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With appropriately chosen sampling probabilities, sampling-based random projection can be used to implement large-scale statistical methods, substantially reducing computational cost while maintaining low statistical error. However,…
The randomized Kaczmarz (RK) method is an iterative method for approximating the least-squares solution of large linear systems of equations. The standard RK method uses sequential updates, making parallel computation difficult. Here, we…
We investigate model reduction of parametric linear time-invariant (LTI) dynamical systems. When posed in the frequency domain, this problem can be formulated as seeking a low-order rational function approximation of a high-order rational…
Loopy Belief Propagation (LBP) is a widely used approximate inference algorithm in probabilistic graphical models, with applications in computer vision, error correction codes, protein folding, program analysis, etc. However, LBP faces…
Linear Predictive Clustering (LPC) partitions samples based on shared linear relationships between feature and target variables, with numerous applications including marketing, medicine, and education. Greedy optimization methods, commonly…
The block-iterative projections (BIP) method of Aharoni and Censor [Block-iterative projection methods for parallel computation of solutions to convex feasibility problems, Linear Algebra and its Applications 120, (1989), 165--175] is an…
This paper introduces generalized Bregman projection algorithms for solving nonlinear split feasibility problems (SF P s) in infinitedimensional Hilbert spaces. The methods integrate Bregman projections, proximal gradient steps, and…
This paper proposes a new algorithm for multiple sparse regression in high dimensions, where the task is to estimate the support and values of several (typically related) sparse vectors from a few noisy linear measurements. Our algorithm is…
*The following abbreviates the abstract. Please refer to the thesis for the full abstract.* After a disaster, locating and extracting victims quickly is critical because mortality rises rapidly after the first two days. To assist search and…
We propose a new yet natural algorithm for learning the graph structure of general discrete graphical models (a.k.a. Markov random fields) from samples. Our algorithm finds the neighborhood of a node by sequentially adding nodes that…
In this paper we analyze the randomized block-coordinate descent (RBCD) methods proposed in [8,11] for minimizing the sum of a smooth convex function and a block-separable convex function. In particular, we extend Nesterov's technique…
We consider the visual feature selection to improve the estimation quality required for the accurate navigation of a robot. We build upon a key property that asserts: contributions of trackable features (landmarks) appear linearly in the…
Approximate dynamic programming is a popular method for solving large Markov decision processes. This paper describes a new class of approximate dynamic programming (ADP) methods- distributionally robust ADP-that address the curse of…
For multi-block alternating direction method of multipliers(ADMM), where the objective function can be decomposed into multiple block components, we show that with block symmetric Gauss-Seidel iteration, the algorithm will converge quickly.…
We propose a computationally efficient alternative to generalized random forests (GRFs) for estimating heterogeneous effects in large dimensions. While GRFs rely on a gradient-based splitting criterion, which in large dimensions is…
Inverse imaging problems rely on limited and indirect measurements, making reconstruction highly dependent on both regularization and sample locations. We introduce a novel greedy framework for the optimal selection of indirect measurements…
Randomized rounding is a standard method, based on the probabilistic method, for designing combinatorial approximation algorithms. In Raghavan's seminal paper introducing the method (1988), he writes: "The time taken to solve the linear…
The optimal robot assembly planning problem is challenging due to the necessity of finding the optimal solution amongst an exponentially vast number of possible plans, all while satisfying a selection of constraints. Traditionally, robotic…
We consider the problem of minimizing the sum of two convex functions: one is smooth and given by a gradient oracle, and the other is separable over blocks of coordinates and has a simple known structure over each block. We develop an…
Partially observable Markov decision processes (POMDPs) have recently become popular among many AI researchers because they serve as a natural model for planning under uncertainty. Value iteration is a well-known algorithm for finding…