Related papers: A first approach to closeness distributions
It is known that statistical model selection as well as identification of dynamical equations from available data are both very challenging tasks. Physical systems behave according to their underlying dynamical equations which, in turn, can…
Probabilistic graphical modeling is a branch of machine learning that uses probability distributions to describe the world, make predictions, and support decision-making under uncertainty. Underlying this modeling framework is an elegant…
Probabilistic graphical models combine the graph theory and probability theory to give a multivariate statistical modeling. They provide a unified description of uncertainty using probability and complexity using the graphical model.…
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…
Probabilistic graphical models (PGMs) have become a popular tool for computational analysis of biological data in a variety of domains. But, what exactly are they and how do they work? How can we use PGMs to discover patterns that are…
We define a class of probability distributions that we call simplicial mixture models, inspired by simplicial complexes from algebraic topology. The parameters of these distributions represent their topology and we show that it is possible…
We describe the geometric notion of distribution in synthetic terms, utilizing the notion of "first neighbourhood of the diagonal" from algebraic geometry. We characterize involutive distributions in combinatorial terms.
First-order statistics of scattered light is described using the representation of probability density cloud which visualizes a two-dimensional distribution for complex amplitude. The geometric parameters of the cloud are studied in detail…
We study the problem of data integration from sources that contain probabilistic uncertain information. Data is modeled by possible-worlds with probability distribution, compactly represented in the probabilistic relation model. Integration…
In physics we often use very simple models to describe systems with many degrees of freedom, but it is not clear why or how this success can be transferred to the more complex biological context. We consider models for the joint…
Various kinds of data are routinely represented as discrete probability distributions. Examples include text documents summarized by histograms of word occurrences and images represented as histograms of oriented gradients. Viewing a…
Graphical model learning and inference are often performed using Bayesian techniques. In particular, learning is usually performed in two separate steps. First, the graph structure is learned from the data; then the parameters of the model…
Approximating complex probability distributions, such as Bayesian posterior distributions, is of central interest in many applications. We study the expressivity of geometric Gaussian approximations. These consist of approximations by…
Models of complex networks are generally defined as graph stochastic processes in which edges and vertices are added or deleted over time to simulate the evolution of networks. Here, we define a unifying framework - probabilistic inductive…
This paper begins with a description of methods for estimating image probability density functions that reflects the observation that such data is usually constrained to lie in restricted regions of the high-dimensional image space-not…
Current theories of perception suggest that the brain represents features of the world as probability distributions, but can such uncertain foundations provide the basis for everyday vision? Perceiving objects and scenes requires knowing…
Global variational approximation methods in graphical models allow efficient approximate inference of complex posterior distributions by using a simpler model. The choice of the approximating model determines a tradeoff between the…
Gaussian Graphical Models provide a convenient framework for representing dependencies between variables. Recently, this tool has received a high interest for the discovery of biological networks. The literature focuses on the case where a…
A typical computational geometry problem begins: Consider a set P of n points in R^d. However, many applications today work with input that is not precisely known, for example when the data is sensed and has some known error model. What if…
A general piecewise (including pointwise) probability distribution with space-saving notation and its hierarchical particular cases are considered. The explicit closed-form normalization, expectation, and variance formulas along with the…