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This paper introduces a novel anomaly detection framework that combines the robust statistical principles of density-estimation-based anomaly detection methods with the representation-learning capabilities of deep learning models. The method originated from this framework is presented in two different versions: a shallow approach employing a density-estimation model based on adaptive Fourier features and density matrices, and a deep approach that integrates an autoencoder to learn a low-dimensional representation of the data. By estimating the density of new samples, both methods are able to find normality scores. The methods can be seamlessly integrated into an end-to-end architecture and optimized using gradient-based optimization techniques. To evaluate their performance, extensive experiments were conducted on various benchmark datasets. The results demonstrate that both versions of the method can achieve comparable or superior performance when compared to other state-of-the-art methods. Notably, the shallow approach performs better on datasets with fewer dimensions, while the autoencoder-based approach shows improved performance on datasets with higher dimensions., Comment: arXiv admin note: substantial text overlap with arXiv:2211.08525

This paper presents a strategy for efficient quantum circuit design for density estimation. The strategy is based on a quantum-inspired algorithm for density estimation and a circuit optimisation routine based on memetic algorithms. The model maps a training dataset to a quantum state represented by a density matrix through a quantum feature map. This training state encodes the probability distribution of the dataset in a quantum state, such that the density of a new sample can be estimated by projecting its corresponding quantum state onto the training state. We propose the application of a memetic algorithm to find the architecture and parameters of a variational quantum circuit that implements the quantum feature map, along with a variational learning strategy to prepare the training state. Demonstrations of the proposed strategy show an accurate approximation of the Gaussian kernel density estimation method through shallow quantum circuits illustrating the feasibility of the algorithm for near-term quantum hardware., Comment: 15 pages, 8 figures, presented at QTML 2023

Despite major advances in artificial intelligence (AI) for medicine and healthcare, the deployment and adoption of AI technologies remain limited in real-world clinical practice. In recent years, concerns have been raised about the technical, clinical, ethical and legal risks associated with medical AI. To increase real world adoption, it is essential that medical AI tools are trusted and accepted by patients, clinicians, health organisations and authorities. This work describes the FUTURE-AI guideline as the first international consensus framework for guiding the development and deployment of trustworthy AI tools in healthcare. The FUTURE-AI consortium was founded in 2021 and currently comprises 118 inter-disciplinary experts from 51 countries representing all continents, including AI scientists, clinicians, ethicists, and social scientists. Over a two-year period, the consortium defined guiding principles and best practices for trustworthy AI through an iterative process comprising an in-depth literature review, a modified Delphi survey, and online consensus meetings. The FUTURE-AI framework was established based on 6 guiding principles for trustworthy AI in healthcare, i.e. Fairness, Universality, Traceability, Usability, Robustness and Explainability. Through consensus, a set of 28 best practices were defined, addressing technical, clinical, legal and socio-ethical dimensions. The recommendations cover the entire lifecycle of medical AI, from design, development and validation to regulation, deployment, and monitoring. FUTURE-AI is a risk-informed, assumption-free guideline which provides a structured approach for constructing medical AI tools that will be trusted, deployed and adopted in real-world practice. Researchers are encouraged to take the recommendations into account in proof-of-concept stages to facilitate future translation towards clinical practice of medical AI.

This paper introduces a novel approach to probabilistic deep learning, kernel density matrices, which provide a simpler yet effective mechanism for representing joint probability distributions of both continuous and discrete random variables. In quantum mechanics, a density matrix is the most general way to describe the state of a quantum system. This work extends the concept of density matrices by allowing them to be defined in a reproducing kernel Hilbert space. This abstraction allows the construction of differentiable models for density estimation, inference, and sampling, and enables their integration into end-to-end deep neural models. In doing so, we provide a versatile representation of marginal and joint probability distributions that allows us to develop a differentiable, compositional, and reversible inference procedure that covers a wide range of machine learning tasks, including density estimation, discriminative learning, and generative modeling. The broad applicability of the framework is illustrated by two examples: an image classification model that can be naturally transformed into a conditional generative model, and a model for learning with label proportions that demonstrates the framework's ability to deal with uncertainty in the training samples. The framework is implemented as a library and is available at: https://github.com/fagonzalezo/kdm.

