Asymptotically unbiased nearest-neighbor estimators for KL divergence have recently been proposed and demonstrated in a number of applications. With small sample sizes, however, these nonparametric methods typically suffer from high estimation bias due to the non-local statistics of empirical nearest-neighbor information. In this paper, we show that this non-local bias can be mitigated by chang...

Divergence functions are the non-symmetric “distance” on the manifold,Mθ, of parametric probability density functions over a measure space, (X,μ). Classical information geometry prescribes, on Mθ: (i) a Riemannian metric given by the Fisher information; (ii) a pair of dual connections (giving rise to the family of α-connections) that preserve the metric under parallel transport by their joint a...

Neutron star constraints and {\it ab initio} pQCD evaluations require the EoS representing cold quark matter to be stiff at intermediate baryonic densities soft high-$n_B$. Here, I suggest that three flavor NJL model with a density dependent repulsive coupling, $G_V(\mu)$, can generate an which interpolates between these two regimes. Such interpolation requires repulsion start decreasing chemic...

In many real-world applications (e.g. social media application), data usually consists of diverse input modalities that originates from various heterogeneous sources. Learning a similarity measure for such data is of great importance for vast number of applications such as classification, clustering, retrieval, etc. Defining an appropriate distance metric between data points with multiple modal...

Combining different metrics into a single measure of quality seems the most direct and natural way to improve over the quality of individual metrics. Recently, several approaches have been suggested (Kulesza and Shieber, 2004; Liu and Gildea, 2007; Albrecht and Hwa, 2007a). Although based on different assumptions, these approaches share the common characteristic of being parametric. Their model...

We clarify the properties of the behavior of classical cosmological perturbations when the Universe experiences a bounce. This is done in the simplest possible case for which gravity is described by general relativity and the matter content has a single component, namely a scalar field in a closed geometry. We show in particular that the spectrum of scalar perturbations can be affected by the b...

We study the problem of learning local metrics for nearest neighbor classification. Most previous works on local metric learning learn a number of local unrelated metrics. While this ”independence” approach delivers an increased flexibility its downside is the considerable risk of overfitting. We present a new parametric local metric learning method in which we learn a smooth metric matrix func...

We study the energy transfer process in quantum battery systems consisting of multiple central spins and bath spins. Here with "quantum battery" we refer to spins, whereas serves as "charger". For single central-spin battery, analytically derive time evolutions charging power arbitrary number case find scaling-law relation between maximum $P_{max}$ $N_B$. It approximately satisfies a scaling la...

We suggest a method for using nonparametric information to modify a parametric model at a low-order level, retaining information in the model only to enhance the nonparametric approach at relatively high orders. Our technique represents an alternative to methods that rst t a parametric model and then adjust it. In particular, relative to a \nonparametric estimator with a parametric start," our ...

In the area of automatic parallelization of programs , analyzing and transforming loop nests with parametric aane loop bounds requires fundamental mathematical results. The most common geometrical model of iteration spaces, called the polytope model, is based on mathematics dealing with convex and discrete geometry, linear programming, combinatorics and geometry of numbers. In this paper, we pr...