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The advantages of discriminative learning algorithms and kernel machines are combined with gen-erative modeling using a novel kernel between distributions. In the probability product kernel, data points in the input space are mapped to distributions over the sample space and a general inner product is then evaluated as the integral of the product of pairs… (More)

Tony Jebara We present a general framework for discriminative estimation based on the maximum entropy principle and its extensions. All calculations involve distributions over structures and/or parameters rather than specific settings and reduce to relative entropy projections. This holds even when the data is not separable within the chosen parametric… (More)

We propose a new technique for direct visual matching of images for the purposes of face recognition and image retrieval, using a probabilistic measure of similarity, based primarily on a Bayesian (MAP) analysis of image di!erences. The performance advantage of this probabilistic matching technique over standard Euclidean nearest-neighbor eigenface matching… (More)

In various application domains, including image recognition, it is natural to represent each example as a set of vectors. With a base kernel we can implicitly map these vectors to a Hilbert space and fit a Gaussian distribution to the whole set using Kernel PCA. We define our kernel between examples as Bhattacharyya's measure of affinity between such… (More)

- David Lazer, Alex Pentland, Lada Adamic, Sinan Aral, Albert-László Barabási, Devon Brewer +12 others
- 2009

centered on a large database, but in this case it is entirely of living organisms, the marine bivalves. Over 28,000 records of bivalve gen-era and subgenera from 322 locations around the world have now been compiled by these authors, giving a global record of some 854 genera and subgenera and 5132 species. No fossils are included in the database, but… (More)

Clustering has recently enjoyed progress via spectral methods which group data using only pairwise affinities and avoid parametric assumptions. While spectral clustering of vector inputs is straightforward , extensions to structured data or time-series data remain less explored. This paper proposes a clustering method for time-series data that couples… (More)

- Tony Jebara, Risi Kondor
- 2003

We introduce a new class of kernels between distributions. These induce a kernel on the input space between data points by associating to each datum a generative model fit to the data point individually. The kernel is then computed by integrating the product of the two generative models corresponding to two data points. This kernel permits discriminative… (More)

We present an efficient algorithm for approximately maintaining and updating a distribution over permutations matching tracks to real world objects. The algorithm hinges on two insights from the theory of harmonic analysis on noncommutative groups. The first is that most of the information in the distribution over permutations is captured by certain " low… (More)

Leading classification methods such as support vector machines (SVMs) and their counterparts achieve strong generalization performance by maximizing the margin of separation between data classes. While the maximum margin approach has achieved promising performance , this article identifies its sensitivity to affine transformations of the data and to… (More)

Graph based semi-supervised learning (SSL) methods play an increasingly important role in practical machine learning systems. A crucial step in graph based SSL methods is the conversion of data into a weighted graph. However, most of the SSL literature focuses on developing label inference algorithms without extensively studying the graph building method… (More)