arXiv subjects

Aritz Pérez

Publications and source records attributed to Aritz Pérez.

At least 19 recordsLinked to original sources

arXiv2026

Minimax Generalized Cross-Entropy

Loss functions play a central role in supervised classification. Cross-entropy (CE) is widely used, whereas the mean absolute error (MAE) loss can offer robustness but is difficult to optimize. Interpolating between the CE and MAE losses, generalized cross-entropy (GCE) has recently been introduced to provide a trade-off between optimization difficulty and robustness. Existing formulations of GCE result in a non-convex optimization over classification margins that is prone to underfitting, leading to poor performances with complex datasets. In this paper, we propose a minimax formulation of generalized cross-entropy (MGCE) that results in a convex optimization over classification margins. Moreover, we show that MGCEs can provide an upper bound on the classification error. The proposed bilevel convex optimization can be efficiently implemented using stochastic gradient computed via implicit differentiation. Using benchmark datasets, we show that MGCE achieves strong accuracy, faster convergence, and better calibration, especially in the presence of label noise.

stat.ML↗

arXiv2026

A Review on Single-Problem Multi-Attempt Heuristic Optimization

In certain real-world optimization scenarios, practitioners are not interested in solving multiple problems but rather in finding the best solution to a single, specific problem. When the computational budget is large relative to the cost of evaluating a candidate solution, multiple heuristic alternatives can be tried to solve the same given problem, each possibly with a different algorithm, parameter configuration, initialization, or stopping criterion. In this practically relevant setting, the sequential selection of which alternative to try next is crucial for efficiently identifying the best possible solution across multiple attempts. However, suitable sequential alternative selection strategies have traditionally been studied separately across different research topics and have not been the exclusive focus of any existing review. As a result, the state-of-the-art remains fragmented for practitioners interested in this setting, with surveys either covering only subsets of relevant strategies or including approaches that rely on assumptions that are not feasible for the single-problem case. This work addresses the identified gap by providing a focused review of single-problem multi-attempt heuristic optimization. It brings together suitable strategies for this setting that have been studied separately through algorithm selection, parameter tuning, multi-start, and resource allocation. These strategies are described using a unified terminology within a common framework, which supports the construction of a taxonomy for systematically organizing and classifying them. The resulting comprehensive review facilitates both the identification and the development of strategies for the single-problem multi-attempt setting in practice.

cs.LG↗

arXiv2025

Efficient Large-Scale Learning of Minimax Risk Classifiers

Supervised learning with large-scale data usually leads to complex optimization problems, especially for classification tasks with multiple classes. Stochastic subgradient methods can enable efficient learning with a large number of samples for classification techniques that minimize the average loss over the training samples. However, recent techniques, such as minimax risk classifiers (MRCs), minimize the maximum expected loss and are not amenable to stochastic subgradient methods. In this paper, we present a learning algorithm based on the combination of constraint and column generation that enables efficient learning of MRCs with large-scale data for classification tasks with multiple classes. Experiments on multiple benchmark datasets show that the proposed algorithm provides upto a 10x speedup for general large-scale data and around a 100x speedup with a sizeable number of classes.

cs.LG↗

arXiv2025

Decentralized Federated Learning of Probabilistic Generative Classifiers

Federated learning is a paradigm of increasing relevance in real world applications, aimed at building a global model across a network of heterogeneous users without requiring the sharing of private data. We focus on model learning over decentralized architectures, where users collaborate directly to update the global model without relying on a central server. In this context, the current paper proposes a novel approach to collaboratively learn probabilistic generative classifiers with a parametric form. The framework is composed by a communication network over a set of local nodes, each of one having its own local data, and a local updating rule. The proposal involves sharing local statistics with neighboring nodes, where each node aggregates the neighbors' information and iteratively learns its own local classifier, which progressively converges to a global model. Extensive experiments demonstrate that the algorithm consistently converges to a globally competitive model across a wide range of network topologies, network sizes, local dataset sizes, and extreme non-i.i.d. data distributions.

