6 research outputs found
Learning Directed Graphical Models with Optimal Transport
Estimating the parameters of a probabilistic directed graphical model from
incomplete data remains a long-standing challenge. This is because, in the
presence of latent variables, both the likelihood function and posterior
distribution are intractable without further assumptions about structural
dependencies or model classes. While existing learning methods are
fundamentally based on likelihood maximization, here we offer a new view of the
parameter learning problem through the lens of optimal transport. This
perspective licenses a general framework that operates on any directed graphs
without making unrealistic assumptions on the posterior over the latent
variables or resorting to black-box variational approximations. We develop a
theoretical framework and support it with extensive empirical evidence
demonstrating the flexibility and versatility of our approach. Across
experiments, we show that not only can our method recover the ground-truth
parameters but it also performs comparably or better on downstream
applications, notably the non-trivial task of discrete representation learning
Mathematical linguistics
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Z-Numbers-Based Approach to Hotel Service Quality Assessment
In this study, we are analyzing the possibility of using Z-numbers for
measuring the service quality and decision-making for quality improvement in the
hotel industry. Techniques used for these purposes are based on consumer evalu-
ations - expectations and perceptions. As a rule, these evaluations are expressed
in crisp numbers (Likert scale) or fuzzy estimates. However, descriptions of the
respondent opinions based on crisp or fuzzy numbers formalism not in all cases
are relevant. The existing methods do not take into account the degree of con-
fidence of respondents in their assessments. A fuzzy approach better describes
the uncertainties associated with human perceptions and expectations. Linguis-
tic values are more acceptable than crisp numbers. To consider the subjective
natures of both service quality estimates and confidence degree in them, the two-
component Z-numbers Z = (A, B) were used. Z-numbers express more adequately
the opinion of consumers. The proposed and computationally efficient approach
(Z-SERVQUAL, Z-IPA) allows to determine the quality of services and iden-
tify the factors that required improvement and the areas for further development.
The suggested method was applied to evaluate the service quality in small and
medium-sized hotels in Turkey and Azerbaijan, illustrated by the example
SIMULATING SEISMIC WAVE PROPAGATION IN TWO-DIMENSIONAL MEDIA USING DISCONTINUOUS SPECTRAL ELEMENT METHODS
We introduce a discontinuous spectral element method for simulating seismic wave in 2- dimensional elastic media. The methods combine the flexibility of a discontinuous finite
element method with the accuracy of a spectral method. The elastodynamic equations are discretized using high-degree of Lagrange interpolants and integration over an element is
accomplished based upon the Gauss-Lobatto-Legendre integration rule. This combination of discretization and integration results in a diagonal mass matrix and the use of discontinuous finite element method makes the calculation can be done locally in each element. Thus, the algorithm is simplified drastically. We validated the results of one-dimensional problem by comparing them with finite-difference time-domain method and exact solution. The comparisons show excellent agreement