30,401 research outputs found
Hypothesis Only Baselines in Natural Language Inference
We propose a hypothesis only baseline for diagnosing Natural Language
Inference (NLI). Especially when an NLI dataset assumes inference is occurring
based purely on the relationship between a context and a hypothesis, it follows
that assessing entailment relations while ignoring the provided context is a
degenerate solution. Yet, through experiments on ten distinct NLI datasets, we
find that this approach, which we refer to as a hypothesis-only model, is able
to significantly outperform a majority class baseline across a number of NLI
datasets. Our analysis suggests that statistical irregularities may allow a
model to perform NLI in some datasets beyond what should be achievable without
access to the context.Comment: Accepted at *SEM 2018 as long paper. 12 page
Takeuti's proof theory in the context of the Kyoto School
Gaisi Takeuti (1926–2017) is one of the most distinguished logicians in proof theory after Hilbert and Gentzen. He extensively extended Hilbert's program in the sense that he formulated Gentzen's sequent calculus, conjectured that cut-elimination holds for it (Takeuti's conjecture), and obtained several stunning results in the 1950–60s towards the solution of his conjecture. Though he has been known chiefly as a great mathematician, he wrote many papers in English and Japanese where he expressed his philosophical thoughts. In particular, he used several keywords such as "active intuition" and "self-reflection" from Nishida's philosophy. In this paper, we aim to describe a general outline of our project to investigate Takeuti's philosophy of mathematics. In particular, after reviewing Takeuti's proof-theoretic results briefly, we describe some key elements in Takeuti's texts. By explaining these texts, we point out the connection between Takeuti's proof theory and Nishida's philosophy and explain the future goals of our project
Hilbert's Program Then and Now
Hilbert's program was an ambitious and wide-ranging project in the philosophy
and foundations of mathematics. In order to "dispose of the foundational
questions in mathematics once and for all, "Hilbert proposed a two-pronged
approach in 1921: first, classical mathematics should be formalized in
axiomatic systems; second, using only restricted, "finitary" means, one should
give proofs of the consistency of these axiomatic systems. Although Godel's
incompleteness theorems show that the program as originally conceived cannot be
carried out, it had many partial successes, and generated important advances in
logical theory and meta-theory, both at the time and since. The article
discusses the historical background and development of Hilbert's program, its
philosophical underpinnings and consequences, and its subsequent development
and influences since the 1930s.Comment: 43 page
An Ordinal View of Independence with Application to Plausible Reasoning
An ordinal view of independence is studied in the framework of possibility
theory. We investigate three possible definitions of dependence, of increasing
strength. One of them is the counterpart to the multiplication law in
probability theory, and the two others are based on the notion of conditional
possibility. These two have enough expressive power to support the whole
possibility theory, and a complete axiomatization is provided for the strongest
one. Moreover we show that weak independence is well-suited to the problems of
belief change and plausible reasoning, especially to address the problem of
blocking of property inheritance in exception-tolerant taxonomic reasoning.Comment: Appears in Proceedings of the Tenth Conference on Uncertainty in
Artificial Intelligence (UAI1994
A Simple Class of Bayesian Nonparametric Autoregression Models
We introduce a model for a time series of continuous outcomes, that can be expressed as fully nonparametric regression or density regression on lagged terms. The model is based on a dependent Dirichlet process prior on a family of random probability measures indexed by the lagged covariates. The approach is also extended to sequences of binary responses. We discuss implementation and applications of the models to a sequence of waiting times between eruptions of the Old Faithful Geyser, and to a dataset consisting of sequences of recurrence indicators for tumors in the bladder of several patients.MIUR 2008MK3AFZFONDECYT 1100010NIH/NCI R01CA075981Mathematic
Global permutation tests for multivariate ordinal data: alternatives, test statistics, and the null dilemma
We discuss two-sample global permutation tests for sets of multivariate ordinal data in possibly high-dimensional setups, motivated by the analysis of data collected by means of the World Health Organisation's International Classification of Functioning,
Disability and Health. The tests do not require any modelling of the multivariate dependence structure. Specifically, we consider testing for marginal inhomogeneity and
direction-independent marginal order. Max-T test statistics are known to lead to good
power against alternatives with few strong individual effects. We propose test statistics that can be seen as their counterparts for alternatives with many weak individual effects. Permutation tests are valid only if the two multivariate distributions are identical under the null hypothesis. By means of simulations, we examine the practical impact of violations of this exchangeability condition. Our simulations suggest that theoretically invalid permutation tests can still be 'practically valid'. In particular, they suggest that the degree of the permutation procedure's failure may be considered as a function of the difference in group-specific covariance matrices, the proportion between group sizes, the number of variables in the set, the test statistic used, and the number of levels per variable
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