Related papers: Structured Prediction with Projection Oracles
In this paper we analyze several new methods for solving nonconvex optimization problems with the objective function formed as a sum of two terms: one is nonconvex and smooth, and another is convex but simple and its structure is known.…
Many important computer vision tasks are naturally formulated to have a non-differentiable objective. Therefore, the standard, dominant training procedure of a neural network is not applicable since back-propagation requires the gradients…
The ability to predict future states of the environment is a central pillar of intelligence. At its core, effective prediction requires an internal model of the world and an understanding of the rules by which the world changes. Here, we…
We consider estimating a compact set from finite data by approximating the support function of that set via sublinear regression. Support functions uniquely characterize a compact set up to closure of convexification, and are sublinear…
Deeply-learned planning methods are often based on learning representations that are optimized for unrelated tasks. For example, they might be trained on reconstructing the environment. These representations are then combined with predictor…
Measuring the accuracy of cross-sectional predictions is a subjective problem. Generally, this problem is avoided. In contrast, this paper confronts subjectivity up front by eliciting an impartial decision-maker's preferences. These…
We build a unifying convex analysis framework characterizing the statistical properties of a large class of penalized estimators, both under a regular and an irregular design. Our framework interprets penalized estimators as proximal…
We propose a geometric algorithm for topic learning and inference that is built on the convex geometry of topics arising from the Latent Dirichlet Allocation (LDA) model and its nonparametric extensions. To this end we study the…
In this paper, we propose a new method based on the Sliding Algorithm from Lan(2016, 2019) for the convex composite optimization problem that includes two terms: smooth one and non-smooth one. Our method uses the stochastic noised…
Recent works have developed new projection-free first-order methods based on utilizing linesearches and normal vector computations to maintain feasibility. These oracles can be cheaper than orthogonal projection or linear optimization…
We present a framework to model the perceived quality of audio signals by combining convolutional architectures, with ideas from classical signal processing, and describe an approach to enhancing perceived acoustical quality. We demonstrate…
A key problem in multiobjective linear programming is to find the set of all efficient extreme points in objective space. In this paper we introduce oriented projective geometry as an efficient and effective framework for solving this…
Projection algorithms are well known for their simplicity and flexibility in solving feasibility problems. They are particularly important in practice due to minimal requirements for software implementation and maintenance. In this work, we…
Recent object detection systems rely on two critical steps: (1) a set of object proposals is predicted as efficiently as possible, and (2) this set of candidate proposals is then passed to an object classifier. Such approaches have been…
We develop and analyze algorithms for distributionally robust optimization (DRO) of convex losses. In particular, we consider group-structured and bounded $f$-divergence uncertainty sets. Our approach relies on an accelerated method that…
Structured prediction is used in areas such as computer vision and natural language processing to predict structured outputs such as segmentations or parse trees. In these settings, prediction is performed by MAP inference or, equivalently,…
A powerful data transformation method named guided projections is proposed creating new possibilities to reveal the group structure of high-dimensional data in the presence of noise variables. Utilising projections onto a space spanned by a…
Folded concave penalization methods have been shown to enjoy the strong oracle property for high-dimensional sparse estimation. However, a folded concave penalization problem usually has multiple local solutions and the oracle property is…
We present a feasibility-seeking approach to neural network training. This mathematical optimization framework is distinct from conventional gradient-based loss minimization and uses projection operators and iterative projection algorithms.…
We consider the problem of projecting a convex set onto a subspace, or equivalently formulated, the problem of computing a set obtained by applying a linear mapping to a convex feasible set. This includes the problem of approximating convex…