相关论文: Two tales for a geometric Jensen--Shannon divergen…
This work studies the Geometric Jensen-Shannon divergence, based on the notion of geometric mean of probability measures, in the setting of Gaussian measures on an infinite-dimensional Hilbert space. On the set of all Gaussian measures…
The Jensen-Shannon divergence is a renown bounded symmetrization of the unbounded Kullback-Leibler divergence which measures the total Kullback-Leibler divergence to the average mixture distribution. However the Jensen-Shannon divergence…
In this report, we derive a non-negative series expansion for the Jensen-Shannon divergence (JSD) between two probability distributions. This series expansion is shown to be useful for numerical calculations of the JSD, when the probability…
Convexity is a key concept in information theory, namely via the many implications of Jensen's inequality, such as the non-negativity of the Kullback-Leibler divergence (KLD). Jensen's inequality also underlies the concept of Jensen-Shannon…
We generalize the Jensen-Shannon divergence by considering a variational definition with respect to a generic mean extending thereby the notion of Sibson's information radius. The variational definition applies to any arbitrary distance and…
Quantifying the difference between probability distributions is crucial in machine learning. However, estimating statistical divergences from empirical samples is challenging due to unknown underlying distributions. This work proposes the…
The Jensen-Shannon divergence is a renown bounded symmetrization of the Kullback-Leibler divergence which does not require probability densities to have matching supports. In this paper, we introduce a vector-skew generalization of the…
The measure of Jensen-Fisher divergence between probability distributions is introduced and its theoretical grounds set up. This quantity, in contrast to the remaining Jensen divergences, is very sensitive to the fluctuations of the…
Jensen-Shannon divergence (JD) is a symmetrized and smoothed version of the most important divergence measure of information theory, Kullback divergence. As opposed to Kullback divergence it determines in a very direct way a metric; indeed,…
Recently, Taneja studied two one parameter generalizations of J-divergence, Jensen-Shannon divergence and Arithmetic-Geometric divergence. These two generalizations in particular contain measures like: Hellinger discrimination, symmetric…
We examine the problem of controlling divergences for latent space regularisation in variational autoencoders. Specifically, when aiming to reconstruct example $x\in\mathbb{R}^{m}$ via latent space $z\in\mathbb{R}^{n}$ ($n\leq m$), while…
There are many information and divergence measures exist in the literature on information theory and statistics. The most famous among them are Kullback-Leibler (1951) relative information and Jeffreys (1951) J-divergence. Sibson (1969)…
The Jensen inequality is a widely used tool in a multitude of fields, such as for example information theory and machine learning. It can be also used to derive other standard inequalities such as the inequality of arithmetic and geometric…
Divergence measures play a central role and become increasingly essential in deep learning, yet efficient measures for multiple (more than two) distributions are rarely explored. This becomes particularly crucial in areas where the…
For testing goodness of fit it is very popular to use either the chi square statistic or G statistics (information divergence). Asymptotically both are chi square distributed so an obvious question is which of the two statistics that has a…
Mapping data from and/or onto a known family of distributions has become an important topic in machine learning and data analysis. Deep generative models (e.g., generative adversarial networks ) have been used effectively to match known and…
Jensen-Shannon divergence is a well known multi-purpose measure of dissimilarity between probability distributions. It has been proven that the square root of this quantity is a true metric in the sense that, in addition to the basic…
In this paper we have considered two one parametric generalizations. These two generalizations have in articular the well known measures such as: J-divergence, Jensen-Shannon divergence and Arithmetic-Geometric mean divergence. These three…
Learning from different data types is a long-standing goal in machine learning research, as multiple information sources co-occur when describing natural phenomena. However, existing generative models that approximate a multimodal ELBO rely…
Sliced-Wasserstein distance (SW) and its variant, Max Sliced-Wasserstein distance (Max-SW), have been used widely in the recent years due to their fast computation and scalability even when the probability measures lie in a very high…