1,720,958 research outputs found
Geodesic gaussian processes for the parametric reconstruction of a free-form surface
Get PDFReconstructing a free-form surface from 3-dimensional (3D) noisy measurements is a central problem in inspection, statistical quality control, and reverse engineering. We present a new method for the statistical reconstruction of a free-form surface patch based on 3D point cloud data. The surface is represented parametrically, with each of the three Cartesian coordinates (x, y, z) a function of surface coordinates (u, v), a model form compatible with computer-aided-design (CAD) models. This model form also avoids having to choose one Euclidean coordinate (say, z) as a “response” function of the other two coordinate “locations” (say, x and y), as commonly used in previous Euclidean kriging models of manufacturing data. The (u, v) surface coordinates are computed using parameterization algorithms from the manifold learning and computer graphics literature. These are then used as locations in a spatial Gaussian process model that considers correlations between two points on the surface a function of their geodesic distance on the surface, rather than a function of their Euclidean distances over the xy plane. We show how the proposed geodesic Gaussian process (GGP) approach better reconstructs the true surface, filtering the measurement noise, than when using a standard Euclidean kriging model of the “heights”, that is, z(x, y). The methodology is applied to simulated surface data and to a real dataset obtained with a noncontact laser scanner. Supplementary materials are available online
Fitting ARMA Time Series Models without Identification: A Proximal Approach
Get PDFFitting autoregressive moving average (ARMA) time series models requires
model identification before parameter estimation. Model identification involves
determining the order of the autoregressive and moving average components which
is generally performed by inspection of the autocorrelation and partial
autocorrelation functions or other offline methods. In this work, we regularize
the parameter estimation optimization problem with a non-smooth hierarchical
sparsity-inducing penalty based on two path graphs that allow performing model
identification and parameter estimation simultaneously. A proximal block
coordinate descent algorithm is then proposed to solve the underlying
optimization problem efficiently. The resulting model satisfies the required
stationarity and invertibility conditions for ARMA models. Numerical results
supporting the proposed method are also presented
Riemannian Stochastic Variance-Reduced Cubic Regularized Newton Method for Submanifold Optimization
Get PDFWe propose a stochastic variance-reduced cubic regularized Newton algorithm
to optimize the finite-sum problem over a Riemannian submanifold of the
Euclidean space. The proposed algorithm requires a full gradient and Hessian
update at the beginning of each epoch while it performs stochastic
variance-reduced updates in the iterations within each epoch. The iteration
complexity of to obtain an
-second-order stationary point, i.e., a point with
the Riemannian gradient norm upper bounded by and minimum eigenvalue
of Riemannian Hessian lower bounded by , is established when
the manifold is embedded in the Euclidean space. Furthermore, the paper
proposes a computationally more appealing modification of the algorithm which
only requires an inexact solution of the cubic regularized Newton subproblem
with the same iteration complexity. The proposed algorithm is evaluated and
compared with three other Riemannian second-order methods over two numerical
studies on estimating the inverse scale matrix of the multivariate
t-distribution on the manifold of symmetric positive definite matrices and
estimating the parameter of a linear classifier on the Sphere manifold
Riemannian Stochastic Gradient Method for Nested Composition Optimization
Get PDFThis work considers optimization of composition of functions in a nested form
over Riemannian manifolds where each function contains an expectation. This
type of problems is gaining popularity in applications such as policy
evaluation in reinforcement learning or model customization in meta-learning.
The standard Riemannian stochastic gradient methods for non-compositional
optimization cannot be directly applied as stochastic approximation of inner
functions create bias in the gradients of the outer functions. For two-level
composition optimization, we present a Riemannian Stochastic Composition
Gradient Descent (R-SCGD) method that finds an approximate stationary point,
with expected squared Riemannian gradient smaller than , in
calls to the stochastic gradient oracle of the outer
function and stochastic function and gradient oracles of the inner function.
Furthermore, we generalize the R-SCGD algorithms for problems with multi-level
nested compositional structures, with the same complexity of
for the first-order stochastic oracle. Finally, the performance of the R-SCGD
method is numerically evaluated over a policy evaluation problem in
reinforcement learning
Stochastic Optimization Algorithms for Problems with Controllable Biased Oracles
Get PDFMotivated by multiple emerging applications in machine learning, we consider
an optimization problem in a general form where the gradient of the objective
function is available through a biased stochastic oracle. We assume a
bias-control parameter can reduce the bias magnitude, however, a lower bias
requires more computation/samples. For instance, for two applications on
stochastic composition optimization and policy optimization for
infinite-horizon Markov decision processes, we show that the bias follows a
power law and exponential decay, respectively, as functions of their
corresponding bias control parameters. For problems with such gradient oracles,
the paper proposes stochastic algorithms that adjust the bias-control parameter
throughout the iterations. We analyze the nonasymptotic performance of the
proposed algorithms in the nonconvex regime and establish their sample or
bias-control computation complexities to obtain a stationary point. Finally, we
numerically evaluate the performance of the proposed algorithms over three
applications
Stochastic Composition Optimization of Functions without Lipschitz Continuous Gradient
Get PDFIn this paper, we study stochastic optimization of two-level composition of
functions without Lipschitz continuous gradient. The smoothness property is
generalized by the notion of relative smoothness which provokes the Bregman
gradient method. We propose three Stochastic Composition Bregman Gradient
algorithms for the three possible relatively smooth compositional scenarios and
provide their sample complexities to achieve an -approximate
stationary point. For the smooth of relatively smooth composition, the first
algorithm requires calls to the stochastic oracles of the
inner function value and gradient as well as the outer function gradient. When
both functions are relatively smooth, the second algorithm requires
calls to the inner function value stochastic oracle and
calls to the inner and outer functions gradients stochastic
oracles. We further improve the second algorithm by variance reduction for the
setting where just the inner function is smooth. The resulting algorithm
requires calls to the inner function value stochastic
oracle, calls to the inner function gradient and
calls to the outer function gradient stochastic oracles.
Finally, we numerically evaluate the performance of these three algorithms over
two different examples
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Get PDFWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
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