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We investigate the continuous non-monotone DR-submodular maximization problem subject to a down-closed convex solvable constraint. Our first contribution is to construct an example to demonstrate that (first-order) stationary points can…
For numerous graph problems in the realm of parameterized algorithms, using the size of a smallest deletion set (called a modulator) into well-understood graph families as parameterization has led to a long and successful line of research.…
We study quasi-modular pseudometric spaces as asymmetric refinements of modular metric structures. To each such space we associate canonical forward and backward quasi-uniformities and the corresponding directional topologies. We introduce…
We develop a general duality-theory framework for revenue maximization in additive Bayesian auctions. The framework extends linear programming duality and complementarity to constraints with partial derivatives. The dual system reveals the…
Adaptive sequential decision making is one of the central challenges in machine learning and artificial intelligence. In such problems, the goal is to design an interactive policy that plans for an action to take, from a finite set of $n$…
The Assouad and quasi-Assouad dimensions of a metric space provide information about the extreme local geometric nature of the set. The Assouad dimension of a set has a measure theoretic analogue, which is also known as the upper regularity…
The Submodular Welfare Maximization problem (SWM) captures an important subclass of combinatorial auctions and has been studied extensively from both computational and economic perspectives. In particular, it has been studied in a natural…
Maximization of {\it non-submodular} functions appears in various scenarios, and many previous works studied it based on some measures that quantify the closeness to being submodular. On the other hand, many practical non-submodular…
We introduce the concept of quotient-convergence for sequences of submodular set functions, providing, among others, a new framework for the study of convergence of matroids through their rank functions. Extending the limit theory of…
Submodular functions are discrete functions that model laws of diminishing returns and enjoy numerous algorithmic applications. They have been used in many areas, including combinatorial optimization, machine learning, and economics. In…
Bridging the gap between data-rich training regimes and observation-sparse deployment conditions remains a central challenge in spatiotemporal field reconstruction, particularly when target domains exhibit distributional shifts,…
Neural networks represent more features than they have dimensions via superposition, forcing features to share representational space. Current methods decompose activations into sparse linear features but discard geometric structure. We…
This work explores the novel idea of learning a submodular scoring function to improve the specificity/selectivity of existing feature attribution methods. Submodular scores are natural for attribution as they are known to accurately model…
We investigate a more generalized form of submodular maximization, referred to as $k$-submodular maximization, with applications across social networks and machine learning domains. In this work, we propose the multilinear extension of…
Similarity search is a fundamental operation for analyzing data series (DS), which are ordered sequences of real values. To enhance efficiency, summarization techniques are employed that reduce the dimensionality of DS. SAX-based approaches…
We study sets of local dimensions for self-similar measures in $\mathbb{R}$ satisfying the finite neighbour condition, which is formally stronger than the weak separation condition but satisfied in all known examples. Under a mild technical…
We propose and analyze batch greedy heuristics for cardinality constrained maximization of non-submodular non-decreasing set functions. We consider the standard greedy paradigm, along with its distributed greedy and stochastic greedy…
We investigate \emph{magnitude} as a new unary and strictly Pareto-compliant quality indicator for finite approximation sets to the Pareto front in multiobjective optimization. Magnitude originates in enriched category theory and metric…
We study constrained versions of the minimal supersymmetric model and investigate the hierarchy between the electroweak scale and the scale of superpartners that can be achieved without relying on specifying model parameters by more than…
Motivated by the problem of reducing the peak to average power ratio (PAPR) of transmitted signals, we consider a design of complementary set matrices whose column sequences satisfy a correlation constraint. The design algorithm recursively…