589 research outputs found

    LIPIcs, Volume 251, ITCS 2023, Complete Volume

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    LIPIcs, Volume 251, ITCS 2023, Complete Volum

    Scalable Distributed Algorithms for Size-Constrained Submodular Maximization in the MapReduce and Adaptive Complexity Models

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    Distributed maximization of a submodular function in the MapReduce model has received much attention, culminating in two frameworks that allow a centralized algorithm to be run in the MR setting without loss of approximation, as long as the centralized algorithm satisfies a certain consistency property - which had only been shown to be satisfied by the standard greedy and continous greedy algorithms. A separate line of work has studied parallelizability of submodular maximization in the adaptive complexity model, where each thread may have access to the entire ground set. For the size-constrained maximization of a monotone and submodular function, we show that several sublinearly adaptive algorithms satisfy the consistency property required to work in the MR setting, which yields highly practical parallelizable and distributed algorithms. Also, we develop the first linear-time distributed algorithm for this problem with constant MR rounds. Finally, we provide a method to increase the maximum cardinality constraint for MR algorithms at the cost of additional MR rounds.Comment: 45 pages, 6 figure

    Independent Sets in Elimination Graphs with a Submodular Objective

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    Maximum weight independent set (MWIS) admits a 1k\frac1k-approximation in inductively kk-independent graphs and a 12k\frac{1}{2k}-approximation in kk-perfectly orientable graphs. These are a a parameterized class of graphs that generalize kk-degenerate graphs, chordal graphs, and intersection graphs of various geometric shapes such as intervals, pseudo-disks, and several others. We consider a generalization of MWIS to a submodular objective. Given a graph G=(V,E)G=(V,E) and a non-negative submodular function f:2VR+f: 2^V \rightarrow \mathbb{R}_+, the goal is to approximately solve maxSIGf(S)\max_{S \in \mathcal{I}_G} f(S) where IG\mathcal{I}_G is the set of independent sets of GG. We obtain an Ω(1k)\Omega(\frac1k)-approximation for this problem in the two mentioned graph classes. The first approach is via the multilinear relaxation framework and a simple contention resolution scheme, and this results in a randomized algorithm with approximation ratio at least 1e(k+1)\frac{1}{e(k+1)}. This approach also yields parallel (or low-adaptivity) approximations. Motivated by the goal of designing efficient and deterministic algorithms, we describe two other algorithms for inductively kk-independent graphs that are inspired by work on streaming algorithms: a preemptive greedy algorithm and a primal-dual algorithm. In addition to being simpler and faster, these algorithms, in the monotone submodular case, yield the first deterministic constant factor approximations for various special cases that have been previously considered such as intersection graphs of intervals, disks and pseudo-disks.Comment: Extended abstract to appear in Proceedings of APPROX 2023. v2 corrects technical typos in few place

    Constrained Submodular Maximization via New Bounds for DR-Submodular Functions

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    Submodular maximization under various constraints is a fundamental problem studied continuously, in both computer science and operations research, since the late 19701970's. A central technique in this field is to approximately optimize the multilinear extension of the submodular objective, and then round the solution. The use of this technique requires a solver able to approximately maximize multilinear extensions. Following a long line of work, Buchbinder and Feldman (2019) described such a solver guaranteeing 0.3850.385-approximation for down-closed constraints, while Oveis Gharan and Vondr\'ak (2011) showed that no solver can guarantee better than 0.4780.478-approximation. In this paper, we present a solver guaranteeing 0.4010.401-approximation, which significantly reduces the gap between the best known solver and the inapproximability result. The design and analysis of our solver are based on a novel bound that we prove for DR-submodular functions. This bound improves over a previous bound due to Feldman et al. (2011) that is used by essentially all state-of-the-art results for constrained maximization of general submodular/DR-submodular functions. Hence, we believe that our new bound is likely to find many additional applications in related problems, and to be a key component for further improvement.Comment: 48 page

    Identifying Spurious Biases Early in Training through the Lens of Simplicity Bias

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    Neural networks trained with (stochastic) gradient descent have an inductive bias towards learning simpler solutions. This makes them highly prone to learning simple spurious features that are highly correlated with a label instead of the predictive but more complex core features. In this work, we show that, interestingly, the simplicity bias of gradient descent can be leveraged to identify spurious correlations, early in training. First, we prove on a two-layer neural network, that groups of examples with high spurious correlation are separable based on the model's output, in the initial training iterations. We further show that if spurious features have a small enough noise-to-signal ratio, the network's output on the majority of examples in a class will be almost exclusively determined by the spurious features and will be nearly invariant to the core feature. Finally, we propose SPARE, which separates large groups with spurious correlations early in training, and utilizes importance sampling to alleviate the spurious correlation, by balancing the group sizes. We show that SPARE achieves up to 5.6% higher worst-group accuracy than state-of-the-art methods, while being up to 12x faster. We also show the applicability of SPARE to discover and mitigate spurious correlations in Restricted ImageNet

