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The joint optimization of the reconstruction and classification error is a hard non convex problem, especially when a non linear mapping is utilized. In order to overcome this obstacle, a novel optimization strategy is proposed, in which a…
In this paper, we propose Neural Spectrum Decomposition, a generic decomposition framework for dataset distillation. Unlike previous methods, we consider the entire dataset as a high-dimensional observation that is low-rank across all…
We present a new scientific machine learning method that learns from data a computationally inexpensive surrogate model for predicting the evolution of a system governed by a time-dependent nonlinear partial differential equation (PDE), an…
In this paper we propose an optimization-based framework to multiple object matching. The framework takes maps computed between pairs of objects as input, and outputs maps that are consistent among all pairs of objects. The central idea of…
The resolution of optical imaging is classically limited by the width of the point-spread function, which in turn is determined by the Rayleigh length. Recently, spatial-mode demultiplexing (SPADE) has been proposed as a method to achieve…
Deep learning based techniques achieve state-of-the-art results in a wide range of image reconstruction tasks like compressed sensing. These methods almost always have hyperparameters, such as the weight coefficients that balance the…
We consider the decomposition of bounded linear operators on Hilbert spaces in terms of functions forming frames. Similar to the singular-value decomposition, the resulting frame decompositions encode information on the structure and…
Optimization decomposition methods are a fundamental tool to develop distributed solution algorithms for large scale optimization problems arising in fields such as machine learning and optimal control. In this paper, we present an…
The ability to differentiate through optimization problems has unlocked numerous applications, from optimization-based layers in machine learning models to complex design problems formulated as bilevel programs. It has been shown that…
Distributed algorithms have been playing an increasingly important role in many applications such as machine learning, signal processing, and control. Significant research efforts have been devoted to developing and analyzing new algorithms…
Prediction models can perform poorly when deployed to target distributions different from the training distribution. To understand these operational failure modes, we develop a method, called DIstribution Shift DEcomposition (DISDE), to…
This paper presents a hybrid algorithm that combines features form both Sqrt(3) and Loop Subdivision schemes. The algorithm aims at preserving sharp features and trim regions, during the surfaces subdivision, using a set of rules. The…
The blind image deconvolution is a challenging, highly ill-posed nonlinear inverse problem. We introduce a Multiscale Hierarchical Decomposition Method (MHDM) that is iteratively solving variational problems with adaptive data and…
Prediction+optimization is a common real-world paradigm where we have to predict problem parameters before solving the optimization problem. However, the criteria by which the prediction model is trained are often inconsistent with the goal…
In computational reinforcement learning, a growing body of work seeks to express an agent's model of the world through predictions about future sensations. In this manuscript we focus on predictions expressed as General Value Functions:…
A novel algorithm for tunable compression to within the precision of reproduction targets, or storage, is proposed. The new algorithm is termed the `Perceptron Algorithm', which utilises simple existing concepts in a novel way, has multiple…
Partition-wise models offer a flexible approach for modeling complex and multidimensional data that are capable of producing interpretable results. They are based on partitioning the observed data into regions, each of which is modeled with…
We introduce sparse random projection, an important dimension-reduction tool from machine learning, for the estimation of discrete-choice models with high-dimensional choice sets. Initially, high-dimensional data are compressed into a…
Most existing studies on evolutionary multi-objective optimization focus on approximating the whole Pareto-optimal front. Nevertheless, rather than the whole front, which demands for too many points (especially in a high-dimensional space),…
Fitting statistical models is computationally challenging when the sample size or the dimension of the dataset is huge. An attractive approach for down-scaling the problem size is to first partition the dataset into subsets and then fit…