Abstract: Cold-start is a notoriously difficult problem which
can occur in recommendation systems, and arises when there is
insufficient information to draw inferences for users or items. To
address this challenge, a contextual bandit algorithm – the Fast
Approximate Bayesian Contextual Cold Start Learning algorithm
(FAB-COST) – is proposed, which is designed to provide improved
accuracy compared to the traditionally used Laplace approximation
in the logistic contextual bandit, while controlling both algorithmic
complexity and computational cost. To this end, FAB-COST uses
a combination of two moment projection variational methods:
Expectation Propagation (EP), which performs well at the cold
start, but becomes slow as the amount of data increases; and
Assumed Density Filtering (ADF), which has slower growth of
computational cost with data size but requires more data to obtain an
acceptable level of accuracy. By switching from EP to ADF when
the dataset becomes large, it is able to exploit their complementary
strengths. The empirical justification for FAB-COST is presented, and
systematically compared to other approaches on simulated data. In a
benchmark against the Laplace approximation on real data consisting
of over 670, 000 impressions from autotrader.co.uk, FAB-COST
demonstrates at one point increase of over 16% in user clicks. On
the basis of these results, it is argued that FAB-COST is likely to
be an attractive approach to cold-start recommendation systems in a
variety of contexts.
Abstract: A formulation of postbuckling analysis of end supported rods under self-weight has been presented by the variational method. The variational formulation involving the strain energy due to bending and the potential energy of the self-weight, are expressed in terms of the intrinsic coordinates. The variational formulation is accomplished by introducing the Lagrange multiplier technique to impose the boundary conditions. The finite element method is used to derive a system of nonlinear equations resulting from the stationary of the total potential energy and then Newton-Raphson iterative procedure is applied to solve this system of equations. The numerical results demonstrate the postbluckled configurations of end supported rods under self-weight. This finite element method based on variational formulation expressed in term of intrinsic coordinate is highly recommended for postbuckling analysis of end-supported rods under self-weight.
Abstract: This paper focuses on a variational formulation of large amplitude free vibration behavior of a very sag marine cable. In the static equilibrium state, the marine cable has a very large sag configuration. In the motion state, the marine cable is assumed to vibrate in in-plane motion with large amplitude from the static equilibrium position. The total virtual work-energy of the marine cable at the dynamic state is formulated which involves the virtual strain energy due to axial deformation, the virtual work done by effective weight, and the inertia forces. The equations of motion for the large amplitude free vibration of marine cable are obtained by taking into account the difference between the Euler’s equation in the static state and the displaced state. Based on the Galerkin finite element procedure, the linear and nonlinear stiffness matrices, and mass matrices of the marine cable are obtained and the eigenvalue problem is solved. The natural frequency spectrum and the large amplitude free vibration behavior of marine cable are presented.
Abstract: Variational methods for optical flow estimation are
known for their excellent performance. The method proposed by Brox
et al. [5] exemplifies the strength of that framework. It combines
several concepts into single energy functional that is then minimized
according to clear numerical procedure. In this paper we propose
a modification of that algorithm starting from the spatiotemporal
gradient constancy assumption. The numerical scheme allows to
establish the connection between our model and the CLG(H) method
introduced in [18]. Experimental evaluation carried out on synthetic
sequences shows the significant superiority of the spatial variant of
the proposed method. The comparison between methods for the realworld
sequence is also enclosed.
Abstract: Evolution of one-dimensional electron system under
high-energy-density (HED) conditions is investigated, using the
principle of least-action and variational method. In a single-mode
modulation model, the amplitude and spatial wavelength of the
modulation are chosen to be general coordinates. Equations of motion
are derived by considering energy conservation and force balance.
Numerical results show that under HED conditions, electron density
modulation could exist. Time dependences of amplitude and
wavelength are both positively related to the rate of energy input.
Besides, initial loading speed has a significant effect on modulation
amplitude, while wavelength relies more on loading duration.
Abstract: A variational method is used to obtain the growth rate of a transverse long-wavelength perturbation applied to the soliton solution of a nonlinear Schr¨odinger equation with a three-half order potential. We demonstrate numerically that this unstable perturbed soliton will eventually transform into a cylindrical soliton.
Abstract: The wave function at the origin is an important quantity in studying many physical problems concerning heavy quarkonia. This is because that it is using for calculating spin state hyperfine splitting and also crucial to evaluating the production and decay amplitude of the heavy quarkonium. In this paper, we present the variational method by using the single-parameter wave function to estimate the WFO for the ground state of heavy mesons.