arXiv subjects

Jose A. Lozano

Publications and source records attributed to Jose A. Lozano.

34 records · Page 2Linked to original sources

arXiv2022

Minimax Classification under Concept Drift with Multidimensional Adaptation and Performance Guarantees

The statistical characteristics of instance-label pairs often change with time in practical scenarios of supervised classification. Conventional learning techniques adapt to such concept drift accounting for a scalar rate of change by means of a carefully chosen learning rate, forgetting factor, or window size. However, the time changes in common scenarios are multidimensional, i.e., different statistical characteristics often change in a different manner. This paper presents adaptive minimax risk classifiers (AMRCs) that account for multidimensional time changes by means of a multivariate and high-order tracking of the time-varying underlying distribution. In addition, differently from conventional techniques, AMRCs can provide computable tight performance guarantees. Experiments on multiple benchmark datasets show the classification improvement of AMRCs compared to the state-of-the-art and the reliability of the presented performance guarantees.

stat.ML↗

arXiv2022

Transitions from P to NP-hardness: the case of the Linear Ordering Problem

In this paper we evaluate how constructive heuristics degrade when a problem transits from P to NP-hard. This is done by means of the linear ordering problem. More specifically, for this problem we prove that the objective function can be expressed as the sum of two objective functions, one of which is associated with a P problem (an exact polynomial time algorithm is proposed to solve it), while the other is associated with an NP-hard problem. We study how different constructive algorithms whose behaviour only depends on univariate information perform depending on the contribution of the P or NP-hard components of the problem. A number of experiments are conducted with reduced dimensions, where the global optimum of the problems is known, giving different weights to the NP-hard component, while the weight of the P component is fixed. It is observed how the performance of the constructive algorithms gets worse as the weight given to the NP-hard component increases.

cs.DM↗

arXiv2021

On Solving Cycle Problems with Branch-and-Cut: Extending Shrinking and Exact Subcycle Elimination Separation Algorithms

In this paper, we extend techniques developed in the context of the Travelling Salesperson Problem for cycle problems. Particularly, we study the shrinking of support graphs and the exact algorithms for subcycle elimination separation problems. The efficient application of the considered techniques has proved to be essential in the Travelling Salesperson Problem when solving large size problems by Branch-and-Cut, and this has been the motivation behind this work. Regarding the shrinking of support graphs, we prove the validity of the Padberg-Rinaldi general shrinking rules and the Crowder-Padberg subcycle-safe shrinking rules. Concerning the subcycle separation problems, we extend two exact separation algorithms, the Dynamic Hong and the Extended Padberg-Grötschel algorithms, which are shown to be superior to the ones used so far in the literature of cycle problems. The proposed techniques are empirically tested in 24 subcycle elimination problem instances generated by solving the Orienteering Problem (involving up to 15112 vertices) with Branch-and-Cut. The experiments suggest the relevance of the proposed techniques for cycle problems. The obtained average speedup for the subcycle separation problems in the Orienteering Problem when the proposed techniques are used together is around 50 times in medium-sized instances and around 250 times in large-sized instances.

cs.DS↗

arXiv2021

A revisited branch-and-cut algorithm for large-scale orienteering problems

The orienteering problem is a route optimization problem which consists in finding a simple cycle that maximizes the total collected profit subject to a maximum distance limitation. In the last few decades, the occurrence of this problem in real-life applications has boosted the development of many heuristic algorithms to solve it. However, during the same period, not much research has been devoted to the field of exact algorithms for the orienteering problem. The aim of this work is to develop an exact method which is able to obtain optimality certification in a wider set of instances than with previous methods, or to improve the lower and upper bounds in its disability. We propose a revisited version of the branch-and-cut algorithm for the orienteering problem which includes new contributions in the separation algorithms of inequalities stemming from the cycle problem, in the separation loop, in the variables pricing, and in the calculation of the lower and upper bounds of the problem. Our proposal is compared to three state-of-the-art algorithms on 258 benchmark instances with up to 7397 nodes. The computational experiments show the relevance of the designed components where 18 new optima, 76 new best-known solutions and 85 new upper-bound values were obtained.

math.OC↗

arXiv2021

Analysis of Dominant Classes in Universal Adversarial Perturbations

The reasons why Deep Neural Networks are susceptible to being fooled by adversarial examples remains an open discussion. Indeed, many different strategies can be employed to efficiently generate adversarial attacks, some of them relying on different theoretical justifications. Among these strategies, universal (input-agnostic) perturbations are of particular interest, due to their capability to fool a network independently of the input in which the perturbation is applied. In this work, we investigate an intriguing phenomenon of universal perturbations, which has been reported previously in the literature, yet without a proven justification: universal perturbations change the predicted classes for most inputs into one particular (dominant) class, even if this behavior is not specified during the creation of the perturbation. In order to justify the cause of this phenomenon, we propose a number of hypotheses and experimentally test them using a speech command classification problem in the audio domain as a testbed. Our analyses reveal interesting properties of universal perturbations, suggest new methods to generate such attacks and provide an explanation of dominant classes, under both a geometric and a data-feature perspective.

