589 research outputs found
LIPIcs, Volume 251, ITCS 2023, Complete Volume
LIPIcs, Volume 251, ITCS 2023, Complete Volum
Scalable Distributed Algorithms for Size-Constrained Submodular Maximization in the MapReduce and Adaptive Complexity Models
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
Maximum weight independent set (MWIS) admits a -approximation in
inductively -independent graphs and a -approximation in
-perfectly orientable graphs. These are a a parameterized class of graphs
that generalize -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 and a non-negative submodular function , the goal is to approximately solve where is the set of independent sets of . We obtain an
-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 . 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 -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
Submodular maximization under various constraints is a fundamental problem
studied continuously, in both computer science and operations research, since
the late '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 -approximation for
down-closed constraints, while Oveis Gharan and Vondr\'ak (2011) showed that no
solver can guarantee better than -approximation. In this paper, we
present a solver guaranteeing -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
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
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
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 subject to a knapsack constraint,
and . is a deterministic algorithm
that provides an approximation factor of while is a
randomized algorithm with an approximation factor of . Both run in
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
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
LIPIcs, Volume 261, ICALP 2023, Complete Volum
Modeling Events and Interactions through Temporal Processes -- A Survey
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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