Related papers: Representation, Approximation and Learning of Subm…
We study the problem of maximizing a monotone submodular function with viability constraints. This problem originates from computational biology, where we are given a phylogenetic tree over a set of species and a directed graph, the…
This paper addresses the problem of sequential submodular maximization: selecting and ranking items in a sequence to optimize some composite submodular function. In contrast to most of the previous works, which assume access to the utility…
It has been a long-standing goal in machine learning, as well as in AI more generally, to develop life-long learning systems that learn many different tasks over time, and reuse insights from tasks learned, "learning to learn" as they do…
Adaptive submodularity is a fundamental concept in stochastic optimization, with numerous applications such as sensor placement, hypothesis identification and viral marketing. We consider the problem of minimum cost cover of…
In a nutshell, submodular functions encode an intuitive notion of diminishing returns. As a result, submodularity appears in many important machine learning tasks such as feature selection and data summarization. Although there has been a…
Neural networks and rational functions efficiently approximate each other. In more detail, it is shown here that for any ReLU network, there exists a rational function of degree $O(\text{polylog}(1/\epsilon))$ which is $\epsilon$-close, and…
We prove lower bounds on complexity measures, such as the approximate degree of a Boolean function and the approximate rank of a Boolean matrix, using quantum arguments. We prove these lower bounds using a quantum query algorithm for the…
We consider the problem of exact identification for read-once functions over arbitrary Boolean bases. We introduce a new type of queries (subcube identity ones), discuss its connection to previously known ones, and study the complexity of…
Submodularity is desirable for a variety of objectives in content selection where the current neural encoder-decoder framework is inadequate. However, it has so far not been explored in the neural encoder-decoder system for text generation.…
In this work we present the first practical $\left(\frac{1}{e}-\epsilon\right)$-approximation algorithm to maximise a general non-negative submodular function subject to a matroid constraint. Our algorithm is based on combining the…
The research problem in this work is the relaxation of maximizing non-negative submodular plus modular with the entire real number domain as its value range over a family of down-closed sets. We seek a feasible point $\mathbf{x}^*$ in the…
While it is widely known that neural networks are universal approximators of continuous functions, a less known and perhaps more powerful result is that a neural network with a single hidden layer can approximate accurately any nonlinear…
This work studies the non-monotone DR-submodular Maximization over a ground set of $n$ subject to a size constraint $k$. We propose two approximation algorithms for solving this problem named FastDrSub and FastDrSub++. FastDrSub offers an…
We study the low rank approximation problem of any given matrix $A$ over $\mathbb{R}^{n\times m}$ and $\mathbb{C}^{n\times m}$ in entry-wise $\ell_p$ loss, that is, finding a rank-$k$ matrix $X$ such that $\|A-X\|_p$ is minimized. Unlike…
First, for the for the submodular $k$-secretary problem with shortlists [1], we provide a near optimal $1-1/e-\epsilon$ approximation using shortlist of size $O(k poly(1/\epsilon))$. In particular, we improve the size of shortlist used in…
We extend the work of Narasimhan and Bilmes [30] for minimizing set functions representable as a dierence between submodular functions. Similar to [30], our new algorithms are guaranteed to monotonically reduce the objective function at…
This paper investigates the approximation properties of shallow neural networks with activation functions that are powers of exponential functions. It focuses on the dependence of the approximation rate on the dimension and the smoothness…
Neural networks are widely used to approximate unknown functions in control. A common neural network architecture uses a single hidden layer (i.e. a shallow network), in which the input parameters are fixed in advance and only the output…
We consider a variant of the prize collecting Steiner tree problem in which we are given a \emph{directed graph} $D=(V,A)$, a monotone submodular prize function $p:2^V \rightarrow \mathbb{R}^+ \cup \{0\}$, a cost function $c:V \rightarrow…
Learning neural set functions becomes increasingly more important in many applications like product recommendation and compound selection in AI-aided drug discovery. The majority of existing works study methodologies of set function…