1,980 research outputs found
Categorical invariance and structural complexity in human concept learning
An alternative account of human concept learning based on an invariance measure of the categorical\ud
stimulus is proposed. The categorical invariance model (CIM) characterizes the degree of structural\ud
complexity of a Boolean category as a function of its inherent degree of invariance and its cardinality or\ud
size. To do this we introduce a mathematical framework based on the notion of a Boolean differential\ud
operator on Boolean categories that generates the degrees of invariance (i.e., logical manifold) of the\ud
category in respect to its dimensions. Using this framework, we propose that the structural complexity\ud
of a Boolean category is indirectly proportional to its degree of categorical invariance and directly\ud
proportional to its cardinality or size. Consequently, complexity and invariance notions are formally\ud
unified to account for concept learning difficulty. Beyond developing the above unifying mathematical\ud
framework, the CIM is significant in that: (1) it precisely predicts the key learning difficulty ordering of\ud
the SHJ [Shepard, R. N., Hovland, C. L.,&Jenkins, H. M. (1961). Learning and memorization of classifications.\ud
Psychological Monographs: General and Applied, 75(13), 1-42] Boolean category types consisting of three\ud
binary dimensions and four positive examples; (2) it is, in general, a good quantitative predictor of the\ud
degree of learning difficulty of a large class of categories (in particular, the 41 category types studied\ud
by Feldman [Feldman, J. (2000). Minimization of Boolean complexity in human concept learning. Nature,\ud
407, 630-633]); (3) it is, in general, a good quantitative predictor of parity effects for this large class of\ud
categories; (4) it does all of the above without free parameters; and (5) it is cognitively plausible (e.g.,\ud
cognitively tractable)
Learning Determinantal Point Processes
Determinantal point processes (DPPs), which arise in random matrix theory and
quantum physics, are natural models for subset selection problems where
diversity is preferred. Among many remarkable properties, DPPs offer tractable
algorithms for exact inference, including computing marginal probabilities and
sampling; however, an important open question has been how to learn a DPP from
labeled training data. In this paper we propose a natural feature-based
parameterization of conditional DPPs, and show how it leads to a convex and
efficient learning formulation. We analyze the relationship between our model
and binary Markov random fields with repulsive potentials, which are
qualitatively similar but computationally intractable. Finally, we apply our
approach to the task of extractive summarization, where the goal is to choose a
small subset of sentences conveying the most important information from a set
of documents. In this task there is a fundamental tradeoff between sentences
that are highly relevant to the collection as a whole, and sentences that are
diverse and not repetitive. Our parameterization allows us to naturally balance
these two characteristics. We evaluate our system on data from the DUC 2003/04
multi-document summarization task, achieving state-of-the-art results
A THEORY OF RATIONAL CHOICE UNDER COMPLETE IGNORANCE
This paper contributes to a theory of rational choice under uncertainty for decision-makers whose preferences are exhaustively described by partial orders representing ""limited information."" Specifically, we consider the limiting case of ""Complete Ignorance"" decision problems characterized by maximally incomplete preferences and important primarily as reduced forms of general decision problems under uncertainty. ""Rationality"" is conceptualized in terms of a ""Principle of Preference-Basedness,"" according to which rational choice should be isomorphic to asserted preference. The main result characterizes axiomatically a new choice-rule called ""Simultaneous Expected Utility Maximization"" which in particular satisfies a choice-functional independence and a context-dependent choice-consistency condition; it can be interpreted as the fair agreement in a bargaining game (Kalai-Smorodinsky solution) whose players correspond to the different possible states (respectively extermal priors in the general case).
A Deductive Verification Framework for Circuit-building Quantum Programs
While recent progress in quantum hardware open the door for significant
speedup in certain key areas, quantum algorithms are still hard to implement
right, and the validation of such quantum programs is a challenge. Early
attempts either suffer from the lack of automation or parametrized reasoning,
or target high-level abstract algorithm description languages far from the
current de facto consensus of circuit-building quantum programming languages.
As a consequence, no significant quantum algorithm implementation has been
currently verified in a scale-invariant manner. We propose Qbricks, the first
formal verification environment for circuit-building quantum programs,
featuring clear separation between code and proof, parametric specifications
and proofs, high degree of proof automation and allowing to encode quantum
programs in a natural way, i.e. close to textbook style. Qbricks builds on best
practice of formal verification for the classical case and tailor them to the
quantum case: we bring a new domain-specific circuit-building language for
quantum programs, namely Qbricks-DSL, together with a new logical specification
language Qbricks-Spec and a dedicated Hoare-style deductive verification rule
named Hybrid Quantum Hoare Logic. Especially, we introduce and intensively
build upon HOPS, a higher-order extension of the recent path-sum symbolic
representation, used for both specification and automation. To illustrate the
opportunity of Qbricks, we implement the first verified parametric
implementations of several famous and non-trivial quantum algorithms, including
the quantum part of Shor integer factoring (Order Finding - Shor-OF), quantum
phase estimation (QPE) - a basic building block of many quantum algorithms, and
Grover search. These breakthroughs were amply facilitated by the specification
and automated deduction principles introduced within Qbricks
Power-law distributions in empirical data
Power-law distributions occur in many situations of scientific interest and
have significant consequences for our understanding of natural and man-made
phenomena. Unfortunately, the detection and characterization of power laws is
complicated by the large fluctuations that occur in the tail of the
distribution -- the part of the distribution representing large but rare events
-- and by the difficulty of identifying the range over which power-law behavior
holds. Commonly used methods for analyzing power-law data, such as
least-squares fitting, can produce substantially inaccurate estimates of
parameters for power-law distributions, and even in cases where such methods
return accurate answers they are still unsatisfactory because they give no
indication of whether the data obey a power law at all. Here we present a
principled statistical framework for discerning and quantifying power-law
behavior in empirical data. Our approach combines maximum-likelihood fitting
methods with goodness-of-fit tests based on the Kolmogorov-Smirnov statistic
and likelihood ratios. We evaluate the effectiveness of the approach with tests
on synthetic data and give critical comparisons to previous approaches. We also
apply the proposed methods to twenty-four real-world data sets from a range of
different disciplines, each of which has been conjectured to follow a power-law
distribution. In some cases we find these conjectures to be consistent with the
data while in others the power law is ruled out.Comment: 43 pages, 11 figures, 7 tables, 4 appendices; code available at
http://www.santafe.edu/~aaronc/powerlaws
Survey of the State of the Art in Natural Language Generation: Core tasks, applications and evaluation
This paper surveys the current state of the art in Natural Language
Generation (NLG), defined as the task of generating text or speech from
non-linguistic input. A survey of NLG is timely in view of the changes that the
field has undergone over the past decade or so, especially in relation to new
(usually data-driven) methods, as well as new applications of NLG technology.
This survey therefore aims to (a) give an up-to-date synthesis of research on
the core tasks in NLG and the architectures adopted in which such tasks are
organised; (b) highlight a number of relatively recent research topics that
have arisen partly as a result of growing synergies between NLG and other areas
of artificial intelligence; (c) draw attention to the challenges in NLG
evaluation, relating them to similar challenges faced in other areas of Natural
Language Processing, with an emphasis on different evaluation methods and the
relationships between them.Comment: Published in Journal of AI Research (JAIR), volume 61, pp 75-170. 118
pages, 8 figures, 1 tabl
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