Efficient approximation of probability distributions with k-order decomposable models

During the last decades several learning algorithms have been proposed to learn probability distributions based on decomposable models. Some of these algorithms can be used to search for a maximum likelihood decomposable model with a given maximum clique size, k. Unfortunately, the problem of learning a maximum likelihood decomposable model given a maximum clique size is NP-hard for k > 2. In this work, we propose the fractal tree family of algorithms which approximates this problem with a computational complexity of O(k 2 · n 2 · N ) in the worst case, where n is the number of implied random variables and N is the size of the training set. The fractal tree algorithms construct a sequence of maximal i-order decomposable graphs, for i = 2, ..., k, in k − 1 steps. At each step, the algorithms follow a divide-and-conquer strategy that decomposes the problem into a set of separator problems. Each separator problem is efficiently solved using the generalized Chow-Liu algorithm. Fractal trees can be considered a natural extension of the Chow-Liu algorithm, from k = 2 to arbitrary values of k, and they have shown a competitive behaviour to deal with the maximum likelihood problem. Due to their competitive behavior, their low computational complexity and their modularity, which allow them to implement different parallelization strategies, the proposed procedures are especially advisable for modelling high dimensional domains.Saiotek and IT609-13 programs (Basque Government) TIN2013-41272-P (Spanish Ministry of Science and Innovation) COMBIOMED network in computational bio-medicine (Carlos III Health Institute

Learning a logistic regression with the help of unknown features at prediction stage

The use of features available at training time, but not at prediction time, as additional information for training models is known as learning using privileged information paradigm. In this paper, the handling of privileged features is addressed from the logistic regression perspective, commonly used in the clinical setting. Two new proposals, LOGIT+ and LRPROB+, learned with the influence of privileged features and preserving the interpretability of conventional logistic regression, are proposed. Experimental results on datasets report improvements of our proposals over the performance of traditional logistic regression learned without privileged information

Efficient approximation of probability distributions with k-order decomposable models

During the last decades several learning algorithms have been proposed to learn probability distributions based on decomposable models. Some of these algorithms can be used to search for a maximum likelihood decomposable model with a given maximum clique size, k. Unfortunately, the problem of learning a maximum likelihood decomposable model given a maximum clique size is NP-hard for $k<2$. In this work, we propose the fractal tree family of algorithms which approximates this problem with a computational complexity of $\mathcal{O}(k \cdot n^2 \log n)$ in the worst case, where $n$ is the number of implied random variables and N is the size of the training set. The fractal tree algorithms construct a sequence of maximal $i$-order decomposable graphs, for $i=2,...,k,$ in $k - 1$ steps. At each step, the algorithms follow a divide-and-conquer strategy that decomposes the problem into a set of separate problems. Each separate problem is efficiently solved using the generalized Chow-Liu algorithm. Fractal trees can be considered a natural extension of the Chow-Liu algorithm, from $k = 2$ to arbitrary values of $k$, and they have shown a competitive behavior to deal with the maximum likelihood problem. Due to their competitive behavior, their low computational complexity and their modularity, which allow them to implement different parallelization strategies, the proposed procedures are especially advisable for modeling high dimensional domains

Analyzing rare event, anomaly, novelty and outlier detection terms under the supervised classification framework

In recent years, a variety of research areas have contributed to a set of related problems with rare event, anomaly, novelty and outlier detection terms as the main actors. These multiple research areas have created a mix-up between terminology and problems. In some research, similar problems have been named differently; while in some other works, the same term has been used to describe different problems. This confusion between terms and problems causes the repetition of research and hinders the advance of the field. Therefore, a standardization is imperative. The goal of this paper is to underline the differences between each term, and organize the area by looking at all these terms under the umbrella of supervised classification. Therefore, a one-to-one assignment of terms to learning scenarios is proposed. In fact, each learning scenario is associated with the term most frequently used in the literature. In order to validate this proposal, a set of experiments retrieving papers from Google Scholar, ACM Digital Library and IEEE Xplore has been carried out

Measuring the Class-imbalance Extent of Multi-class Problems

Since many important real-world classification problems involve learning from unbalanced data, the challenging class-imbalance problem has lately received con- siderable attention in the community. Most of the methodological contributions proposed in the literature carry out a set of experiments over a battery of specific datasets. In these cases, in order to be able to draw meaningful conclusions from the experiments, authors often measure the class-imbalance extent of each tested dataset using imbalance-ratio, i.e. dividing the frequencies of the majority class by the minority class. In this paper, we argue that, although imbalance-ratio is an informative measure for binary problems, it is not adequate for the multi-class scenario due to the fact that, in that scenario, it groups problems with disparate class-imbalance extents under the same numerical value. Thus, in order to overcome this drawback, in this paper, we propose imbalance-degree as a novel and normalised measure which is capable of properly measuring the class-imbalance extent of a multi-class problem. Experimental results show that imbalance-degree is more adequate than imbalance- ratio since it is more sensitive in reflecting the hindrance produced by skewed multi- class distributions to the learning processes.TIN2013-41272P, IT609-13, AP2008-0076

