26,338 research outputs found
Noisy Tensor Completion for Tensors with a Sparse Canonical Polyadic Factor
In this paper we study the problem of noisy tensor completion for tensors
that admit a canonical polyadic or CANDECOMP/PARAFAC (CP) decomposition with
one of the factors being sparse. We present general theoretical error bounds
for an estimate obtained by using a complexity-regularized maximum likelihood
principle and then instantiate these bounds for the case of additive white
Gaussian noise. We also provide an ADMM-type algorithm for solving the
complexity-regularized maximum likelihood problem and validate the theoretical
finding via experiments on synthetic data set
Multi-Entity Dependence Learning with Rich Context via Conditional Variational Auto-encoder
Multi-Entity Dependence Learning (MEDL) explores conditional correlations
among multiple entities. The availability of rich contextual information
requires a nimble learning scheme that tightly integrates with deep neural
networks and has the ability to capture correlation structures among
exponentially many outcomes. We propose MEDL_CVAE, which encodes a conditional
multivariate distribution as a generating process. As a result, the variational
lower bound of the joint likelihood can be optimized via a conditional
variational auto-encoder and trained end-to-end on GPUs. Our MEDL_CVAE was
motivated by two real-world applications in computational sustainability: one
studies the spatial correlation among multiple bird species using the eBird
data and the other models multi-dimensional landscape composition and human
footprint in the Amazon rainforest with satellite images. We show that
MEDL_CVAE captures rich dependency structures, scales better than previous
methods, and further improves on the joint likelihood taking advantage of very
large datasets that are beyond the capacity of previous methods.Comment: The first two authors contribute equall
A General Framework for Fast Stagewise Algorithms
Forward stagewise regression follows a very simple strategy for constructing
a sequence of sparse regression estimates: it starts with all coefficients
equal to zero, and iteratively updates the coefficient (by a small amount
) of the variable that achieves the maximal absolute inner product
with the current residual. This procedure has an interesting connection to the
lasso: under some conditions, it is known that the sequence of forward
stagewise estimates exactly coincides with the lasso path, as the step size
goes to zero. Furthermore, essentially the same equivalence holds
outside of least squares regression, with the minimization of a differentiable
convex loss function subject to an norm constraint (the stagewise
algorithm now updates the coefficient corresponding to the maximal absolute
component of the gradient).
Even when they do not match their -constrained analogues, stagewise
estimates provide a useful approximation, and are computationally appealing.
Their success in sparse modeling motivates the question: can a simple,
effective strategy like forward stagewise be applied more broadly in other
regularization settings, beyond the norm and sparsity? The current
paper is an attempt to do just this. We present a general framework for
stagewise estimation, which yields fast algorithms for problems such as
group-structured learning, matrix completion, image denoising, and more.Comment: 56 pages, 15 figure
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