Related papers: Surprises in approximating Levenshtein distances
Methods of high-dimensional probability play a central role in applications for statistics, signal processing theoretical computer science and related fields. These lectures present a sample of particularly useful tools of high-dimensional…
The Johnson-Lindenstrauss lemma allows dimension reduction on real vectors with low distortion on their pairwise Euclidean distances. This result is often used in algorithms such as $k$-means or $k$ nearest neighbours since they only use…
The purpose of this paper is twofold. First, the definition of new statistical convergence with Fibonacci sequence is given and some fundamental properties of statistical convergence are examined. Second, approximation theory worked as a…
As subjects perceive the sensory world, different stimuli elicit a number of neural representations. Here, a subjective distance between stimuli is defined, measuring the degree of similarity between the underlying representations. As an…
A variety of network modeling problems begin by generating a degree sequence drawn from a given probability distribution. If the randomly generated sequence is not graphic, we give a new approach for generating a graphic approximation of…
The Fr\'echet distance is a popular similarity measure between curves. For some applications, it is desirable to match the curves under translation before computing the Fr\'echet distance between them. This variant is called the Translation…
The Wasserstein distance is an attractive tool for data analysis but statistical inference is hindered by the lack of distributional limits. To overcome this obstacle, for probability measures supported on finitely many points, we derive…
In this paper, a sample-based procedure for obtaining simple and computable approximations of chance-constrained sets is proposed. The procedure allows to control the complexity of the approximating set, by defining families of…
Since the introduction of the Sliced Wasserstein distance in the literature, its simplicity and efficiency have made it one of the most interesting surrogate for the Wasserstein distance in image processing and machine learning. However,…
The classification of DNA sequences is a key research area in bioinformatics as it enables researchers to conduct genomic analysis and detect possible diseases. In this paper, three state-of-the-art algorithms, namely Convolutional Neural…
In previous work cite{Ha98:Towards} we presented a case-based approach to eliciting and reasoning with preferences. A key issue in this approach is the definition of similarity between user preferences. We introduced the probabilistic…
We introduce the discrete Fr\'echet gap and its variants as an alternative measure of similarity between polygonal curves. We believe that for some applications the new measure (and its variants) may better reflect our intuitive notion of…
We define a modified Wasserstein distance for distribution clustering which inherits many of the properties of the Wasserstein distance but which can be estimated easily and computed quickly. The modified distance is the sum of two terms.…
The question of optimally approximating an arbitrary probability measure in the Wasserstein distance by a discrete one with uniform weights is considered. Estimates are obtained for the optimal approximation distance, with an explicit rate…
The basic idea of importance sampling is to use independent samples from a proposal measure in order to approximate expectations with respect to a target measure. It is key to understand how many samples are required in order to guarantee…
Symbolic regression is a nonlinear regression method which is commonly performed by an evolutionary computation method such as genetic programming. Quantification of uncertainty of regression models is important for the interpretation of…
Wasserstein distances are increasingly used in a wide variety of applications in machine learning. Sliced Wasserstein distances form an important subclass which may be estimated efficiently through one-dimensional sorting operations. In…
The problem of guessing a random string is revisited. A close relation between guessing and compression is first established. Then it is shown that if the sequence of distributions of the information spectrum satisfies the large deviation…
String similarity, longest common subsequence and shortest edit scripts are the triplets of problem that related to each other. There are different algorithms exist to generate edit script by solving longest common subsequence problem. This…
Most classifiers rely on discriminative boundaries that separate instances of each class from everything else. We argue that discriminative boundaries are counter-intuitive as they define semantics by what-they-are-not; and should be…