cs.LG↗

arXiv2025

Risk-based Calibration for Generative Classifiers

Generative classifiers are constructed on the basis of a joint probability distribution and are typically learned using closed-form procedures that rely on data statistics and maximize scores related to data fitting. However, these scores are not directly linked to supervised classification metrics such as the error, i.e., the expected 0-1 loss. To address this limitation, we propose a learning procedure called risk-based calibration (RC) that iteratively refines the generative classifier by adjusting its joint probability distribution according to the 0-1 loss in training samples. This is achieved by reinforcing data statistics associated with the true classes while weakening those of incorrect classes. As a result, the classifier progressively assigns higher probability to the correct labels, improving its training error. Results on 20 heterogeneous datasets using both naïve Bayes and quadratic discriminant analysis show that RC significantly outperforms closed-form learning procedures in terms of both training error and generalization error. In this way, RC bridges the gap between traditional generative approaches and learning procedures guided by performance measures, ensuring a closer alignment with supervised classification objectives.

cs.LG↗

arXiv2024

PAC-Bayes-Chernoff bounds for unbounded losses

We introduce a new PAC-Bayes oracle bound for unbounded losses that extends Cramér-Chernoff bounds to the PAC-Bayesian setting. The proof technique relies on controlling the tails of certain random variables involving the Cramér transform of the loss. Our approach naturally leverages properties of Cramér-Chernoff bounds, such as exact optimization of the free parameter in many PAC-Bayes bounds. We highlight several applications of the main theorem. Firstly, we show that our bound recovers and generalizes previous results. Additionally, our approach allows working with richer assumptions that result in more informative and potentially tighter bounds. In this direction, we provide a general bound under a new \textit{model-dependent} assumption from which we obtain bounds based on parameter norms and log-Sobolev inequalities. Notably, many of these bounds can be minimized to obtain distributions beyond the Gibbs posterior and provide novel theoretical coverage to existing regularization techniques.

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arXiv2024

MRCpy: A Library for Minimax Risk Classifiers

Libraries for supervised classification have enabled the wide-spread usage of machine learning methods. Existing libraries, such as scikit-learn, caret, and mlpack, implement techniques based on the classical empirical risk minimization (ERM) approach. We present a Python library, MRCpy, that implements minimax risk classifiers (MRCs) based on the robust risk minimization (RRM) approach. The library offers multiple variants of MRCs that can provide performance guarantees, enable efficient learning in high dimensions, and adapt to distribution shifts. MRCpy follows an object-oriented approach and adheres to the standards of popular Python libraries, such as scikit-learn, facilitating readability and easy usage together with a seamless integration with other libraries. The source code is available under the GPL-3.0 license at https://github.com/MachineLearningBCAM/MRCpy.

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arXiv2024

Large-scale unsupervised spatio-temporal semantic analysis of vast regions from satellite images sequences

Temporal sequences of satellite images constitute a highly valuable and abundant resource for analyzing regions of interest. However, the automatic acquisition of knowledge on a large scale is a challenging task due to different factors such as the lack of precise labeled data, the definition and variability of the terrain entities, or the inherent complexity of the images and their fusion. In this context, we present a fully unsupervised and general methodology to conduct spatio-temporal taxonomies of large regions from sequences of satellite images. Our approach relies on a combination of deep embeddings and time series clustering to capture the semantic properties of the ground and its evolution over time, providing a comprehensive understanding of the region of interest. The proposed method is enhanced by a novel procedure specifically devised to refine the embedding and exploit the underlying spatio-temporal patterns. We use this methodology to conduct an in-depth analysis of a 220 km$^2$ region in northern Spain in different settings. The results provide a broad and intuitive perspective of the land where large areas are connected in a compact and well-structured manner, mainly based on climatic, phytological, and hydrological factors.

cs.CV↗

arXiv2024

Speeding-up Evolutionary Algorithms to solve Black-Box Optimization Problems

Population-based evolutionary algorithms are often considered when approaching computationally expensive black-box optimization problems. They employ a selection mechanism to choose the best solutions from a given population after comparing their objective values, which are then used to generate the next population. This iterative process explores the solution space efficiently, leading to improved solutions over time. However, these algorithms require a large number of evaluations to provide a quality solution, which might be computationally expensive when the evaluation cost is high. In some cases, it is possible to replace the original objective function with a less accurate approximation of lower cost. This introduces a trade-off between the evaluation cost and its accuracy. In this paper, we propose a technique capable of choosing an appropriate approximate function cost during the execution of the optimization algorithm. The proposal finds the minimum evaluation cost at which the solutions are still properly ranked, and consequently, more evaluations can be computed in the same amount of time with minimal accuracy loss. An experimental section on four very different problems reveals that the proposed approach can reach the same objective value in less than half of the time in certain cases.

