247 research outputs found
Stochastic Majorization-Minimization Algorithms for Large-Scale Optimization
Majorization-minimization algorithms consist of iteratively minimizing a
majorizing surrogate of an objective function. Because of its simplicity and
its wide applicability, this principle has been very popular in statistics and
in signal processing. In this paper, we intend to make this principle scalable.
We introduce a stochastic majorization-minimization scheme which is able to
deal with large-scale or possibly infinite data sets. When applied to convex
optimization problems under suitable assumptions, we show that it achieves an
expected convergence rate of after iterations, and of
for strongly convex functions. Equally important, our scheme almost
surely converges to stationary points for a large class of non-convex problems.
We develop several efficient algorithms based on our framework. First, we
propose a new stochastic proximal gradient method, which experimentally matches
state-of-the-art solvers for large-scale -logistic regression. Second,
we develop an online DC programming algorithm for non-convex sparse estimation.
Finally, we demonstrate the effectiveness of our approach for solving
large-scale structured matrix factorization problems.Comment: accepted for publication for Neural Information Processing Systems
(NIPS) 2013. This is the 9-pages version followed by 16 pages of appendices.
The title has changed compared to the first technical repor
End-to-End Kernel Learning with Supervised Convolutional Kernel Networks
In this paper, we introduce a new image representation based on a multilayer
kernel machine. Unlike traditional kernel methods where data representation is
decoupled from the prediction task, we learn how to shape the kernel with
supervision. We proceed by first proposing improvements of the
recently-introduced convolutional kernel networks (CKNs) in the context of
unsupervised learning; then, we derive backpropagation rules to take advantage
of labeled training data. The resulting model is a new type of convolutional
neural network, where optimizing the filters at each layer is equivalent to
learning a linear subspace in a reproducing kernel Hilbert space (RKHS). We
show that our method achieves reasonably competitive performance for image
classification on some standard "deep learning" datasets such as CIFAR-10 and
SVHN, and also for image super-resolution, demonstrating the applicability of
our approach to a large variety of image-related tasks.Comment: to appear in Advances in Neural Information Processing Systems (NIPS
Group Invariance, Stability to Deformations, and Complexity of Deep Convolutional Representations
The success of deep convolutional architectures is often attributed in part
to their ability to learn multiscale and invariant representations of natural
signals. However, a precise study of these properties and how they affect
learning guarantees is still missing. In this paper, we consider deep
convolutional representations of signals; we study their invariance to
translations and to more general groups of transformations, their stability to
the action of diffeomorphisms, and their ability to preserve signal
information. This analysis is carried by introducing a multilayer kernel based
on convolutional kernel networks and by studying the geometry induced by the
kernel mapping. We then characterize the corresponding reproducing kernel
Hilbert space (RKHS), showing that it contains a large class of convolutional
neural networks with homogeneous activation functions. This analysis allows us
to separate data representation from learning, and to provide a canonical
measure of model complexity, the RKHS norm, which controls both stability and
generalization of any learned model. In addition to models in the constructed
RKHS, our stability analysis also applies to convolutional networks with
generic activations such as rectified linear units, and we discuss its
relationship with recent generalization bounds based on spectral norms
On the Inductive Bias of Neural Tangent Kernels
State-of-the-art neural networks are heavily over-parameterized, making the
optimization algorithm a crucial ingredient for learning predictive models with
good generalization properties. A recent line of work has shown that in a
certain over-parameterized regime, the learning dynamics of gradient descent
are governed by a certain kernel obtained at initialization, called the neural
tangent kernel. We study the inductive bias of learning in such a regime by
analyzing this kernel and the corresponding function space (RKHS). In
particular, we study smoothness, approximation, and stability properties of
functions with finite norm, including stability to image deformations in the
case of convolutional networks, and compare to other known kernels for similar
architectures.Comment: NeurIPS 201
Stochastic Optimization with Variance Reduction for Infinite Datasets with Finite-Sum Structure
Stochastic optimization algorithms with variance reduction have proven
