Context-free inference is a standard part of many NLP pipelines. Most approaches use a variant of the CYK dynamic programming algorithm to populate a chart structure with predicted nonterminals over each span. We can extract a parse tree from this chart in several ways. In this work, we compare two commonly-used decoding approaches (Viterbi and max-rule) with a minimum-bayes-risk (MBR) method w...

This paper develops tools for analyzing properties of stochastic objective functions that take the form ( , ) ( , ) ( ; ) V u dF ≡ ∫s x x s s θ θ . The paper analyzes the relationship between properties of the primitive functions, such as the utility functions u and probability distributions F, and properties of the stochastic objective. The methods are designed to address problems where the ut...

Clustering is often formulated as a discrete optimization problem. The objective is to find, among all partitions of the data set, the best one according to some quality measure. However, in the statistical setting where we assume that the finite data set has been sampled from some underlying space, the goal is not to find the best partition of the given sample, but to approximate the true part...

We introduce a parameterized version of set cover that generalizes several previously studied problems. Given a ground set V and a collection of subsets Si of V , a feasible solution is a partition of V such that each subset of the partition is included in one of the Si. The problem involves maximizing the mean subset size of the partition, where the mean is the generalized mean of parameter p,...

Hierarchical clustering is a recursive partitioning of a dataset into clusters at an increasingly finer granularity. Motivated by the fact that most work on hierarchical clustering was based on providing algorithms, rather than optimizing a specific objective, [19] framed similarity-based hierarchical clustering as a combinatorial optimization problem, where a ‘good’ hierarchical clustering is ...

Most static mixers are designed to maximize radial mixing to achieve compositional and thermal homogeneity. Flow inverters maximize heat transfer. Axial mixers that closely approximate an exponential distribution of residence times have been devised as well. More recent papers describe static mixers for surge dampening in industrial swing-cycle processes (Smith, Graham, and Palamara, 2006). An ...

We present the first fast route planning algorithm that answers shortest paths queries for a customizable linear combination of two different metrics, e. g. travel time and energy cost, on large scale road networks. The precomputation receives as input a directed graph, two edge weight functions t(e) and c(e), and a discrete interval [L,U ]. The resulting flexible query algorithm finds for a pa...