Various supervised inference methods can be analyzed as convex duals of the generalized maximum entropy (MaxEnt) framework. Generalized MaxEnt aims to find a distribution that maximizes an entropy function while respecting prior information represented as potential functions in miscellaneous forms of constraints and/or penalties. We extend this framework to semi-supervised learning by incorpora...

Various supervised inference methods can be analyzed as convex duals of a generalized maximum entropy framework, where the goal is to find a distribution with maximum entropy subject to the moment matching constraints on the data. We extend this framework to semi-supervised learning using two approaches: 1) by incorporating unlabeled data into the data constraints and 2) by imposing similarity ...

As a first-order method, the augmented Lagrangian method (ALM) is a benchmark solver for linearly constrained convex programming, and in practice some semi-definite proximal terms are often added to its primal variable's subproblem to make it more implementable. In this paper, we propose an accelerated PALM with indefinite proximal regularization (PALM-IPR) for convex programming with linear co...

For arbitrary real matrices F and G, the positive semi-deenite Procrustes problem is minimization of the Frr obenius norm of F ? PG with respect to positive semi-deenite symmetric P. Existing solution algorithms are based on a convex programming approach. Here an unconstrained non-convex approach is taken, namely writing P = E 0 E and optimizing with respect to E. The main result is that all lo...

Matrix completion is a well-studied problem with many machine learning applications. In practice, the problem is often solved by non-convex optimization algorithms. However, the current theoretical analysis for non-convex algorithms relies crucially on the assumption that each entry of the matrix is observed with exactly the same probability p, which is not realistic in practice. In this paper,...

A general duality framework in convex multiobjective optimization is established using the scalarization with K-strongly increasing functions and the conjugate duality for composed convex cone-constrained optimization problems. Other scalarizations used in the literature arise as particular cases and the general duality is specialized for some of them, namely linear scalarization, maximum(-line...

This paper concerns parameterized convex infinite (or semi-infinite) inequality systems whose decision variables run over general infinite-dimensional Banach (resp. finite-dimensional) spaces and that are indexed by an arbitrary fixed set T . Parameter perturbations on the right-hand side of the inequalities are measurable and bounded, and thus the natural parameter space is l∞(T ). Based on ad...

We address the problem of aggregating an ensemble of predictors with known loss bounds in a semi-supervised binary classification setting, to minimize prediction loss incurred on the unlabeled data. We find the minimax optimal predictions for a very general class of loss functions including all convex and many non-convex losses, extending a recent analysis of the problem for misclassification e...

We prove that in a convex metric space (X, d), an existence set K having a lower semi continuous metric projection is a δ-sun and in a complete M -space, a Chebyshev set K with a continuous metric projection is a γ-sun as well as almost convex.

We provide a specific representation of convex polynomials nonnegative on a convex (not necessarily compact) basic closed semi-algebraic set K ⊂ Rn. Namely, they belong to a specific subset of the quadratic module generated by the concave polynomials that define K. Mathematics Subject Classification (2000). Primary 14P10; Secondary 11E25 12D15 90C25.