Statistical Learning
Solving a Class of Non-Convex Min-Max Games Using Iterative First Order Methods
Maher Nouiehed, Maziar Sanjabi, Tianjian Huang, Jason D. Lee, Meisam Razaviyayn
Neural Information Processing Systems http://nips.cc/
Escaping from saddle points on Riemannian manifolds
Yue Sun, Nicolas Flammarion, Maryam Fazel
Neural Information Processing Systems http://nips.cc/
A Latent Variational Framework for Stochastic Optimization
Neural Information Processing Systems http://nips.cc/
Sample Complexity of Learning Mixture of Sparse Linear Regressions
Akshay Krishnamurthy, Arya Mazumdar, Andrew McGregor, Soumyabrata Pal
Learning mixtures of linear regressions is a natural generalization of the basic linear regression problem.
Supplementary Material for " Partial Optimal Transport with Applications on Positive-Unlabeled Learning '
The proof involves 3 steps: 1. A null 5 (with a constant A > 2ξ) the GW formulation involves pairs of points. This yields the following cases: Case 1: a > 0. In that case, φ (γ) is a convex function, whose minimum on [0, 1] is reached for γ Using the development in Section 1.2.2 of the supplemental, we can establish that The partial-OT computation is based on a augmented problem with a dummy point and, as such, is convex. On the contrary, the GW problem is non-convex and, although the algorithm is proved to converge, there is no guarantee that the global optimum is reached. The quality of the solution is therefore highly dependent on the initialization.
A Gaussian Process Model of Quasar Spectral Energy Distributions Andrew Miller
We propose a method for combining two sources of astronomical data, spectroscopy and photometry, that carry information about sources of light (e.g., stars, galaxies, and quasars) at extremely different spectral resolutions. Our model treats the spectral energy distribution (SED) of the radiation from a source as a latent variable that jointly explains both photometric and spectroscopic observations. We place a flexible, nonparametric prior over the SED of a light source that admits a physically interpretable decomposition, and allows us to tractably perform inference. We use our model to predict the distribution of the redshift of a quasar from five-band (low spectral resolution) photometric data, the so called "photo-z" problem. Our method shows that tools from machine learning and Bayesian statistics allow us to leverage multiple resolutions of information to make accurate predictions with well-characterized uncertainties.
Efficient Exact Gradient Update for training Deep Networks with Very Large Sparse Targets
Pascal Vincent, Alexandre de Brébisson, Xavier Bouthillier
An important class of problems involves training deep neural networks with sparse prediction targets of very high dimension D . These occur naturally in e.g.
Partially View-aligned Clustering
In this paper, we study one challenging issue in multi-view data clustering.