Machine Learning (ML) is being used in multiple disciplines due to its powerful capability to infer relationships within data. In particular, Software Engineering (SE) is one of those disciplines in which ML has been used for multiple tasks, like software categorization, bugs prediction, and testing. In addition to the multiple ML applications, some studies have been conducted to detect and understand possible pitfalls and issues when using ML. However, to the best of our knowledge, only a few studies have focused on presenting ML best practices or guidelines for the application of ML in different domains. In addition, the practices and literature presented in previous literature (i) are domain-specific (e.g., concrete practices in biomechanics), (ii) describe few practices, or (iii) the practices lack rigorous validation and are presented in gray literature. In this paper, we present a study listing 127 ML best practices systematically mining 242 posts of 14 different Stack Exchange (STE) websites and validated by four independent ML experts. The list of practices is presented in a set of categories related to different stages of the implementation process of an ML-enabled system; for each practice, we include explanations and examples. In all the practices, the provided examples focus on SE tasks. We expect this list of practices could help practitioners to understand better the practices and use ML in a more informed way, in particular newcomers to this new area that sits at the intersection of software engineering and machine learning.

This paper presents an anomaly detection model that combines the strong statistical foundation of density-estimation-based anomaly detection methods with the representation-learning ability of deep-learning models. The method combines an autoencoder, for learning a low-dimensional representation of the data, with a density-estimation model based on random Fourier features and density matrices in an end-to-end architecture that can be trained using gradient-based optimization techniques. The method predicts a degree of normality for new samples based on the estimated density. A systematic experimental evaluation was performed on different benchmark datasets. The experimental results show that the method performs on par with or outperforms other state-of-the-art methods., Comment: 10 pages

This paper presents a novel density estimation method for anomaly detection using density matrices (a powerful mathematical formalism from quantum mechanics) and Fourier features. The method can be seen as an efficient approximation of Kernel Density Estimation (KDE). A systematic comparison of the proposed method with eleven state-of-the-art anomaly detection methods on various data sets is presented, showing competitive performance on different benchmark data sets. The method is trained efficiently and it uses optimization to find the parameters of data embedding. The prediction phase complexity of the proposed algorithm is constant relative to the training data size, and it performs well in data sets with different anomaly rates. Its architecture allows vectorization and can be implemented on GPU/TPU hardware., Comment: 10 pages, 1 figure

Streaming anomaly detection refers to the problem of detecting anomalous data samples in streams of data. This problem poses challenges that classical and deep anomaly detection methods are not designed to cope with, such as conceptual drift and continuous learning. State-of-the-art flow anomaly detection methods rely on fixed memory using hash functions or nearest neighbors that may not be able to constrain high-frequency values as in a moving average or remove seamless outliers and cannot be trained in an end-to-end deep learning architecture. We present a new incremental anomaly detection method that performs continuous density estimation based on random Fourier features and the mechanism of quantum measurements and density matrices that can be viewed as an exponential moving average density. It can process potentially endless data and its update complexity is constant $O(1)$. A systematic evaluation against 12 state-of-the-art streaming anomaly detection algorithms using 12 streaming datasets is presented., Comment: 15 pages, 3 figures

Governments have to supervise and inspect social economy enterprises (SEEs). However, inspecting all SEEs is not possible due to the large number of SEEs and the low number of inspectors in general. We proposed a prediction model based on a machine learning approach. The method was trained with the random forest algorithm with historical data provided by each SEE. Three consecutive periods of data were concatenated. The proposed method uses these periods as input data and predicts the risk of each SEE in the fourth period. The model achieved 76\% overall accuracy. In addition, it obtained good accuracy in predicting the high risk of a SEE. We found that the legal nature and the variation of the past-due portfolio are good predictors of the future risk of a SEE. Thus, the risk of a SEE in a future period can be predicted by a supervised machine learning method. Predicting the high risk of a SEE improves the daily work of each inspector by focusing only on high-risk SEEs., Comment: 8 pages, 1 figure

