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The existence of strongly polynomial-time algorithm for linear programming is a cross-century international mathematical problem, whose breakthrough will solve a major theoretical crisis for the development of artificial intelligence. In…
Convolution neural networks (CNNs) have shown great success in various applications. However, the computational complexity and memory storage of CNNs is a bottleneck for their deployment on resource-constrained devices. Recent efforts…
We develop several efficient algorithms for the classical \emph{Matrix Scaling} problem, which is used in many diverse areas, from preconditioning linear systems to approximation of the permanent. On an input $n\times n$ matrix $A$, this…
Kernel methods provide a principled way to perform non linear, nonparametric learning. They rely on solid functional analytic foundations and enjoy optimal statistical properties. However, at least in their basic form, they have limited…
Identification of model parameters in computer simulations is an important topic in computer experiments. We propose a new method, called the projected kernel calibration method, to estimate these model parameters. The proposed method is…
We present a novel algorithm which can overcome the drawbacks of the conventional linear scaling method with minimal computational overhead. This is achieved by introducing additional constraints, thus eliminating the redundancy of the…
The number of non-negative integer matrices with given row and column sums appears in a variety of problems in mathematics and statistics but no closed-form expression for it is known, so we rely on approximations of various kinds. Here we…
We introduce a new method for speeding up the inference of deep neural networks. It is somewhat inspired by the reduced-order modeling techniques for dynamical systems.The cornerstone of the proposed method is the maximum volume algorithm.…
We develop algorithms for inner approximating the cone of positive semidefinite matrices via linear programming and second order cone programming. Starting with an initial linear algebraic approximation suggested recently by Ahmadi and…
Random projections have proven extremely useful in many signal processing and machine learning applications. However, they often require either to store a very large random matrix, or to use a different, structured matrix to reduce the…
We study the problem of instance segmentation in biological images with crowded and compact cells. We formulate this task as an integer program where variables correspond to cells and constraints enforce that cells do not overlap. To solve…
Kernel logistic regression (KLR) is a conventional nonlinear classifier in machine learning. With the explosive growth of data size, the storage and computation of large dense kernel matrices is a major challenge in scaling KLR. Even the…
Reduced modeling of a computationally demanding dynamical system aims at approximating its trajectories, while optimizing the trade-off between accuracy and computational complexity. In this work, we propose to achieve such an approximation…
Deep networks are nowadays becoming popular in many computer vision and pattern recognition tasks. Among these networks, deep kernels are particularly interesting and effective, however, their computational complexity is a major issue…
The CUR decomposition is a technique for low-rank approximation that selects small subsets of the columns and rows of a given matrix to use as bases for its column and rowspaces. It has recently attracted much interest, as it has several…
The proximal bundle method (PBM) is a fundamental and computationally effective algorithm for solving nonsmooth optimization problems. In this paper, we present the first variant of the PBM for smooth objectives, achieving an accelerated…
We study the problem of exact completion for $m \times n$ sized matrix of rank $r$ with the adaptive sampling method. We introduce a relation of the exact completion problem with the sparsest vector of column and row spaces (which we call…
Multiple-input multiple-output (MIMO) systems are playing an important role in the recent wireless communication. The complexity of the different systems models challenge different researches to get a good complexity to performance balance.…
A matrix algorithm is said to be superfast (that is, runs at sublinear cost) if it involves much fewer scalars and flops than the input matrix has entries. Such algorithms have been extensively studied and widely applied in modern…
Kernel approximation via nonlinear random feature maps is widely used in speeding up kernel machines. There are two main challenges for the conventional kernel approximation methods. First, before performing kernel approximation, a good…