8,951 research outputs found
Learning Moore Machines from Input-Output Traces
The problem of learning automata from example traces (but no equivalence or
membership queries) is fundamental in automata learning theory and practice. In
this paper we study this problem for finite state machines with inputs and
outputs, and in particular for Moore machines. We develop three algorithms for
solving this problem: (1) the PTAP algorithm, which transforms a set of
input-output traces into an incomplete Moore machine and then completes the
machine with self-loops; (2) the PRPNI algorithm, which uses the well-known
RPNI algorithm for automata learning to learn a product of automata encoding a
Moore machine; and (3) the MooreMI algorithm, which directly learns a Moore
machine using PTAP extended with state merging. We prove that MooreMI has the
fundamental identification in the limit property. We also compare the
algorithms experimentally in terms of the size of the learned machine and
several notions of accuracy, introduced in this paper. Finally, we compare with
OSTIA, an algorithm that learns a more general class of transducers, and find
that OSTIA generally does not learn a Moore machine, even when fed with a
characteristic sample
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
Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives
Part 2 of this monograph builds on the introduction to tensor networks and
their operations presented in Part 1. It focuses on tensor network models for
super-compressed higher-order representation of data/parameters and related
cost functions, while providing an outline of their applications in machine
learning and data analytics. A particular emphasis is on the tensor train (TT)
and Hierarchical Tucker (HT) decompositions, and their physically meaningful
interpretations which reflect the scalability of the tensor network approach.
Through a graphical approach, we also elucidate how, by virtue of the
underlying low-rank tensor approximations and sophisticated contractions of
core tensors, tensor networks have the ability to perform distributed
computations on otherwise prohibitively large volumes of data/parameters,
thereby alleviating or even eliminating the curse of dimensionality. The
usefulness of this concept is illustrated over a number of applied areas,
including generalized regression and classification (support tensor machines,
canonical correlation analysis, higher order partial least squares),
generalized eigenvalue decomposition, Riemannian optimization, and in the
optimization of deep neural networks. Part 1 and Part 2 of this work can be
used either as stand-alone separate texts, or indeed as a conjoint
comprehensive review of the exciting field of low-rank tensor networks and
tensor decompositions.Comment: 232 page
Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives
Part 2 of this monograph builds on the introduction to tensor networks and
their operations presented in Part 1. It focuses on tensor network models for
super-compressed higher-order representation of data/parameters and related
cost functions, while providing an outline of their applications in machine
learning and data analytics. A particular emphasis is on the tensor train (TT)
and Hierarchical Tucker (HT) decompositions, and their physically meaningful
interpretations which reflect the scalability of the tensor network approach.
Through a graphical approach, we also elucidate how, by virtue of the
underlying low-rank tensor approximations and sophisticated contractions of
core tensors, tensor networks have the ability to perform distributed
computations on otherwise prohibitively large volumes of data/parameters,
thereby alleviating or even eliminating the curse of dimensionality. The
usefulness of this concept is illustrated over a number of applied areas,
including generalized regression and classification (support tensor machines,
canonical correlation analysis, higher order partial least squares),
generalized eigenvalue decomposition, Riemannian optimization, and in the
optimization of deep neural networks. Part 1 and Part 2 of this work can be
used either as stand-alone separate texts, or indeed as a conjoint
comprehensive review of the exciting field of low-rank tensor networks and
tensor decompositions.Comment: 232 page
On Completeness of Cost Metrics and Meta-Search Algorithms in \$-Calculus
In the paper we define three new complexity classes for Turing Machine
undecidable problems inspired by the famous Cook/Levin's NP-complete complexity
class for intractable problems. These are U-complete (Universal complete),
D-complete (Diagonalization complete) and H-complete (Hypercomputation
complete) classes. We started the population process of these new classes. We
justify that some super-Turing models of computation, i.e., models going beyond
Turing machines, are tremendously expressive and they allow to accept arbitrary
languages over a given alphabet including those undecidable ones. We prove also
that one of such super-Turing models of computation -- the \$-Calculus,
designed as a tool for automatic problem solving and automatic programming, has
also such tremendous expressiveness. We investigate also completeness of cost
metrics and meta-search algorithms in \$-calculus
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