We present improved methods of using structured SVMs in a large-scale hierarchical classification problem, that is when labels are leaves, or sets of leaves, in a tree or a DAG. We examine the need to normalize both the regularization and the margin and show how doing so significantly improves performance, including allowing achieving state-of-the-art results where unnormalized structured SVMs ...

We propose a new segmentation or clustering model that combines Markov Random Field (MRF) and Normalized Cut (NC) objectives. Both NC and MRF models are widely used in machine learning and computer vision, but they were not combined before due to significant differences in the corresponding optimization, e.g. spectral relaxation and combinatorial max-flow techniques. On the one hand, we show th...

We prove the existence of solutions ( λ , v ) ∈ R × H 1 Ω elliptic problem { − Δ + V x = p in Ω, > 0 ∫ 2 d ρ . Any solving such (for some is called a normalized solution, where normalization settled L Here either whole space N or bounded smooth domain which case we assume ≡ and homogeneous Dirichlet Neumann boundary conditions. Moreover, < if ≥ 3 Normalized appear different contexts, as study N...

For the Randall-Sundrum brane world where a positive tension Minkowski brane is embedded in AdS 5 , two candidate propagators have been suggested in the literature, one being based on the normalized mode solutions to the source-free volcano potential fluctuation equation, and the other being the Giddings, Katz and Randall outgoing Hankel function based one. We show that while both of these two ...

Optimization algorithms for training deep models not only affects the convergence rate and stability of the training process, but are also highly related to the generalization performance of the models. While adaptive algorithms, such as Adam and RMSprop, have shown better optimization performance than stochastic gradient descent (SGD) in many scenarios, they often lead to worse generalization ...

Estimating maps among large collections of objects (e.g., dense correspondences across images and 3D shapes) is a fundamental problem across a wide range of domains. In this paper, we provide theoretical justifications of spectral techniques for the map synchronization problem, i.e., it takes as input a collection of objects and noisy maps estimated between pairs of objects along a connected ob...

Dependent Dirichlet processes (DPs) are dependent sets of random measures, each being marginally DP distributed. They are used in Bayesian nonparametric models when the usual exchangeability assumption does not hold. We propose a simple and general framework to construct dependent DPs by marginalizing and normalizing a single gamma process over an extended space. The result is a set of DPs, eac...

A new mark-up programming language is introduced in order to facilitate and improve the visualization of ISO/EN 13606 dual model-based normalized medical information. This is the first time that visualization of normalized medical information is addressed and the programming language is intended to be used by medical non-IT professionals.

Rapid progress has been made towards question answering (QA) systems that can extract answers from text. Existing neural approaches make use of expensive bidirectional attention mechanisms or score all possible answer spans, limiting scalability. We propose instead to cast extractive QA as an iterative search problem: select the answer’s sentence, start word, and end word. This representation r...

Let G be a graph and let A and D be the adjacency matrix of G and diagonal matrix of vertex degrees of G respectively. If each vertex degree is positive, then the normalized adjacency matrix of G is  = D−1/2AD−1/2. A classification is given of those graphs for which the all eigenvalues of the normalized adjacency matrix are integral. The problem of determining those graphs G for which λ ∈ Q fo...