The importance of features interactions for classification tasks between two classes is proven by the abundance of high-performance machine learning methods using them. In this paper, we take our inspiration from Bayesian Networks (BNs), a famous classification method whose main asset is the graphical representation of links between features. In the case of discrete feature, we assume that the features follow a tree-based distribution under each class. Then, we show that the optimal Bayes classifier coincides with a logistic regression whose features are one-hot encoded with a specific scheme. We show the advantages of such an approach both theoretically and numerically, especially showing that the learning step always converges toward a unique solution. Simulated experiments confirm the efficiency of the one-hot logistic regression with feature interaction encoding.

Radiomics maps digital medical images into quantitative data with the end goal of generating imaging biomarkers as decision support tools for clinical practice. Radiomics features are extracted from biomedical images and then process with machine learning algorithms. Logistic regression is a very common machine learning technique to investigate radiomics features but its linearity limits its performance. In this paper, we propose a non-linear logistic regression based on features binning. It is shown that this non-linear regression coincides with the naive Bayes classifier. Furthermore, it is shown that each radiomics feature is associated with a reliable feature profile. This profile allows us to interpret the importance of the feature in the original biomedical image. We illustrate our theoretical results with two radiomics datasets.

ReLU neural networks suffer from a problem of explainability because they partition the input space into a lot of polyhedrons. This paper proposes a constrained neural network model that replaces polyhedrons by orthotopes: each hidden neuron processes only a single component of the input signal. When the number of hidden neurons is large, we show that our neural network is equivalent to a logistic regression whose input is a non-linear transformation of the processed signal. Hence, the training of our neural network always converges to a unique solution. Numerical simulations show that the loss of performance with respect to state-of-the-art methods is negligible even though our neural network is strongly constrained on robustness and explainability.

This paper proposes an understandable neural network whose score function is modeled as an additive sum of univariate spline functions. It extends usual understandable models like generative additive models, spline-based models, and neural additive models. It is shown that this neural network can be approximated by a logistic regression whose inputs are obtained with a non-linear preprocessing of input data. This preprocessing depends on the neural network initialization but this paper establishes that it can be replaced by a non random kernel-based preprocessing that no longer depends on the initialization. Hence, the convergence of the training process is guaranteed and the solution is unique for a given training dataset.

This paper aims to build a supervised classifier for dealing with imbalanced datasets, uncertain class proportions, dependencies between features, the presence of both numeric and categorical features, and arbitrary loss functions. The Bayes classifier suffers when prior probability shifts occur between the training and testing sets. A solution is to look for an equalizer decision rule whose class-conditional risks are equal. Such a classifier corresponds to a minimax classifier when it maximizes the Bayes risk. We develop a novel box-constrained minimax classifier which takes into account some constraints on the priors to control the risk maximization. We analyze the empirical Bayes risk with respect to the box-constrained priors for discrete inputs. We show that this risk is a concave non-differentiable multivariate piecewise affine function. A projected subgradient algorithm is derived to maximize this empirical Bayes risk over the box-constrained simplex. Its convergence is established and its speed is bounded. The optimization algorithm is scalable when the number of classes is large. The robustness of our classifier is studied on diverse databases. Our classifier, jointly applied with a clustering algorithm to process mixed attributes, tends to equalize the class-conditional risks while being not too pessimistic.

