Related papers: Modelling conditional probabilities with Riemann-T…
We propose two nonparametric statistical tests of goodness of fit for conditional distributions: given a conditional probability density function $p(y|x)$ and a joint sample, decide whether the sample is drawn from $p(y|x)r_x(x)$ for some…
Learning invariant representations is a critical task in computer vision. In this paper, we propose the Theta-Restricted Boltzmann Machine ({\theta}-RBM in short), which builds upon the original RBM formulation and injects the notion of…
In order to develop reliable services using machine learning, it is important to understand the uncertainty of the model outputs. Often the probability distribution that the prediction target follows has a complex shape, and a mixture…
We outline an efficient method for the reconstruction of a probability density function from the knowledge of its infinite sequence of ordinary moments. The approximate density is obtained resorting to maximum entropy technique, under the…
We present several results on smoothness in $L_{p}$ sense of filtering densities under the Lipschitz continuity assumption on the coefficients of a partially observable diffusion processes. We obtain them by rewriting in divergence form…
Algorithms for jointly obtaining projection estimates of the density and distribution function of a random variable using Legendre polynomials are proposed. For these algorithms, a problem of the conditional optimization is solved. Such…
We consider here together the inference questions and the change-point problem in Poisson autoregressions (see Tj{\o}stheim, 2012). The conditional mean (or intensity) of the process is involved as a non-linear function of it past values…
The density operator of a quantum state can be represented as a complex joint probability of any two observables whose eigenstates have non-zero mutual overlap. Transformations to a new basis set are then expressed in terms of complex…
If two random variables X and A are functionally related via f(X)=A for some strictly monotone continuously differentiable function f:R->R, the distribution of X may easily be computed from the distribution of A.
The restricted Boltzmann machine is a graphical model for binary random variables. Based on a complete bipartite graph separating hidden and observed variables, it is the binary analog to the factor analysis model. We study this graphical…
Construction methods for prior densities are investigated from a predictive viewpoint. Predictive densities for future observables are constructed by using observed data. The simultaneous distribution of future observables and observed data…
We calculate the discrete moments of the characteristic polynomial of a random unitary matrix, evaluated a small distance away from an eigenangle. Such results allow us to make conjectures about similar moments for the Riemann zeta…
This paper introduces and describes the R package ts.extend, which adds probability functions for stationary Gaussian ARMA models and some related utility functions for time-series. We show how to use the package to compute the density and…
This paper proposes probabilistic conformal prediction (PCP), a predictive inference algorithm that estimates a target variable by a discontinuous predictive set. Given inputs, PCP construct the predictive set based on random samples from…
The density operator of the arbitrary physical system must be positive definite. Employing the general master equation technique which preserves this property we derive equations of motion for the density operator of an active atom which…
We present explicit classes of probability distributions that can be learned by Restricted Boltzmann Machines (RBMs) depending on the number of units that they contain, and which are representative for the expressive power of the model. We…
The random matrix model is popular in extended object tracking, due to its relative simplicity and versatility. In this model, the extended object state consists of a kinematic vector for the position and motion parameters (velocity, etc),…
The deep extension of the restricted Boltzmann machine (RBM), known as the deep Boltzmann machine (DBM), is an expressive family of machine learning models which can serve as compact representations of complex probability distributions.…
This paper presents a new approach to conditional inference, based on the simulation of samples conditioned by a statistics of the data. Also an explicit expression for the approximation of the conditional likelihood of long runs of the…
Probabilistic model checking for systems with large or unbounded state space is a challenging computational problem in formal modelling and its applications. Numerical algorithms require an explicit representation of the state space, while…