Nonlinear embedding algorithms such as stochastic neighbor embedding do dimensionality reduction by optimizing an objective function involving similarities between pairs of input patterns. The result is a low-dimensional projection of each input pattern. A common way to define an out-of-sample mapping is to optimize the objective directly over a parametric mapping of the inputs, such as a neura...

Joint distributions over many variables are frequently modeled by decomposing them into products of simpler, lower-dimensional conditional distributions, such as in sparsely connected Bayesian networks. However, au­ tomatically learning such models can be very computationally expensive when there are many datapoints and many continuous vari­ ables with complex nonlinear relationships, particula...

We present an algorithm for the inference of context-free graph grammars from examples. The algorithm builds on an earlier system for frequent substructure discovery, and is biased toward grammars that minimize description length. Grammar features include recursion, variables and relationships. We present an illustrative example, demonstrate the algorithm’s ability to learn in the presence of n...

We present an algorithm for the inference of context-free graph grammars from examples. The algorithm builds on an earlier system for frequent substructure discovery, and is biased toward grammars that minimize description length. Grammar features include recursion, variables and relationships. We present an illustrative example, demonstrate the algorithm’s ability to learn in the presence of n...

in this paper, the variational iteration method proposed by ji-huan he is applied to solve both linear and nonlinear schrodinger equations. the main property of the method is in its flexibility and ability to solve linear and nonlinear equations accurately and conveniently. in this method, general lagrange multipliers are introduced to construct correction functionals to the problems. the multi...

Children learn causal relationships quickly and make far-reaching causal inferences from what they observe. Acquiring abstract causal principles that allow generalization across different causal relationships could support these abilities. We examine children's ability to acquire abstract knowledge about the forms of causal relationships and show that in some cases they learn better than adults...