Improvements to message computation in lazy propagation

Even though existing algorithms for belief update in Bayesian networks (BNs) have exponential time and space complexity, belief update in many real-world BNs is feasible. However, in some cases the efficiency of belief update may be insufficient. In such cases minor improvements in efficiency may be important or even necessary to make a task tractable. This paper introduces two improvements to the message computation in Lazy propagation (LP): (1) we introduce myopic methods for sorting the operations involved in a variable elimination using arc-reversal and (2) extend LP with the any-space property. The performance impacts of the methods are assessed empirically.     

Examples of Sweedler Cohomology in Positive Characteristic

There have been few examples of computations of Sweedler cohomology, or its generalization in low degrees known as lazy cohomology, for Hopf algebras of positive characteristic. In this paper we first provide a detailed calculation of the Sweedler cohomology of the algebra of functions on (?/2) ^r , in all degrees, over a field of characteristic 2. Here the result is strikingly different from the characteristic zero analog.

Then we show that there is a variant in characteristic p of the result obtained by Kassel and the author in characteristic zero, which provides a near-complete calculation of the second lazy cohomology group in the case of function algebras over a finite group; in positive characteristic, the statement is, rather surprisingly, simpler.     

Improvements to Variable Elimination and Symbolic Probabilistic Inference for evaluating Influence Diagrams

An Influence Diagram is a probabilistic graphical model used to represent and solve decision problems under uncertainty. Its evaluation requires performing several combinations and marginalizations on the potentials attached to the Influence Diagram. Finding an optimal order for these operations, which is NP-hard, is an element of crucial importance for the efficiency of the evaluation. In this paper, two methods for optimizing this order are proposed. The first one is an improvement of the Variable Elimination algorithm while the second is the adaptation of the Symbolic Probabilistic Inference for evaluating Influence Diagrams. Both algorithms can be used for the direct evaluation of IDs but also for the computation of clique-to-clique messages in Lazy Evaluation of Influence Diagrams. In the experimental work, the efficiency of these algorithms is tested with several Influence Diagrams from the literature.     

Quantitative analysis of less soluble form IV in commercial carbamazepine (form III) by diffuse reflectance fourier transform spectroscopy (DRIFTS) and lazy learning algorithm

Carbamazepine is a poorly soluble drug, with known bioavailability problems related to its polymorphism, and a form (C-monoclinic or form IV) less soluble than the pharmaceutically acceptable (P-monoclinic or form III) can be formed under various conditions, possible to occur during drug formulation. Therefore, quantitative analysis of form IV in form III is important to the drug formulators. In the present study, a fast and simple non-destructive method was developed for quantification of form IV in form III, by using DRIFTS spectral data subjected to the standard normal variate transformation (row centering and scaling) and to the lazy learning algorithm. Fast principal component (fast PCR) and partial least squares (PLS) regression methods of multivariate calibration were also used, which were compared with lazy learning. The lazy learning algorithm was performing better than the fast PCR and PLS methods (root mean squared error of cross-validation 1.318% versus 3.337 and 3.058%, respectively). Even with a small number of calibration samples it gave satisfactory predictive performance (root mean squared error of prediction <2.0% versus >3.3% of fast PCR and >2.6% of PLS), in the concentration range below 30% (w/w) of form IV. This is attributed to the capability of handling non-linearity in the relation of reflectance and concentration as well as to local modeling using a pre-selected number of nearest neighbor concentrations.     

交换代数的lazy上循环

该文对于Hopf代数H和交换代数A, 给出了lazy左2 -上循环$\sigma$的定义, 并且证得lazy 2 -上循环和lazy H-cleft对象之间存在着对应关系.     

Explicit error bounds for lazy reversible Markov chain Monte Carlo

We prove explicit, i.e., non-asymptotic, error bounds for Markov Chain Monte Carlo methods, such as the Metropolis algorithm. The problem is to compute the expectation (or integral) of f$f$ with respect to a measure π$\pi$ which can be given by a density ?$?$ with respect to another measure. A straight simulation of the desired distribution by a random number generator is in general not possible. Thus it is reasonable to use Markov chain sampling with a burn-in. We study such an algorithm and extend the analysis of Lovasz and Simonovits [L. Lovász, M. Simonovits, Random walks in a convex body and an improved volume algorithm, Random Structures Algorithms 4 (4) (1993) 359–412] to obtain an explicit error bound.