32,072 research outputs found
Recovering Latent Signals from a Mixture of Measurements using a Gaussian Process Prior
In sensing applications, sensors cannot always measure the latent quantity of
interest at the required resolution, sometimes they can only acquire a blurred
version of it due the sensor's transfer function. To recover latent signals
when only noisy mixed measurements of the signal are available, we propose the
Gaussian process mixture of measurements (GPMM), which models the latent signal
as a Gaussian process (GP) and allows us to perform Bayesian inference on such
signal conditional to a set of noisy mixture of measurements. We describe how
to train GPMM, that is, to find the hyperparameters of the GP and the mixing
weights, and how to perform inference on the latent signal under GPMM;
additionally, we identify the solution to the underdetermined linear system
resulting from a sensing application as a particular case of GPMM. The proposed
model is validated in the recovery of three signals: a smooth synthetic signal,
a real-world heart-rate time series and a step function, where GPMM
outperformed the standard GP in terms of estimation error, uncertainty
representation and recovery of the spectral content of the latent signal.Comment: Published on IEEE Signal Processing Letters on Dec. 201
Sliced Wasserstein Distance for Learning Gaussian Mixture Models
Gaussian mixture models (GMM) are powerful parametric tools with many
applications in machine learning and computer vision. Expectation maximization
(EM) is the most popular algorithm for estimating the GMM parameters. However,
EM guarantees only convergence to a stationary point of the log-likelihood
function, which could be arbitrarily worse than the optimal solution. Inspired
by the relationship between the negative log-likelihood function and the
Kullback-Leibler (KL) divergence, we propose an alternative formulation for
estimating the GMM parameters using the sliced Wasserstein distance, which
gives rise to a new algorithm. Specifically, we propose minimizing the
sliced-Wasserstein distance between the mixture model and the data distribution
with respect to the GMM parameters. In contrast to the KL-divergence, the
energy landscape for the sliced-Wasserstein distance is more well-behaved and
therefore more suitable for a stochastic gradient descent scheme to obtain the
optimal GMM parameters. We show that our formulation results in parameter
estimates that are more robust to random initializations and demonstrate that
it can estimate high-dimensional data distributions more faithfully than the EM
algorithm
End-to-End Kernel Learning with Supervised Convolutional Kernel Networks
In this paper, we introduce a new image representation based on a multilayer
kernel machine. Unlike traditional kernel methods where data representation is
decoupled from the prediction task, we learn how to shape the kernel with
supervision. We proceed by first proposing improvements of the
recently-introduced convolutional kernel networks (CKNs) in the context of
unsupervised learning; then, we derive backpropagation rules to take advantage
of labeled training data. The resulting model is a new type of convolutional
neural network, where optimizing the filters at each layer is equivalent to
learning a linear subspace in a reproducing kernel Hilbert space (RKHS). We
show that our method achieves reasonably competitive performance for image
classification on some standard "deep learning" datasets such as CIFAR-10 and
SVHN, and also for image super-resolution, demonstrating the applicability of
our approach to a large variety of image-related tasks.Comment: to appear in Advances in Neural Information Processing Systems (NIPS
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