Optimizing different loss functions in multilabel classifications

Multilabel classification (ML) aims to assign a set of labels to an instance. This generalization of multiclass classification yields to the redefinition of loss functions and the learning tasks become harder. The objective of this paper is to gain insights into the relations of optimization aims and some of the most popular performance measures: subset (or 0/1), Hamming, and the example-based F-measure. To make a fair comparison, we implemented three ML learners for optimizing explicitly each one of these measures in a common framework. This can be done considering a subset of labels as a structured output. Then, we use structured output support vector machines tailored to optimize a given loss function. The paper includes an exhaustive experimental comparison. The conclusion is that in most cases, the optimization of the Hamming loss produces the best or competitive scores. This is a practical result since the Hamming loss can be minimized using a bunch of binary classifiers, one for each label separately, and therefore, it is a scalable and fast method to learn ML tasks. Additionally, we observe that in noise-free learning tasks optimizing the subset loss is the best option, but the differences are very small. We have also noticed that the biggest room for improvement can be found when the goal is to optimize an F-measure in noisy learning task

Semantic Information G Theory and Logical Bayesian Inference for Machine Learning

An important problem with machine learning is that when label number n\u3e2, it is very difficult to construct and optimize a group of learning functions, and we wish that optimized learning functions are still useful when prior distribution P(x) (where x is an instance) is changed. To resolve this problem, the semantic information G theory, Logical Bayesian Inference (LBI), and a group of Channel Matching (CM) algorithms together form a systematic solution. MultilabelMultilabel A semantic channel in the G theory consists of a group of truth functions or membership functions. In comparison with likelihood functions, Bayesian posteriors, and Logistic functions used by popular methods, membership functions can be more conveniently used as learning functions without the above problem. In Logical Bayesian Inference (LBI), every label’s learning is independent. For Multilabel learning, we can directly obtain a group of optimized membership functions from a big enough sample with labels, without preparing different samples for different labels. A group of Channel Matching (CM) algorithms are developed for machine learning. For the Maximum Mutual Information (MMI) classification of three classes with Gaussian distributions on a two-dimensional feature space, 2-3 iterations can make mutual information between three classes and three labels surpass 99% of the MMI for most initial partitions. For mixture models, the Expectation-Maxmization (EM) algorithm is improved and becomes the CM-EM algorithm, which can outperform the EM algorithm when mixture ratios are imbalanced, or local convergence exists. The CM iteration algorithm needs to combine neural networks for MMI classifications on high-dimensional feature spaces. LBI needs further studies for the unification of statistics and logic

Multilabel Consensus Classification

In the era of big data, a large amount of noisy and incomplete data can be collected from multiple sources for prediction tasks. Combining multiple models or data sources helps to counteract the effects of low data quality and the bias of any single model or data source, and thus can improve the robustness and the performance of predictive models. Out of privacy, storage and bandwidth considerations, in certain circumstances one has to combine the predictions from multiple models or data sources to obtain the final predictions without accessing the raw data. Consensus-based prediction combination algorithms are effective for such situations. However, current research on prediction combination focuses on the single label setting, where an instance can have one and only one label. Nonetheless, data nowadays are usually multilabeled, such that more than one label have to be predicted at the same time. Direct applications of existing prediction combination methods to multilabel settings can lead to degenerated performance. In this paper, we address the challenges of combining predictions from multiple multilabel classifiers and propose two novel algorithms, MLCM-r (MultiLabel Consensus Maximization for ranking) and MLCM-a (MLCM for microAUC). These algorithms can capture label correlations that are common in multilabel classifications, and optimize corresponding performance metrics. Experimental results on popular multilabel classification tasks verify the theoretical analysis and effectiveness of the proposed methods

The Lov\'asz Hinge: A Novel Convex Surrogate for Submodular Losses

Learning with non-modular losses is an important problem when sets of predictions are made simultaneously. The main tools for constructing convex surrogate loss functions for set prediction are margin rescaling and slack rescaling. In this work, we show that these strategies lead to tight convex surrogates iff the underlying loss function is increasing in the number of incorrect predictions. However, gradient or cutting-plane computation for these functions is NP-hard for non-supermodular loss functions. We propose instead a novel surrogate loss function for submodular losses, the Lov\'asz hinge, which leads to O(p log p) complexity with O(p) oracle accesses to the loss function to compute a gradient or cutting-plane. We prove that the Lov\'asz hinge is convex and yields an extension. As a result, we have developed the first tractable convex surrogates in the literature for submodular losses. We demonstrate the utility of this novel convex surrogate through several set prediction tasks, including on the PASCAL VOC and Microsoft COCO datasets

A multi-label approach for diagnosis problems in energy systems using LAMDA algorithm

2022 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), 18-23 July 2022, Italia.In this paper, we propose a supervised multilabel algorithm called Learning Algorithm for Multivariate Data Analysis for Multilabel Classification (LAMDA-ML). This algorithm is based on the algorithms of the LAMDA family, in particular, on the LAMDA-HAD (Higher Adequacy Grade) algorithm. Unlike previous algorithms in a multi-label context, LAMDA-ML is based on the Global Adequacy Degree (GAD) of an individual in multiple classes. In our proposal, we define a membership threshold (Gt), such that for all GAD values above this threshold, it implies that an individual will be assigned to the respective classes. For the evaluation of the performance of this proposal, a solar power generation dataset is used, with very encouraging results according to several metrics in the context of multiple labels.European CommissionAgencia Estatal de InvestigaciónJunta de Comunidades de Castilla-La Manch

Simpler is better: a novel genetic algorithm to induce compact multi-label chain classifiers

Multi-label classification (MLC) is the task of assigning multiple class labels to an object based on the features that describe the object. One of the most effective MLC methods is known as Classifier Chains (CC). This approach consists in training q binary classifiers linked in a chain, y1 → y2 → ... → yq, with each responsible for classifying a specific label in {l1, l2, ..., lq}. The chaining mechanism allows each individual classifier to incorporate the predictions of the previous ones as additional information at classification time. Thus, possible correlations among labels can be automatically exploited. Nevertheless, CC suffers from two important drawbacks: (i) the label ordering is decided at random, although it usually has a strong effect on predictive accuracy; (ii) all labels are inserted into the chain, although some of them might carry irrelevant information to discriminate the others. In this paper we tackle both problems at once, by proposing a novel genetic algorithm capable of searching for a single optimized label ordering, while at the same time taking into consideration the utilization of partial chains. Experiments on benchmark datasets demonstrate that our approach is able to produce models that are both simpler and more accurate