Streaming method improves weakly submodular function approximation.
problem Optimizing weakly submodular functions with streaming algorithms.
method Streaming algorithm for RSC and RSM functions.
result Constant factor approximation for weakly submodular functions.
Submodular functions are a broad class of set functions, which naturally arise in diverse areas. Many algorithms have been suggested for the maximization of these functions. Unfortunately, once the function deviates from submodularity, the known algorithms may perform arbitrarily poorly. Amending this issue, by obtaini…
A derivative-free algorithm improves continuous submodular maximization.
problem Maximizing monotone DR-submodular continuous functions without gradient information.
method LDGM algorithm for continuous DR-submodular maximization, with β and α parameters. result LDGM achieves (1−e−β−ϵ)-approximation guarantee with O(1/ϵ) iterations. New algorithm speeds up feature selection and experimental design.
problem Designing efficient parallel algorithms for statistical subset selection.
method Differential submodularity and adaptive sampling.
result Logarithmic parallel runtime for feature selection and experimental design.
In this paper, we consider adaptive decision-making problems for stochastic state estimation with partial observations. First, we introduce the concept of weak adaptive submodularity, a generalization of adaptive submodularity, which has found great success in solving challenging adaptive state estimation problems. The…
In this paper, we consider an online optimization process, where the objective functions are not convex (nor concave) but instead belong to a broad class of continuous submodular functions. We first propose a variant of the Frank-Wolfe algorithm that has access to the full gradient of the objective functions. We show t…
In many machine learning applications, it is important to explain the predictions of a black-box classifier. For example, why does a deep neural network assign an image to a particular class? We cast interpretability of black-box classifiers as a combinatorial maximization problem and propose an efficient streaming alg…
The paper studies continuous submodular functions and their optimization.
problem Maximizing continuous submodular functions in poly. time.
method Characterization of continuous submodularity, operations preserving it, and algorithms for constrained maximization.
result Continuous submodularity is equivalent to a weak DR property, leading to continuous DR-submodular functions with the full DR property.
New method approximates non-submodular functions, offering first guarantees.
problem Minimizing non-submodular functions without theoretical guarantees.
method Extends submodularity relations to non-submodular functions, offering approximation guarantees.
result First approximation guarantees for non-submodular minimization, optimal under noise.
New method for probabilistic modeling of integer submodular functions.
problem Lack of probabilistic modeling for integer submodular functions.
method Proposed Generalized Multilinear Extension and block-coordinate ascent algorithm.
result Demonstrated effectiveness and viability on real-world datasets.
Differentially private algorithms for submodular maximization under various constraints.
problem Maximizing decomposable submodular functions under constraints while preserving privacy.
method Designing differentially private algorithms for both monotone and non-monotone decomposable submodular maximization under general matroid constraints.
result Improved utility guarantees and competitive performance compared to non-private algorithms.
We introduce a method to learn a mixture of submodular "shells" in a large-margin setting. A submodular shell is an abstract submodular function that can be instantiated with a ground set and a set of parameters to produce a submodular function. A mixture of such shells can then also be so instantiated to produce a mor…
Study private submodular maximization in streaming data.
problem Private maximization of submodular functions in streaming data.
method Established differentially private baselines and derived better trade-offs for decomposable submodular functions.
result Improved trade-offs between privacy and utility for decomposable submodular functions.
Paper tackles stochastic k-submodular bandits with full feedback, achieving sublinear regret.
problem Online optimization of k-submodular functions with full-bandit feedback. method Proposes online algorithms for various k-submodular stochastic combinatorial multi-armed bandit problems. result Achieves sublinear α-regret bounds for multiple k-submodular stochastic combinatorial multi-armed bandit problems. Submodularity is studied for convex risk measures, including Expected Shortfall.
problem Characterizing submodularity in convex risk measures.
method Analyzing submodularity properties of law-invariant coherent risk measures, including Expected Shortfall and Value-at-Risk.
result AES is submodular only when it reduces to ES, and empirical analysis shows AES violations are less frequent than VaR and ES violations.
The paper introduces submodular information measures for machine learning applications.
problem Generalizing information-theoretic measures to non-random variables.
method Developing combinatorial information measures based on submodular functions.
result Submodular mutual information is submodular in one argument for certain submodular functions.