successful for minimizing large finite sums of functions. Unfortunately, these
techniques are unable to deal with stochastic perturbations of input data,
induced for example by data augmentation. In such cases, the objective is no
longer a finite sum, and the main candidate for optimization is the stochastic
gradient descent method (SGD). In this paper, we introduce a variance reduction
approach for these settings when the objective is composite and strongly
convex. The convergence rate outperforms SGD with a typically much smaller
constant factor, which depends on the variance of gradient estimates only due
to perturbations on a single example.Comment: Advances in Neural Information Processing Systems (NIPS), Dec 2017,
Long Beach, CA, United State
On the Importance of Visual Context for Data Augmentation in Scene Understanding
Performing data augmentation for learning deep neural networks is known to be
important for training visual recognition systems. By artificially increasing
the number of training examples, it helps reducing overfitting and improves
generalization. While simple image transformations can already improve
predictive performance in most vision tasks, larger gains can be obtained by
leveraging task-specific prior knowledge. In this work, we consider object
detection, semantic and instance segmentation and augment the training images
by blending objects in existing scenes, using instance segmentation
annotations. We observe that randomly pasting objects on images hurts the
performance, unless the object is placed in the right context. To resolve this
issue, we propose an explicit context model by using a convolutional neural
network, which predicts whether an image region is suitable for placing a given
object or not. In our experiments, we show that our approach is able to improve
object detection, semantic and instance segmentation on the PASCAL VOC12 and
COCO datasets, with significant gains in a limited annotation scenario, i.e.
when only one category is annotated. We also show that the method is not
limited to datasets that come with expensive pixel-wise instance annotations
and can be used when only bounding boxes are available, by employing
weakly-supervised learning for instance masks approximation.Comment: Updated the experimental section. arXiv admin note: substantial text
overlap with arXiv:1807.0742
Task-Driven Dictionary Learning
Modeling data with linear combinations of a few elements from a learned
dictionary has been the focus of much recent research in machine learning,
neuroscience and signal processing. For signals such as natural images that
admit such sparse representations, it is now well established that these models
are well suited to restoration tasks. In this context, learning the dictionary
amounts to solving a large-scale matrix factorization problem, which can be
done efficiently with classical optimization tools. The same approach has also
been used for learning features from data for other purposes, e.g., image
classification, but tuning the dictionary in a supervised way for these tasks
has proven to be more difficult. In this paper, we present a general
formulation for supervised dictionary learning adapted to a wide variety of
tasks, and present an efficient algorithm for solving the corresponding
optimization problem. Experiments on handwritten digit classification, digital
art identification, nonlinear inverse image problems, and compressed sensing
demonstrate that our approach is effective in large-scale settings, and is well
suited to supervised and semi-supervised classification, as well as regression
tasks for data that admit sparse representations.Comment: final draft post-refereein
Catalyst Acceleration for First-order Convex Optimization: from Theory to Practice
We introduce a generic scheme for accelerating gradient-based optimization
methods in the sense of Nesterov. The approach, called Catalyst, builds upon
the inexact accelerated proximal point algorithm for minimizing a convex
objective function, and consists of approximately solving a sequence of
well-chosen auxiliary problems, leading to faster convergence. One of the keys
to achieve acceleration in theory and in practice is to solve these
sub-problems with appropriate accuracy by using the right stopping criterion
and the right warm-start strategy. We give practical guidelines to use Catalyst
and present a comprehensive analysis of its global complexity. We show that
Catalyst applies to a large class of algorithms, including gradient descent,
block coordinate descent, incremental algorithms such as SAG, SAGA, SDCA, SVRG,
MISO/Finito, and their proximal variants. For all of these methods, we
establish faster rates using the Catalyst acceleration, for strongly convex and
non-strongly convex objectives. We conclude with extensive experiments showing
that acceleration is useful in practice, especially for ill-conditioned
problems.Comment: link to publisher website:
http://jmlr.org/papers/volume18/17-748/17-748.pd
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