Kernel density estimation (KDE) is one of the most widely used nonparametric density estimation methods. The fact that it is a memory-based method, i.e., it uses the entire training data set for prediction, makes it unsuitable for most current big data applications. Several strategies, such as tree-based or hashing-based estimators, have been proposed to improve the efficiency of the kernel density estimation method. The novel density kernel density estimation method (DMKDE) uses density matrices, a quantum mechanical formalism, and random Fourier features, an explicit kernel approximation, to produce density estimates. This method has its roots in the KDE and can be considered as an approximation method, without its memory-based restriction. In this paper, we systematically evaluate the novel DMKDE algorithm and compare it with other state-of-the-art fast procedures for approximating the kernel density estimation method on different synthetic data sets. Our experimental results show that DMKDE is on par with its competitors for computing density estimates and advantages are shown when performed on high-dimensional data. We have made all the code available as an open source software repository., Comment: 9 pages, 3 figures, 1 table

Density estimation is a fundamental task in statistics and machine learning applications. Kernel density estimation is a powerful tool for non-parametric density estimation in low dimensions; however, its performance is poor in higher dimensions. Moreover, its prediction complexity scale linearly with more training data points. This paper presents a method for neural density estimation that can be seen as a type of kernel density estimation, but without the high prediction computational complexity. The method is based on density matrices, a formalism used in quantum mechanics, and adaptive Fourier features. The method can be trained without optimization, but it could be also integrated with deep learning architectures and trained using gradient descent. Thus, it could be seen as a form of neural density estimation method. The method was evaluated in different synthetic and real datasets, and its performance compared against state-of-the-art neural density estimation methods, obtaining competitive results., Comment: 14 pages, 6 figures, 2 tables

We consider the Feynman-Kitaev formalism applied to a spin chain described by the transverse field Ising model. This formalism consists of building a Hamiltonian whose ground state encodes the time evolution of the spin chain at discrete time steps. To find this ground state, variational wave functions parameterised by artificial neural networks -- also known as neural quantum states (NQSs) -- are used. Our work focuses on assessing, in the context of the Feynman-Kitaev formalism, two properties of NQSs: expressivity (the possibility that variational parameters can be set to values such that the NQS is faithful to the true ground state of the system) and trainability (the process of reaching said values). We find that the considered NQSs are capable of accurately approximating the true ground state of the system, i.e., they are expressive enough ans\"atze. However, extensive hyperparameter tuning experiments show that, empirically, reaching the set of values for the variational parameters that correctly describe the ground state becomes ever more difficult as the number of time steps increase because the true ground state becomes more entangled, and the probability distribution starts to spread across the Hilbert space canonical basis., Comment: 20 pages, 4 figures

We demonstrate the implementation of a novel machine learning framework for probability density estimation and classification using quantum circuits. The framework maps a training data set or a single data sample to the quantum state of a physical system through quantum feature maps. The quantum state of the arbitrarily large training data set summarises its probability distribution in a finite-dimensional quantum wave function. By projecting the quantum state of a new data sample onto the quantum state of the training data set, one can derive statistics to classify or estimate the density of the new data sample. Remarkably, the implementation of our framework on a real quantum device does not require any optimisation of quantum circuit parameters. Nonetheless, we discuss a variational quantum circuit approach that could leverage quantum advantage for our framework., Comment: Paper condensing experiments shown in QTML 2021

This paper presents a hybrid classical-quantum program for density estimation and supervised classification. The program is implemented as a quantum circuit in a high-dimensional quantum computer simulator. We show that the proposed quantum protocols allow to estimate probability density functions and to make predictions in a supervised learning manner. This model can be generalized to find expected values of density matrices in high-dimensional quantum computers. Experiments on various data sets are presented. Results show that the proposed method is a viable strategy to implement supervised classification and density estimation in a high-dimensional quantum computer., Comment: 15 pages, 10 figures

This paper presents the Deep Bag-of-Sub-Emotions (DeepBoSE), a novel deep learning model for depression detection in social media. The model is formulated such that it internally computes a differentiable Bag-of-Features (BoF) representation that incorporates emotional information. This is achieved by a reinterpretation of classical weighting schemes like term frequency-inverse document frequency into probabilistic deep learning operations. An important advantage of the proposed method is that it can be trained under the transfer learning paradigm, which is useful to enhance conventional BoF models that cannot be directly integrated into deep learning architectures. Experiments were performed in the eRisk17 and eRisk18 datasets for the depression detection task; results show that DeepBoSE outperforms conventional BoF representations and it is competitive with the state of the art, achieving a F1-score over the positive class of 0.64 in eRisk17 and 0.65 in eRisk18.

