相关论文: Probabilistic Alternatives to the Gower Distance: …
This paper presents a new distance metric to compare two continuous probability density functions. The main advantage of this metric is that, unlike other statistical measurements, it can provide an analytic, closed-form expression for a…
The ideas here are a continuation of a previous article. Some of the applications of the main ideas in the previous article are explained, along with some limitations of the general ideas. There are situations where additional hypotheses…
To what extent can we distinguish one probability distribution from another? Are there quantitative measures of distinguishability? The goal of this tutorial is to approach such questions by introducing the notion of the "distance" between…
In this paper, we propose a method to build a sequence of generalized empirical principal curves, with selected length, so that, in Hausdor distance, the images of the estimating principal curves converge in probability to the image of g.
The goal of this note is to provide a geometric setting in which generalized arithmetic means are best predictors in an appropriate metric. This characterization provides a geometric interpretation to the concept of certainty equivalent.…
The metric properties of the set in which random variables take their values lead to relevant probabilistic concepts. For example, the mean of a random variable is a best predictor in that it minimizes the standard Euclidean distance or…
A basic feasible probabilistic purification of unknown noisy coherent states, outgoing from different state preparations with unknown mean number of thermal photons, is proposed. The scheme is based only on a linear-optical network with an…
Gibbs-type random probability measures, or Gibbs-type priors, are arguably the most "natural" generalization of the celebrated Dirichlet prior. Among them the two parameter Poisson-Dirichlet prior certainly stands out for the mathematical…
We show on theoretical grounds that, even in the presence of noise, probabilistic measurement strategies (which have a certain probability of failure or abstention) can provide, upon a heralded successful outcome, estimates with a precision…
We study the distinguishability notion given by Wootters for states represented by probability density functions. This presents the particularity that it can also be used for defining a distance in chaotic unidimensional maps. Based on that…
The Gromov-Wasserstein distances were proposed a few years ago to compare distributions which do not lie in the same space. In particular, they offer an interesting alternative to the Wasserstein distances for comparing probability measures…
Expressive human speech generally abounds with rich and flexible speech prosody variations. The speech prosody predictors in existing expressive speech synthesis methods mostly produce deterministic predictions, which are learned by…
The aim of this article is to promote the use of probabilistic methods in the study of problems in mathematical general relativity. Two new and simple singularity theorems, whose features are different from the classical singularity…
Estimating mutual information between continuous random variables is often intractable and extremely challenging for high-dimensional data. Recent progress has leveraged neural networks to optimize variational lower bounds on mutual…
We present an improvement of the phase distance correlation (PDC) periodogram to account for uncertainties in the time-series data. The PDC periodogram introduced in our previous papers is based on the statistical concept of distance…
Quantum walks are quantum counterparts of random walks and their probability distributions are different from each other. A quantum walker distributes on a Hilbert space and it is observed at a location with a probability. The finding…
A novel switching differentiator that has considerably simple form is proposed. Under the assumption that time-derivatives of the signal are norm-bounded, it is shown that estimation errors are convergent to the zeros asymptotically. The…
In previous work cite{Ha98:Towards} we presented a case-based approach to eliciting and reasoning with preferences. A key issue in this approach is the definition of similarity between user preferences. We introduced the probabilistic…
Probabilistic Spacetime is a simple generalization of the classical model of spacetime in General Relativity, such that it allows to consider multiple metric field realizations endowed with probabilities. The motivation for such a…
Inspired by applications in sports where the skill of players or teams competing against each other varies over time, we propose a probabilistic model of pairwise-comparison outcomes that can capture a wide range of time dynamics. We…