261 research outputs found
Learning Mixtures of Bernoulli Templates by Two-Round EM with Performance Guarantee
Dasgupta and Shulman showed that a two-round variant of the EM algorithm can
learn mixture of Gaussian distributions with near optimal precision with high
probability if the Gaussian distributions are well separated and if the
dimension is sufficiently high. In this paper, we generalize their theory to
learning mixture of high-dimensional Bernoulli templates. Each template is a
binary vector, and a template generates examples by randomly switching its
binary components independently with a certain probability. In computer vision
applications, a binary vector is a feature map of an image, where each binary
component indicates whether a local feature or structure is present or absent
within a certain cell of the image domain. A Bernoulli template can be
considered as a statistical model for images of objects (or parts of objects)
from the same category. We show that the two-round EM algorithm can learn
mixture of Bernoulli templates with near optimal precision with high
probability, if the Bernoulli templates are sufficiently different and if the
number of features is sufficiently high. We illustrate the theoretical results
by synthetic and real examples.Comment: 27 pages, 8 figure
Discussion of "EQUI-energy sampler" by Kou, Zhou and Wong
Discussion of ``EQUI-energy sampler'' by Kou, Zhou and Wong [math.ST/0507080]Comment: Published at http://dx.doi.org/10.1214/009053606000000506 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Interpretable Convolutional Neural Networks
This paper proposes a method to modify traditional convolutional neural
networks (CNNs) into interpretable CNNs, in order to clarify knowledge
representations in high conv-layers of CNNs. In an interpretable CNN, each
filter in a high conv-layer represents a certain object part. We do not need
any annotations of object parts or textures to supervise the learning process.
Instead, the interpretable CNN automatically assigns each filter in a high
conv-layer with an object part during the learning process. Our method can be
applied to different types of CNNs with different structures. The clear
knowledge representation in an interpretable CNN can help people understand the
logics inside a CNN, i.e., based on which patterns the CNN makes the decision.
Experiments showed that filters in an interpretable CNN were more semantically
meaningful than those in traditional CNNs.Comment: In this version, we release the website of the code. Compared to the
previous version, we have corrected all values of location instability in
Table 3--6 by dividing the values by sqrt(2), i.e., a=a/sqrt(2). Such
revisions do NOT decrease the significance of the superior performance of our
method, because we make the same correction to location-instability values of
all baseline
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