Related papers: Exact uniform sampling over catalan structures
We develop a novel, fundamental and surprisingly simple randomized iterative method for solving consistent linear systems. Our method has six different but equivalent interpretations: sketch-and-project, constrain-and-approximate, random…
Combinatorial samplers are algorithmic schemes devised for the approximate- and exact-size generation of large random combinatorial structures, such as context-free words, various tree-like data structures, maps, tilings, RNA molecules.…
This work presents a unified framework that combines global approximations with locally built models to handle challenging nonconvex and nonsmooth composite optimization problems, including cases involving extended real-valued functions. We…
In low-dimensional topology, many important decision algorithms are based on normal surface enumeration, which is a form of vertex enumeration over a high-dimensional and highly degenerate polytope. Because this enumeration is subject to…
Strict inequalities in mixed-integer linear optimization can cause difficulties in guaranteeing convergence and exactness. Utilizing that optimal vertex solutions follow a lattice structure we propose a rounding rule for strict inequalities…
Tree search algorithms, such as branch-and-bound, are the most widely used tools for solving combinatorial and nonconvex problems. For example, they are the foremost method for solving (mixed) integer programs and constraint satisfaction…
This paper deals with the problem of robust matrix completion -- retrieving a low-rank matrix and a sparse matrix from the compressed counterpart of their superposition. Though seemingly not an unresolved issue, we point out that the…
Linear-parametric optimization, where multiple objectives are combined into a single objective using linear combinations with parameters as coefficients, has numerous links to other fields in optimization and a wide range of application…
We define a weighted analog for the multidimensional Catalan numbers, obtain matrix-based recurrences for some of them, and give conditions under which they are periodic. Building on this framework, we introduce two new sequences of…
We consider a notion of uniform thinning for a finite sequence of random variables $(X_1,...,X_n)$ obtained by removing one random variable, uniformly at random. If a triangular array of random variables $(X_{n,k} : n \in \mathbb{N}_+, 1…
We present a new algorithm for the exact uniform sampling of proper \(k\)-colorings of a graph on \(n\) vertices with maximum degree~\(\Delta\). The algorithm is based on partial rejection sampling (PRS) and introduces a soft relaxation of…
We propose two algorithms for interpretation and boosting of tree-based ensemble methods. Both algorithms make use of mathematical programming models that are constructed with a set of rules extracted from an ensemble of decision trees. The…
We resolve a long-standing open question, about the existence of a constant-factor approximation algorithm for the average-case \textsc{Decision Tree} problem with uniform probability distribution over the hypotheses. We answer the question…
The uniform distribution on matrices with specified row and column sums is often a natural choice of null model when testing for structure in two-way tables (binary or nonnegative integer). Due to the difficulty of sampling from this…
Efficient sampling from constraint manifolds, and thereby generating a diverse set of solutions for feasibility problems, is a fundamental challenge. We consider the case where a problem is factored, that is, the underlying nonlinear…
We present a general and modular algorithmic framework for path planning of robots. Our framework combines geometric methods for exact and complete analysis of low-dimensional configuration spaces, together with practical, considerably…
We address the collective matrix completion problem of jointly recovering a collection of matrices with shared structure from partial (and potentially noisy) observations. To ensure well--posedness of the problem, we impose a joint low rank…
Generalized sampling is a recently developed linear framework for sampling and reconstruction in separable Hilbert spaces. It allows one to recover any element in any finite-dimensional subspace given finitely many of its samples with…
Sampling from very large spatial populations is challenging. The solutions suggested in recent literature on this subject often require that the randomly selected units are well distributed across the study region by using complex…
A probabilistic representation for initial value semilinear parabolic problems based on generalized random trees has been derived. Two different strategies have been proposed, both requiring generating suitable random trees combined with a…