This paper introduces a novel coding/decoding mechanism that mimics one of the most important properties of the human visual system: its ability to enhance the visual perception quality in time. In other words, the brain takes advantage of time to process and clarify the details of the visual scene. This characteristic is yet to be considered by the state-of-the-art quantization mechanisms that process the visual information regardless the duration of time it appears in the visual scene. We propose a compression architecture built of neuroscience models; it first uses the leaky integrate-and-fire (LIF) model to transform the visual stimulus into a spike train and then it combines two different kinds of spike interpretation mechanisms (SIM), the time-SIM and the rate-SIM for the encoding of the spike train. The time-SIM allows a high quality interpretation of the neural code and the rate-SIM allows a simple decoding mechanism by counting the spikes. For that reason, the proposed mechanisms is called Dual-SIM quantizer (Dual-SIMQ). We show that (i) the time-dependency of Dual-SIMQ automatically controls the reconstruction accuracy of the visual stimulus, (ii) the numerical comparison of Dual-SIMQ to the state-of-the-art shows that the performance of the proposed algorithm is similar to the uniform quantization schema while it approximates the optimal behavior of the non-uniform quantization schema and (iii) from the perceptual point of view the reconstruction quality using the Dual-SIMQ is higher than the state-of-the-art.

This paper presents a novel neuro-inspired quantization model which is the extension of the recently released perfect-Leaky Integrate and Fire (LIF) model. We propose that the LIF, which is a very efficient neuromathematical model that describes the spike generation neural mechanism, can lead to a groundbreaking and above all dynamic compression algorithm which is called LIF encoder/decoder. We also prove that under some assumptions, there is a link between the novel LIF encoder/decoder and the conventional Uniform Deadzone Quantizer (UDQ).

This paper introduces a novel filter, which is inspired by the human retina. The human retina consists of three different layers: the Outer Plexiform Layer (OPL), the inner plexiform layer, and the ganglionic layer. Our inspiration is the linear transform which takes place in the OPL and has been mathematically described by the neuroscientific model "virtual retina." This model is the cornerstone to derive the non-separable spatio-temporal OPL retina-inspired filter, briefly renamed retina-inspired filter, studied in this paper. This filter is connected to the dynamic behavior of the retina, which enables the retina to increase the sharpness of the visual stimulus during filtering before its transmission to the brain. We establish that this retina-inspired transform forms a group of spatio-temporal Weighted Difference of Gaussian (WDoG) filters when it is applied to a still image visible for a given time. We analyze the spatial frequency bandwidth of the retina-inspired filter with respect to time. It is shown that the WDoG spectrum varies from a lowpass filter to a bandpass filter. Therefore, while time increases, the retina-inspired filter enables to extract different kinds of information from the input image. Finally, we discuss the benefits of using the retina-inspired filter in image processing applications such as edge detection and compression.

This paper studies the problem of classifying some Gaussian samples into one of two parametric probabilistic models, also called sources, when the parameter and the a priori probability of each source are unknown. Each source is governed by an univariate normal distribution whose mean is unknown. A training sequence is available for each source in order to compensate the lack of prior information. An almost optimal most stringent test is proposed to solve this classification problem subject to a constrained false alarm probability. This learning-based test minimizes its maximum shortcoming with respect to the most powerful test which knows exactly the parameters of the sources. It also guarantees a prescribed false alarm probability whatever the size of the training sequences. The threshold, the probability of false alarm and the probability of correct detection are calculated analytically.

This paper addresses the detection of a suddenly arriving dynamic profile of a finite duration often called a transient change. In contrast to the traditional abrupt change detection, where the post-change period is assumed to be infinitely long, the detection of a suddenly arriving transient change should be done before it disappears. The detection of transient changes after their disappearance is considered as missed. Hence, the traditional quickest change detection criterion, minimizing the average detection delays provided a prescribed false alarm rate, is compromised. The proposed optimality criterion minimizes the worst case probability of missed detection provided that the worst case probability of false alarm during a certain period is upper bounded. A suboptimal CUSUM-type transient change detection algorithm, based on a subclass of truncated Sequential Probability Ratio Tests, is proposed. The optimization of the proposed algorithm in this subclass leads to a specially designed Finite Moving Average Test. The proposed method is analyzed theoretically and by simulation. A special attention is paid to the case of Gaussian observations with a dynamic profile.

