395,035 research outputs found
Regularized Regression Problem in hyper-RKHS for Learning Kernels
This paper generalizes the two-stage kernel learning framework, illustrates
its utility for kernel learning and out-of-sample extensions, and proves
{asymptotic} convergence results for the introduced kernel learning model.
Algorithmically, we extend target alignment by hyper-kernels in the two-stage
kernel learning framework. The associated kernel learning task is formulated as
a regression problem in a hyper-reproducing kernel Hilbert space (hyper-RKHS),
i.e., learning on the space of kernels itself. To solve this problem, we
present two regression models with bivariate forms in this space, including
kernel ridge regression (KRR) and support vector regression (SVR) in the
hyper-RKHS. By doing so, it provides significant model flexibility for kernel
learning with outstanding performance in real-world applications. Specifically,
our kernel learning framework is general, that is, the learned underlying
kernel can be positive definite or indefinite, which adapts to various
requirements in kernel learning. Theoretically, we study the convergence
behavior of these learning algorithms in the hyper-RKHS and derive the learning
rates. Different from the traditional approximation analysis in RKHS, our
analyses need to consider the non-trivial independence of pairwise samples and
the characterisation of hyper-RKHS. To the best of our knowledge, this is the
first work in learning theory to study the approximation performance of
regularized regression problem in hyper-RKHS.Comment: 25 pages, 3 figure
On Learning with Finite Memory
We consider an infinite collection of agents who make decisions,
sequentially, about an unknown underlying binary state of the world. Each
agent, prior to making a decision, receives an independent private signal whose
distribution depends on the state of the world. Moreover, each agent also
observes the decisions of its last K immediate predecessors. We study
conditions under which the agent decisions converge to the correct value of the
underlying state. We focus on the case where the private signals have bounded
information content and investigate whether learning is possible, that is,
whether there exist decision rules for the different agents that result in the
convergence of their sequence of individual decisions to the correct state of
the world. We first consider learning in the almost sure sense and show that it
is impossible, for any value of K. We then explore the possibility of
convergence in probability of the decisions to the correct state. Here, a
distinction arises: if K equals 1, learning in probability is impossible under
any decision rule, while for K greater or equal to 2, we design a decision rule
that achieves it. We finally consider a new model, involving forward looking
strategic agents, each of which maximizes the discounted sum (over all agents)
of the probabilities of a correct decision. (The case, studied in previous
literature, of myopic agents who maximize the probability of their own decision
being correct is an extreme special case.) We show that for any value of K, for
any equilibrium of the associated Bayesian game, and under the assumption that
each private signal has bounded information content, learning in probability
fails to obtain
Using Hybrid Effectively in Christian Higher Education
Hybrid is just one of a number of terms used for the convergence of face-to-face and online learning, At the University of Central Florida (UCF) they are called mixed mode courses, In the corporate world the most common language used for hybrid is blended learning, Blended learning, says Bob Mosher, is about using multiple learning modalities, which include, but are not limited to, the Web.7 The blended learning term is also being used more frequently within academic circles,8 Because of the inconsistency in how blended learning is employed, though, and because our goal is not to describe learning in general but to focus on individual courses, this article will use the term hybrid and will apply it more narrowly to mean a course in which face-to-face and online learning are integrated in such a way that the seat time of the course is reduced
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