Generalized Bhattacharyya and Chernoff upper bounds on Bayes error using quasi-arithmetic means

Revisiting Chernoff Information with Likelihood Ratio Exponential Families

The Chernoff information between two probability measures is a statistical divergence measuring their deviation defined as their maximally skewed Bhattacharyya distance. Although the Chernoff information was originally introduced for bounding the Bayes error in statistical hypothesis testing, the divergence found many other applications due to its empirical robustness property found in applications ranging from information fusion to quantum information. From the viewpoint of information theory, the Chernoff information can also be interpreted as a minmax symmetrization of the Kullback-Leibler divergence. In this paper, we first revisit the Chernoff information between two densities of a measurable Lebesgue space by considering the exponential families induced by their geometric mixtures: The so-called likelihood ratio exponential families. Second, we show how to (i) solve exactly the Chernoff information between any two univariate Gaussian distributions or get a closed-form formula using symbolic computing, (ii) report a closed-form formula of the Chernoff information of centered Gaussians with scaled covariance matrices and (iii) use a fast numerical scheme to approximate the Chernoff information between any two multivariate Gaussian distributions.

On Training Road Surface Classifiers by Data Augmentation

It is demonstrated that data augmentation is a promising approach to reduce the size of the captured dataset required for training automatic road surface classifiers. The context is on-board systems for autonomous or semi-autonomous driving assistance: automatic power-assisted steering. Evidence is obtained by extensive experiments involving multiple captures from a 10-channel multisensor deployment: three channels from the accelerometer (acceleration in the X, Y, and Z axes); three microphone channels; two speed channels; and the torque and position of the handwheel. These captures were made under different settings: three worm-gear interface configurations; hands on or off the wheel; vehicle speed (constant speed of 10, 15, 20, 30 km/h, or accelerating from 0 to 30 km/h); and road surface (smooth flat asphalt, stripes, or cobblestones). It has been demonstrated in the experiments that data augmentation allows a reduction by an approximate factor of 1.5 in the size of the captured training dataset.

Two-dimensional Bhattacharyya bound linear discriminant analysis with its applications

The recently proposed L2-norm linear discriminant analysis criterion based on Bhattacharyya error bound estimation (L2BLDA) was an effective improvement over linear discriminant analysis (LDA) and was used to handle vector input samples. When faced with two-dimensional (2D) inputs, such as images, converting two-dimensional data to vectors, regardless of the inherent structure of the image, may result in some loss of useful information. In this paper, we propose a novel two-dimensional Bhattacharyya bound linear discriminant analysis (2DBLDA). 2DBLDA maximizes the matrix-based between-class distance, which is measured by the weighted pairwise distances of class means and minimizes the matrix-based within-class distance. The criterion of 2DBLDA is equivalent to optimizing the upper bound of the Bhattacharyya error. The weighting constant between the between-class and within-class terms is determined by the involved data that make the proposed 2DBLDA adaptive. The construction of 2DBLDA avoids the small sample size (SSS) problem, is robust, and can be solved through a simple standard eigenvalue decomposition problem. The experimental results on image recognition and face image reconstruction demonstrate the effectiveness of 2DBLDA.

Sensitivity Analysis of Sentinel-1 Backscatter to Oil Palm Plantations at Pluriannual Scale: A Case Study in Gabon, Africa

The present paper focuses on a sensitivity analysis of Sentinel-1 backscattering signatures from oil palm canopies cultivated in Gabon, Africa. We employed one Sentinel-1 image per year during the 2015–2021 period creating two separated time series for both the wet and dry seasons. The first images were almost simultaneously acquired to the initial growth stage of oil palm plants. The VH and VV backscattering signatures were analysed in terms of their corresponding statistics for each date and compared to the ones corresponding to tropical forests. The times series for the wet season showed that, in a time interval of 2–3 years after oil palm plantation, the VV/VH ratio in oil palm parcels increases above the one for forests. Backscattering and VV/VH ratio time series for the dry season exhibit similar patterns as for the wet season but with a more stable behaviour. The separability of oil palm and forest classes was also quantitatively addressed by means of the Jeffries–Matusita distance, which seems to point to the C-band VV/VH ratio as a potential candidate for discrimination between oil palms and natural forests, although further analysis must still be carried out. In addition, issues related to the effect of the number of samples in this particular scenario were also analysed. Overall, the outcomes presented here can contribute to the understanding of the radar signatures from this scenario and to potentially improve the accuracy of mapping techniques for this type of ecosystems by using remote sensing. Nevertheless, further research is still to be done as no classification method was performed due to the lack of the required geocoded reference map. In particular, a statistical assessment of the radar signatures should be carried out to statistically characterise the observed trends.

