A pattern of a sequence is a sequence of integer indices with each index describing the order of first occurrence of the respective symbol in the original sequence. In a recent paper, tight general bounds on the block entropy of patterns of sequences generated by independent and identically distributed (i.i.d.) sources were derived. In this paper, precise approximations are provided for the pat...

We prove that an ergodic free action of a countable discrete amenable group with completely positive entropy has a countable Lebesgue spectrum. Our approach is based on the Rudolph-Weiss result on the equality of conditional entropies for actions of countable amenable groups with the same orbits. Relative completely positive entropy actions are also considered. An application to the entropic pr...

Kaufmann has recently argued that the thesis according to which the probability of an indicative conditional equals the conditional probability of the consequent given the antecedent under certain specifiable circumstances deviates from intuition. He presents a method for calculating the probability of a conditional that does seem to give the intuitively correct result under those circumstances...

According to the Principle of Conditional Non-Contradiction (CNC), conditionals of the form “If p, q” and “If p, not q” cannot both be true, unless p is inconsistent. This principle is widely regarded as an adequacy constraint on any semantics that attributes truth conditions to conditionals. Gibbard has presented an example of a pair of conditionals that, in the context he describes, appear to...

Chain rules for Tsallis type entropies are proven, as including the famous pseudoadditivity in nonextensive statistics as a special case. They give important relations between Tsallis conditional entropy and Tsallis joint entropy. Moreover the subadditivity of Tsallis type entropies is shown for the correlated two random variables in the case of q ≥ 1 with the help of the generalized Shannon in...

In this work, we propose a new approach of deriving the bounds between entropy and error from a joint distribution through an optimization means. The specific case study is given on binary classifications. Two basic types of classification errors are investigated, namely, the Bayesian and non-Bayesian errors. The consideration of non-Bayesian errors is due to the facts that most classifiers res...

The paper proposes an information-theorybased method for feature types analysis in probabilistic evaluation modelling for statistical parsing. The basic idea is that we use entropy and conditional entropy to measure whether a feature type grasps some of the information for syntactic structure prediction. Our experiment quantitatively analyzes several feature types’ power for syntactic structure...

One of the obstacles to fully ensure the semantic contents of words is how to grab the meanings of a word from various probabilities it associates with other words. According to Shannon’s (1948) information theory, entropy can provide indications of amount of information and extent of uncertainty of a given variable by calculating the probability distributions of event occurrence. Therefore, en...

A basic property of the entropy of a discrete random variable x is that: 0 ≤ H(x) ≤ log |X | In fact, the entropy is maximal for the discrete uniform distribution. That is, (∀x ∈ X ) p(x) = 1/|X |, in which case H(x) = log |X |. Definition 3.2 (Conditional entropy). The conditional entropy of y given x is defined as: H(y|x) = ∑ v∈X px(v)H(y|x = v) = − ∑ v∈X px(v) ∑ y∈Y py|x(y|v) log py|x(y|v) =...

We study the effect of the mandatory adoption of IFRS in Europe in 2005 on conditional conservatism. To capture conditional conservatism, we use three measures: the Basu (1997) measure, the Khan and Watts (2009) measure, and a measure controlling for potential shifts in unconditional conservatism and cost of capital after the adoption of IFRS. From a sample of 7,251 firm-year observations drawn...