A density matrix describes the statistical state of a quantum system. It is a powerful formalism to represent both the quantum and classical uncertainty of quantum systems and to express different statistical operations such as measurement, system combination and expectations as linear algebra operations. This paper explores how density matrices can be used as a building block for machine learning models exploiting their ability to straightforwardly combine linear algebra and probability. One of the main results of the paper is to show that density matrices coupled with random Fourier features could approximate arbitrary probability distributions over $\mathbb{R}^n$. Based on this finding the paper builds different models for density estimation, classification and regression. These models are differentiable, so it is possible to integrate them with other differentiable components, such as deep learning architectures and to learn their parameters using gradient-based optimization. In addition, the paper presents optimization-less training strategies based on estimation and model averaging. The models are evaluated in benchmark tasks and the results are reported and discussed., Comment: Final version published in Quantum Mach. Intell. 4, 23 (2022)

Diabetic Retinopathy (DR) is one of the microvascular complications of Diabetes Mellitus, which remains as one of the leading causes of blindness worldwide. Computational models based on Convolutional Neural Networks represent the state of the art for the automatic detection of DR using eye fundus images. Most of the current work address this problem as a binary classification task. However, including the grade estimation and quantification of predictions uncertainty can potentially increase the robustness of the model. In this paper, a hybrid Deep Learning-Gaussian process method for DR diagnosis and uncertainty quantification is presented. This method combines the representational power of deep learning, with the ability to generalize from small datasets of Gaussian process models. The results show that uncertainty quantification in the predictions improves the interpretability of the method as a diagnostic support tool. The source code to replicate the experiments is publicly available at https://github.com/stoledoc/DLGP-DR-Diagnosis.

The dissimilarity mixture autoencoder (DMAE) is a neural network model for feature-based clustering that incorporates a flexible dissimilarity function and can be integrated into any kind of deep learning architecture. It internally represents a dissimilarity mixture model (DMM) that extends classical methods like K-Means, Gaussian mixture models, or Bregman clustering to any convex and differentiable dissimilarity function through the reinterpretation of probabilities as neural network representations. DMAE can be integrated with deep learning architectures into end-to-end models, allowing the simultaneous estimation of the clustering and neural network's parameters. Experimental evaluation was performed on image and text clustering benchmark datasets showing that DMAE is competitive in terms of unsupervised classification accuracy and normalized mutual information. The source code with the implementation of DMAE is publicly available at: https://github.com/juselara1/dmae, Comment: 20 pages (2.5 pages of references)

This paper reports a novel method for supervised machine learning based on the mathematical formalism that supports quantum mechanics. The method uses projective quantum measurement as a way of building a prediction function. Specifically, the relationship between input and output variables is represented as the state of a bipartite quantum system. The state is estimated from training samples through an averaging process that produces a density matrix. Prediction of the label for a new sample is made by performing a projective measurement on the bipartite system with an operator, prepared from the new input sample, and applying a partial trace to obtain the state of the subsystem representing the output. The method can be seen as a generalization of Bayesian inference classification and as a type of kernel-based learning method. One remarkable characteristic of the method is that it does not require learning any parameters through optimization. We illustrate the method with different 2-D classification benchmark problems and different quantum information encodings., Comment: Supplementary material integrated into main text. Typos corrected

The main goal of this paper is to explore latent topic analysis (LTA), in the context of quantum information retrieval. LTA is a valuable technique for document analysis and representation, which has been extensively used in information retrieval and machine learning. Different LTA techniques have been proposed, some based on geometrical modeling (such as latent semantic analysis, LSA) and others based on a strong statistical foundation. However, these two different approaches are not usually mixed. Quantum information retrieval has the remarkable virtue of combining both geometry and probability in a common principled framework. We built on this quantum framework to propose a new LTA method, which has a clear geometrical motivation but also supports a well-founded probabilistic interpretation. An initial exploratory experimentation was performed on three standard data sets. The results show that the proposed method outperforms LSA on two of the three datasets. These results suggests that the quantum-motivated representation is an alternative for geometrical latent topic modeling worthy of further exploration., Comment: ICTIR2011 International Conference on the Theory of Information Retrieval