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Solving large-scale optimization problems is a bottleneck and is very important for machine learning and multiple kinds of scientific problems. Subspace-based methods using the local approximation strategy are one of the most important…
Mainstream deep models for three-dimensional MRI synthesis are either cross-sectional or volumetric depending on the input. Cross-sectional models can decrease the model complexity, but they may lead to discontinuity artifacts. On the other…
This paper addresses smooth convexly constrained optimization problems where the Euclidean projection onto the feasible set is computationally tractable. Although momentum techniques like Polyak's heavy-ball are known for accelerating…
Recent progress in deep learning has been driven by increasingly larger models. However, their computational and energy demands have grown proportionally, creating significant barriers to their deployment and to a wider adoption of deep…
Recent advances in deep reinforcement learning (deep RL) enable researchers to solve challenging control problems, from simulated environments to real-world robotic tasks. However, deep RL algorithms are known to be sensitive to the problem…
This paper proposes a new general technique for maximal subgraph enumeration which we call proximity search, whose aim is to design efficient enumeration algorithms for problems that could not be solved by existing frameworks. To support…
In this paper, we propose a new algorithm for exploratory projection pursuit. The basis of the algorithm is the insight that previous approaches used fairly narrow definitions of interestingness / non interestingness. We argue that allowing…
Convex hulls are fundamental objects in computational geometry. In moderate dimensions or for large numbers of vertices, computing the convex hull can be impractical due to the computational complexity of convex hull algorithms. In this…
Due to the explosive growth of large-scale data sets, tensors have been a vital tool to analyze and process high-dimensional data. Different from the matrix case, tensor decomposition has been defined in various formats, which can be…
We study the existing algorithms that solve the multidimensional martingale optimal transport. Then we provide a new algorithm based on entropic regularization and Newton's method. Then we provide theoretical convergence rate results and we…
We study strategies of approximate pattern matching that exploit bidirectional text indexes, extending and generalizing ideas of Lam et al. We introduce a formalism, called search schemes, to specify search strategies of this type, then…
A novel approach is proposed to establish a sharp upper bound on the expected supremum of a separable martingale random field, serving as an alternative to classical universal chaining-based methods. The proposed approach begins by deriving…
Recently, sparsity-based algorithms are proposed for super-resolution spectrum estimation. However, to achieve adequately high resolution in real-world signal analysis, the dictionary atoms have to be close to each other in frequency,…
This paper presents new approaches for finding the determinant and inverse of a matrix. The choice of pivot selection is kept arbitrary and can be made according to the users need. So the ill conditioned matrices can be handled easily. The…
DR-submodular continuous functions are important objectives with wide real-world applications spanning MAP inference in determinantal point processes (DPPs), and mean-field inference for probabilistic submodular models, amongst others.…
We propose a nonconvex estimator for joint multivariate regression and precision matrix estimation in the high dimensional regime, under sparsity constraints. A gradient descent algorithm with hard thresholding is developed to solve the…
A Random SubMatrix method (RSM) is proposed to calculate the low-rank decomposition of large-scale matrices with known entry percentage \rho. RSM is very fast as the floating-point operations (flops) required are compared favorably with the…
In recent years there has been much interest in the Monte Carlo tree search algorithm, a new, adaptive, randomized optimization algorithm. In fields as diverse as Artificial Intelligence, Operations Research, and High Energy Physics,…
This paper proposes and develops new Newton-type methods to solve structured nonconvex and nonsmooth optimization problems with justifying their fast local and global convergence by means of advanced tools of variational analysis and…
Local search has recently been applied to SMT problems over various arithmetic theories. Among these, nonlinear real arithmetic poses special challenges due to its uncountable solution space and potential need to solve higher-degree…