Related papers: Randomized Group-Greedy Method for Large-Scale Sen…
In this article, we derive a novel convergence estimate for the weak POD-Greedy method with multiple POD modes and variable greedy thresholds in terms of the entropy numbers of the parametric solution manifold. Combining the POD with the…
Many robotic systems deal with uncertainty by performing a sequence of information gathering actions. In this work, we focus on the problem of efficiently constructing such a sequence by drawing an explicit connection to submodularity.…
Motivated by a wide range of applications in data mining and machine learning, we consider the problem of maximizing a submodular function subject to supermodular cost constraints. In contrast to the well-understood setting of cardinality…
In this article, we present a family of numerical approaches to solve high-dimensional linear non-symmetric problems. The principle of these methods is to approximate a function which depends on a large number of variates by a sum of tensor…
The Long Term Evolution (LTE) as a mobile broadband technology supports a wide domain of communication services with different requirements. Therefore, scheduling of all flows from various applications in overload states in which the…
Reduced bases have been introduced for the approximation of parametrized PDEs in applications where many online queries are required. Their numerical efficiency for such problems has been theoretically confirmed in \cite{BCDDPW,DPW}, where…
Submodular maximization has been widely studied over the past decades, mostly because of its numerous applications in real-world problems. It is well known that the standard greedy algorithm guarantees a worst-case approximation factor of…
Determinantal point processes (DPPs) are popular probabilistic models that arise in many machine learning tasks, where distributions of diverse sets are characterized by matrix determinants. In this paper, we develop fast algorithms to find…
We consider the problem of collaborative distributed estimation in a large scale sensor network with statistically dependent sensor observations. In collaborative setup, the aim is to maximize the overall estimation performance by modeling…
We present a greedy algorithm for computing selected eigenpairs of a large sparse matrix $H$ that can exploit localization features of the eigenvector. When the eigenvector to be computed is localized, meaning only a small number of its…
In this paper, we propose a new greedy algorithm for sparse approximation, called SLS for Single L_1 Selection. SLS essentially consists of a greedy forward strategy, where the selection rule of a new component at each iteration is based on…
Many important problems in discrete optimization require maximization of a monotonic submodular function subject to matroid constraints. For these problems, a simple greedy algorithm is guaranteed to obtain near-optimal solutions. In this…
We study the problem of sampling a bandlimited graph signal in the presence of noise, where the objective is to select a node subset of prescribed cardinality that minimizes the signal reconstruction mean squared error (MSE). To that end,…
Motivated by, e.g., sensitivity analysis and end-to-end learning, the demand for differentiable optimization algorithms has been significantly increasing. In this paper, we establish a theoretically guaranteed versatile framework that makes…
In this paper, we study the following robust optimization problem. Given an independence system and candidate objective functions, we choose an independent set, and then an adversary chooses one objective function, knowing our choice. Our…
When solving PDEs, classical numerical solvers are often computationally expensive, while machine learning methods can suffer from spectral bias, failing to capture high-frequency components. Designing an optimal hybrid iterative…
We study an iterative selection problem over N i.i.d. discrete-time stochastic processes with independent increments. At each stage, a fixed number of processes are retained based on their observed values. Under this simple model, we prove…
Informed sampling techniques accelerate the convergence of sampling-based motion planners by biasing sampling toward regions of the state space that are most likely to yield better solutions. However, when the current solution path contains…
Motivated by the successful use of greedy algorithms for Reduced Basis Methods, a greedy method is proposed that selects N input data in an asymptotically optimal way to solve well-posed operator equations using these N data. The operator…
We consider forward-backward greedy algorithms for solving sparse feature selection problems with general convex smooth functions. A state-of-the-art greedy method, the Forward-Backward greedy algorithm (FoBa-obj) requires to solve a large…