α-Geodesical Skew Divergence

The asymmetric skew divergence smooths one of the distributions by mixing it, to a degree determined by the parameter λ, with the other distribution. Such divergence is an approximation of the KL divergence that does not require the target distribution to be absolutely continuous with respect to the source distribution. In this paper, an information geometric generalization of the skew divergence called the α-geodesical skew divergence is proposed, and its properties are studied.

On a Variational Definition for the Jensen-Shannon Symmetrization of Distances Based on the Information Radius

We generalize the Jensen-Shannon divergence and the Jensen-Shannon diversity index by considering a variational definition with respect to a generic mean, thereby extending the notion of Sibson's information radius. The variational definition applies to any arbitrary distance and yields a new way to define a Jensen-Shannon symmetrization of distances. When the variational optimization is further constrained to belong to prescribed families of probability measures, we get relative Jensen-Shannon divergences and their equivalent Jensen-Shannon symmetrizations of distances that generalize the concept of information projections. Finally, we touch upon applications of these variational Jensen-Shannon divergences and diversity indices to clustering and quantization tasks of probability measures, including statistical mixtures.

Strongly Convex Divergences

We consider a sub-class of the f-divergences satisfying a stronger convexity property, which we refer to as strongly convex, or κ-convex divergences. We derive new and old relationships, based on convexity arguments, between popular f-divergences.

An Elementary Introduction to Information Geometry

In this survey, we describe the fundamental differential-geometric structures of information manifolds, state the fundamental theorem of information geometry, and illustrate some use cases of these information manifolds in information sciences. The exposition is self-contained by concisely introducing the necessary concepts of differential geometry. Proofs are omitted for brevity.

On the Jensen-Shannon Symmetrization of Distances Relying on Abstract Means

The Jensen-Shannon divergence is a renowned bounded symmetrization of the unbounded Kullback-Leibler divergence which measures the total Kullback-Leibler divergence to the average mixture distribution. However, the Jensen-Shannon divergence between Gaussian distributions is not available in closed form. To bypass this problem, we present a generalization of the Jensen-Shannon (JS) divergence using abstract means which yields closed-form expressions when the mean is chosen according to the parametric family of distributions. More generally, we define the JS-symmetrizations of any distance using parameter mixtures derived from abstract means. In particular, we first show that the geometric mean is well-suited for exponential families, and report two closed-form formula for (i) the geometric Jensen-Shannon divergence between probability densities of the same exponential family; and (ii) the geometric JS-symmetrization of the reverse Kullback-Leibler divergence between probability densities of the same exponential family. As a second illustrating example, we show that the harmonic mean is well-suited for the scale Cauchy distributions, and report a closed-form formula for the harmonic Jensen-Shannon divergence between scale Cauchy distributions. Applications to clustering with respect to these novel Jensen-Shannon divergences are touched upon.

Integration of in vitro and in silico Models Using Bayesian Optimization With an Application to Stochastic Modeling of Mesenchymal 3D Cell Migration

Cellular migration plays a crucial role in many aspects of life and development. In this paper, we propose a computational model of 3D migration that is solved by means of the tau-leaping algorithm and whose parameters have been calibrated using Bayesian optimization. Our main focus is two-fold: to optimize the numerical performance of the mechano-chemical model as well as to automate the calibration process of in silico models using Bayesian optimization. The presented mechano-chemical model allows us to simulate the stochastic behavior of our chemically reacting system in combination with mechanical constraints due to the surrounding collagen-based matrix. This numerical model has been used to simulate fibroblast migration. Moreover, we have performed in vitro analysis of migrating fibroblasts embedded in 3D collagen-based fibrous matrices (2 mg/ml). These in vitro experiments have been performed with the main objective of calibrating our model. Nine model parameters have been calibrated testing 300 different parametrizations using a completely automatic approach. Two competing evaluation metrics based on the Bhattacharyya coefficient have been defined in order to fit the model parameters. These metrics evaluate how accurately the in silico model is replicating in vitro measurements regarding the two main variables quantified in the experimental data (number of protrusions and the length of the longest protrusion). The selection of an optimal parametrization is based on the balance between the defined evaluation metrics. Results show how the calibrated model is able to predict the main features observed in the in vitro experiments.

Pedestrian Tracking Based on Camshift with Kalman Prediction for Autonomous Vehicles

Pedestrian detection and tracking is the key to autonomous vehicle navigation systems avoiding potentially dangerous situations. Firstly, the probability distribution of colour information is established after a pedestrian is located in an image. Then the detected results are utilized to initialize a Kalman filter to predict the possible position of the pedestrian centroid in the future frame. A Camshift tracking algorithm is used to track the pedestrian in the specific search window of the next frame based on the prediction results. The actual position of the pedestrian centroid is output from the Camshift tracking algorithm to update the gain and error covariance matrix of the Kalman filter. Experimental results in real traffic situations show the proposed pedestrian tracking algorithm can achieve good performance even when they are partly occluded in inconsistent illumination circumstances.