13,951 research outputs found
Sample Complexity Analysis for Learning Overcomplete Latent Variable Models through Tensor Methods
We provide guarantees for learning latent variable models emphasizing on the
overcomplete regime, where the dimensionality of the latent space can exceed
the observed dimensionality. In particular, we consider multiview mixtures,
spherical Gaussian mixtures, ICA, and sparse coding models. We provide tight
concentration bounds for empirical moments through novel covering arguments. We
analyze parameter recovery through a simple tensor power update algorithm. In
the semi-supervised setting, we exploit the label or prior information to get a
rough estimate of the model parameters, and then refine it using the tensor
method on unlabeled samples. We establish that learning is possible when the
number of components scales as , where is the observed
dimension, and is the order of the observed moment employed in the tensor
method. Our concentration bound analysis also leads to minimax sample
complexity for semi-supervised learning of spherical Gaussian mixtures. In the
unsupervised setting, we use a simple initialization algorithm based on SVD of
the tensor slices, and provide guarantees under the stricter condition that
(where constant can be larger than ), where the
tensor method recovers the components under a polynomial running time (and
exponential in ). Our analysis establishes that a wide range of
overcomplete latent variable models can be learned efficiently with low
computational and sample complexity through tensor decomposition methods.Comment: Title change
Color Constancy Convolutional Autoencoder
In this paper, we study the importance of pre-training for the generalization
capability in the color constancy problem. We propose two novel approaches
based on convolutional autoencoders: an unsupervised pre-training algorithm
using a fine-tuned encoder and a semi-supervised pre-training algorithm using a
novel composite-loss function. This enables us to solve the data scarcity
problem and achieve competitive, to the state-of-the-art, results while
requiring much fewer parameters on ColorChecker RECommended dataset. We further
study the over-fitting phenomenon on the recently introduced version of
INTEL-TUT Dataset for Camera Invariant Color Constancy Research, which has both
field and non-field scenes acquired by three different camera models.Comment: 6 pages, 1 figure, 3 table
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