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The main goal of this paper is to describe a new pruning method for solving decision trees and game trees. The pruning method for decision trees suggests a slight variant of decision trees that we call scenario trees. In scenario trees, we…
Score-based algorithms that learn Bayesian Network (BN) structures provide solutions ranging from different levels of approximate learning to exact learning. Approximate solutions exist because exact learning is generally not applicable to…
Pruning is one of the predominant approaches for compressing deep neural networks (DNNs). Lately, coresets (provable data summarizations) were leveraged for pruning DNNs, adding the advantage of theoretical guarantees on the trade-off…
We present an algorithm for sampling tightly confined random equilateral closed polygons in three-space which has runtime linear in the number of edges. Using symplectic geometry, sampling such polygons reduces to sampling a moment…
How to develop slim and accurate deep neural networks has become crucial for real- world applications, especially for those employed in embedded systems. Though previous work along this research line has shown some promising results, most…
This paper discusses the graph covering problem in which a set of edges in an edge- and node-weighted graph is chosen to satisfy some covering constraints while minimizing the sum of the weights. In this problem, because of the large…
We develop a probabilistic algorithm for computing elimination ideals of likelihood equations, which is for larger models by far more efficient than directly computing Groebner bases or the interpolation method proposed in the first…
Zeroth-order local optimisation algorithms are essential for solving real-valued black-box optimisation problems. Among these, Natural Evolution Strategies (NES) represent a prominent class, particularly well-suited for scenarios where…
We propose a randomized algorithm for enumerating the vertices of a zonotope, which is a low-dimensional linear projection of a hypercube. The algorithm produces a pair of the zonotope's vertices by sampling a random linear combination of…
Polytopes are the basic finite data structures for convex sets: they appear as feasible regions in linear optimization, as geometric summaries in algorithms, and as random objects in stochastic geometry. A natural geometric question is…
We explain how to encode an algebraic series by finite data and how to do effective arithmetic on the level of these encodings. The reasoning is based on the Newton-Puiseux algorithm and an effective equality test for algebraic series.…
First, we study geometric variants of the standard set cover motivated by assignment of directional antenna and shipping with deadlines, providing the first known polynomial-time exact solutions. Next, we consider the following general…
Graph polynomials encode fundamental combinatorial invariants of graphs. Their computation is investigated using tree and path decomposition frameworks, with formal definitions of treewidth, k-trees, and pathwidth establishing the…
We present an efficient algorithm to reduce the size of nondeterministic tree automata, while retaining their language. It is based on new transition pruning techniques, and quotienting of the state space w.r.t. suitable equivalences. It…
Deep learning algorithms are increasingly employed at the edge. However, edge devices are resource constrained and thus require efficient deployment of deep neural networks. Pruning methods are a key tool for edge deployment as they can…
We give an efficient perfect sampling algorithm for weighted, connected induced subgraphs (or graphlets) of rooted, bounded degree graphs. Our algorithm utilizes a vertex-percolation process with a carefully chosen rejection filter and…
We have designed a new symbolic-numeric strategy to compute efficiently and accurately floating point Puiseux series defined by a bivariate polynomial over an algebraic number field. In essence, computations modulo a well chosen prime $p$…
Quantization is an essential technique for making neural networks more efficient, yet our theoretical understanding of it remains limited. Previous works demonstrated that extremely low-precision networks, such as binary networks, can be…
In this paper we consider the problem of constructing numerical algorithms for approximating of convex compact bodies in d-dimensional Euclidean space by polytopes with any given accuracy. It is well known that optimal with respect to the…
We present a polynomial time algorithm to approximately scale tensors of any format to arbitrary prescribed marginals (whenever possible). This unifies and generalizes a sequence of past works on matrix, operator and tensor scaling. Our…