1,413 research outputs found
Evolutionary Algorithms in Decision Tree Induction
One of the biggest problem that many data analysis techniques have to deal with nowadays is Combinatorial Optimization that, in the past, has led many methods to be taken apart. Actually, the (still not enough!) higher computing power available makes it possible to apply such techniques within certain bounds. Since other research fields like Artificial Intelligence have been (and still are) dealing with such problems, their contribute to
statistics has been very significant.
This chapter tries to cast the Combinatorial Optimization methods into the Artificial Intelligence framework, particularly with respect Decision Tree Induction, which is considered a powerful instrument for the knowledge extraction and the decision making support. When the exhaustive enumeration and evaluation of all the possible candidate solution to a Tree-based Induction problem is not computationally affordable, the use of Nature Inspired Optimization Algorithms, which have been proven to be powerful instruments for attacking many combinatorial optimization problems, can be of great help.
In this respect, the attention is focused on three main problems involving Decision Tree Induction by mainly focusing the attention on the Classification and Regression Tree-CART (Breiman et al., 1984) algorithm. First, the problem of splitting complex predictors such a multi-attribute ones is faced through the use of Genetic Algorithms. In addition, the possibility of growing “optimal” exploratory trees is also investigated by making use of Ant Colony Optimization (ACO) algorithm. Finally, the derivation of a subset of decision trees for modelling multi-attribute response on the basis of a data-driven heuristic is also described. The proposed approaches might be useful for knowledge extraction from large databases as well as for data mining applications. The solution they offer for complicated data modelling and data analysis problems might be considered for a possible implementation in a Decision Support System (DSS).
The remainder of the chapter is as follows. Section 2 describes the main features and the recent developments of Decision Tree Induction. An overview of Combinatorial Optimization with a particular focus on Genetic Algorithms and Ant Colony Optimization is presented in section 3. The use of these two algorithms within the Decision Tree Induction Framework is described in section 4, together with the description of the algorithm for modelling multi-attribute response. Section 5 summarizes the results of the proposed method on real and simulated datasets. Concluding remarks are presented in section 6. The chapter also includes an appendix that presents J-Fast, a Java-based software for Decision Tree that currently implements Genetic Algorithms and Ant Colony Optimization
Two-dimensional placement compaction using an evolutionary approach: a study
The placement problem of two-dimensional objects over planar surfaces optimizing
given utility functions is a combinatorial optimization problem. Our main drive is that of
surveying genetic algorithms and hybrid metaheuristics in terms of final positioning area
compaction of the solution. Furthermore, a new hybrid evolutionary approach, combining
a genetic algorithm merged with a non-linear compaction method is introduced and
compared with referenced literature heuristics using both randomly generated instances
and benchmark problems. A wide variety of experiments is made, and the respective
results and discussions are presented. Finally, conclusions are drawn, and future research
is defined
Integrating Learning from Examples into the Search for Diagnostic Policies
This paper studies the problem of learning diagnostic policies from training
examples. A diagnostic policy is a complete description of the decision-making
actions of a diagnostician (i.e., tests followed by a diagnostic decision) for
all possible combinations of test results. An optimal diagnostic policy is one
that minimizes the expected total cost, which is the sum of measurement costs
and misdiagnosis costs. In most diagnostic settings, there is a tradeoff
between these two kinds of costs. This paper formalizes diagnostic decision
making as a Markov Decision Process (MDP). The paper introduces a new family of
systematic search algorithms based on the AO* algorithm to solve this MDP. To
make AO* efficient, the paper describes an admissible heuristic that enables
AO* to prune large parts of the search space. The paper also introduces several
greedy algorithms including some improvements over previously-published
methods. The paper then addresses the question of learning diagnostic policies
from examples. When the probabilities of diseases and test results are computed
from training data, there is a great danger of overfitting. To reduce
overfitting, regularizers are integrated into the search algorithms. Finally,
the paper compares the proposed methods on five benchmark diagnostic data sets.
The studies show that in most cases the systematic search methods produce
better diagnostic policies than the greedy methods. In addition, the studies
show that for training sets of realistic size, the systematic search algorithms
are practical on todays desktop computers
Statistical mechanics approaches to optimization and inference
Nowadays, typical methodologies employed in statistical physics are successfully applied to a huge set of problems arising from different research fields. In this thesis I will propose several statistical mechanics based models able to deal with two types of problems: optimization and inference problems. The intrinsic difficulty that characterizes both problems is that, due to the hard combinatorial nature of optimization and inference, finding exact solutions would require hard and impractical computations. In fact, the time needed to perform these calculations, in almost all cases, scales exponentially with respect to relevant parameters of the system and thus cannot be accomplished in practice. As combinatorial optimization addresses the problem of finding a fair configuration of variables able to minimize/maximize an objective function, inference seeks a posteriori the most fair assignment of a set of variables given a partial knowledge of the system. These two problems can be re-phrased in a statistical mechanics framework where elementary components of a physical system interact according to the constraints of the original problem. The information at our disposal can be encoded in the Boltzmann distribution of the new variables which, if properly investigated, can provide the solutions to the original problems. As a consequence, the methodologies originally adopted in statistical mechanics to study and, eventually, approximate the Boltzmann distribution can be fruitfully applied for solving inference and optimization problems.