A new framework speeds up submodular optimization for large problems.
problem Large scale submodular optimization problems are hard to solve.
method Memoization framework for submodular functions with precomputed statistics.
result Significant speedups for various submodular optimization problems.
This thesis explores how submodularity aids in optimizing non-convex functions and validating algorithms.
problem Understanding which functions can be optimized efficiently in non-convex settings.
method Introducing continuous submodularity and developing algorithms for maximizing these functions.
result Characterization and optimization of continuous submodular functions with strong guarantees.
Algorithm improves recommendation subset selection in the presence of biases.
problem Maximizing submodular functions for recommendation in the presence of social biases.
method Algorithm for submodular maximization with fairness constraints.
result Algorithm provably outputs subsets with near-optimal utility and proportional representation.
Derives an approximation algorithm for continuous submodular maximization without derivative information.
problem Maximizing a continuous submodular function with only function values and no derivative information.
method Black-box Continuous Greedy algorithm for DR-submodular functions, extended to stochastic setting.
result Achieves a (1−1/e)OPT−ε approximation guarantee with O(d/ε3) function evaluations. Scalable methods for maximizing regularized submodular functions with improved memory and communication complexity.
problem Maximizing submodular functions with negative values and constraints.
method Developed one-pass streaming and distributed algorithms for maximizing regularized submodular functions.
result Improved memory and communication complexity by a factor of O(1/ε) compared to existing work.
Paper improves greedy algorithm for non-submodular matroid constraints.
problem Maximizing non-submodular functions subject to matroid constraints.
method Developed and analyzed a greedy algorithm with approximation guarantees.
result Greedy algorithm offers approximation factors for matroid constraints.
Optimal algorithms for continuous non-monotone submodular and DR-submodular maximization.
problem Maximizing continuous non-monotone submodular and DR-submodular functions.
method Developed novel algorithms for both continuous submodular and DR-submodular maximization problems.
result First $ rac{1}{2}$-approximation algorithm for continuous submodular maximization.
IoU is not submodular, impacting machine learning applications.
problem IoU's submodularity assumption in machine learning is incorrect.
method Demonstrated through counterexamples and analysis of function properties.
result IoU is not a submodular function, invalidating its use in certain applications.
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 every step. We empirically and theoretically show that the per-iteration cost of ou…
New method improves submodular maximization for machine learning applications.
problem Inexact monotonicity in submodular functions limits traditional algorithms' performance.
method Introduces monotonicity ratio as a continuous version of monotonicity, leading to improved approximation guarantees.
result Improved approximation ratios for movie recommendation, quadratic programming, and image summarization.
New technique improves submodular maximization with barrier functions.
problem Maximizing submodular functions under complex constraints.
method Inspired by barrier functions in continuous optimization, a novel potential function is proposed for approximate minimization.
result Guaranteed 2(k+1+ε)-approximation factor for feasible sets. New algorithms solve DR-submodular maximization with faster convergence.
problem Maximizing monotone DR-submodular functions under convex constraints.
method Introduced strongly DR-submodular functions and proposed SDRFW and PGA algorithms.
result SDRFW achieves optimal approximation ratio after fewer iterations.
New algorithm maximizes non-monotone adaptive submodular functions in linear time.
problem Maximizing non-monotone adaptive submodular functions subject to a cardinality constraint.
method Developed a linear-time algorithm for non-monotone adaptive submodular maximization.
result Achieved a 1/e−ε approximation ratio with O(nε−2logε−1) value oracle queries. The scalability of submodular optimization methods is critical for their usability in practice. In this paper, we study the reducibility of submodular functions, a property that enables us to reduce the solution space of submodular optimization problems without performance loss. We introduce the concept of reducibility…
Set-functions appear in many areas of computer science and applied mathematics, such as machine learning, computer vision, operations research or electrical networks. Among these set-functions, submodular functions play an important role, similar to convex functions on vector spaces. In this tutorial, the theory of sub…
New algorithms reduce regret for online submodular maximization under various conditions.
problem Online optimization of submodular functions with adversarial or random utilities.
method Characterized strongly DR-submodular functions and derived bounds for different utility classes.
result Logarithmic regret bounds for adversarial strongly DR-submodular functions and submodular functions with random order.
