A Weakest Pre-Expectation Semantics for Mixed-Sign Expectations

We present a weakest-precondition-style calculus for reasoning about the expected values (pre-expectations) of \emph{mixed-sign unbounded} random variables after execution of a probabilistic program. The semantics of a while-loop is well-defined as the limit of iteratively applying a functional to a zero-element just as in the traditional weakest pre-expectation calculus, even though a standard least fixed point argument is not applicable in this context. A striking feature of our semantics is that it is always well-defined, even if the expected values do not exist. We show that the calculus is sound, allows for compositional reasoning, and present an invariant-based approach for reasoning about pre-expectations of loops

Treebank-based acquisition of a Chinese lexical-functional grammar

Scaling wide-coverage, constraint-based grammars such as Lexical-Functional Grammars (LFG) (Kaplan and Bresnan, 1982; Bresnan, 2001) or Head-Driven Phrase Structure Grammars (HPSG) (Pollard and Sag, 1994) from fragments to naturally occurring unrestricted text is knowledge-intensive, time-consuming and (often prohibitively) expensive. A number of researchers have recently presented methods to automatically acquire wide-coverage, probabilistic constraint-based grammatical resources from treebanks (Cahill et al., 2002, Cahill et al., 2003; Cahill et al., 2004; Miyao et al., 2003; Miyao et al., 2004; Hockenmaier and Steedman, 2002; Hockenmaier, 2003), addressing the knowledge acquisition bottleneck in constraint-based grammar development. Research to date has concentrated on English and German. In this paper we report on an experiment to induce wide-coverage, probabilistic LFG grammatical and lexical resources for Chinese from the Penn Chinese Treebank (CTB) (Xue et al., 2002) based on an automatic f-structure annotation algorithm. Currently 96.751% of the CTB trees receive a single, covering and connected f-structure, 0.112% do not receive an f-structure due to feature clashes, while 3.137% are associated with multiple f-structure fragments. From the f-structure-annotated CTB we extract a total of 12975 lexical entries with 20 distinct subcategorisation frame types. Of these 3436 are verbal entries with a total of 11 different frame types. We extract a number of PCFG-based LFG approximations. Currently our best automatically induced grammars achieve an f-score of 81.57% against the trees in unseen articles 301-325; 86.06% f-score (all grammatical functions) and 73.98% (preds-only) against the dependencies derived from the f-structures automatically generated for the original trees in 301-325 and 82.79% (all grammatical functions) and 67.74% (preds-only) against the dependencies derived from the manually annotated gold-standard f-structures for 50 trees randomly selected from articles 301-325

Philosophy and the practice of Bayesian statistics

A substantial school in the philosophy of science identifies Bayesian inference with inductive inference and even rationality as such, and seems to be strengthened by the rise and practical success of Bayesian statistics. We argue that the most successful forms of Bayesian statistics do not actually support that particular philosophy but rather accord much better with sophisticated forms of hypothetico-deductivism. We examine the actual role played by prior distributions in Bayesian models, and the crucial aspects of model checking and model revision, which fall outside the scope of Bayesian confirmation theory. We draw on the literature on the consistency of Bayesian updating and also on our experience of applied work in social science. Clarity about these matters should benefit not just philosophy of science, but also statistical practice. At best, the inductivist view has encouraged researchers to fit and compare models without checking them; at worst, theorists have actively discouraged practitioners from performing model checking because it does not fit into their framework.Comment: 36 pages, 5 figures. v2: Fixed typo in caption of figure 1. v3: Further typo fixes. v4: Revised in response to referee

Evaluation of an automatic f-structure annotation algorithm against the PARC 700 dependency bank

An automatic method for annotating the Penn-II Treebank (Marcus et al., 1994) with high-level Lexical Functional Grammar (Kaplan and Bresnan, 1982; Bresnan, 2001; Dalrymple, 2001) f-structure representations is described in (Cahill et al., 2002; Cahill et al., 2004a; Cahill et al., 2004b; O’Donovan et al., 2004). The annotation algorithm and the automatically-generated f-structures are the basis for the automatic acquisition of wide-coverage and robust probabilistic approximations of LFG grammars (Cahill et al., 2002; Cahill et al., 2004a) and for the induction of LFG semantic forms (O’Donovan et al., 2004). The quality of the annotation algorithm and the f-structures it generates is, therefore, extremely important. To date, annotation quality has been measured in terms of precision and recall against the DCU 105. The annotation algorithm currently achieves an f-score of 96.57% for complete f-structures and 94.3% for preds-only f-structures. There are a number of problems with evaluating against a gold standard of this size, most notably that of overfitting. There is a risk of assuming that the gold standard is a complete and balanced representation of the linguistic phenomena in a language and basing design decisions on this. It is, therefore, preferable to evaluate against a more extensive, external standard. Although the DCU 105 is publicly available, 1 a larger well-established external standard can provide a more widely-recognised benchmark against which the quality of the f-structure annotation algorithm can be evaluated. For these reasons, we present an evaluation of the f-structure annotation algorithm of (Cahill et al., 2002; Cahill et al., 2004a; Cahill et al., 2004b; O’Donovan et al., 2004) against the PARC 700 Dependency Bank (King et al., 2003). Evaluation against an external gold standard is a non-trivial task as linguistic analyses may differ systematically between the gold standard and the output to be evaluated as regards feature geometry and nomenclature. We present conversion software to automatically account for many (but not all) of the systematic differences. Currently, we achieve an f-score of 87.31% for the f-structures generated from the original Penn-II trees and an f-score of 81.79% for f-structures from parse trees produced by Charniak’s (2000) parser in our pipeline parsing architecture against the PARC 700