cs.NE↗

arXiv2023

Time-dependent Probabilistic Generative Models for Disease Progression

Electronic health records contain valuable information for monitoring patients' health trajectories over time. Disease progression models have been developed to understand the underlying patterns and dynamics of diseases using these data as sequences. However, analyzing temporal data from EHRs is challenging due to the variability and irregularities present in medical records. We propose a Markovian generative model of treatments developed to (i) model the irregular time intervals between medical events; (ii) classify treatments into subtypes based on the patient sequence of medical events and the time intervals between them; and (iii) segment treatments into subsequences of disease progression patterns. We assume that sequences have an associated structure of latent variables: a latent class representing the different subtypes of treatments; and a set of latent stages indicating the phase of progression of the treatments. We use the Expectation-Maximization algorithm to learn the model, which is efficiently solved with a dynamic programming-based method. Various parametric models have been employed to model the time intervals between medical events during the learning process, including the geometric, exponential, and Weibull distributions. The results demonstrate the effectiveness of our model in recovering the underlying model from data and accurately modeling the irregular time intervals between medical actions.

stat.ML↗

arXiv2023

On the Fair Comparison of Optimization Algorithms in Different Machines

An experimental comparison of two or more optimization algorithms requires the same computational resources to be assigned to each algorithm. When a maximum runtime is set as the stopping criterion, all algorithms need to be executed in the same machine if they are to use the same resources. Unfortunately, the implementation code of the algorithms is not always available, which means that running the algorithms to be compared in the same machine is not always possible. And even if they are available, some optimization algorithms might be costly to run, such as training large neural-networks in the cloud. In this paper, we consider the following problem: how do we compare the performance of a new optimization algorithm B with a known algorithm A in the literature if we only have the results (the objective values) and the runtime in each instance of algorithm A? Particularly, we present a methodology that enables a statistical analysis of the performance of algorithms executed in different machines. The proposed methodology has two parts. First, we propose a model that, given the runtime of an algorithm in a machine, estimates the runtime of the same algorithm in another machine. This model can be adjusted so that the probability of estimating a runtime longer than what it should be is arbitrarily low. Second, we introduce an adaptation of the one-sided sign test that uses a modified p-value and takes into account that probability. Such adaptation avoids increasing the probability of type I error associated with executing algorithms A and B in different machines.

cs.PF↗

arXiv2023

Structural Restricted Boltzmann Machine for image denoising and classification

Restricted Boltzmann Machines are generative models that consist of a layer of hidden variables connected to another layer of visible units, and they are used to model the distribution over visible variables. In order to gain a higher representability power, many hidden units are commonly used, which, in combination with a large number of visible units, leads to a high number of trainable parameters. In this work we introduce the Structural Restricted Boltzmann Machine model, which taking advantage of the structure of the data in hand, constrains connections of hidden units to subsets of visible units in order to reduce significantly the number of trainable parameters, without compromising performance. As a possible area of application, we focus on image modelling. Based on the nature of the images, the structure of the connections is given in terms of spatial neighbourhoods over the pixels of the image that constitute the visible variables of the model. We conduct extensive experiments on various image domains. Image denoising is evaluated with corrupted images from the MNIST dataset. The generative power of our models is compared to vanilla RBMs, as well as their classification performance, which is assessed with five different image domains. Results show that our proposed model has a faster and more stable training, while also obtaining better results compared to an RBM with no constrained connections between its visible and hidden units.

cs.CV↗

arXiv2023

Efficient Learning of Minimax Risk Classifiers in High Dimensions

High-dimensional data is common in multiple areas, such as health care and genomics, where the number of features can be tens of thousands. In such scenarios, the large number of features often leads to inefficient learning. Constraint generation methods have recently enabled efficient learning of L1-regularized support vector machines (SVMs). In this paper, we leverage such methods to obtain an efficient learning algorithm for the recently proposed minimax risk classifiers (MRCs). The proposed iterative algorithm also provides a sequence of worst-case error probabilities and performs feature selection. Experiments on multiple high-dimensional datasets show that the proposed algorithm is efficient in high-dimensional scenarios. In addition, the worst-case error probability provides useful information about the classifier performance, and the features selected by the algorithm are competitive with the state-of-the-art.

