Related papers: Fast Greedy MAP Inference for Determinantal Point …
We study the problem of selecting a subset of vectors from a large set, to obtain the best signal representation over a family of functions. Although greedy methods have been widely used for tackling this problem and many of those have been…
Maximum Inner Product Search (MIPS) is an important task in many machine learning applications such as the prediction phase of a low-rank matrix factorization model for a recommender system. There have been some works on how to perform MIPS…
Identifying cause-effect relations among variables is a key step in the decision-making process. While causal inference requires randomized experiments, researchers and policymakers are increasingly using observational studies to test…
Users of industrial recommender systems are normally suggesteda list of items at one time. Ideally, such list-wise recommendationshould provide diverse and relevant options to the users. However, in practice, list-wise recommendation is…
In this paper we prove the efficacy of a simple greedy algorithm for a finite horizon online resource allocation/matching problem, when the corresponding static planning linear program (SPP) exhibits a non-degeneracy condition called the…
Determinantal Point Processes (DPPs) are probabilistic models over all subsets a ground set of $N$ items. They have recently gained prominence in several applications that rely on "diverse" subsets. However, their applicability to large…
Determinantal point processes (DPPs) are point process models that naturally encode diversity between the points of a given realization, through a positive definite kernel $K$. DPPs possess desirable properties, such as exact sampling or…
The standard Monte Carlo estimator $\widehat{I}_N^{\mathrm{MC}}$ of $\int fd\omega$ relies on independent samples from $\omega$ and has variance of order $1/N$. Replacing the samples with a determinantal point process (DPP), a repulsive…
Active learning is increasingly adopted for expensive multi-objective combinatorial optimization problems, but it involves a challenging subset selection problem, optimizing the batch acquisition score that quantifies the goodness of a…
In a standard NP-complete optimization problem we introduce an interpolating algorithm between the quick decrease along the gradient (greedy dynamics) and a slow decrease close to the level curves (reluctant dynamics). We find that for a…
Determinantal point processes (DPPs) are an elegant model for encoding probabilities over subsets, such as shopping baskets, of a ground set, such as an item catalog. They are useful for a number of machine learning tasks, including product…
It is known that greedy methods perform well for maximizing monotone submodular functions. At the same time, such methods perform poorly in the face of non-monotonicity. In this paper, we show - arguably, surprisingly - that invoking the…
Randomized Numerical Linear Algebra (RandNLA) uses randomness to develop improved algorithms for matrix problems that arise in scientific computing, data science, machine learning, etc. Determinantal Point Processes (DPPs), a seemingly…
Unstructured neural network pruning algorithms have achieved impressive compression rates. However, the resulting - typically irregular - sparse matrices hamper efficient hardware implementations, leading to additional memory usage and…
In the design of algorithms, the greedy paradigm provides a powerful tool for solving efficiently classical computational problems, within the framework of procedural languages. However, expressing these algorithms within the declarative…
Determinantal point processes (DPPs), which arise in random matrix theory and quantum physics, are natural models for subset selection problems where diversity is preferred. Among many remarkable properties, DPPs offer tractable algorithms…
``Composable core-sets'' are an efficient framework for solving optimization problems in massive data models. In this work, we consider efficient construction of composable core-sets for the determinant maximization problem. This can also…
The Set Cover problem (SCP) and Set Packing problem (SPP) are standard NP-hard combinatorial optimization problems. Their decision problem versions are shown to be NP-Complete in Karp's 1972 paper. We specify a rough guide to constructing…
Random restart of a given algorithm produces many partitions to yield a consensus clustering. Ensemble methods such as consensus clustering have been recognized as more robust approaches for data clustering than single clustering…
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…