case 8% of questions were answered affirmatively, 60% negatively and 26% were marked as nonsensical.