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We present an efficient algorithm for recent generalizations of optimal mass transport theory to matrix-valued and vector-valued densities. These generalizations lead to several applications including diffusion tensor imaging, color images…
In this paper, we compare the performance of different numerical schemes in approximating Pontryagin's Maximum Principle's necessary conditions for the optimal control of nonholonomic systems. Retraction maps are used as a seed to construct…
Our approach to higher order Fourier analysis is to study the ultra product of finite (or compact) Abelian groups on which a new algebraic theory appears. This theory has consequences on finite (or compact) groups usually in the form of…
We reconsider the variational integration of optimal control problems for mechanical systems based on a direct discretization of the Lagrange-d'Alembert principle. This approach yields discrete dynamical constraints which by construction…
Deep neural networks do not discriminate between spurious and causal patterns, and will only learn the most predictive ones while ignoring the others. This shortcut learning behaviour is detrimental to a network's ability to generalize to…
We consider the problem of estimating a low-rank signal matrix from noisy measurements under the assumption that the distribution of the data matrix belongs to an exponential family. In this setting, we derive generalized Stein's unbiased…
Asymptotic expressions of the mutual information between any discrete input and the corresponding output of the scalar additive white Gaussian noise channel are presented in the limit as the signal-to-noise ratio (SNR) tends to infinity.…
The inference of a large symmetric signal-matrix $\mathbf{S} \in \mathbb{R}^{N\times N}$ corrupted by additive Gaussian noise, is considered for two regimes of growth of the rank $M$ as a function of $N$. For sub-linear ranks…
We develop Brenier theorems on iterated Wasserstein spaces. For a separable Hilbert space $H$ and $N\geq 1$, we construct a full-support probability $\Lambda$ on $P_2^{N}(H)= P_2(... P_2(H)...)$ that is transport regular: for every $Q$ with…
I--MR charts commonly estimate the process standard deviation $\sigma$ via the span-2 average moving range divided by the unbiasing constant $d_2$; unlike the unbiased sample standard deviation ($S/c_4$), this estimator depends on ordering…
We consider the problem of finding the subset of order statistics that contains the most information about a sample of random variables drawn independently from some known parametric distribution. We leverage information-theoretic…
The estimation of correspondences between two images resp. point sets is a core problem in computer vision. One way to formulate the problem is graph matching leading to the quadratic assignment problem which is NP-hard. Several so called…
Three classes of algorithms to learn the structure of Bayesian networks from data are common in the literature: constraint-based algorithms, which use conditional independence tests to learn the dependence structure of the data; score-based…
We study how to utilize (possibly erroneous) predictions in a model for computing under uncertainty in which an algorithm can query unknown data. Our aim is to minimize the number of queries needed to solve the minimum spanning tree…
Optimization problems that include regularization functions in their objectives are regularly solved in many applications. When one seeks second-order methods for such problems, it may be desirable to exploit specific properties of some of…
Estimating optimal transport (OT) maps (a.k.a. Monge maps) between two measures $P$ and $Q$ is a problem fraught with computational and statistical challenges. A promising approach lies in using the dual potential functions obtained when…
Graphical models use the intuitive and well-studied methods of graph theory to implicitly represent dependencies between variables in large systems. They can model the global behaviour of a complex system by specifying only local factors.…
Second order information is useful in many ways in smooth optimization problems, including for the design of step size rules and descent directions, or the analysis of the local properties of the objective functional. However, the…
With observational data alone, causal structure learning is a challenging problem. The task becomes easier when having access to data collected from perturbations of the underlying system, even when the nature of these is unknown. Existing…
In the statistical problem of denoising, Bayes and empirical Bayes methods can "overshrink" their output relative to the latent variables of interest. This work is focused on constrained denoising problems which mitigate such phenomena. At…