The Grow-Shrink strategy for learning Markov network structures constrained by context-specific independences

Markov networks are models for compactly representing complex probability distributions. They are composed by a structure and a set of numerical weights. The structure qualitatively describes independences in the distribution, which can be exploited to factorize the distribution into a set of compact functions. A key application for learning structures from data is to automatically discover knowledge. In practice, structure learning algorithms focused on "knowledge discovery" present a limitation: they use a coarse-grained representation of the structure. As a result, this representation cannot describe context-specific independences. Very recently, an algorithm called CSPC was designed to overcome this limitation, but it has a high computational complexity. This work tries to mitigate this downside presenting CSGS, an algorithm that uses the Grow-Shrink strategy for reducing unnecessary computations. On an empirical evaluation, the structures learned by CSGS achieve competitive accuracies and lower computational complexity with respect to those obtained by CSPC.Comment: 12 pages, and 8 figures. This works was presented in IBERAMIA 201

Linear canonical transformations and quantum phase:a unified canonical and algebraic approach

The algebra of generalized linear quantum canonical transformations is examined in the prespective of Schwinger's unitary-canonical basis. Formulation of the quantum phase problem within the theory of quantum canonical transformations and in particular with the generalized quantum action-angle phase space formalism is established and it is shown that the conceptual foundation of the quantum phase problem lies within the algebraic properties of the quantum canonical transformations in the quantum phase space. The representations of the Wigner function in the generalized action-angle unitary operator pair for certain Hamiltonian systems with the dynamical symmetry are examined. This generalized canonical formalism is applied to the quantum harmonic oscillator to examine the properties of the unitary quantum phase operator as well as the action-angle Wigner function.Comment: 19 pages, no figure

On the Relation between Operator Constraint --, Master Constraint --, Reduced Phase Space --, and Path Integral Quantisation

Path integral formulations for gauge theories must start from the canonical formulation in order to obtain the correct measure. A possible avenue to derive it is to start from the reduced phase space formulation. In this article we review this rather involved procedure in full generality. Moreover, we demonstrate that the reduced phase space path integral formulation formally agrees with the Dirac's operator constraint quantisation and, more specifically, with the Master constraint quantisation for first class constraints. For first class constraints with non trivial structure functions the equivalence can only be established by passing to Abelian(ised) constraints which is always possible locally in phase space. Generically, the correct configuration space path integral measure deviates from the exponential of the Lagrangian action. The corrections are especially severe if the theory suffers from second class secondary constraints. In a companion paper we compute these corrections for the Holst and Plebanski formulations of GR on which current spin foam models are based.Comment: 43 page

Ground states of integrable quantum liquids

Based on a recently introduced operator algebra for the description of a class of integrable quantum liquids we define the ground states for all canonical ensembles of these systems. We consider the particular case of the Hubbard chain in a magnetic field and chemical potential. The ground states of all canonical ensembles of the model can be generated by acting onto the electron vacuum (densities $n1$), suitable pseudoparticle creation operators. We also evaluate the energy gaps of the non-lowest-weight states (non - LWS's) and non-highest-weight states (non - HWS's) of the eta-spin and spin algebras relative to the corresponding ground states. For all sectors of parameter space and symmetries the {\it exact ground state} of the many-electron problem is in the pseudoparticle basis the non-interacting pseudoparticle ground state. This plays a central role in the pseudoparticle perturbation theory.Comment: RevteX 3.0, 43 pages, preprint Univ.Evora, Portuga