Related papers: On Sampling and Greedy MAP Inference of Constraine…
We consider the problem of simultaneously learning to linearly combine a very large number of kernels and learn a good predictor based on the learnt kernel. When the number of kernels $d$ to be combined is very large, multiple kernel…
We consider a class of optimization problems that involve determining the maximum value that a function in a particular class can attain subject to a collection of difference constraints. We show that a particular linear programming…
Stochastic iterative algorithms have gained recent interest in machine learning and signal processing for solving large-scale systems of equations, $Ax=b$. One such example is the Randomized Kaczmarz (RK) algorithm, which acts only on…
We study the problem of differentially private constrained maximization of decomposable submodular functions. A submodular function is decomposable if it takes the form of a sum of submodular functions. The special case of maximizing a…
We consider the problem of compressed sensing and of (real-valued) phase retrieval with random measurement matrix. We derive sharp asymptotics for the information-theoretically optimal performance and for the best known polynomial algorithm…
We consider determinantal point processes (DPPs) constrained by spanning trees. Given a graph $G=(V,E)$ and a positive semi-definite matrix $\mathbf{A}$ indexed by $E$, a spanning-tree DPP defines a distribution such that we draw…
We introduce the \emph{submodular objectives chasing problem}, which generalizes many natural and previously-studied problems: a sequence of constrained submodular maximization problems is revealed over time, with both the objective and…
Motivated by the emerging role of interpolating machines in signal processing and machine learning, this work considers the computational aspects of over-parametrized matrix factorization. In this context, the optimization landscape may…
A wide variety of problems in machine learning, including exemplar clustering, document summarization, and sensor placement, can be cast as constrained submodular maximization problems. A lot of recent effort has been devoted to developing…
The constrained linear representability problem (CLRP) for polymatroids determines whether there exists a polymatroid that is linear over a specified field while satisfying a collection of constraints on the rank function. Using a computer…
In Diffusion Probabilistic Models (DPMs), the task of modeling the score evolution via a single time-dependent neural network necessitates extended training periods and may potentially impede modeling flexibility and capacity. To counteract…
Constrained submodular maximization problems have long been studied, with near-optimal results known under a variety of constraints when the submodular function is monotone. The case of non-monotone submodular maximization is less…
We consider the energy minimization problem for undirected graphical models, also known as MAP-inference problem for Markov random fields which is NP-hard in general. We propose a novel polynomial time algorithm to obtain a part of its…
The convergence speed of stochastic gradient descent (SGD) can be improved by actively selecting mini-batches. We explore sampling schemes where similar data points are less likely to be selected in the same mini-batch. In particular, we…
The randomized group-greedy method and its customized method for large-scale sensor selection problems are proposed. The randomized greedy sensor selection algorithm is applied straightforwardly to the group-greedy method, and a customized…
In this paper, we consider a subset selection problem in a spatial field where we seek to find a set of k locations whose observations provide the best estimate of the field value at a finite set of prediction locations. The measurements…
Centralized training with decentralized execution has become an important paradigm in multi-agent learning. Though practical, current methods rely on restrictive assumptions to decompose the centralized value function across agents for…
To make machine learning (ML) sustainable and apt to run on the diverse devices where relevant data is, it is essential to compress ML models as needed, while still meeting the required learning quality and time performance. However, how…
In the Determinant Maximization problem, given an $n\times n$ positive semi-definite matrix $\bf{A}$ in $\mathbb{Q}^{n\times n}$ and an integer $k$, we are required to find a $k\times k$ principal submatrix of $\bf{A}$ having the maximum…
Combining kernel-based collocation methods with time-stepping methods to solve parabolic partial differential equations can potentially introduce challenges in balancing temporal and spatial discretization errors. Typically, using kernels…