Multivariate-Normal Classification with Covariances Known

Multidimensional random processes with normal covariances

where R(*) is a weakly stationary covariance. Thanks to the facts that R(s, s) ^ 0 for every seU1 and R (0) ^ 0 this definition yields R(s) !> 0 for every s e (R__. The definition of local stationarity for random sequences is given in [4]. In this case a covariance function R(-, •), defined on Z x Z (Cartesian product of integers), can be expressed as R(n, m) = R(n + m) R(n m) where R(*) is a s...

2 Sample Size Considerations in Multivariate Normal Classification by Seymour

Optimal Classification with Multivariate Losses

A. Appendix A A.1. Proof of Theorem 1 The proof is by contradiction. Fix a distribution P satisfying conditional independence, and let x denote a fixed set of instances. Denote P(Y = 1|xi) = ηi and the optimal classifier by s∗ ∈ {0, 1}n. Suppose there exist indices j, k such that sj = 1, sk = 0 and ηj < ηk. Let s′ ∈ {0, 1}n be such that sj = 0 and sk = 1, but identical to s∗ otherwise i.e. si =...

Optimal Classification with Multivariate Losses

Multivariate loss functions are extensively employed in several prediction tasks arising in Information Retrieval. Often, the goal in the tasks is to minimize expected loss when retrieving relevant items from a presented set of items, where the expectation is with respect to the joint distribution over item sets. Our key result is that for most multivariate losses, the expected loss is provably...

Multivariate Stochastic Simulation with Subjective Multivariate Normal Distributions1

-In many applications of Monte Carlo simulation in forestry or forest products, it may be known that some variables are correlated. However, for simplicity, in most simulations it has been assumed that random variables are independently distributed. This report describes an alternative Monte Carlo simulation technique for subjectively assessed multivariate normal distributions. The method requi...