cs.LG↗

arXiv2020

A review on outlier/anomaly detection in time series data

Recent advances in technology have brought major breakthroughs in data collection, enabling a large amount of data to be gathered over time and thus generating time series. Mining this data has become an important task for researchers and practitioners in the past few years, including the detection of outliers or anomalies that may represent errors or events of interest. This review aims to provide a structured and comprehensive state-of-the-art on outlier detection techniques in the context of time series. To this end, a taxonomy is presented based on the main aspects that characterize an outlier detection technique.

cs.LG↗

arXiv2019

Sentiment analysis with genetically evolved Gaussian kernels

Sentiment analysis consists of evaluating opinions or statements from the analysis of text. Among the methods used to estimate the degree in which a text expresses a given sentiment, are those based on Gaussian Processes. However, traditional Gaussian Processes methods use a predefined kernel with hyperparameters that can be tuned but whose structure can not be adapted. In this paper, we propose the application of Genetic Programming for evolving Gaussian Process kernels that are more precise for sentiment analysis. We use use a very flexible representation of kernels combined with a multi-objective approach that simultaneously considers two quality metrics and the computational time spent by the kernels. Our results show that the algorithm can outperform Gaussian Processes with traditional kernels for some of the sentiment analysis tasks considered.

cs.CL↗

arXiv2019

Evolving Gaussian Process kernels from elementary mathematical expressions

Choosing the most adequate kernel is crucial in many Machine Learning applications. Gaussian Process is a state-of-the-art technique for regression and classification that heavily relies on a kernel function. However, in the Gaussian Process literature, kernels have usually been either ad hoc designed, selected from a predefined set, or searched for in a space of compositions of kernels which have been defined a priori. In this paper, we propose a Genetic-Programming algorithm that represents a kernel function as a tree of elementary mathematical expressions. By means of this representation, a wider set of kernels can be modeled, where potentially better solutions can be found, although new challenges also arise. The proposed algorithm is able to overcome these difficulties and find kernels that accurately model the characteristics of the data. This method has been tested in several real-world time-series extrapolation problems, improving the state-of-the-art results while reducing the complexity of the kernels.

cs.LG↗

arXiv2019

Taxonomization of Combinatorial Optimization Problems in Fourier Space

We propose and develop a novel framework for analyzing permutation-based combinatorial optimization problems, which could eventually be extended to other types of problems. Our approach is based on the decomposition of the objective functions via the generalized Fourier transform. We characterize the Fourier coefficients of three different problems: the Traveling Salesman Problem, the Linear Ordering Problem and the Quadratic Assignment Problem. This implies that these three problems can be viewed in a homogeneous space, such as the Fourier domain. Our final target would be to create a taxonomy of problem instances, so that functions which are treated similarly under the same search algorithms are grouped together. For this purpose, we simplify the representations of the objective functions by considering them as permutations of the elements of the search space, and study the permutations that are associated with different problems.

cs.DM↗

arXiv2019

A data-driven approach to precipitation parameterizations using convolutional encoder-decoder neural networks

Numerical Weather Prediction (NWP) models represent sub-grid processes using parameterizations, which are often complex and a major source of uncertainty in weather forecasting. In this work, we devise a simple machine learning (ML) methodology to learn parameterizations from basic NWP fields. Specifically, we demonstrate how encoder-decoder Convolutional Neural Networks (CNN) can be used to derive total precipitation using geopotential height as the only input. Several popular neural network architectures, from the field of image processing, are considered and a comparison with baseline ML methodologies is provided. We use NWP reanalysis data to train different ML models showing how encoder-decoder CNNs are able to interpret the spatial information contained in the geopotential field to infer total precipitation with a high degree of accuracy. We also provide a method to identify the levels of the geopotential height that have a higher influence on precipitation through a variable selection process. As far as we know, this paper covers the first attempt to model NWP parameterizations using CNN methodologies.

physics.ao-ph↗

arXiv2018

Merge Non-Dominated Sorting Algorithm for Many-Objective Optimization

Many Pareto-based multi-objective evolutionary algorithms require to rank the solutions of the population in each iteration according to the dominance principle, what can become a costly operation particularly in the case of dealing with many-objective optimization problems. In this paper, we present a new efficient algorithm for computing the non-dominated sorting procedure, called Merge Non-Dominated Sorting (MNDS), which has a best computational complexity of $Θ(NlogN)$ and a worst computational complexity of $Θ(MN^2)$. Our approach is based on the computation of the dominance set of each solution by taking advantage of the characteristics of the merge sort algorithm. We compare the MNDS against four well-known techniques that can be considered as the state-of-the-art. The results indicate that the MNDS algorithm outperforms the other techniques in terms of number of comparisons as well as the total running time.

