We analyze the performance of the top-down multiclass classification algorithm for decision tree learning called LOMtree, recently proposed in the literature Choromanska and Langford (2014) for solving efficiently classification problems with very large number of classes. The algorithm online optimizes the objective function which simultaneously controls the depth of the tree and its statistica...

This manual describes the Fortran 90 implementation of maximum-entropy basis functions. The main ingredients of the theory are presented, and then the numerical implementation is touched upon. Instructions on the installation and execution of the code, as well as on writing an interface to the library are presented. Each program module and the most important functions in each module are discuss...

We demonstrate a direct mapping of max k-SAT problems (and weighted max k-SAT) to a Chimera graph, which is the non-planar hardware graph of the devices built by D-Wave Systems Inc. We further show that this mapping can be used to map a similar class of maximum satisfiability problems where the clauses are replaced by parity checks over potentially large numbers of bits. The latter is of specif...

We consider the problem of approximating the empirical Shannon entropy of a highfrequency data stream under the relaxed strict-turnstile model, when space limitations make exact computation infeasible. An equivalent measure of entropy is the Rényi entropy that depends on a constant α. This quantity can be estimated efficiently and unbiasedly from a low-dimensional synopsis called an α-stable da...

By combining the explicit formula of the Shannon informational entropy ) , ( Y X H for two random variables X and Y , with the entropy )) ( ( X f H of ) (X f where (.) f is a real-valued differentiable function, we have shown that the density of the amount of information in Shannon sense involved in a non-random differentiable function is defined by the logarithm of the absolute value of its de...

The weak law of large numbers implies that, under mild assumptions on the source, the Renyi entropy per produced symbol converges (in probability) towards the Shannon entropy rate. This paper quantifies the speed of this convergence for sources with independent (but not iid) outputs, generalizing and improving the result of Holenstein and Renner (IEEE Trans. Inform. Theory, 2011). (a) we charac...

let $g$ be a finite simple graph whose vertices and edges are weighted by two functions. in this paper we shall define and calculate entropy of a dynamical system on weights of the graph $g$, by using the weights of vertices and edges of $g$. we examine the conditions under which entropy of the dynamical system is zero, possitive or $+infty$. at the end it is shown that, for $rin [0,+infty]$, t...

Beyond the local constraints imposed by grammar, words concatenated in long sequences carrying a complex message show statistical regularities that may reflect their linguistic role in the message. In this paper, we perform a systematic statistical analysis of the use of words in literary English corpora. We show that there is a quantitative relation between the role of content words in literar...

BACKGROUND AND OBJECTIVE Equality in distribution of health care facilities is the main cause for access and enjoyment to the health. The aim of this study was to examine the regional disparities in health care facilities across the Markazi province. METHODS This was a cross-sectional study. Study sample included the cities of Markazi province, ranked based on 15 health indices. Data was coll...