1,339 research outputs found
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
Optimization with Sparsity-Inducing Penalties
Sparse estimation methods are aimed at using or obtaining parsimonious
representations of data or models. They were first dedicated to linear variable
selection but numerous extensions have now emerged such as structured sparsity
or kernel selection. It turns out that many of the related estimation problems
can be cast as convex optimization problems by regularizing the empirical risk
with appropriate non-smooth norms. The goal of this paper is to present from a
general perspective optimization tools and techniques dedicated to such
sparsity-inducing penalties. We cover proximal methods, block-coordinate
descent, reweighted -penalized techniques, working-set and homotopy
methods, as well as non-convex formulations and extensions, and provide an
extensive set of experiments to compare various algorithms from a computational
point of view
Supervised Classification: Quite a Brief Overview
The original problem of supervised classification considers the task of
automatically assigning objects to their respective classes on the basis of
numerical measurements derived from these objects. Classifiers are the tools
that implement the actual functional mapping from these measurements---also
called features or inputs---to the so-called class label---or output. The
fields of pattern recognition and machine learning study ways of constructing
such classifiers. The main idea behind supervised methods is that of learning
from examples: given a number of example input-output relations, to what extent
can the general mapping be learned that takes any new and unseen feature vector
to its correct class? This chapter provides a basic introduction to the
underlying ideas of how to come to a supervised classification problem. In
addition, it provides an overview of some specific classification techniques,
delves into the issues of object representation and classifier evaluation, and
(very) briefly covers some variations on the basic supervised classification
task that may also be of interest to the practitioner
A survey on online active learning
Online active learning is a paradigm in machine learning that aims to select
the most informative data points to label from a data stream. The problem of
minimizing the cost associated with collecting labeled observations has gained
a lot of attention in recent years, particularly in real-world applications
where data is only available in an unlabeled form. Annotating each observation
can be time-consuming and costly, making it difficult to obtain large amounts
of labeled data. To overcome this issue, many active learning strategies have
been proposed in the last decades, aiming to select the most informative
observations for labeling in order to improve the performance of machine
learning models. These approaches can be broadly divided into two categories:
static pool-based and stream-based active learning. Pool-based active learning
involves selecting a subset of observations from a closed pool of unlabeled
data, and it has been the focus of many surveys and literature reviews.
However, the growing availability of data streams has led to an increase in the
number of approaches that focus on online active learning, which involves
continuously selecting and labeling observations as they arrive in a stream.
This work aims to provide an overview of the most recently proposed approaches
for selecting the most informative observations from data streams in the
context of online active learning. We review the various techniques that have
been proposed and discuss their strengths and limitations, as well as the
challenges and opportunities that exist in this area of research. Our review
aims to provide a comprehensive and up-to-date overview of the field and to
highlight directions for future work
Learning to compare nodes in branch and bound with graph neural networks
En informatique, la résolution de problèmes NP-difficiles en un temps raisonnable est d’une grande importance : optimisation de la chaîne d’approvisionnement, planification, routage, alignement de séquences biologiques multiples, inference dans les modèles graphiques pro- babilistes, et même certains problèmes de cryptographie sont tous des examples de la classe NP-complet. En pratique, nous modélisons beaucoup d’entre eux comme un problème d’op- timisation en nombre entier, que nous résolvons à l’aide de la méthodologie séparation et évaluation. Un algorithme de ce style divise un espace de recherche pour l’explorer récursi- vement (séparation), et obtient des bornes d’optimalité en résolvant des relaxations linéaires sur les sous-espaces (évaluation). Pour spécifier un algorithme, il faut définir plusieurs pa- ramètres, tel que la manière d’explorer les espaces de recherche, de diviser une recherche l’espace une fois exploré, ou de renforcer les relaxations linéaires. Ces politiques peuvent influencer considérablement la performance de résolution.