In this paper, we aim to propose a video codec based on the novel retina-inspired filter and retina-inspired quantizer which both perform according to the early visual system. The recently released non-separable spatiotemporal OPL retina-inspired filter enables to progressively extract different kind of information from the input signal which is the sequence of pictures of a video stream. This retina inspired transform has been proven to be a redundant frame which ensures a perfect reconstruction when no quantization appears. The reduction of this redundancy is achieved by a quantization which is inspired by the spike generation mechanism of ganglion cells. This mechanism has been approximated by the Rank Order Coder (ROC) and the Leaky-Integrate and Fire (LIF) models. The ROC model encodes the rank of the spikes and it has been proposed as a complete and very efficient codec for still-images. However, its limitations concerning the reconstruction method forced us to focus our attention on LIF which encodes the spike delays. We approximate the LIF by a scalar quantizer with a dead-zone. This is the first attempt to build a complete retina-inspired video codec which gives promising reconstruction results at low bitrate and high reconstruction quality.

This paper introduces a novel non-Separable sPAtioteMporal filter (non-SPAM) which enables the spatiotemporal decomposition of a still-image. The construction of this filter is inspired by the model of the retina which is able to selectively transmit information to the brain. The non-SPAM filter mimics the retinal-way to extract necessary information for a dynamic encoding/decoding system. We applied the non-SPAM filter on a still image which is flashed for a long time. We prove that the non-SPAM filter decomposes the still image over a set of time-varying difference of Gaussians, which form a frame. We simulate the analysis and synthesis system based on this frame. This system results in a progressive reconstruction of the input image. Both the theoretical and numerical results show that the quality of the reconstruction improves while the time increases.

This paper addresses the problem of discriminating two different vector lines from a non-zero mean Gaussian noise vector. Under each hypothesis, the Gaussian noise vector is completely characterized by its expected value which belongs to a known vector line. A new criterion of optimality, namely the epsilon most stringent test, is proposed and studied. This criterion consists in minimizing the maximum shortcoming of the test, up to a small loss, subject to a constrained false alarm probability. The maximum shortcoming corresponds to the maximum gap between the power function of the test and the envelope power function which is defined as the supremum of the power over all tests satisfying the prescribed false alarm probability. It is numerically shown that the proposed test outperforms the generalized likelihood ratio test.

The paper addresses random field time series analysis and simulation. The analysis constrains a spatial isotropic fractional Brownian field to a dynamic temporal behavior from separable time varying Hurst parameters. The constrained dynamic applies by embedding the wavelet packet spectrum of the input random field into different spectra associated with the same random family (exponential spectrum decay). The paper highlights the relevance of the approach for representing and simulating isotropic light source and cloud dynamics.

Asynchronous event-based cameras use time encoding to code the pixel intensity values. A time encoding of a random valued pixel is a representation of the intensity of this pixel as a random sequence of strictly increasing times. The goal of this paper is the estimation of the pixel mean value from asynchronous samples given by the integrate and fire time encoding. The optimal uniformly minimum variance unbiased estimator is calculated and its statistical performance is compared with a conventional frame-based estimator which exploits regular samples of the pixel intensity. Time encoding significantly reduces the mean number of bits needed to minimize the mean square error of the estimate. Hence, time encoding saves power compared to regular sampling.

This paper deals with stego-image steganalysis to detect hidden information in natural images. Hidden bits are embedded by using the Least Significant Bit (LSB) replacement mechanism. We address the problem of learning the weights which characterize the structure and the performance of the standard Weighted Stego-image (WS) detector. In this paper we propose a new Hybrid Weighted Stego-detection (HWS) algorithm. We assume that the WS weights are related to the image pixels variance through an unknown function which is decomposed onto a set of known basis functions. This yields a linear detector which consists of a linear combination of parametric features derived from the structure of the standard WS detector. The coefficients of the linear combination are learnt by minimizing calibrated losses using stochastic gradient descent or a more efficient stochastic Newton descent approach. Thus, the HWS algorithm benefits from two fundamental advantages: the posterior probability of detection is well estimated and the numerical complexity of the algorithm is linear with the number of samples and the dimension of the features. The benchmark on real images shows that HWS method outperforms standard WS baseline method.

