Henrique K. Miyamoto

Université Paris-Saclay · Laboratory of Signals and Systems (L2S)

We present a new systematic approach to constructing spherical codes in dimensions $2^{k}$ , based on Hopf foliations. Using the fact that a sphere $S^{2n-1}$ is foliated by manifolds $S_{\cos \eta }^{n-1} \times S_{\sin \eta }^{n-1}$ , $\eta \in [0,\pi /2]$ , we distribute points in dimension $2^{k}$ via a recursive algorithm from a basi...

We propose novel compression algorithms for time-varying channel state information (CSI) in wireless communications. The proposed scheme combines (lossy) vector quantisation and (lossless) compression. First, the new vector quantisation technique is based on a class of parametrised companders applied on each component of the normalised CSI vector....

A lattice tiling decomposition induces dual operations: quantisation and wrapping, which map the Euclidean space to the lattice and to one of its fundamental domains, respectively. Applying such decomposition to random variables over the Euclidean space produces quantised and wrapped random variables. In studying the characteristic function of thos...

The Fisher-Rao distance is the geodesic distance between probability distributions in a statistical manifold equipped with the Fisher metric, which is the natural choice of Riemannian metric on such manifolds. Finding closed-form expressions for the Fisher-Rao distance is a non-trivial task, and those are available only for a few families of probab...

A full-rank lattice in the Euclidean space is a discrete set formed by all integer linear combinations of a basis. Given a probability distribution on Rn, two operations can be induced by considering the quotient of the space by such a lattice: wrapping and quantization. For a lattice Λ, and a fundamental domain D, which tiles Rn through Λ, the wra...

Choosing a suitable loss function is essential when learning by empirical risk minimisation. In many practical cases, the datasets used for training a classifier may contain incorrect labels, which prompts the interest for using loss functions that are inherently robust to label noise. In this paper, we study the Fisher–Rao loss function, which eme...

A full-rank lattice in the Euclidean space is a discrete set formed by all integer linear combinations of a basis. Given a probability distribution on $\mathbb{R}^n$, two operations can be induced by considering the quotient of the space by such a lattice: wrapping and quantization. For a lattice $\Lambda$, and a fundamental domain $D$ which tiles...

Choosing a suitable loss function is essential when learning by empirical risk minimisation. In many practical cases, the datasets used for training a classifier may contain incorrect labels, which prompts the interest for using loss functions that are inherently robust to label noise. In this paper, we study the Fisher-Rao loss function, which eme...

We study the Fisher-Rao loss function, which emerges from the Fisher-Rao distance in the statistical manifold of discrete distributions, especially in the presence of label noise.

This dissertation is composed of three contributions, which have in common the use of tools from geometry and/or statistics in applications to communications and learning. The first of them concerns the construction of spherical codes from a recursive procedure based on the sphere foliations given by the Hopf fibration. In the second one, we propos...

We propose novel compression algorithms for timevarying channel state information (CSI) in wireless communications. The proposed schemes combine (lossy) vector quantisation and (lossless) compression. The vector quantisation technique is based on data-adapted parametrised companders applied on each component of the normalised vector. Then, the sequ...

We propose novel compression algorithms to time-varying channel state information (CSI) for wireless communications. The proposed scheme combines (lossy) vector quantisation and (lossless) compression. First, the new vector quantisation technique is based on a class of parametrised companders applied on each component of the normalised vector. Our...

We present a new systematic approach to constructing spherical codes in dimensions $2^k$, based on Hopf foliations. Using the fact that a sphere $S^{2n-1}$ is foliated by manifolds $S_{\cos\eta}^{n-1} \times S_{\sin\eta}^{n-1}$, $\eta\in[0,\pi/2]$, we distribute points in dimension $2^k$ via a recursive algorithm from a basic construction in $\math...

Apresentamos uma nova construção para códigos esféricos, baseada em folheações de esferas obtidas a partir da fibração de Hopf e inspirada pela construção em camadas de toros planares (TLSC). No caso base (ℝ4), a 3-esfera é folheada por toros para realizar a construção em um algoritmo de dois passos: (i) escolher uma família de toros afastados de u...

A new approach to construct spherical codes in R4 is presented, based on properties of the Hopf fibration and inspired by a previous construction on layers of flat tori [1][2]. We use the Hopf foliation of the 3-sphere by tori to construct a two-step algorithm: (i) to choose a torus parametrised by height and (ii) to distribute points in each torus...