1,629 research outputs found
Piecewise Latent Variables for Neural Variational Text Processing
Advances in neural variational inference have facilitated the learning of
powerful directed graphical models with continuous latent variables, such as
variational autoencoders. The hope is that such models will learn to represent
rich, multi-modal latent factors in real-world data, such as natural language
text. However, current models often assume simplistic priors on the latent
variables - such as the uni-modal Gaussian distribution - which are incapable
of representing complex latent factors efficiently. To overcome this
restriction, we propose the simple, but highly flexible, piecewise constant
distribution. This distribution has the capacity to represent an exponential
number of modes of a latent target distribution, while remaining mathematically
tractable. Our results demonstrate that incorporating this new latent
distribution into different models yields substantial improvements in natural
language processing tasks such as document modeling and natural language
generation for dialogue.Comment: 19 pages, 2 figures, 8 tables; EMNLP 201
Evaluating Data Assimilation Algorithms
Data assimilation leads naturally to a Bayesian formulation in which the
posterior probability distribution of the system state, given the observations,
plays a central conceptual role. The aim of this paper is to use this Bayesian
posterior probability distribution as a gold standard against which to evaluate
various commonly used data assimilation algorithms.
A key aspect of geophysical data assimilation is the high dimensionality and
low predictability of the computational model. With this in mind, yet with the
goal of allowing an explicit and accurate computation of the posterior
distribution, we study the 2D Navier-Stokes equations in a periodic geometry.
We compute the posterior probability distribution by state-of-the-art
statistical sampling techniques. The commonly used algorithms that we evaluate
against this accurate gold standard, as quantified by comparing the relative
error in reproducing its moments, are 4DVAR and a variety of sequential
filtering approximations based on 3DVAR and on extended and ensemble Kalman
filters.
The primary conclusions are that: (i) with appropriate parameter choices,
approximate filters can perform well in reproducing the mean of the desired
probability distribution; (ii) however they typically perform poorly when
attempting to reproduce the covariance; (iii) this poor performance is
compounded by the need to modify the covariance, in order to induce stability.
Thus, whilst filters can be a useful tool in predicting mean behavior, they
should be viewed with caution as predictors of uncertainty. These conclusions
are intrinsic to the algorithms and will not change if the model complexity is
increased, for example by employing a smaller viscosity, or by using a detailed
NWP model
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