The structure of the thesis follows the path covered during the three years of my Ph.D. At first, I will propose a set of combinatorial optimization problems on graphs, the Prize collecting and the Packing of Steiner trees problems. The tools used to face these hard problems rely on the zero-temperature implementation of the Belief Propagation algorithm, called Max Sum algorithm. The second set of problems proposed in this thesis falls under the name of linear estimation problems. One of them, the compressed sensing problem, will guide us in the modelling of these problems within a Bayesian framework along with the introduction of a powerful algorithm known as Expectation Propagation or Expectation Consistent in statistical physics. I will propose a similar approach to other challenging problems: the inference of metabolic fluxes, the inverse problem of the electro-encephalography and the reconstruction of tomographic images
ForestHash: Semantic Hashing With Shallow Random Forests and Tiny Convolutional Networks
Hash codes are efficient data representations for coping with the ever
growing amounts of data. In this paper, we introduce a random forest semantic
hashing scheme that embeds tiny convolutional neural networks (CNN) into
shallow random forests, with near-optimal information-theoretic code
aggregation among trees. We start with a simple hashing scheme, where random
trees in a forest act as hashing functions by setting `1' for the visited tree
leaf, and `0' for the rest. We show that traditional random forests fail to
generate hashes that preserve the underlying similarity between the trees,
rendering the random forests approach to hashing challenging. To address this,
we propose to first randomly group arriving classes at each tree split node
into two groups, obtaining a significantly simplified two-class classification
problem, which can be handled using a light-weight CNN weak learner. Such
random class grouping scheme enables code uniqueness by enforcing each class to
share its code with different classes in different trees. A non-conventional
low-rank loss is further adopted for the CNN weak learners to encourage code
consistency by minimizing intra-class variations and maximizing inter-class
distance for the two random class groups. Finally, we introduce an
information-theoretic approach for aggregating codes of individual trees into a
single hash code, producing a near-optimal unique hash for each class. The
proposed approach significantly outperforms state-of-the-art hashing methods
for image retrieval tasks on large-scale public datasets, while performing at
the level of other state-of-the-art image classification techniques while
utilizing a more compact and efficient scalable representation. This work
proposes a principled and robust procedure to train and deploy in parallel an
ensemble of light-weight CNNs, instead of simply going deeper.Comment: Accepted to ECCV 201
Optimization bounds from the branching dual
We present a general method for obtaining strong bounds for discrete optimization problems that is based on a concept of branching duality. It can be applied when no useful integer programming model is available, and we illustrate this with the minimum bandwidth problem. The method strengthens a known bound for a given problem by formulating a dual problem whose feasible solutions are partial branching trees. It solves the dual problem with a “worst-bound” local search heuristic that explores neighboring partial trees. After proving some optimality properties of the heuristic, we show that it substantially improves known combinatorial bounds for the minimum bandwidth problem with a modest amount of computation. It also obtains significantly tighter bounds than depth-first and breadth-first branching, demonstrating that the dual perspective can lead to better branching strategies when the object is to find valid bounds.Accepted manuscrip
Recent Advances in Graph Partitioning
We survey recent trends in practical algorithms for balanced graph
partitioning together with applications and future research directions
The development and application of metaheuristics for problems in graph theory: A computational study
This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.It is known that graph theoretic models have extensive application
to real-life discrete optimization problems. Many of these models
are NP-hard and, as a result, exact methods may be impractical for
large scale problem instances. Consequently, there is a great interest
in developing e±cient approximate methods that yield near-optimal
solutions in acceptable computational times. A class of such methods,
known as metaheuristics, have been proposed with success.
This thesis considers some recently proposed NP-hard combinatorial
optimization problems formulated on graphs. In particular, the min-
imum labelling spanning tree problem, the minimum labelling Steiner
tree problem, and the minimum quartet tree cost problem, are inves-
tigated. Several metaheuristics are proposed for each problem, from
classical approximation algorithms to novel approaches. A compre-
hensive computational investigation in which the proposed methods
are compared with other algorithms recommended in the literature is
reported. The results show that the proposed metaheuristics outper-
form the algorithms recommended in the literature, obtaining optimal
or near-optimal solutions in short computational running times. In
addition, a thorough analysis of the implementation of these methods
provide insights for the implementation of metaheuristic strategies for
other graph theoretic problems
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