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1. Optimizing Sparsity over Lattices and Semigroups

   https://doi.org/10.1007/978-3-030-45771-6_4  

   Aliev, I. (April 2020, Integer Programming and Combinatorial Optimization. IPCO 2020. Lecture Notes in Computer Science)

   Bienstock, D. (Ed.)

   Motivated by problems in optimization we study the sparsity of the solutions to systems of linear Diophantine equations and linear integer programs, i.e., the number of non-zero entries of a solution, which is often referred to as the ℓ0-norm. Our main results are improved bounds on the ℓ0-norm of sparse solutions to systems 𝐴𝑥=𝑏, where 𝐴∈ℤ𝑚×𝑛, 𝑏∈ℤ𝑚 and 𝑥 is either a general integer vector (lattice case) or a non-negative integer vector (semigroup case). In the lattice case and certain scenarios of the semigroup case, we give polynomial time algorithms for computing solutions with ℓ0-norm satisfying the obtained bounds. 

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2. Improving Decision Sparsity

   Sun, Yiyang; Wang, Tong; Rudin, Cynthia (December 2024, Advances in Neural Information Processing Systems)

   Sparsity is a central aspect of interpretability in machine learning. Typically, sparsity is measured in terms of the size of a model globally, such as the number of variables it uses. However, this notion of sparsity is not particularly relevant for decision-making; someone subjected to a decision does not care about variables that do not contribute to the decision. In this work, we dramatically expand a notion of decision sparsity called the Sparse Explanation Value(SEV) so that its explanations are more meaningful. SEV considers movement along a hypercube towards a reference point. By allowing flexibility in that reference and by considering how distances along the hypercube translate to distances in feature space, we can derive sparser and more meaningful explanations for various types of function classes. We present cluster-based SEV and its variant tree-based SEV, introduce a method that improves credibility of explanations, and propose algorithms that optimize decision sparsity in machine learning models. 

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3. Improving Decision Sparsity

   Sun, Yiyang; Wang, Tong; Rudin, Cynthia (December 2024, Advances in Neural Information Processing Systems)

   Sparsity is a central aspect of interpretability in machine learning. Typically, sparsity is measured in terms of the size of a model globally, such as the number of variables it uses. However, this notion of sparsity is not particularly relevant for decision-making; someone subjected to a decision does not care about variables that do not contribute to the decision. In this work, we dramatically expand a notion of decision sparsity called the Sparse Explanation Value(SEV) so that its explanations are more meaningful. SEV considers movement along a hypercube towards a reference point. By allowing flexibility in that reference and by considering how distances along the hypercube translate to distances in feature space, we can derive sparser and more meaningful explanations for various types of function classes. We present cluster-based SEV and its variant tree-based SEV, introduce a method that improves credibility of explanations, and propose algorithms that optimize decision sparsity in machine learning models. 

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4. Improving Decision Sparsity

   Sun, Yiyang; Wang, Tong; Rudin, Cynthia (December 2024, Advances in Neural Information Processing Systems)

   Sparsity is a central aspect of interpretability in machine learning. Typically, sparsity is measured in terms of the size of a model globally, such as the number of variables it uses. However, this notion of sparsity is not particularly relevant for decision-making; someone subjected to a decision does not care about variables that do not contribute to the decision. In this work, we dramatically expand a notion of decision sparsity called the Sparse Explanation Value(SEV) so that its explanations are more meaningful. SEV considers movement along a hypercube towards a reference point. By allowing flexibility in that reference and by considering how distances along the hypercube translate to distances in feature space, we can derive sparser and more meaningful explanations for various types of function classes. We present cluster-based SEV and its variant tree-based SEV, introduce a method that improves credibility of explanations, and propose algorithms that optimize decision sparsity in machine learning models. 

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5. Improving Decision Sparsity

   Sun, Y; Wang, T; Rudin, C (December 2024, NeurIPS)

   Sparsity is a central aspect of interpretability in machine learning. Typically, sparsity is measured in terms of the size of a model globally, such as the number of variables it uses. However, this notion of sparsity is not particularly relevant for decision making; someone subjected to a decision does not care about variables that do not contribute to the decision. In this work, we dramatically expand a notion of decision sparsity called the Sparse Explanation Value (SEV) so that its explanations are more meaningful. SEV considers movement along a hypercube towards a reference point. By allowing flexibility in that reference and by considering how distances along the hypercube translate to distances in feature space, we can derive sparser and more meaningful explanations for various types of function classes. We present cluster-based SEV and its variant tree-based SEV, introduce a method that improves credibility of explanations, and propose algorithms that optimize decision sparsity in machine learning models. 

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