The sum. difference, product and quotient of two functions with different domains are usually defined only on their common domain. This paper extends these definitions so that the sum and other operations are essentially defined anywhere that at least one of the components is defined. This idea is applied to propositions and events, expressed as indicator functions, to define conditional propos...

Conditional expectations are not commonly used outside of probability and statistics. We present here a short introduction and list of their properties. For a random variable Z and a random vector X, the conditional expectation E[Z|X] is itself a random variable because it is a function of the random variables in X. For continuous random variables, E[Z|X] is defined as E[Z|X = x] = ∫ dz z p(z|x...

This paper proposes a joint random field (JRF) model for moving vehicle detection in video sequences. The JRF model extends the conditional random field (CRF) by introducing auxiliary latent variables to characterize the structure and evolution of visual scene. Hence detection labels (e.g. vehicle/roadway) and hidden variables (e.g. pixel intensity under shadow) are jointly estimated to enhance...

the notion of a $d$-poset was introduced in a connection withquantum mechanical models. in this paper, we introduce theconditional expectation of  random variables on thek^{o}pka's $d$-poset and prove the basic properties ofconditional expectation on this  structure.

Abstract Random Forests were introduced as a Machine Learning tool in Breiman (2001) and have since proven to be very popular and powerful for high-dimensional regression and classification. For regression, Random Forests give an accurate approximation of the conditional mean of a response variable. It is shown here that Random Forests provide information about the full conditional distribution...