This paper adresses the voice activity detection problem within a semiparametric hypothesis testing framework. Semiparametric detection consists in combining the statistical optimality of a parametric test with the robustness regarding the learning data of a nonparametric test. The proposed semiparametric approach splits the frame vector into two parts such that the first part has a known statistical distribution. The second part is processed by a non-parametric detector producing a binary decision. A likelihood ratio test, based on the first part and the nonparametric binary decision, is then applied to classify the frame as either speech or nonspeech. The statistical performance of the resulting fusion test is analytically established and validated using real speech signals.

Semiparametric detection consists of combining the statistical optimality of a parametric test to the robustness regarding the data of a nonparametric test. This approach is specially interesting in presence of statistical hypotheses depending on unknown probability distributions. The proposed semiparametric approach consists of splitting the measurement vector into two parts such that the first part has a known statistical distribution. Then, it is proposed to calculate a likelihood ratio test based both on the first part and the detection result of a nonparametric test applied to the second part. The statistical performance of the proposed test is analytically established.

The goal of this paper is to propose the optimal statistical test based on the modeling of discrete cosine transform (DCT) coefficients with a quantified Laplacian distribution. This paper focuses on the detection of hidden information embedded in bits of the DCT coefficients of a JPEG image. This problem is difficult, in terms of statistical decision, for two main reasons: first, the number of DCT coefficients used to conceal the hidden bits is random; second, the JPEG image compression induces a strong quantization of DCT coefficients. The proposed test explicitly takes into account the randomness of the number of DCT coefficients used. It maximizes the probability of hidden information detection by ensuring a prescribed level of false alarm.

A new estimator, optimal in the frequency domain with respect to the masking properties of the human auditory system, is proposed. This new filtering technique prevents the emergence of post-filtering isolated tonals that increase the musical noise perception. Experimental results by means of objective tests show that this technique improves the enhanced speech quality.

This paper addresses the problem of anomaly detection and classification by using a noisy measurement vector corrupted by some linear unknown nuisance parameters. An invariant constrained asymptotically uniformly minimax test is proposed. It minimizes the maximum false classification probability as the signal-to-noise ratio becomes arbitrary large, uniformly with respect to the unknown anomaly amplitude and independently on the nuisance parameters. The probability of maximum classification error is calculated in a closed-form.

In the last two decades substantial progress has been made in the detection of hidden information or hidden communication channels in media files or streams. Typically, it is necessary to reliably detect in a huge set of files (image, audio, and video) which of these files contain the hidden information. The goal of this paper is to study the problem of hypothesis testing based on quantized observations by using a parametric statistical model with nuisance parameters and to apply the obtained tests to the hidden information detection.

A constrained epsilon-equalizer test is proposed to detect and classify non-orthogonal vectors in Gaussian noise. The classification error probabilities of this test are equalized up to a negligible difference, subject to a constraint on the false alarm probability. It has a small loss of optimality with respect to the purely theoretical and incalculable constrained equalizer test provided that the norms of vectors to classify are sufficiently large. A numerical example confirms the theoretical findings.

A constrained epsilon-minimax test is proposed to detect and classify nonorthogonal vectors in Gaussian noise, with a general covariance matrix, and in presence of linear interferences. This test is epsilon-minimax in the sense that it has a small loss of optimality with respect to the purely theoretical and incalculable constrained minimax test which minimizes the maximum classification error probability subject to a constraint on the false alarm probability. This loss is even more negligible as the signal-to-noise ratio is large. Furthermore, it is also an epsilon-equalizer test since its classification error probabilities are equalized up to a negligible difference. When the signal-to-noise ratio is sufficiently large, an asymptotically equivalent test with a very simple form is proposed. This equivalent test coincides with the generalized likelihood ratio test when the vectors to classify are strongly separated in term of Euclidean distance. Numerical experiments on active user identification in a multiuser system confirm the theoretical findings.