cs.NE↗

arXiv2018

A review on distance based time series classification

Time series classification is an increasing research topic due to the vast amount of time series data that are being created over a wide variety of fields. The particularity of the data makes it a challenging task and different approaches have been taken, including the distance based approach. 1-NN has been a widely used method within distance based time series classification due to it simplicity but still good performance. However, its supremacy may be attributed to being able to use specific distances for time series within the classification process and not to the classifier itself. With the aim of exploiting these distances within more complex classifiers, new approaches have arisen in the past few years that are competitive or which outperform the 1-NN based approaches. In some cases, these new methods use the distance measure to transform the series into feature vectors, bridging the gap between time series and traditional classifiers. In other cases, the distances are employed to obtain a time series kernel and enable the use of kernel methods for time series classification. One of the main challenges is that a kernel function must be positive semi-definite, a matter that is also addressed within this review. The presented review includes a taxonomy of all those methods that aim to classify time series using a distance based approach, as well as a discussion of the strengths and weaknesses of each method.

stat.ML↗

arXiv2018

An efficient K -means clustering algorithm for massive data

The analysis of continously larger datasets is a task of major importance in a wide variety of scientific fields. In this sense, cluster analysis algorithms are a key element of exploratory data analysis, due to their easiness in the implementation and relatively low computational cost. Among these algorithms, the K -means algorithm stands out as the most popular approach, besides its high dependency on the initial conditions, as well as to the fact that it might not scale well on massive datasets. In this article, we propose a recursive and parallel approximation to the K -means algorithm that scales well on both the number of instances and dimensionality of the problem, without affecting the quality of the approximation. In order to achieve this, instead of analyzing the entire dataset, we work on small weighted sets of points that mostly intend to extract information from those regions where it is harder to determine the correct cluster assignment of the original instances. In addition to different theoretical properties, which deduce the reasoning behind the algorithm, experimental results indicate that our method outperforms the state-of-the-art in terms of the trade-off between number of distance computations and the quality of the solution obtained.

stat.ML↗

arXiv2016

Towards Competitive Classifiers for Unbalanced Classification Problems: A Study on the Performance Scores

Although a great methodological effort has been invested in proposing competitive solutions to the class-imbalance problem, little effort has been made in pursuing a theoretical understanding of this matter. In order to shed some light on this topic, we perform, through a novel framework, an exhaustive analysis of the adequateness of the most commonly used performance scores to assess this complex scenario. We conclude that using unweighted Hölder means with exponent $p \leq 1$ to average the recalls of all the classes produces adequate scores which are capable of determining whether a classifier is competitive. Then, we review the major solutions presented in the class-imbalance literature. Since any learning task can be defined as an optimisation problem where a loss function, usually connected to a particular score, is minimised, our goal, here, is to find whether the learning tasks found in the literature are also oriented to maximise the previously detected adequate scores. We conclude that they usually maximise the unweighted Hölder mean with $p = 1$ (a-mean). Finally, we provide bounds on the values of the studied performance scores which guarantee a classifier with a higher recall than the random classifier in each and every class.

stat.ML↗

arXiv2015

Computing factorized approximations of Pareto-fronts using mNM-landscapes and Boltzmann distributions

NM-landscapes have been recently introduced as a class of tunable rugged models. They are a subset of the general interaction models where all the interactions are of order less or equal $M$. The Boltzmann distribution has been extensively applied in single-objective evolutionary algorithms to implement selection and study the theoretical properties of model-building algorithms. In this paper we propose the combination of the multi-objective NM-landscape model and the Boltzmann distribution to obtain Pareto-front approximations. We investigate the joint effect of the parameters of the NM-landscapes and the probabilistic factorizations in the shape of the Pareto front approximations.

cs.NE↗

arXiv2013

Combinatorial Optimization by Learning and Simulation of Bayesian Networks

This paper shows how the Bayesian network paradigm can be used in order to solve combinatorial optimization problems. To do it some methods of structure learning from data and simulation of Bayesian networks are inserted inside Estimation of Distribution Algorithms (EDA). EDA are a new tool for evolutionary computation in which populations of individuals are created by estimation and simulation of the joint probability distribution of the selected individuals. We propose new approaches to EDA for combinatorial optimization based on the theory of probabilistic graphical models. Experimental results are also presented.

cs.AI↗