Figure 6

Statistical learning: Log-likelihood estimation procedure for unsupervised clustering of class-specific observations in a one-dimensional example. The histograms of two distinct classes of observations show substantial overlap between their distributions that are Gaussian with unit variance and means 0 and 2 respectively (top). The initial estimates of the log-likelihood ratio at the observations using the k-means strategy reveal the structure of the unknown true log likelihood ratio shown in the continuous line but are degraded by heavy noise (middle). The final estimates achieved using support vector machine regression accurately capture the unknown log-likelihood ratio and identify the samples that are specific to classes 1 and 2 along with those that are non-specific according to their log-likelihoods with respect to the 95% specificity thresholds given by ± log(95/5) (bottom).