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

Learning Active Basis Models by EM-Type Algorithms

EM algorithm is a convenient tool for maximum likelihood model fitting when the data are incomplete or when there are latent variables or hidden states. In this review article we explain that EM algorithm is a natural computational scheme for learning image templates of object categories where the learning is not fully supervised. We represent an image template by an active basis model, which is a linear composition of a selected set of localized, elongated and oriented wavelet elements that are allowed to slightly perturb their locations and orientations to account for the deformations of object shapes. The model can be easily learned when the objects in the training images are of the same pose, and appear at the same location and scale. This is often called supervised learning. In the situation where the objects may appear at different unknown locations, orientations and scales in the training images, we have to incorporate the unknown locations, orientations and scales as latent variables into the image generation process, and learn the template by EM-type algorithms. The E-step imputes the unknown locations, orientations and scales based on the currently learned template. This step can be considered self-supervision, which involves using the current template to recognize the objects in the training images. The M-step then relearns the template based on the imputed locations, orientations and scales, and this is essentially the same as supervised learning. So the EM learning process iterates between recognition and supervised learning. We illustrate this scheme by several experiments.Comment: Published in at http://dx.doi.org/10.1214/09-STS281 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Mining Object Parts from CNNs via Active Question-Answering

Given a convolutional neural network (CNN) that is pre-trained for object classification, this paper proposes to use active question-answering to semanticize neural patterns in conv-layers of the CNN and mine part concepts. For each part concept, we mine neural patterns in the pre-trained CNN, which are related to the target part, and use these patterns to construct an And-Or graph (AOG) to represent a four-layer semantic hierarchy of the part. As an interpretable model, the AOG associates different CNN units with different explicit object parts. We use an active human-computer communication to incrementally grow such an AOG on the pre-trained CNN as follows. We allow the computer to actively identify objects, whose neural patterns cannot be explained by the current AOG. Then, the computer asks human about the unexplained objects, and uses the answers to automatically discover certain CNN patterns corresponding to the missing knowledge. We incrementally grow the AOG to encode new knowledge discovered during the active-learning process. In experiments, our method exhibits high learning efficiency. Our method uses about 1/6-1/3 of the part annotations for training, but achieves similar or better part-localization performance than fast-RCNN methods.Comment: Published in CVPR 201