Anomaly detection is addressed within a statistical framework. Often the statistical model is composed of two types of parameters : the informative parameters and the nuisance ones. The nuisance parameters are of no interest for detection but they are necessary to complete the model. In the case of unknown, non-random nuisance parameters, their elimination is unavoidable. Some approaches addressing the cases where the nuisance parameters, belonging to a subspace, interfere with the informative ones in a linear manner, use the theory of invariance to reject the nuisance. Sometimes this leads to a certain degradation of the detector performances because some faults become undetectable, masked by the nuisance. Nevertheless, in many cases the physical nature of nuisance parameters is (partially) known, and this knowledge may allow us to define inequality bounds to limit the variations of these parameters. The goal of this paper is to study the statistical performances of the constrained generalized likelihood ratio test used to detect an additive anomaly in the case of bounded nuisance parameters. An example of the integrity monitoring of GNSS train navigation illustrates the relevance of the proposed method.

Traffic Engineering (TE) has become a challenging mechanism for network management and resources optimization due to the uncertainty and the difficulty to predict current traffic patterns. Recent works have proposed robust optimization techniques to cope with uncertain traffic, computing a stable routing configuration that is immune to demand variations within certain uncertainty set. However, using a single routing configuration for long-time periods can be highly inefficient. Even more, the presence of abnormal and malicious traffic has magnified the network operation problem, claiming for solutions which not only deal with traffic uncertainty but also allow to identify faulty traffic. In this paper, we propose two complementary methods to tackle both problems. Based on expected traffic patterns, we adapt the uncertainty set and build a multi-hour yet robust routing scheme that outperforms the stable approach. For the case of anomalous and unexpected traffic, we propose a fast anomaly detection/isolation algorithm which relies on a novel linear spline-based model of traffic demands to identify traffic problems and decide routing changes. This algorithm is optimal in the sense that it minimizes the decision delay for a given mean false alarm rate and false isolation probabilities. Both proposals are validated using real traffic data from two Internet backbone networks.

The non-Bayesian detection of an anomaly from a single or a few noisy tomographic projections is considered as a statistical hypotheses testing problem. It is supposed that a radiography is composed of an imaged nonanomalous background medium, considered as a deterministic nuisance parameter, with a possibly hidden anomaly. Because the full voxel-by-voxel reconstruction is impossible, an original tomographic method based on the parametric models of the nonanomalous background medium and radiographic process is proposed to fill up the gap in the missing data. Exploiting this "parametric tomography," a new detection scheme with a limited loss of optimality is proposed as an alternative to the nonlinear generalized likelihood ratio test, which is untractable in the context of nondestructive testing for the objects with uncertainties in their physical/geometrical properties. The theoretical results are illustrated by the processing of real radiographies for the nuclear fuel rod inspection.

The paper concerns the radiographic non-destructive testing of well-manufactured objects. The detection of anomalies is addressed from the statistical point of view as a binary hypothesis testing problem with nonlinear nuisance parameters. A new detection scheme is proposed as an alternative to the classical GLR test. It is shown that this original decision rule detects anomalies with a loss of a negligible (epsiv) part of optimality with respect to an optimal invariant test designed for the "closest" hypothesis testing problem with linear nuisance parameters

The problem of detecting an anomaly/target from a limited number of noisy tomographic projections is addressed from the statistical point of view. An unknown 2D (or 3D) scene is composed of an environment, considered as a nuisance parameter, with a possibly hidden anomaly/target. A parametric approach is proposed to reduce the lack of a priori information and two statistical tests are discussed : the first one, invariant, is devoted to simply detect the presence of an unspecified anomaly and the second one is able to simultaneously detect and localize the projection of a size limited anomaly.