734 research outputs found
Empirical Risk Minimization with Approximations of Probabilistic Grammars
Probabilistic grammars are generative statistical models that are useful for compositional and sequential structures. We present a framework, reminiscent of structural risk minimization, for empirical risk minimization of the parameters of a fixed probabilistic grammar using the log-loss. We derive sample complexity bounds in this framework that apply both to the supervised setting and the unsupervised setting.
Empirical Risk Minimization for Probabilistic Grammars: Sample Complexity and Hardness of Learning
Probabilistic grammars are generative statistical models that are useful for compositional and sequential structures. They are used ubiquitously in computational linguistics. We present a framework, reminiscent of structural risk minimization, for empirical risk minimization of probabilistic grammars using the log-loss. We derive sample complexity bounds in this framework that apply both to the supervised setting and the unsupervised setting. By making assumptions about the underlying distribution that are appropriate for natural language scenarios, we are able to derive distribution-dependent sample complexity bounds for probabilistic grammars. We also give simple algorithms for carrying out empirical risk minimization using this framework in both the supervised and unsupervised settings. In the unsupervised case, we show that the problem of minimizing empirical risk is NP-hard. We therefore suggest an approximate algorithm, similar to expectation-maximization, to minimize the empirical risk. Learning from data is central to contemporary computational linguistics. It is in common in such learning to estimate a model in a parametric family using the maximum likelihood principle. This principle applies in the supervised case (i.e., using annotate
In Language and Information Technologies
With the rising amount of available multilingual text data, computational linguistics faces an opportunity and a challenge. This text can enrich the domains of NLP applications and improve their performance. Traditional supervised learning for this kind of data would require annotation of part of this text for induction of natural language structure. For these large amounts of rich text, such an annotation task can be daunting and expensive. Unsupervised learning of natural language structure can compensate for the need for such annotation. Natural language structure can be modeled through the use of probabilistic grammars, generative statistical models which are useful for compositional and sequential structures. Probabilistic grammars are widely used in natural language processing, but they are also used in other fields as well, such as computer vision, computational biology and cognitive science. This dissertation focuses on presenting a theoretical and an empirical analysis for the learning of these widely used grammars in the unsupervised setting. We analyze computational properties involved in estimation of probabilisti
Learning Efficient Disambiguation
This dissertation analyses the computational properties of current
performance-models of natural language parsing, in particular Data Oriented
Parsing (DOP), points out some of their major shortcomings and suggests
suitable solutions. It provides proofs that various problems of probabilistic
disambiguation are NP-Complete under instances of these performance-models, and
it argues that none of these models accounts for attractive efficiency
properties of human language processing in limited domains, e.g. that frequent
inputs are usually processed faster than infrequent ones. The central
hypothesis of this dissertation is that these shortcomings can be eliminated by
specializing the performance-models to the limited domains. The dissertation
addresses "grammar and model specialization" and presents a new framework, the
Ambiguity-Reduction Specialization (ARS) framework, that formulates the
necessary and sufficient conditions for successful specialization. The
framework is instantiated into specialization algorithms and applied to
specializing DOP. Novelties of these learning algorithms are 1) they limit the
hypotheses-space to include only "safe" models, 2) are expressed as constrained
optimization formulae that minimize the entropy of the training tree-bank given
the specialized grammar, under the constraint that the size of the specialized
model does not exceed a predefined maximum, and 3) they enable integrating the
specialized model with the original one in a complementary manner. The
dissertation provides experiments with initial implementations and compares the
resulting Specialized DOP (SDOP) models to the original DOP models with
encouraging results.Comment: 222 page
Theoretical Interpretations and Applications of Radial Basis Function Networks
Medical applications usually used Radial Basis Function Networks just as Artificial Neural Networks. However, RBFNs are Knowledge-Based Networks that can be interpreted in several way: Artificial Neural Networks, Regularization Networks, Support Vector Machines, Wavelet Networks, Fuzzy Controllers, Kernel Estimators, Instanced-Based Learners. A survey of their interpretations and of their corresponding learning algorithms is provided as well as a brief survey on dynamic learning algorithms. RBFNs' interpretations can suggest applications that are particularly interesting in medical domains
Kernel methods in machine learning
We review machine learning methods employing positive definite kernels. These
methods formulate learning and estimation problems in a reproducing kernel
Hilbert space (RKHS) of functions defined on the data domain, expanded in terms
of a kernel. Working in linear spaces of function has the benefit of
facilitating the construction and analysis of learning algorithms while at the
same time allowing large classes of functions. The latter include nonlinear
functions as well as functions defined on nonvectorial data. We cover a wide
range of methods, ranging from binary classifiers to sophisticated methods for
estimation with structured data.Comment: Published in at http://dx.doi.org/10.1214/009053607000000677 the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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