Ce travail se concentre sur une nouvelle manière de dériver politique de recherche, c’est à dire le choix du prochain sous-espace à séparer étant donné une partition en cours, en nous servant de l’apprentissage automatique profond. Premièrement, nous collectons des données résumant, sur une collection de problèmes donnés, quels sous-espaces contiennent l’optimum et quels ne le contiennent pas. En représentant ces sous-espaces sous forme de graphes bipartis qui capturent leurs caractéristiques, nous entraînons un réseau de neurones graphiques à déterminer la probabilité qu’un sous-espace contienne la solution optimale par apprentissage supervisé. Le choix d’un tel modèle est particulièrement utile car il peut s’adapter à des problèmes de différente taille sans modifications. Nous montrons que notre approche bat celle de nos concurrents, consistant à des modèles d’apprentissage automatique plus simples entraînés à partir des statistiques du solveur, ainsi que la politique par défaut de SCIP, un solveur open-source compétitif, sur trois familles NP-dures: des problèmes de recherche de stables de taille maximum, de flots de réseau multicommodité à charge fixe, et de satisfiabilité maximum.In computer science, solving NP-hard problems in a reasonable time is of great importance, such as in supply chain optimization, scheduling, routing, multiple biological sequence align- ment, inference in probabilistic graphical models, and even some problems in cryptography. In practice, we model many of them as a mixed integer linear optimization problem, which we solve using the branch and bound framework. An algorithm of this style divides a search space to explore it recursively (branch) and obtains optimality bounds by solving linear relaxations in such sub-spaces (bound). To specify an algorithm, one must set several pa- rameters, such as how to explore search spaces, how to divide a search space once it has been explored, or how to tighten these linear relaxations. These policies can significantly influence resolution performance.
This work focuses on a novel method for deriving a search policy, that is, a rule for select- ing the next sub-space to explore given a current partitioning, using deep machine learning. First, we collect data summarizing which subspaces contain the optimum, and which do not. By representing these sub-spaces as bipartite graphs encoding their characteristics, we train a graph neural network to determine the probability that a subspace contains the optimal so- lution by supervised learning. The choice of such design is particularly useful as the machine learning model can automatically adapt to problems of different sizes without modifications. We show that our approach beats the one of our competitors, consisting of simpler machine learning models trained from solver statistics, as well as the default policy of SCIP, a state- of-the-art open-source solver, on three NP-hard benchmarks: generalized independent set, fixed-charge multicommodity network flow, and maximum satisfiability problems
Thirty Years of Machine Learning: The Road to Pareto-Optimal Wireless Networks
Future wireless networks have a substantial potential in terms of supporting
a broad range of complex compelling applications both in military and civilian
fields, where the users are able to enjoy high-rate, low-latency, low-cost and
reliable information services. Achieving this ambitious goal requires new radio
techniques for adaptive learning and intelligent decision making because of the
complex heterogeneous nature of the network structures and wireless services.
Machine learning (ML) algorithms have great success in supporting big data
analytics, efficient parameter estimation and interactive decision making.
Hence, in this article, we review the thirty-year history of ML by elaborating
on supervised learning, unsupervised learning, reinforcement learning and deep
learning. Furthermore, we investigate their employment in the compelling
applications of wireless networks, including heterogeneous networks (HetNets),
cognitive radios (CR), Internet of things (IoT), machine to machine networks
(M2M), and so on. This article aims for assisting the readers in clarifying the
motivation and methodology of the various ML algorithms, so as to invoke them
for hitherto unexplored services as well as scenarios of future wireless
networks.Comment: 46 pages, 22 fig
DC Proximal Newton for Non-Convex Optimization Problems
We introduce a novel algorithm for solving learning problems where both the
loss function and the regularizer are non-convex but belong to the class of
difference of convex (DC) functions. Our contribution is a new general purpose
proximal Newton algorithm that is able to deal with such a situation. The
algorithm consists in obtaining a descent direction from an approximation of
the loss function and then in performing a line search to ensure sufficient
descent. A theoretical analysis is provided showing that the iterates of the
proposed algorithm {admit} as limit points stationary points of the DC
objective function. Numerical experiments show that our approach is more
efficient than current state of the art for a problem with a convex loss
functions and non-convex regularizer. We have also illustrated the benefit of
our algorithm in high-dimensional transductive learning problem where both loss
function and regularizers are non-convex
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