5,870 research outputs found
Variational Inference in Nonconjugate Models
Mean-field variational methods are widely used for approximate posterior
inference in many probabilistic models. In a typical application, mean-field
methods approximately compute the posterior with a coordinate-ascent
optimization algorithm. When the model is conditionally conjugate, the
coordinate updates are easily derived and in closed form. However, many models
of interest---like the correlated topic model and Bayesian logistic
regression---are nonconjuate. In these models, mean-field methods cannot be
directly applied and practitioners have had to develop variational algorithms
on a case-by-case basis. In this paper, we develop two generic methods for
nonconjugate models, Laplace variational inference and delta method variational
inference. Our methods have several advantages: they allow for easily derived
variational algorithms with a wide class of nonconjugate models; they extend
and unify some of the existing algorithms that have been derived for specific
models; and they work well on real-world datasets. We studied our methods on
the correlated topic model, Bayesian logistic regression, and hierarchical
Bayesian logistic regression
Nested Hierarchical Dirichlet Processes
We develop a nested hierarchical Dirichlet process (nHDP) for hierarchical
topic modeling. The nHDP is a generalization of the nested Chinese restaurant
process (nCRP) that allows each word to follow its own path to a topic node
according to a document-specific distribution on a shared tree. This alleviates
the rigid, single-path formulation of the nCRP, allowing a document to more
easily express thematic borrowings as a random effect. We derive a stochastic
variational inference algorithm for the model, in addition to a greedy subtree
selection method for each document, which allows for efficient inference using
massive collections of text documents. We demonstrate our algorithm on 1.8
million documents from The New York Times and 3.3 million documents from
Wikipedia.Comment: To appear in IEEE Transactions on Pattern Analysis and Machine
Intelligence, Special Issue on Bayesian Nonparametric
Stochastic Variational Inference
We develop stochastic variational inference, a scalable algorithm for
approximating posterior distributions. We develop this technique for a large
class of probabilistic models and we demonstrate it with two probabilistic
topic models, latent Dirichlet allocation and the hierarchical Dirichlet
process topic model. Using stochastic variational inference, we analyze several
large collections of documents: 300K articles from Nature, 1.8M articles from
The New York Times, and 3.8M articles from Wikipedia. Stochastic inference can
easily handle data sets of this size and outperforms traditional variational
inference, which can only handle a smaller subset. (We also show that the
Bayesian nonparametric topic model outperforms its parametric counterpart.)
Stochastic variational inference lets us apply complex Bayesian models to
massive data sets
From zonal flow to convection rolls in Rayleigh-B\'enard convection with free-slip plates
Rayleigh-B\'enard (RB) convection with free-slip plates and horizontally
periodic boundary conditions is investigated using direct numerical
simulations. Two configurations are considered, one is two-dimension (2D) RB
convection and the other one three-dimension (3D) RB convection with a rotating
axis parallel to the plate. We explore the parameter range of Rayleigh numbers
Ra from 10^9Pr1100. We show
that zonal flow, which was observed, for example, by Goluskin \emph{et al}.
\emph{J. Fluid. Mech.} 759, 360-385 (2014) for \Gamma=2\GammaRaPr\Gamma\GammaRa=10^7Pr=0.71\Gamma=8\Gamma = 16\Gamma\Gamma=2\pi by von
Hardenberg \emph{et al}. \emph{Phys. Rev. Lett.} 15, 134501 (2015), completely
disappears for \Gamma=16\Gamma\Gamma =
8$, the convection roll state and the zonal flow state are both statistically
stable. What state is taken depends on the initial conditions, similarly as we
found for the 2D case.Comment: 26 pages, 12 figure
Electrical control of metallic heavy-metal/ferromagnet interfacial states
Voltage control effects provide an energy-efficient means of tailoring
material properties, especially in highly integrated nanoscale devices.
However, only insulating and semiconducting systems can be controlled so far.
In metallic systems, there is no electric field due to electron screening
effects and thus no such control effect exists. Here we demonstrate that
metallic systems can also be controlled electrically through ionic not
electronic effects. In a Pt/Co structure, the control of the metallic Pt/Co
interface can lead to unprecedented control effects on the magnetic properties
of the entire structure. Consequently, the magnetization and perpendicular
magnetic anisotropy of the Co layer can be independently manipulated to any
desired state, the efficient spin toques can be enhanced about 3.5 times, and
the switching current can be reduced about one order of magnitude. This ability
to control a metallic system may be extended to control other physical
phenomena.Comment: 20 pages, 7 figures, Accepted by Physical Review Applied (2017
Top quark rare three-body decays in the littlest Higgs model with T-parity
In the littlest Higgs model with T-parity (LHT), the mirror quarks have
flavor structures and will contribute to the top quark flavor changing neutral
current. In this work, we perform an extensive investigation of the top quark
rare three-body decays and at one-loop level. Our results show that the branching ratios
of and could reach in the
favorite parameter space of the littlest Higgs model with T-parity, which
implies that these decays may be detectable at the LHC or ILC, while for the
other decays, their rates are too small to be observable at the present or
future colliders.Comment: 12 pages, 10 figure
Computation of the maximal invariant set of discrete-time linear systems subject to a class of non-convex constraints
We consider the problem of computing the maximal invariant set of
discrete-time linear systems subject to a class of non-convex constraints that
admit quadratic relaxations. These non-convex constraints include semialgebraic
sets and other smooth constraints with Lipschitz gradient. With these quadratic
relaxations, a sufficient condition for set invariance is derived and it can be
formulated as a set of linear matrix inequalities. Based on the sufficient
condition, a new algorithm is presented with finite-time convergence to the
actual maximal invariant set under mild assumptions. This algorithm can be also
extended to switched linear systems and some special nonlinear systems. The
performance of this algorithm is demonstrated on several numerical examples.Comment: Accepted in Automatic
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