Inner-product operators, often referred to as kernels in statistical learning, define a mapping from some input space into a feature space. The focus of this letter is the construction of biologically motivated kernels for cortical activities. The kernels we derive, termed Spikernels, map spike count sequences into an abstract vector space in which we can perform various prediction tasks. We discuss in detail the derivation of Spikernels and describe an efficient algorithm for computing their value on any two sequences of neural population spike counts. We demonstrate the merits of our modeling approach by comparing the Spikernel to various standard kernels in the task of predicting hand movement velocities from cortical recordings. All of the kernels that we tested in our experiments outperform the standard scalar product used in linear regression, with the Spikernel consistently achieving the best performance.

We discuss the problem of ranking instances. In our framework, each instance is associated with a rank or a rating, which is an integer in 1 to k . Our goal is to find a rank-prediction rule that assigns each instance a rank that is as close as possible to the instance's true rank. We discuss a group of closely related online algorithms, analyze their performance in the mistake-bound model, and prove their correctness. We describe two sets of experiments, with synthetic data and with the Each Movie data set for collaborative filtering. In the experiments we performed, our algorithms outperform online algorithms for regression and classification applied to ranking.

We describe and analyze a mixture model for supervised learning of probabilistic transducers. We devise an online learning algorithm that efficiently infers the structure and estimates the parameters of each probabilistic transducer in the mixture. Theoretical analysis and comparative simulations indicate that the learning algorithm tracks the best transducer from an arbitrarily large (possibly infinite) pool of models. We also present an application of the model for inducing a noun phrase recognizer.