Restricting the Weak-Generative Capacity of Synchronous Tree-Adjoining Grammars

The formalism of synchronous tree-adjoining grammars, a variant of standard tree-adjoining grammars (TAG), was intended to allow the use of TAGs for language transduction in addition to language specification. In previous work, the definition of the transduction relation defined by a synchronous TAG was given by appeal to an iterative rewriting process. The rewriting definition of derivation is problematic in that it greatly extends the expressivity of the formalism and makes the design of parsing algorithms difficult if not impossible. We introduce a simple, natural definition of synchronous tree-adjoining derivation, based on isomorphisms between standard tree-adjoining derivations, that avoids the expressivity and implementability problems of the original rewriting definition. The decrease in expressivity, which would otherwise make the method unusable, is offset by the incorporation of an alternative definition of standard tree-adjoining derivation, previously proposed for completely separate reasons, thereby making it practical to entertain using the natural definition of synchronous derivation. Nonetheless, some remaining problematic cases call for yet more flexibility in the definition; the isomorphism requirement may have to be relaxed. It remains for future research to tune the exact requirements on the allowable mappings.Comment: 21 pages, uses lingmacros.sty, psfig.sty, fullname.sty; minor typographical changes onl

Roasting the Pig to Burn Down the House: A Modest Proposal

This essay addresses the question whether one should support regulatory proposals that one believes are, standing alone, bad public policy in the hope that they will do such harm that they will ultimately produce (likely unintended) good results. For instance, one may regard a set of proposed regulations as foolish and likely to hobble the industry regulated, but perhaps desirable if one believes that we would be better off without that industry. I argue that television broadcasting is such an industry, and thus that we should support new regulations that will make broadcasting unprofitable, to hasten its demise. But it cannot be just any costly regulation: if a regulation would tend to entrench broadcasting\u27s place on the airwaves, then the regulation will not help to free up the spectrum and should be avoided. Ideal regulations for this purpose are probably those that are pure deadweight loss - regulations that cost broadcasters significant amounts of money but have no impact on their behavior. Am I serious in writing all this? Not entirely, but mostly. I do think that society would benefit if the wireless frequencies currently devoted to broadcast could be used for other services, and the first-best ways of achieving that goal may not be realistic. I am proposing a second-best - a fairly cynical second-best, but a second-best all the same. I would prefer not to go down this path, but if that is the only way to hasten the shriveling of television broadcasting\u27s spectrum usage, then it is probably a path worth taking

Analysis of the ensemble Kalman filter for inverse problems

The ensemble Kalman filter (EnKF) is a widely used methodology for state estimation in partial, noisily observed dynamical systems, and for parameter estimation in inverse problems. Despite its widespread use in the geophysical sciences, and its gradual adoption in many other areas of application, analysis of the method is in its infancy. Furthermore, much of the existing analysis deals with the large ensemble limit, far from the regime in which the method is typically used. The goal of this paper is to analyze the method when applied to inverse problems with fixed ensemble size. A continuous-time limit is derived and the long-time behavior of the resulting dynamical system is studied. Most of the rigorous analysis is confined to the linear forward problem, where we demonstrate that the continuous time limit of the EnKF corresponds to a set of gradient flows for the data misfit in each ensemble member, coupled through a common pre-conditioner which is the empirical covariance matrix of the ensemble. Numerical results demonstrate that the conclusions of the analysis extend beyond the linear inverse problem setting. Numerical experiments are also given which demonstrate the benefits of various extensions of the basic methodology

Judicial Retirements and the Staying Power of U.S. Supreme Court Decisions

The influence of U.S. Supreme Court majority opinions depends critically on how these opinions are received and treated by lower courts, which decide the vast majority of legal disputes. We argue that the retirement of Justices on the Supreme Court serves as a simple heuristic device for lower court judges in deciding how much deference to show to Supreme Court precedent. Using a unique dataset of the treatment of all Supreme Court majority opinions in the courts of appeals from 1953 to 2012, we find that negative treatments of Supreme Court opinions increase, and positive treatments decrease, as the Justices who supported a decision retire from the Court. Importantly, this effect exists over and above the impact of retirements on the ideological makeup of the Supreme Court

The Bayesian Formulation of EIT: Analysis and Algorithms

We provide a rigorous Bayesian formulation of the EIT problem in an infinite dimensional setting, leading to well-posedness in the Hellinger metric with respect to the data. We focus particularly on the reconstruction of binary fields where the interface between different media is the primary unknown. We consider three different prior models - log-Gaussian, star-shaped and level set. Numerical simulations based on the implementation of MCMC are performed, illustrating the advantages and disadvantages of each type of prior in the reconstruction, in the case where the true conductivity is a binary field, and exhibiting the properties of the resulting posterior distribution.Comment: 30 pages, 10 figure

Recognizing Uncertainty in Speech

We address the problem of inferring a speaker's level of certainty based on prosodic information in the speech signal, which has application in speech-based dialogue systems. We show that using phrase-level prosodic features centered around the phrases causing uncertainty, in addition to utterance-level prosodic features, improves our model's level of certainty classification. In addition, our models can be used to predict which phrase a person is uncertain about. These results rely on a novel method for eliciting utterances of varying levels of certainty that allows us to compare the utility of contextually-based feature sets. We elicit level of certainty ratings from both the speakers themselves and a panel of listeners, finding that there is often a mismatch between speakers' internal states and their perceived states, and highlighting the importance of this distinction.Comment: 11 page