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Artificial Neuronal Networks are models widely used for many scientific tasks. One of the well-known field of application is the approximation of high-dimensional problems via Deep Learning. In the present paper we investigate the Deep…
The notion of probability density for a random function is not as straightforward as in finite-dimensional cases. While a probability density function generally does not exist for functional data, we show that it is possible to develop the…
It is common practice in deep learning to represent a measurement of the world on a discrete grid, e.g. a 2D grid of pixels. However, the underlying signal represented by these measurements is often continuous, e.g. the scene depicted in an…
Aggregation of large databases in a specific format is a frequently used process to make the data easily manageable. Interval-valued data is one of the data types that is generated by such an aggregation process. Using traditional methods…
This is a tutorial introduction to the functional analysis mathematics needed in many physical problems, such as in waves in continuous media. Functional analysis takes us beyond finite matrices, allowing us to work with infinite sets of…
We introduce derivation depth-a computable metric of the reasoning effort needed to answer a query based on a given set of premises. We model information as a two-layered structure linking abstract knowledge with physical carriers, and…
Image Segmentation has been an active field of research as it has a wide range of applications, ranging from automated disease detection to self-driving cars. In the past five years, various papers came up with different objective loss…
Deep learning (DL) shows promise of advantages over conventional signal processing techniques in a variety of imaging applications. The networks' being trained from examples of data rather than explicitly designed allows them to learn…
Given a statistical functional of interest such as the mean or median, a (strict) identification function is zero in expectation at (and only at) the true functional value. Identification functions are key objects in forecast validation,…
Depth perception is fundamental for robots to understand the surrounding environment. As the view of cognitive neuroscience, visual depth perception methods are divided into three categories, namely binocular, active, and pictorial. The…
Deep learning has arguably achieved tremendous success in recent years. In simple words, deep learning uses the composition of many nonlinear functions to model the complex dependency between input features and labels. While neural networks…
Situations of a functional predictor paired with a scalar response are increasingly encountered in data analysis. Predictors are often appropriately modeled as square integrable smooth random functions. Imposing minimal assumptions on the…
The applications of traditional statistical feature selection methods to high-dimension, low sample-size data often struggle and encounter challenging problems, such as overfitting, curse of dimensionality, computational infeasibility, and…
Centrality descriptors are widely used to rank nodes according to specific concept(s) of importance. Despite the large number of centrality measures available nowadays, it is still poorly understood how to identify the node which can be…
Functional Spectral Imaging (FSI) models image formation as the recovery of tissue surrogates such as density and stiffness from spectral perturbations of a self-adjoint elliptic operator. Rather than relying on reflectivity or relaxation…
In the last years, deep learning has dramatically improved the performances in a variety of medical image analysis applications. Among different types of deep learning models, convolutional neural networks have been among the most…
For the purpose of monitoring the behavior of complex infrastructures (e.g. aircrafts, transport or energy networks), high-rate sensors are deployed to capture multivariate data, generally unlabeled, in quasi continuous-time to detect…
Various 3D semantic attributes such as segmentation masks, geometric features, keypoints, and materials can be encoded as per-point probe functions on 3D geometries. Given a collection of related 3D shapes, we consider how to jointly…
The popularity of transformer-based text embeddings calls for better statistical tools for measuring distributions of such embeddings. One such tool would be a method for ranking texts within a corpus by centrality, i.e. assigning each text…
Functional Principal Component Analysis is a reference method for dimension reduction of curve data. Its theoretical properties are now well understood in the simplified case where the sample curves are fully observed without noise.…