852 research outputs found
Unlabeled sample compression schemes and corner peelings for ample and maximum classes
We examine connections between combinatorial notions that arise in machine
learning and topological notions in cubical/simplicial geometry. These
connections enable to export results from geometry to machine learning.
Our first main result is based on a geometric construction by Tracy Hall
(2004) of a partial shelling of the cross-polytope which can not be extended.
We use it to derive a maximum class of VC dimension 3 that has no corners. This
refutes several previous works in machine learning from the past 11 years. In
particular, it implies that all previous constructions of optimal unlabeled
sample compression schemes for maximum classes are erroneous.
On the positive side we present a new construction of an unlabeled sample
compression scheme for maximum classes. We leave as open whether our unlabeled
sample compression scheme extends to ample (a.k.a. lopsided or extremal)
classes, which represent a natural and far-reaching generalization of maximum
classes. Towards resolving this question, we provide a geometric
characterization in terms of unique sink orientations of the 1-skeletons of
associated cubical complexes
Multiclass Learnability Does Not Imply Sample Compression
A hypothesis class admits a sample compression scheme, if for every sample
labeled by a hypothesis from the class, it is possible to retain only a small
subsample, using which the labels on the entire sample can be inferred. The
size of the compression scheme is an upper bound on the size of the subsample
produced. Every learnable binary hypothesis class (which must necessarily have
finite VC dimension) admits a sample compression scheme of size only a finite
function of its VC dimension, independent of the sample size. For multiclass
hypothesis classes, the analog of VC dimension is the DS dimension. We show
that the analogous statement pertaining to sample compression is not true for
multiclass hypothesis classes: every learnable multiclass hypothesis class,
which must necessarily have finite DS dimension, does not admit a sample
compression scheme of size only a finite function of its DS dimension
GhostVLAD for set-based face recognition
The objective of this paper is to learn a compact representation of image
sets for template-based face recognition. We make the following contributions:
first, we propose a network architecture which aggregates and embeds the face
descriptors produced by deep convolutional neural networks into a compact
fixed-length representation. This compact representation requires minimal
memory storage and enables efficient similarity computation. Second, we propose
a novel GhostVLAD layer that includes {\em ghost clusters}, that do not
contribute to the aggregation. We show that a quality weighting on the input
faces emerges automatically such that informative images contribute more than
those with low quality, and that the ghost clusters enhance the network's
ability to deal with poor quality images. Third, we explore how input feature
dimension, number of clusters and different training techniques affect the
recognition performance. Given this analysis, we train a network that far
exceeds the state-of-the-art on the IJB-B face recognition dataset. This is
currently one of the most challenging public benchmarks, and we surpass the
state-of-the-art on both the identification and verification protocols.Comment: Accepted by ACCV 201
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