    Human-AI complex task planning

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    The process of complex task planning is ubiquitous and arises in a variety of compelling applications. A few leading examples include designing a personalized course plan or trip plan, designing music playlists/work sessions in web applications, or even planning routes of naval assets to collaboratively discover an unknown destination. For all of these aforementioned applications, creating a plan requires satisfying a basic construct, i.e., composing a sequence of sub-tasks (or items) that optimizes several criteria and satisfies constraints. For instance, in course planning, sub-tasks or items are core and elective courses, and degree requirements capture their complex dependencies as constraints. In trip planning, sub-tasks are points of interest (POIs) and constraints represent time and monetary budget, or user-specified requirements. Needless to say, task plans are to be individualized and designed considering uncertainty. When done manually, the process is human-intensive and tedious, and unlikely to scale. The goal of this dissertation is to present computational frameworks that synthesize the capabilities of human and AI algorithms to enable task planning at scale while satisfying multiple objectives and complex constraints. This dissertation makes significant contributions in four main areas, (i) proposing novel models, (ii) designing principled scalable algorithms, (iii) conducting rigorous experimental analysis, and (iv) deploying designed solutions in the real-world. A suite of constrained and multi-objective optimization problems has been formalized, with a focus on their applicability across diverse domains. From an algorithmic perspective, the dissertation proposes principled algorithms with theoretical guarantees adapted from discrete optimization techniques, as well as Reinforcement Learning based solutions. The memory and computational efficiency of these algorithms have been studied, and optimization opportunities have been proposed. The designed solutions are extensively evaluated on various large-scale real-world and synthetic datasets and compared against multiple baseline solutions after appropriate adaptation. This dissertation also presents user study results involving human subjects to validate the effectiveness of the proposed models. Lastly, a notable outcome of this dissertation is the deployment of one of the developed solutions at the Naval Postgraduate School. This deployment enables simultaneous route planning for multiple assets that are robust to uncertainty under multiple contexts

    Linear Query Approximation Algorithms for Non-monotone Submodular Maximization under Knapsack Constraint

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    This work, for the first time, introduces two constant factor approximation algorithms with linear query complexity for non-monotone submodular maximization over a ground set of size nn subject to a knapsack constraint, DLA\mathsf{DLA} and RLA\mathsf{RLA}. DLA\mathsf{DLA} is a deterministic algorithm that provides an approximation factor of 6+ϵ6+\epsilon while RLA\mathsf{RLA} is a randomized algorithm with an approximation factor of 4+ϵ4+\epsilon. Both run in O(nlog(1/ϵ)/ϵ)O(n \log(1/\epsilon)/\epsilon) query complexity. The key idea to obtain a constant approximation ratio with linear query lies in: (1) dividing the ground set into two appropriate subsets to find the near-optimal solution over these subsets with linear queries, and (2) combining a threshold greedy with properties of two disjoint sets or a random selection process to improve solution quality. In addition to the theoretical analysis, we have evaluated our proposed solutions with three applications: Revenue Maximization, Image Summarization, and Maximum Weighted Cut, showing that our algorithms not only return comparative results to state-of-the-art algorithms but also require significantly fewer queries

    Beyond Submodularity: A Unified Framework of Randomized Set Selection with Group Fairness Constraints

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    Machine learning algorithms play an important role in a variety of important decision-making processes, including targeted advertisement displays, home loan approvals, and criminal behavior predictions. Given the far-reaching impact of these algorithms, it is crucial that they operate fairly, free from bias or prejudice towards certain groups in the population. Ensuring impartiality in these algorithms is essential for promoting equality and avoiding discrimination. To this end we introduce a unified framework for randomized subset selection that incorporates group fairness constraints. Our problem involves a global utility function and a set of group utility functions for each group, here a group refers to a group of individuals (e.g., people) sharing the same attributes (e.g., gender). Our aim is to generate a distribution across feasible subsets, specifying the selection probability of each feasible set, to maximize the global utility function while meeting a predetermined quota for each group utility function in expectation. Note that there may not necessarily be any direct connections between the global utility function and each group utility function. We demonstrate that this framework unifies and generalizes many significant applications in machine learning and operations research. Our algorithmic results either improves the best known result or provide the first approximation algorithms for new applications.Comment: This paper has been accepted for publication in the Journal on Combinatorial Optimizatio

    LIPIcs, Volume 261, ICALP 2023, Complete Volume

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    LIPIcs, Volume 261, ICALP 2023, Complete Volum

    Modeling Events and Interactions through Temporal Processes -- A Survey

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    In real-world scenario, many phenomena produce a collection of events that occur in continuous time. Point Processes provide a natural mathematical framework for modeling these sequences of events. In this survey, we investigate probabilistic models for modeling event sequences through temporal processes. We revise the notion of event modeling and provide the mathematical foundations that characterize the literature on the topic. We define an ontology to categorize the existing approaches in terms of three families: simple, marked, and spatio-temporal point processes. For each family, we systematically review the existing approaches based based on deep learning. Finally, we analyze the scenarios where the proposed techniques can be used for addressing prediction and modeling aspects.Comment: Image replacement
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