We present a novel approach to efficiently learn a label tree for large scale classification with many classes. The key contribution of the approach is a technique to simultaneously determine the structure of the tree and learn the classifiers for each node in the tree. This approach also allows fine grained control over the efficiency vs accuracy trade-off in designing a label tree, leading to more balanced trees. Experiments are performed on large scale image classification with 10184 classes and 9 million images. We demonstrate significant improvements in test accuracy and efficiency with less training time and more balanced trees compared to the previous state of the art by Bengio et al.

Many applications in computer vision measure the similarity between images or image patches based on some statistics such as oriented gradients. These are often modeled implicitly or explicitly with a Gaussian noise assumption, leading to the use of the Euclidean distance when comparing image descriptors. In this paper, we show that the statistics of gradient based image descriptors often follow a heavy-tailed distribution, which undermines any principled motivation for the use of Euclidean distances. We advocate for the use of a distance measure based on the likelihood ratio test with appropriate probabilistic models that fit the empirical data distribution. We instantiate this similarity measure with the Gammacompound-Laplace distribution, and show significant improvement over existing distance measures in the application of SIFT feature matching, at relatively low computational cost.

Multiclass prediction is the problem of classifying an object into a relevant target class. We consider the problem of learning a multiclass predictor that uses only few features, and in particular, the number of used features should increase sublinearly with the number of possible classes. This implies that features should be shared by several classes. We describe and analyze the ShareBoost algorithm for learning a multiclass predictor that uses few shared features. We prove that Share-Boost efficiently finds a predictor that uses few shared features (if such a predictor exists) and that it has a small generalization error. We also describe how to use ShareBoost for learning a non-linear predictor that has a fast evaluation time. In a series of experiments with natural data sets we demonstrate the benefits of Share-Boost and evaluate its success relatively to other state-of-the-art approaches.

Clustering is a popular problem with many applications. We consider the k-means problem in the situation where the data is too large to be stored in main memory and must be accessed sequentially, such as from a disk, and where we must use as little memory as possible. Our algorithm is based on recent theoretical results, with significant improvements to make it practical. Our approach greatly simplifies a recently developed algorithm, both in design and in analysis, and eliminates large constant factors in the approximation guarantee, the memory requirements, and the running time. We then incorporate approximate nearest neighbor search to compute k-means in o( nk) (where n is the number of data points; note that computing the cost, given a solution, takes 8(nk) time). We show that our algorithm compares favorably to existing algorithms - both theoretically and experimentally, thus providing state-of-the-art performance in both theory and practice.

We prove a new oracle inequality for support vector machines with Gaussian RBF kernels solving the regularized least squares regression problem. To this end, we apply the modulus of smoothness. With the help of the new oracle inequality we then derive learning rates that can also be achieved by a simple data-dependent parameter selection method. Finally, it turns out that our learning rates are asymptotically optimal for regression functions satisfying certain standard smoothness conditions.

We consider the problem of Ising and Gaussian graphical model selection given n i.i.d.

We introduce a Gaussian process model of functions which are additive. An additive function is one which decomposes into a sum of low-dimensional functions, each depending on only a subset of the input variables. Additive GPs generalize both Generalized Additive Models, and the standard GP models which use squared-exponential kernels. Hyperparameter learning in this model can be seen as Bayesian Hierarchical Kernel Learning (HKL). We introduce an expressive but tractable parameterization of the kernel function, which allows efficient evaluation of all input interaction terms, whose number is exponential in the input dimension. The additional structure discoverable by this model results in increased interpretability, as well as state-of-the-art predictive power in regression tasks.

For a learning problem whose associated excess loss class is (β, B)-Bernstein, we show that it is theoretically possible to track the same classification performance of the best (unknown) hypothesis in our class, provided that we are free to abstain from prediction in some region of our choice.

We introduce hierarchically supervised latent Dirichlet allocation (HSLDA), a model for hierarchically and multiply labeled bag-of-word data. Examples of such data include web pages and their placement in directories, product descriptions and associated categories from product hierarchies, and free-text clinical records and their assigned diagnosis codes. Out-of-sample label prediction is the primary goal of this work, but improved lower-dimensional representations of the bagof-word data are also of interest. We demonstrate HSLDA on large-scale data from clinical document labeling and retail product categorization tasks. We show that leveraging the structure from hierarchical labels improves out-of-sample label prediction substantially when compared to models that do not.

This paper proposes a novel boosting algorithm called VadaBoost which is motivated by recent empirical Bernstein bounds. VadaBoost iteratively minimizes a cost function that balances the sample mean and the sample variance of the exponential loss. Each step of the proposed algorithm minimizes the cost efficiently by providing weighted data to a weak learner rather than requiring a brute force evaluation of all possible weak learners. Thus, the proposed algorithm solves a key limitation of previous empirical Bernstein boosting methods which required brute force enumeration of all possible weak learners. Experimental results confirm that the new algorithm achieves the performance improvements of EBBoost yet goes beyond decision stumps to handle any weak learner. Significant performance gains are obtained over AdaBoost for arbitrary weak learners including decision trees (CART).