Computing the Kullback-Leibler Divergence between two Weibull Distributions

We derive a closed form solution for the Kullback-Leibler divergence between two Weibull distributions. These notes are meant as reference material and intended to provide a guided tour towards a result that is often mentioned but seldom made explicit in the literature

Retinal metric: a stimulus distance measure derived from population neural responses

The ability of the organism to distinguish between various stimuli is limited by the structure and noise in the population code of its sensory neurons. Here we infer a distance measure on the stimulus space directly from the recorded activity of 100 neurons in the salamander retina. In contrast to previously used measures of stimulus similarity, this "neural metric" tells us how distinguishable a pair of stimulus clips is to the retina, given the noise in the neural population response. We show that the retinal distance strongly deviates from Euclidean, or any static metric, yet has a simple structure: we identify the stimulus features that the neural population is jointly sensitive to, and show the SVM-like kernel function relating the stimulus and neural response spaces. We show that the non-Euclidean nature of the retinal distance has important consequences for neural decoding.Comment: 5 pages, 4 figures, to appear in Phys Rev Let

Direct Ensemble Estimation of Density Functionals

Estimating density functionals of analog sources is an important problem in statistical signal processing and information theory. Traditionally, estimating these quantities requires either making parametric assumptions about the underlying distributions or using non-parametric density estimation followed by integration. In this paper we introduce a direct nonparametric approach which bypasses the need for density estimation by using the error rates of k-NN classifiers asdata-driven basis functions that can be combined to estimate a range of density functionals. However, this method is subject to a non-trivial bias that dramatically slows the rate of convergence in higher dimensions. To overcome this limitation, we develop an ensemble method for estimating the value of the basis function which, under some minor constraints on the smoothness of the underlying distributions, achieves the parametric rate of convergence regardless of data dimension.Comment: 5 page

An on-line speaker adaptation method for HMM-based speech recognizers

In the past few years numerous techniques have been proposed to improve the efficiency of basic adaptation methods like MLLR and MAP. These adaptation methods have a common aim, which is to increase the likelihood of the phoneme models for a particular speaker. During their operation, these speaker adaptation methods need precise phonetic segmentation information of the actual utterance, but these data samples are often faulty. To improve the overall performance, only those frames from the spoken sentence which are well segmented should be retained, while the incorrectly segmented data should not be used during adaptation. Several heuristic algorithms have been proposed in the literature for the selection of the reliably segmented data blocks, and here we would like to suggest some new heuristics that discriminate between faulty and well-segmented data. The effect of these methods on the efficiency of speech recognition using speaker adaptation is examined, and conclusions for each will be drawn. Besided post-filtering the set of the segmented adaptation examples, another way of improving the efficiency of the adaptation method might be to create a more precise segmentation, which should then reduce the chance of faulty data samples being included. We suggest a method like this here as well which is based on a scoring procedure for the N-best lists, taking into account phoneme duration

Beyond Gauss: Image-Set Matching on the Riemannian Manifold of PDFs

State-of-the-art image-set matching techniques typically implicitly model each image-set with a Gaussian distribution. Here, we propose to go beyond these representations and model image-sets as probability distribution functions (PDFs) using kernel density estimators. To compare and match image-sets, we exploit Csiszar f-divergences, which bear strong connections to the geodesic distance defined on the space of PDFs, i.e., the statistical manifold. Furthermore, we introduce valid positive definite kernels on the statistical manifolds, which let us make use of more powerful classification schemes to match image-sets. Finally, we introduce a supervised dimensionality reduction technique that learns a latent space where f-divergences reflect the class labels of the data. Our experiments on diverse problems, such as video-based face recognition and dynamic texture classification, evidence the benefits of our approach over the state-of-the-art image-set matching methods