We consider active, semi-supervised learning in an offline transductive setting. We show that a previously proposed error bound for active learning on undirected weighted graphs can be generalized by replacing graph cut with an arbitrary symmetric submodular function. Arbitrary non-symmetric submodular functions can be…
Paper tackles non-monotone DR-submodular maximization with approximation and regret guarantees.
problem Maximizing non-monotone DR-submodular functions over specific sets.
method Frank-Wolfe algorithm for general convex sets, Stochastic Gradient Ascent for down-closed convex sets.
result First approximation guarantees for both offline and online settings.
A new method learns interpretable decision rules using submodular optimization.
problem Learning interpretable decision rules from data.
method Submodular optimization approach for selecting rules from a large set.
result The method effectively learns interpretable rule sets from real datasets.
Fast algorithms developed for adaptive and fully adaptive submodular maximization problems.
problem Maximizing submodular functions subject to constraints in linear time.
method Developed linear-time algorithms for two submodular maximization problems: adaptive and fully adaptive.
result Achieved (1−1/e−ε) approximation ratio for adaptive submodular maximization and $ rac{1-1/e-ε}{4-2/e-2ε}$ for fully adaptive submodular maximization. Adaptive cascade submodular maximization tackles sequential selection under uncertainty.
problem Maximizing expected utility from a set of items with unknown states and continuation probabilities.
method Proposed adaptive cascade submodular functions and a 0.12 approximation algorithm.
result Identified a class of functions (adaptive cascade submodular) that many practical applications satisfy.
Paper tackles online DR-submodular maximization with various convex sets.
problem Maximizing DR-submodular functions online over different convex sets.
method Develops online algorithms with approximation guarantees for various convex sets.
result Achieves 1/e-approximation ratio with O(T2/3) regret for down-closed sets. Greedy algorithms are widely used for problems in machine learning such as feature selection and set function optimization. Unfortunately, for large datasets, the running time of even greedy algorithms can be quite high. This is because for each greedy step we need to refit a model or calculate a function using the pre…
This paper presents quantum and classical algorithms for approximate submodular function minimization.
problem Approximate minimization of submodular functions.
method Classical and quantum algorithms for submodular minimization, with a new quantum sampling method.
result Quantum algorithm for approximate submodular minimization with improved time complexity.
We address the problem of maximizing an unknown submodular function that can only be accessed via noisy evaluations. Our work is motivated by the task of summarizing content, e.g., image collections, by leveraging users' feedback in form of clicks or ratings. For summarization tasks with the goal of maximizing coverage…
An optimal algorithm maximizes submodular functions online with no-1/2 regret.
problem Maximizing submodular functions in an online setting with limited information.
method Polynomial-time no-1/2-regret algorithm for online unconstrained submodular maximization.
result Achieves 1/2 times the maximum total value of a fixed subset in hindsight, up to a sublinear error term.
A number of discrete and continuous optimization problems in machine learning are related to convex minimization problems under submodular constraints. In this paper, we deal with a submodular function with a directed graph structure, and we show that a wide range of convex optimization problems under submodular constr…
Submodular extensions of an energy function can be used to efficiently compute approximate marginals via variational inference. The accuracy of the marginals depends crucially on the quality of the submodular extension. To identify the best possible extension, we show an equivalence between the submodular extensions of…
DR-submodular continuous functions are important objectives with wide real-world applications spanning MAP inference in determinantal point processes (DPPs), and mean-field inference for probabilistic submodular models, amongst others. DR-submodularity captures a subclass of non-convex functions that enables both exact…
New method improves neural network generalization and robustness.
problem Improving neural network generalization and robustness to input perturbations.
method Co-Mixup with supermodular diversity, optimizing data saliency and diversity.
result Achieves state-of-the-art generalization, calibration, and localization results.
New algorithm for maximizing submodular functions in real-time data changes.
problem Maximizing submodular functions under dynamic constraints.
method Randomized algorithm with O(k2) amortized update time. result 4-approximate solution to submodular maximization problem.
Submodular functions have applications throughout machine learning, but in many settings, we do not have direct access to the underlying function f. We focus on stochastic functions that are given as an expectation of functions over a distribution P. In practice, we often have only a limited set of samples fi fr…