Related papers: Simultaneous off-the-grid learning of mixtures iss…
We consider a general non-linear model where the signal is a finite mixture of an unknown, possibly increasing, number of features issued from a continuous dictionary parameterized by a real non-linear parameter. The signal is observed with…
We consider a model where a signal (discrete or continuous) is observed with an additive Gaussian noise process. The signal is issued from a linear combination of a finite but increasing number of translated features. The features are…
Signal extraction out of background noise is a common challenge in high precision physics experiments, where the measurement output is often a continuous data stream. To improve the signal to noise ratio of the detection, witness sensors…
A central question in modern machine learning and imaging sciences is to quantify the number of effective parameters of vastly over-parameterized models. The degrees of freedom is a mathematically convenient way to define this number of…
A popular approach within the signal processing and machine learning communities consists in modelling signals as sparse linear combinations of atoms selected from a learned dictionary. While this paradigm has led to numerous empirical…
The explicit regularization and optimality of deep neural networks estimators from independent data have made considerable progress recently. The study of such properties on dependent data is still a challenge. In this paper, we carry out…
In this paper we analyze the asymptotic properties of l1 penalized maximum likelihood estimation of signals with piece-wise constant mean values and/or variances. The focus is on segmentation of a non-stationary time series with respect to…
We study the problem of learning a directed acyclic graph from data generated according to an additive, non-linear structural equation model with Gaussian noise. We express each non-linear function through a basis expansion, and derive a…
Anomalies and outliers are common in real-world data, and they can arise from many sources, such as sensor faults. Accordingly, anomaly detection is important both for analyzing the anomalies themselves and for cleaning the data for further…
Off-the-grid regularisation has been extensively employed over the last decade in the context of ill-posed inverse problems formulated in the continuous setting of the space of Radon measures $\mathcal{M}(\mathcal{X})$. These approaches…
The multivariate linear regression model with shuffled data and additive Gaussian noise arises in various correspondence estimation and matching problems. Focusing on the denoising aspect of this problem, we provide a characterization the…
We study the problem of estimating multiple linear regression equations for the purpose of both prediction and variable selection. Following recent work on multi-task learning Argyriou et al. [2008], we assume that the regression vectors…
Many empirical studies suggest that samples of continuous-time signals taken at locations randomly deviated from an equispaced grid (i.e., off-the-grid) can benefit signal acquisition, e.g., undersampling and anti-aliasing. However,…
Mixtures of Linear Regressions (MLR) is an important mixture model with many applications. In this model, each observation is generated from one of the several unknown linear regression components, where the identity of the generated…
We consider the analysis of continuous repeated measurement outcomes that are collected through time, also known as longitudinal data. A standard framework for analysing data of this kind is a linear Gaussian mixed-effects model within…
While graphical models for continuous data (Gaussian graphical models) and discrete data (Ising models) have been extensively studied, there is little work on graphical models linking both continuous and discrete variables (mixed data),…
Machine learning in the context of noise is a challenging but practical setting to plenty of real-world applications. Most of the previous approaches in this area focus on the pairwise relation (casual or correlational relationship) with…
The task of robust linear estimation in the presence of outliers is of particular importance in signal processing, statistics and machine learning. Although the problem has been stated a few decades ago and solved using classical…
A low-complexity model for signal quality prediction in a nonlinear fiber-optical network is developed. The model, which builds on the Gaussian noise model, takes into account the signal degradation caused by a combination of chromatic…
A large set of signals can sometimes be described sparsely using a dictionary, that is, every element can be represented as a linear combination of few elements from the dictionary. Algorithms for various signal processing applications,…