Huge data sets containing millions of training examples (tall data) with a large number of attributes (fat data) are relatively easy to gather. However one of the bottlenecks for successful inference of useful information from the data is the computational complexity of machine learning algorithms

We describe a point of view about the parameterized computational complexity framework in the broad context of one of the central issues of theoretical computer science as a field: the problem of systematically coping with computational intractability. Those already familiar with the basic ideas

Terminological Logics are knowledge representation formalisms of enormous applicative interest, as they are specifically oriented to the vast class of application domains that are describable by means of taxonomic organizations of complex objects. A number of results relative to the computational

TerminologicalLogicsareknowledgerepresentationformalismsofenormous applicative interest,astheyarespeciflcallyorientedtothevast classofapplicationdomainsthataredescribableby meansoftaxonomicorganizationsofcomplexobjects. A numberofresultsrelative tothecomputationalcomplexity ofterminologicallogicshave recentlyappearedintheliterature. Unfortunately,mostoftheseresults are\negative"innature,astheyshow that,inthelogicstheyrefer to,decidingsubsumption(i.e.themetalinguisticrelationwhich correspondstovalidity instandardlogics)iscomputationallyintractable. Inthispaper,after briey introducingthefundamentalconceptsunderlyingterminological logics,we show thatcomputingsubsumption isO (n logn)intheALN logic,an extensionofBrachman andLevesque 'sF L logic.ALN isobtainedby endowingF L withthetwo operatorsatleastandatmost,which allow thespeciflcationofnumberrestrictions, and theoperatora-not,which introducesa limited formofnegation.The resultwe presentisoftheoreticalsigniflcance, inthatALN isoneof...

of language. The dialogue model is based on an extensive analysis of collected dialogues from various application domains. Issues concerning computational tractability has also been decisive for its development. It is concluded that a simple dialogue grammar based model is sufficient for the management

assumption can have, and one of great importance in exploratory data analysis and mining where the underlying distribution is decidedly unknown. To date, however, despite a wealth of advanced underlying statistical theory, the use of nonparametric methods has been limited by their computational

and investigated with respect to the trade-off between efficiency and computational tractability. All of the mechanisms provetohave a common basis: the Vickrey Auction.

of alternative operators in the inference network framework must contend with the issue of computational tractability. We define a flexible class of link matrices that are natural candidates for the implementation of Boolean operators and an O(n²) algorithm for the computation of probabilities involving link

We study the computational complexity of Bayesian inference through the lens of simulating probabilistic programs. Our approach is grounded in new conceptual hypotheses about some intrinsic drivers of computational complexity, drawn from the experience of computational Bayesian statisticians. We

or losing. It is well known that computing Banzhaf indices in a weighted voting game is #P-complete. We give a comprehensive characterization of weighted voting games which can be solved in polynomial time. Among other results, we provide a polynomial (O(k ( n k)k)) algorithm to compute the Banzhaf indices