7797628
Bayesian Networks and Inner Product Spaces
In connection with two-label classification tasks over the Boolean domain, we consider the possibility to combine the key advantages of Bayesian networks and of kernel-based learning systems. This leads us to the basic question whether the class of decision functions induced by a given Bayesian network can be represented within a low-dimensional inner product space. For Bayesian networks with an explicitly given (full or reduced) parameter collection, we show that the “natural” inner product space has the smallest possible dimension up to factor 2 (even up to an additive term 1 in many cases). For a slight modification of the so-called logistic autoregressive Bayesian network with n nodes, we show that every sufficiently expressive inner product space has dimension at least 2 n/4. The main technical contribution of our work consists in uncovering combinatorial and algebraic structures within Bayesian networks such that known techniques for proving lower bounds on the dimension of inner product spaces can be brought into play.
45719384
A Characterization of Strong Learnability in the Statistical Query Model
In this paper, we consider Kearns' [4] Statistical Query Model of learning. It is well known [3] that the number of statistical queries, needed for "weakly learning" an unknown target concept (i.e. for gaining significant advantage over random guessing) is polynomially related to the so-called Statistical Query dimension of the concept class. In this paper, we provide a similar characterization for "strong learning" where the learners final hypothesis is required to approximate the unknown target concept up to a small rate of misclassification. The quantity that characterizes strong learnability in the Statistical Query model is a surprisingly close relative of (though not identical to) the Statistical Query dimension. For the purpose of proving the main result, we provide other characterizations of strong learnability which are given in terms of covering numbers and related notions. These results might find some interest in their own right. All characterizations are purely information-theoretical and ignore computational issues.
31930258
How Many Missing Answers Can Be Tolerated by Query Learners?
We consider the model of exact learning using an equivalence oracle and an incomplete membership oracle. In this model, a random subset of the learners membership queries is left unanswered. Our results are as follows. First, we analyze the obvious method for coping with missing answers: search exhaustively through all possible "answer patterns" associated with the unanswered queries. Thereafter, we present two specific concept classes that are efficiently learnable using an equivalence oracle and a (completely reliable) membership oracle, but are provably not polynomially learnable if the membership oracle becomes slightly incomplete. The first class will demonstrate that the aforementioned method of exhaustively searching through all possible answer patterns cannot be substantially improved in general (despite its apparent simplicity). The second class will demonstrate that the incomplete membership oracle can be rendered useless even if it leaves only a fraction 1/poly(n) of all queries unanswered. Finally, we present a learning algorithm for monotone DNF formulas that can cope with a relatively large fraction of missing answers (more than sixty percent), but is as efficient (in terms of run-time and number of queries) as the classical algorithm whose questions are always answered reliably.
427643
A MIMD implementation of a parallel Euler solver for unstructured grids
A mesh-vertex finite volume scheme for solving the Euler equations on triangular unstructured meshes is implemented on a MIMD (multiple instruction/multiple data stream) parallel computer. Three partitioning strategies for distributing the work load onto the processors are discussed. Issues pertaining to the communication costs are also addressed. We find that the spectral bisection strategy yields the best performance. The performance of this unstructured computation on the Intel iPSC/860 compares very favorably with that on a one-processor CRAY Y-MP/1 and an earlier implementation on the Connection Machine.
14801431
Causality in Bayesian Belief Networks
We address the problem of causal interpretation of the graphical structure of Bayesian belief networks (BBNs). We review the concept of causality explicated in the domain of structural equations models and show that it is applicable to BBNs. In this view, which we call mechanism-based, causality is defined within models and causal asymmetries arise when mechanisms are placed in the context of a system. We lay the link between structural equations models and BBNs models and formulate the conditions under which the latter can be given causal interpretation.
62731399
NAS parallel benchmark results
The NAS (Numerical Aerodynamic Simulation) parallel benchmarks have been developed at NASA Ames Research Center to study the performance of parallel supercomputer. The eight benchmark problems are specified in a 'pencil and paper' fashion. The performance results of various systems using the NAS parallel benchmarks are presented. These results represent the best results that have been reported to the authors for the specific systems listed. They represent implementation efforts performed by personnel in both the NAS Applied Research Branch of NASA Ames Research Center and in other organizations.<<ETX>>
36371266
Some Further Notes on a Class of Skew Distribution Functions
This note takes issue with a recent criticism by Dr. B. Mandelbrot of a certain stochastic model to explain word-frequency data. Dr. Mandelbrot's principal empirical and mathematical objections to the model are shown to be unfounded. A central question is whether the basic parameter of the distributions is larger or smaller than unity. The empirical data show it is almost always very close to unity, sometimes slightly larger, sometimes smaller. Simple stochastic models can be constructed for either case, and give a special status, as a limiting case, to instances where the parameter is unity. More generally, the empirical data can be explained by two types of stochastic models as well as by models assuming efficient information coding. The three types of models are briefly characterized and compared.
1494125
Gordon Bell prize lectures
No abstract available