Earlier we assumed estimates x lived in RD and that (squared) Euclidean distance was a meaningful distance measure. However, for many quantities of interest, such as angles, Euclidean distance is not appropriate (e.g., given two angles θ1 = 5◦ and θ2 = 355◦ the difference between them is 10◦ not 350◦). Below we extend our approach to angular data. We begin by introducing a distance measure betw...

Derivation of tight bounds on f -divergences and related distances is of interest in information theory and statistics. This paper improves some existing bounds on f -divergences. In some cases, an alternative approach leads to a simplified proof of an existing bound. Following bounds on the chi-squared divergence, an improved version of a reversed Pinsker’s inequality is derived for an arbitra...

Derivation of tight bounds on f -divergences and related distances is of interest in information theory and statistics. This paper improves some existing bounds on f -divergences. In some cases, an alternative approach leads to a simplified proof of an existing bound. Following bounds on the chi-squared divergence, an improved version of a reversed Pinsker’s inequality is derived for an arbitra...

This paper presents an Acoustic-to-Articulatory inversion method based on local regression. Two types of local regression, a non-parametric and a local linear regression have been applied on a corpus containing simultaneous recordings of positions of articulators and the corresponding acoustics. A maximum likelihood trajectory smoothing using the estimated dynamics of the articulators is also a...

We calculate the effect of nonlinear interactions among solar acoustic modes upon the modal frequencies and energy loss rates (or line widths). The frequency shift for a radial p-mode of frequency 3 mHz is found to be about -0.5 JlHz. The magnitude of nonlinear frequency shift increases more rapidly with frequency than the inverse mode mass (mode mass is defined as the ratio of energy in the mo...

This paper applies time distance, suggested by Granger and Jeon (1997), to models of in ation. The commonly used metric of forecast performance, mean squared forecasting error, measures how vertically close the forecast is to the series to be predicted; time distance instead measures the leading and lagging properties, often leading to significantly di erent conclusions about relative performan...

The squared eigenfunctions of the spectral problem associated to the Camassa-Holm equation represent a complete basis of functions, which helps to describe the Inverse Scattering Transform for the Camassa-Holm hierarchy as a Generalised Fourier transform. The main result of this work is the derivation of the completeness relation for the squared solutions of the Camassa-Holm spectral problem. W...

Vectored data frequently occur in a variety of fields, which are easy to handle since they can be mathematically abstracted as points residing in a Euclidean space. An appropriate distance metric in the data space is quite demanding for a great number of applications. In this paper, we pose robust and tractable metric learning under pairwise constraints that are expressed as similarity judgemen...