We propose an independence criterion based on the eigenspectrum of covariance operators in reproducing kernel Hilbert spaces (RKHSs), consisting of an empirical estimate of the Hilbert-Schmidt norm of the cross-covariance operator (we term this a Hilbert-Schmidt Independence Criterion, or HSIC). This approach has several advantages, compared with previous kernel-based independence criteria. First, the empirical estimate is simpler than any other kernel dependence test, and requires no user-defined regularisation. Second, there is a clearly defined population quantity which the empirical estimate approaches in the large sample limit, with exponential convergence guaranteed between the two: this ensures that independence tests based on HSIC do not suffer from slow learning rates. Finally, we show in the context of independent component analysis (ICA) that the performance of HSIC is competitive with that of previously published kernel-based criteria, and of other recently published ICA methods.

http://www.dbs.ifi.lmu.de/~borgward/MMD.

Given sets of observations of training and test data, we consider the problem of re-weighting the training data such that its distribution more closely matches that of the test data. We achieve this goal by matching covariate distributions between training and test sets in a high dimensional feature space (specifically, a reproducing kernel Hilbert space). This approach does not require distribution estimation. Instead, the sample weights are obtained by a simple quadratic programming procedure. We provide a uniform convergence bound on the distance between the reweighted training feature mean and the test feature mean, a transductive bound on the expected loss of an algorithm trained on the reweighted data, and a connection to single class SVMs. While our method is designed to deal with the case of simple covariate shift (in the sense of Chapter ??), we have also found benefits for sample selection bias on the labels. Our correction procedure yields its greatest and most consistent advantages when the learning algorithm returns a classifier/regressor that is "simpler" than the data might suggest.

Local field potentials (LFPs) reflect subthreshold integrative processes that complement spike train measures. However, little is yet known about the differences between how LFPs and spikes encode rich naturalistic sensory stimuli. We addressed this question by recording LFPs and spikes from the primary visual cortex of anesthetized macaques while presenting a color movie. We then determined how the power of LFPs and spikes at different frequencies represents the visual features in the movie. We found that the most informative LFP frequency ranges were 1-8 and 60 -100 Hz. LFPs in the range of 12-40 Hz carried little information about the stimulus, and may primarily reflect neuromodulatory inputs. Spike power was informative only at frequencies Ͻ12 Hz. We further quantified "signal correlations" (correlations in the trial-averaged power response to different stimuli) and "noise correlations" (trial-by-trial correlations in the fluctuations around the average) of LFPs and spikes recorded from the same electrode. We found positive signal correlation between high-gamma LFPs (60 -100 Hz) and spikes, as well as strong positive signal correlation within high-gamma LFPs, suggesting that high-gamma LFPs and spikes are generated within the same network. LFPs Ͻ24 Hz shared strong positive noise correlations, indicating that they are influenced by a common source, such as a diffuse neuromodulatory input. LFPs Ͻ40 Hz showed very little signal and noise correlations with LFPs Ͼ40 Hz and with spikes, suggesting that low-frequency LFPs reflect neural processes that in natural conditions are fully decoupled from those giving rise to spikes and to high-gamma LFPs.