A note on the behavior of majority voting in multi-class domains with biased annotators

Majority voting is a popular and robust strategy to aggregate different opinions in learning from crowds, where each worker labels examples ac- cording to their own criteria. Although it has been extensively studied in the binary case, its behavior with multiple classes is not completely clear, specifically when annotations are biased. This paper attempts to fill that gap. The behavior of the majority voting strategy is studied in-depth in multi-class domains, emphasizing the effect of annotation bias. By means of a complete experimental setting, we show the limitations of the stan- dard majority voting strategy. The use of three simple techniques that infer global information from the annotations and annotators allows us to put the performance of the majority voting strategy in context.TIN2016-78365-

A system for airport weather forecasting based on circular regression trees

This paper describes a suite of tools and a model for improving the accuracy of airport weather forecasts produced by numerical weather prediction (NWP) products, by learning from the relationships between previously modelled and observed data. This is based on a new machine learning methodology that allows circular variables to be naturally incorporated into regression trees, producing more accurate results than linear and previous circular regression tree methodologies. The software has been made publicly available as a Python package, which contains all the necessary tools to extract historical NWP and observed weather data and to generate forecasts for different weather variables for any airport in the world. Several examples are presented where the results of the proposed model significantly improve those produced by NWP and also by previous regression tree models.TIN2016-78365-R, IT609-1

Optimization of deep learning precipitation models using categorical binary metrics

This work introduces a methodology for optimizing neural network models using a combination of continuous and categorical binary indices in the context of precipitation forecasting. Probability of detection or false alarm rate are popular metrics used in the verification of precipitation models. However, machine learning models trained using gradient descent cannot be optimized based on these metrics, as they are not differentiable. We propose an alternative formulation for these categorical indices that are differentiable and we demonstrate how they can be used to optimize the skill of precipitation neural network models defined as a multi-objective optimization problem. To our knowledge, this is the first proposal of a methodology for optimizing weather neural network models based on categorical indices.TIN2016-78365-

Learning to classify software defects from crowds: a novel approach

In software engineering, associating each reported defect with a cate- gory allows, among many other things, for the appropriate allocation of resources. Although this classification task can be automated using stan- dard machine learning techniques, the categorization of defects for model training requires expert knowledge, which is not always available. To cir- cumvent this dependency, we propose to apply the learning from crowds paradigm, where training categories are obtained from multiple non-expert annotators (and so may be incomplete, noisy or erroneous) and, dealing with this subjective class information, classifiers are efficiently learnt. To illustrate our proposal, we present two real applications of the IBM’s or- thogonal defect classification working on the issue tracking systems from two different real domains. Bayesian network classifiers learnt using two state-of-the-art methodologies from data labeled by a crowd of annotators are used to predict the category (impact) of reported software defects. The considered methodologies show enhanced performance regarding the straightforward solution (majority voting) according to different metrics. This shows the possibilities of using non-expert knowledge aggregation techniques when expert knowledge is unavailable

Learning a Battery of COVID-19 Mortality Prediction Models by Multi-objective Optimization

The COVID-19 pandemic is continuously evolving with drastically changing epidemiological situations which are approached with different decisions: from the reduction of fatalities to even the selection of patients with the highest probability of survival in critical clinical situations. Motivated by this, a battery of mortality prediction models with different performances has been developed to assist physicians and hospital managers. Logistic regression, one of the most popular classifiers within the clinical field, has been chosen as the basis for the generation of our models. Whilst a standard logistic regression only learns a single model focusing on improving accuracy, we propose to extend the possibilities of logistic regression by focusing on sensitivity and specificity. Hence, the log-likelihood function, used to calculate the coefficients in the logistic model, is split into two objective functions: one representing the survivors and the other for the deceased class. A multi-objective optimization process is undertaken on both functions in order to find the Pareto set, composed of models not improved by another model in both objective functions simultaneously. The individual optimization of either sensitivity (deceased patients) or specificity (survivors) criteria may be conflicting objectives because the improvement of one can imply the worsening of the other. Nonetheless, this conflict guarantees the output of a battery of diverse prediction models. Furthermore, a specific methodology for the evaluation of the Pareto models is proposed. As a result, a battery of COVID-19 mortality prediction models is obtained to assist physicians in decision-making for specific epidemiological situations.This research is supported by the Basque Government (IT1504- 22, Elkartek) through the BERC 2022–2025 program and BMTF project, and by the Ministry of Science, Innovation and Universities: BCAM Severo Ochoa accreditation SEV-2017-0718 and PID2019-104966GB-I00. Furthermore, the work is also supported by the AXA Research Fund project “Early prognosis of COVID-19 infections via machine learning”