Related papers: Towards Better Compressed Representations
A criterion for pruning parameters from N-gram backoff language models is developed, based on the relative entropy between the original and the pruned model. It is shown that the relative entropy resulting from pruning a single N-gram can…
State-space search with explicit abstraction heuristics is at the state of the art of cost-optimal planning. These heuristics are inherently limited, nonetheless, because the size of the abstract space must be bounded by some, even if a…
In this paper, we consider a well-known sparse optimization problem that aims to find a sparse solution of a possibly noisy underdetermined system of linear equations. Mathematically, it can be modeled in a unified manner by minimizing…
In this paper we study the classical problem of throughput maximization. In this problem we have a collection $J$ of $n$ jobs, each having a release time $r_j$, deadline $d_j$, and processing time $p_j$. They have to be scheduled…
This paper introduces a heuristic framework for the Best Secretary Problem, where one item must be selected using rank information only. We develop five data-responsive rules extending classical fixed-cutoff methods: an expected-record…
Compressed Sensing decoding algorithms can efficiently recover an N dimensional real-valued vector x to within a factor of its best k-term approximation by taking m = 2klog(N/k) measurements y = Phi x. If the sparsity or approximate…
We propose a general framework for solving quantum state estimation problems using the minimum relative entropy criterion. A convex optimization approach allows us to decide the feasibility of the problem given the data and, whenever…
The hm admissible heuristics for (sequential and temporal) regression planning are defined by a parameterized relaxation of the optimal cost function in the regression search space, where the parameter m offers a trade-off between the…
We investigate the complexity of three optimization problems in Boolean propositional logic related to information theory: Given a conjunctive formula over a set of relations, find a satisfying assignment with minimal Hamming distance to a…
Music summarization allows for higher efficiency in processing, storage, and sharing of datasets. Machine-oriented approaches, being agnostic to human consumption, optimize these aspects even further. Such summaries have already been…
It is well known that sparse approximation problem is \textsf{NP}-hard under general dictionaries. Several algorithms have been devised and analyzed in the past decade under various assumptions on the \emph{coherence} $\mu$ of the…
Current state-of-the-art solvers for mixed-integer programming (MIP) problems are designed to perform well on a wide range of problems. However, for many real-world use cases, problem instances come from a narrow distribution. This has…
We introduce the first differentiable approximation of range-partition entropy, a complexity measure from computational geometry that directly bounds algorithmic runtime. Unlike architectural modifications, our method is a complementary…
Optimisation problems in science and engineering typically involve finding the ground state (i.e. the minimum energy configuration) of a cost function with respect to many variables. If the variables are corrupted by noise then this…
Building on the blueprint from Goemans and Williamson (1995) for the Max-Cut problem, we construct a polynomial-time approximation algorithm for orthogonally constrained quadratic optimization problems. First, we derive a semidefinite…
Extracting dense representations for terms and phrases is a task of great importance for knowledge discovery platforms targeting highly-technical fields. Dense representations are used as features for downstream components and have multiple…
We present a new methodology for utilising machine learning technology in symbolic computation research. We explain how a well known human-designed heuristic to make the choice of variable ordering in cylindrical algebraic decomposition may…
We apply the stabilizer formalism to the Maximum Cut problem, and obtain a new greedy construction heuristic. It turns out to be an elegant synthesis of the edge-contraction and differencing edge-contraction approaches. Utilizing the…
We suggest a compositional vector representation of parse trees that relies on a recursive combination of recurrent-neural network encoders. To demonstrate its effectiveness, we use the representation as the backbone of a greedy, bottom-up…
We study the approximation of high-dimensional rank one tensors using point evaluations and consider deterministic as well as randomized algorithms. We prove that for certain parameters (smoothness and norm of the $r$th derivative) this…