Related papers: Joint Continuous and Discrete Model Selection via …
Regularization techniques are widely employed in optimization-based approaches for solving ill-posed inverse problems in data analysis and scientific computing. These methods are based on augmenting the objective with a penalty function,…
Identifying and understanding modular organizations is centrally important in the study of complex systems. Several approaches to this problem have been advanced, many framed in information-theoretic terms. Our treatment starts from the…
Submodular optimization plays a key role in many real-world problems. In many real-world scenarios, it is also necessary to handle uncertainty, and potentially disruptive events that violate constraints in stochastic settings need to be…
Rule sets are highly interpretable logical models in which the predicates for decision are expressed in disjunctive normal form (DNF, OR-of-ANDs), or, equivalently, the overall model comprises an unordered collection of if-then decision…
We investigate two new optimization problems -- minimizing a submodular function subject to a submodular lower bound constraint (submodular cover) and maximizing a submodular function subject to a submodular upper bound constraint…
A fundamental task underlying many important optimization problems, from influence maximization to sensor placement to content recommendation, is to select the optimal group of $k$ items from a larger set. Submodularity has been very…
Constrained submodular function maximization has been used in subset selection problems such as selection of most informative sensor locations. While these models have been quite popular, the solutions Constrained submodular function…
Regularization is used in many different areas of optimization when solutions are sought which not only minimize a given function, but also possess a certain degree of regularity. Popular applications are image denoising, sparse regression…
In this paper, we propose the first exact algorithm for minimizing the difference of two submodular functions (D.S.), i.e., the discrete version of the D.C. programming problem. The developed algorithm is a branch-and-bound-based algorithm…
Submodular functions are an important class of functions in combinatorial optimization which satisfy the natural properties of decreasing marginal costs. The study of these functions has led to strong structural properties with applications…
Submodular functions and their optimization have found applications in diverse settings ranging from machine learning and data mining to game theory and economics. In this work, we consider the constrained maximization of a submodular…
We connect high-dimensional subset selection and submodular maximization. Our results extend the work of Das and Kempe (2011) from the setting of linear regression to arbitrary objective functions. For greedy feature selection, this…
We study a class of convex-concave min-max problems in which the coupled component of the objective is linear in at least one of the two decision vectors. We identify such problem structure as interpolating between the bilinearly and…
The way that people make choices or exhibit preferences can be strongly affected by the set of available alternatives, often called the choice set. Furthermore, there are usually heterogeneous preferences, either at an individual level…
Structured pruning is an effective approach for compressing large pre-trained neural networks without significantly affecting their performance. However, most current structured pruning methods do not provide any performance guarantees, and…
Training materials through periodic drive allows to endow materials and structures with complex elastic functions. As a result of the driving, the system explores the high dimensional space of structures, ultimately converging to a…
Submodular optimization generalizes many classic problems in combinatorial optimization and has recently found a wide range of applications in machine learning (e.g., feature engineering and active learning). For many large-scale…
Submodular function maximization has been studied extensively in recent years under various constraints and models. The problem plays a major role in various disciplines. We study a natural online variant of this problem in which elements…
Submodularity is an important concept in integer and combinatorial optimization. A classical submodular set function models the utility of selecting homogenous items from a single ground set, and such selections can be represented by binary…
Chance constraints are frequently used to limit the probability of constraint violations in real-world optimization problems where the constraints involve stochastic components. We study chance-constrained submodular optimization problems,…