We provide novel theoretical insights on structured prediction in the context of efficient convex surrogate loss minimization with consistency guarantees. For any task loss, we construct a convex surrogate that can be optimized via stochastic gradient descent and we prove tight bounds on the so-called "calibration function" relating the excess surrogate risk to the actual risk. In contrast to prior related work, we carefully monitor the effect of the exponential number of classes in the learning guarantees as well as on the optimization complexity. As an interesting consequence, we formalize the intuition that some task losses make learning harder than others, and that the classical 0-1 loss is ill-suited for general structured prediction.

This (https://arxiv.org/abs/1703.02403) is joint work with Anton Osokin and Francis Bach.

Authors: Matej Balog, Ilya Tolstikhin, Bernhard Schölkopf.

Authors: Ho Chung Leon Law, Dougal J. Sutherland, Dino Sejdinovic, Seth Flaxman.

Authors: Bo Dai, Niao He, Yunpeng Pan, Byron Boots, Le Song. Poster session continues at 14:50 - 15:50.

Author: Tomasz Arodz. Poster session continues at 14:50 - 15:50.

Authors: Le Hou, Chen-Ping Yu, Dimitris Samaras. Poster session continues at 14:50 - 15:50.

Authors: Thosini K. Bamunu Mudiyanselage, Yanqing Zhang. Poster session continues at 14:50 - 15:50.

Author: Jorge Luis Guevara Diaz. Poster session continues at 14:50 - 15:50.

Authors: Rune K. Nielsen, Aasa Feragen, Andreas Holm. Poster session continues at 14:50 - 15:50.

Authors: Sainyam Galhotra, Arya Mazumdar, Soumyabrata Pal, Barna Saha. Poster session continues at 14:50 - 15:50.

Authors: Ashwin Pananjady, Cheng Mao, Vidya Muthukumar, Martin Wainwright, Thomas Courtade. Poster session continues at 14:50 - 15:50.

Authors: Denny Wu, Makoto Yamada, Ichiro Takeuchi, Kenji Fukumizu. Poster session continues at 14:50 - 15:50.

Authors: Daniel Hsu, Kevin Shi, Xiaorui Sun. Poster session continues at 14:50 - 15:50.

Authors: Vassilis Kalofolias, Nathanael Perraudin. Poster session continues at 14:50 - 15:50.

Authors: Matej Balog, Ilya Tolstikhin, Bernhard Schölkopf. Poster session continues at 14:50 - 15:50.

Authors: Nguyen Quang Tran, Alexander Jung, Saeed Basirian. Poster session continues at 14:50 - 15:50.

Authors: Ho Chung Leon Law, Dougal J Sutherland, Dino Sejdinovic, Seth Flaxman. Poster session continues at 14:50 - 15:50.

Authors: Yunlong Jiao, Jean-Philippe Vert. Poster session continues at 14:50 - 15:50.

Authors: Horia Mania, Aaditya Ramdas, Martin Wainwright, Michael Jordan, Benjamin Recht. Poster session continues at 14:50 - 15:50.

Authors: Nguyen Quang Tran, Alexander Jung, Saeed Basirian.

Authors: Ashwin Pananjady, Cheng Mao, Vidya Muthukumar, Martin Wainwright, Thomas Courtade.

Authors: Yunlong Jiao, Jean-Philippe Vert.

Authors: Horia Mania, Aaditya Ramdas, Martin Wainwright, Michael Jordan, Benjamin Recht.

Topological data analysis (TDA) is a recent methodology for extracting topological and geometrical features from complex geometric data structures. Persistent homology, a new mathematical notion proposed by Edelsbrunner (2002), provides a multiscale descriptor for the topology of data, and has been recently applied to a variety of data analysis. In this talk I will introduce a machine learning framework of TDA by combining persistence homology and kernel methods. As an expression of persistent homology, persistence diagrams are widely used to express the lifetimes of generators of homology groups. While they serve as a compact representation of data, it is not straightforward to apply standard data analysis to persistence diagrams, since they consist of a set of points in 2D space expressing the lifetimes. We introduce a method of kernel embedding of the persistence diagrams to obtain their vector representation, which enables one to apply any kernel methods in topological data analysis, and propose a persistence weighted Gaussian kernel as a suitable kernel for vectorization of persistence diagrams. Some theoretical properties including Lipschitz continuity of the embedding are also discussed. I will also present applications to change point detection and time series analysis in the field of material sciences and biochemistry.

Positive semidefinite operator-valued kernel generalizes the well-known notion of reproducing kernel, and is a main concept underlying many kernel-based vector-valued learning algorithms. In this talk I will give a brief introduction to learning with operator-valued kernels, discuss current challenges in the field, and describe convenient schemes to overcome them. I'll overview our recent work on learning with functional data in the case where both attributes and labels are functions. In this setting, a set of rigorously defined infinite-dimensional operator-valued kernels that can be valuably applied when the data are functions is described, and a learning scheme for nonlinear functional data analysis is introduced. The methodology is illustrated through speech and audio signal processing experiments.

The most common machine learning algorithms operate on finite-dimensional vectorial feature representations. In many applications, however, the natural representation of the data consists of distributions, sets, and other complex objects rather than finite-dimensional vectors. In this talk we will review machine learning algorithms that can operate directly on these complex objects. We will discuss applications in various scientific problems including estimating the cosmological parameters of our Universe, dynamical mass measurements of galaxy clusters, finding anomalous events in fluid dynamics, and estimating phenotypes in agriculturally important plants.

Most existing neural networks for learning graphs deal with the issue of permutation invariance by conceiving of the network as a message passing scheme, where each node sums the feature vectors coming from its neighbors. We argue that this imposes a limitation on their representation power, and instead propose a new general architecture for representing objects consisting of a hierarchy of parts, which we call covariant compositional networks (CCNs). Here covariance means that the activation of each neuron must transform in a specific way under permutations, similarly to steerability in CNNs. We achieve covariance by making each activation transform according to a tensor representation of the permutation group, and derive the corresponding tensor aggregation rules that each neuron must implement. Experiments show that CCNs can outperform competing methods on some standard graph learning benchmarks.