19 research outputs found
Binary Independent Component Analysis with OR Mixtures
Independent component analysis (ICA) is a computational method for separating
a multivariate signal into subcomponents assuming the mutual statistical
independence of the non-Gaussian source signals. The classical Independent
Components Analysis (ICA) framework usually assumes linear combinations of
independent sources over the field of realvalued numbers R. In this paper, we
investigate binary ICA for OR mixtures (bICA), which can find applications in
many domains including medical diagnosis, multi-cluster assignment, Internet
tomography and network resource management. We prove that bICA is uniquely
identifiable under the disjunctive generation model, and propose a
deterministic iterative algorithm to determine the distribution of the latent
random variables and the mixing matrix. The inverse problem concerning
inferring the values of latent variables are also considered along with noisy
measurements. We conduct an extensive simulation study to verify the
effectiveness of the propose algorithm and present examples of real-world
applications where bICA can be applied.Comment: Manuscript submitted to IEEE Transactions on Signal Processin
Are v1 simple cells optimized for visual occlusions? : A comparative study
Abstract: Simple cells in primary visual cortex were famously found to respond to low-level image components such as edges. Sparse coding and independent component analysis (ICA) emerged as the standard computational models for simple cell coding because they linked their receptive fields to the statistics of visual stimuli. However, a salient feature of image statistics, occlusions of image components, is not considered by these models. Here we ask if occlusions have an effect on the predicted shapes of simple cell receptive fields. We use a comparative approach to answer this question and investigate two models for simple cells: a standard linear model and an occlusive model. For both models we simultaneously estimate optimal receptive fields, sparsity and stimulus noise. The two models are identical except for their component superposition assumption. We find the image encoding and receptive fields predicted by the models to differ significantly. While both models predict many Gabor-like fields, the occlusive model predicts a much sparser encoding and high percentages of ‘globular’ receptive fields. This relatively new center-surround type of simple cell response is observed since reverse correlation is used in experimental studies. While high percentages of ‘globular’ fields can be obtained using specific choices of sparsity and overcompleteness in linear sparse coding, no or only low proportions are reported in the vast majority of studies on linear models (including all ICA models). Likewise, for the here investigated linear model and optimal sparsity, only low proportions of ‘globular’ fields are observed. In comparison, the occlusive model robustly infers high proportions and can match the experimentally observed high proportions of ‘globular’ fields well. Our computational study, therefore, suggests that ‘globular’ fields may be evidence for an optimal encoding of visual occlusions in primary visual cortex.
Author Summary: The statistics of our visual world is dominated by occlusions. Almost every image processed by our brain consists of mutually occluding objects, animals and plants. Our visual cortex is optimized through evolution and throughout our lifespan for such stimuli. Yet, the standard computational models of primary visual processing do not consider occlusions. In this study, we ask what effects visual occlusions may have on predicted response properties of simple cells which are the first cortical processing units for images. Our results suggest that recently observed differences between experiments and predictions of the standard simple cell models can be attributed to occlusions. The most significant consequence of occlusions is the prediction of many cells sensitive to center-surround stimuli. Experimentally, large quantities of such cells are observed since new techniques (reverse correlation) are used. Without occlusions, they are only obtained for specific settings and none of the seminal studies (sparse coding, ICA) predicted such fields. In contrast, the new type of response naturally emerges as soon as occlusions are considered. In comparison with recent in vivo experiments we find that occlusive models are consistent with the high percentages of center-surround simple cells observed in macaque monkeys, ferrets and mice
Infinite Divisibility of Information
We study an information analogue of infinitely divisible probability
distributions, where the i.i.d. sum is replaced by the joint distribution of an
i.i.d. sequence. A random variable is called informationally infinitely
divisible if, for any , there exists an i.i.d. sequence of random
variables that contains the same information as , i.e.,
there exists an injective function such that .
While there does not exist informationally infinitely divisible discrete random
variable, we show that any discrete random variable has a bounded
multiplicative gap to infinite divisibility, that is, if we remove the
injectivity requirement on , then there exists i.i.d.
and satisfying , and the entropy satisfies
. We also study a new class of discrete
probability distributions, called spectral infinitely divisible distributions,
where we can remove the multiplicative gap . Furthermore, we study the
case where is itself an i.i.d. sequence, , for
which the multiplicative gap can be replaced by .
This means that as increases, becomes closer to
being spectral infinitely divisible in a uniform manner. This can be regarded
as an information analogue of Kolmogorov's uniform theorem. Applications of our
result include independent component analysis, distributed storage with a
secrecy constraint, and distributed random number generation.Comment: 22 page