stat.ML↗

arXiv2022

Dirichlet process mixture models for non-stationary data streams

In recent years, we have seen a handful of work on inference algorithms over non-stationary data streams. Given their flexibility, Bayesian non-parametric models are a good candidate for these scenarios. However, reliable streaming inference under the concept drift phenomenon is still an open problem for these models. In this work, we propose a variational inference algorithm for Dirichlet process mixture models. Our proposal deals with the concept drift by including an exponential forgetting over the prior global parameters. Our algorithm allows to adapt the learned model to the concept drifts automatically. We perform experiments in both synthetic and real data, showing that the proposed model is competitive with the state-of-the-art algorithms in the density estimation problem, and it outperforms them in the clustering problem.

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arXiv2022

Comparing Two Samples Through Stochastic Dominance: A Graphical Approach

Non-deterministic measurements are common in real-world scenarios: the performance of a stochastic optimization algorithm or the total reward of a reinforcement learning agent in a chaotic environment are just two examples in which unpredictable outcomes are common. These measures can be modeled as random variables and compared among each other via their expected values or more sophisticated tools such as null hypothesis statistical tests. In this paper, we propose an alternative framework to visually compare two samples according to their estimated cumulative distribution functions. First, we introduce a dominance measure for two random variables that quantifies the proportion in which the cumulative distribution function of one of the random variables stochastically dominates the other one. Then, we present a graphical method that decomposes in quantiles i) the proposed dominance measure and ii) the probability that one of the random variables takes lower values than the other. With illustrative purposes, we re-evaluate the experimentation of an already published work with the proposed methodology and we show that additional conclusions (missed by the rest of the methods) can be inferred. Additionally, the software package RVCompare was created as a convenient way of applying and experimenting with the proposed framework.

stat.ML↗

arXiv2021

Generalized Maximum Entropy for Supervised Classification

The maximum entropy principle advocates to evaluate events' probabilities using a distribution that maximizes entropy among those that satisfy certain expectations' constraints. Such principle can be generalized for arbitrary decision problems where it corresponds to minimax approaches. This paper establishes a framework for supervised classification based on the generalized maximum entropy principle that leads to minimax risk classifiers (MRCs). We develop learning techniques that determine MRCs for general entropy functions and provide performance guarantees by means of convex optimization. In addition, we describe the relationship of the presented techniques with existing classification methods, and quantify MRCs performance in comparison with the proposed bounds and conventional methods.

stat.ML↗

arXiv2021

K-means for Evolving Data Streams

Currently the amount of data produced worldwide is increasing beyond measure, thus a high volume of unsupervised data must be processed continuously. One of the main unsupervised data analysis is clustering. In streaming data scenarios, the data is composed by an increasing sequence of batches of samples where the concept drift phenomenon may happen. In this paper, we formally define the Streaming $K$-means(S$K$M) problem, which implies a restart of the error function when a concept drift occurs. We propose a surrogate error function that does not rely on concept drift detection. We proof that the surrogate is a good approximation of the S$K$M error. Hence, we suggest an algorithm which minimizes this alternative error each time a new batch arrives. We present some initialization techniques for streaming data scenarios as well. Besides providing theoretical results, experiments demonstrate an improvement of the converged error for the non-trivial initialization methods.

stat.ML↗

arXiv2018

Candidate Labeling for Crowd Learning

Crowdsourcing has become very popular among the machine learning community as a way to obtain labels that allow a ground truth to be estimated for a given dataset. In most of the approaches that use crowdsourced labels, annotators are asked to provide, for each presented instance, a single class label. Such a request could be inefficient, that is, considering that the labelers may not be experts, that way to proceed could fail to take real advantage of the knowledge of the labelers. In this paper, the use of candidate labeling for crowd learning is proposed, where the annotators may provide more than a single label per instance to try not to miss the real label. The main hypothesis is that, by allowing candidate labeling, knowledge can be extracted from the labelers more efficiently by than in the standard crowd learning scenario. Empirical evidence which supports that hypothesis is presented.

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