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We show a general relation between the spatially disjoint product of probability density functions and the sum of their Fisher information metric tensors. We then utilise this result to give a method for constructing the probability density…
Suppose we are given the conditional probability of one variable given some other variables.Normally the full joint distribution over the conditioning variablesis required to determine the probability of the conditioned variable.Under what…
The notion of probability density for a random function is not as straightforward as in finite-dimensional cases. While a probability density function generally does not exist for functional data, we show that it is possible to develop the…
Conditional Density Estimation (CDE) models deal with estimating conditional distributions. The conditions imposed on the distribution are the inputs of the model. CDE is a challenging task as there is a fundamental trade-off between model…
Based on a quantum mechanical approach, we investigate moment- (or M-) indeterminate probability densities by way of the characteristic function and self-adjoint operators. The approach leads to new methods to construct classes of…
We present a theoretical analysis of Gaussian-binary restricted Boltzmann machines (GRBMs) from the perspective of density models. The key aspect of this analysis is to show that GRBMs can be formulated as a constrained mixture of…
Probabilistic programming allows specification of probabilistic models in a declarative manner. Recently, several new software systems and languages for probabilistic programming have been developed on the basis of newly developed and…
The spectral density function describes the second-order properties of a stationary stochastic process on $\mathbb{R}^d$. This paper considers the nonparametric estimation of the spectral density of a continuous-time stochastic process…
In this paper we will turn our attention to the problem of obtaining phase-space probability density functions. We will show that it is possible to obtain functions which assume only positive values over all its domain of definition.
The indistinguishability of many bosons undergoing passive linear transformations followed by number basis measurements is fully characterized by the visible state of the bosons. However, measuring all the parameters in the visible state is…
Observed clusters should be modelled by considering the distribution function to be a random variable that quantifies the degree of excitation of the system's normal modes. A system of canonical coordinates for the space of DFs is…
We develop a general approach to estimating the derivative of a function-valued parameter $\theta_o(u)$ that is identified for every value of $u$ as the solution to a moment condition. This setup in particular covers many interesting models…
U-statistics constitute a large class of estimators, generalizing the empirical mean of a random variable $X$ to sums over every $k$-tuple of distinct observations of $X$. They may be used to estimate a regular functional $\theta(P_{X})$ of…
Motivated by a probabilistic analysis of a simple game (itself inspired by a problem in computational learning theory) we introduce the \emph{moment zeta function} of a probability distribution, and study in depth some asymptotic properties…
Semantic composition remains an open problem for vector space models of semantics. In this paper, we explain how the probabilistic graphical model used in the framework of Functional Distributional Semantics can be interpreted as a…
Modern datasets are becoming heterogeneous. To this end, we present in this paper Mixed-Variate Restricted Boltzmann Machines for simultaneously modelling variables of multiple types and modalities, including binary and continuous…
This paper generalizes recent proposals of density forecasting models and it develops theory for this class of models. In density forecasting, the density of observations is estimated in regions where the density is not observed.…
Conditional density estimation generalizes regression by modeling a full density f(yjx) rather than only the expected value E(yjx). This is important for many tasks, including handling multi-modality and generating prediction intervals.…
The projection of sample measurements onto a reconstruction space represented by a basis on a regular grid is a powerful and simple approach to estimate a probability density function. In this paper, we focus on Riesz bases and propose a…
Probability density estimation is a classical and well studied problem, but standard density estimation methods have historically lacked the power to model complex and high-dimensional image distributions. More recent generative models…