Related papers: Marking and re-marking
A vertex colouring of a given graph $G$ can be considered as a random experiment. A discrete random variable $X$, corresponding to this random experiment, can be defined as the colour of a randomly chosen vertex of $G$ and a probability…
In this article, we consider a collection of geometric problems involving points colored by two colors (red and blue), referred to as bichromatic problems. The motivation behind studying these problems is two fold; (i) these problems appear…
Categorical random variables are a common staple in machine learning methods and other applications across disciplines. Many times, correlation within categorical predictors exists, and has been noted to have an effect on various algorithm…
Binomial coefficients have been used for centuries in a variety of fields and have accumulated numerous definitions. In this paper, we introduce a new way of defining binomial coefficients as repeated sums of ones. A multitude of binomial…
The automorphisms of a graph act naturally on its set of labeled imbeddings to produce its unlabeled imbeddings. The imbedding sum of a graph is a polynomial that contains useful information about a graph's labeled and unlabeled imbeddings.…
Automatic colorization of gray images with objects of different colors and sizes is challenging due to inter- and intra-object color variation and the small area of the main objects due to extensive backgrounds. The learning process often…
The existing methods for image search reranking suffer from the unfaithfulness of the assumptions under which the text-based images search result. The resulting images contain more irrelevant images. Hence the re ranking concept arises to…
Colouring the vertices of a graph $G$ according to certain conditions can be considered as a random experiment and a discrete random variable $X$ can be defined as the number of vertices having a particular colour in the proper colouring of…
Set-coloring a graph means giving each vertex a subset of a fixed color set so that no two adjacent subsets have the same cardinality. When the graph is complete one gets a new distribution problem with an interesting generating function.…
Convolutions of independent random variables often arise in a natural way in many applied problems. In this article, we compare convolutions of two sets of gamma (negative binomial) random variables in the convolution order and the usual…
We prove an important property of the binomial transform: it converts multiplication by the discrete variable into a certain difference operator. We also consider the case of dividing by the discrete variable. The properties presented here…
Multiple binomial sums form a large class of multi-indexed sequences, closed under partial summation, which contains most of the sequences obtained by multiple summation of products of binomial coefficients and also all the sequences with…
Disentangled distributed representations of data are desirable for machine learning, since they are more expressive and can generalize from fewer examples. However, for complex data, the distributed representations of multiple objects…
Matrix-valued polynomials in any finite number of freely noncommuting variables that enjoy certain canonical partial convexity properties are characterized, via an algebraic certificate, in terms of Linear Matrix Inequalities and Bilinear…
Classification is a major tool of statistics and machine learning. A classification method first processes a training set of objects with given classes (labels), with the goal of afterward assigning new objects to one of these classes. When…
The number of possible methods of generalizing binary classification to multi-class classification increases exponentially with the number of class labels. Often, the best method of doing so will be highly problem dependent. Here we present…
We seek to learn a representation on a large annotated data source that generalizes to a target domain using limited new supervision. Many prior approaches to this problem have focused on learning "disentangled" representations so that as…
We propose a new approach to designing visual markers (analogous to QR-codes, markers for augmented reality, and robotic fiducial tags) based on the advances in deep generative networks. In our approach, the markers are obtained as color…
Inpainting is a learned interpolation technique that is based on generative modeling and used to populate masked or missing pieces in an image; it has wide applications in picture editing and retouching. Recently, inpainting started being…
We initiate the study of what we refer to as random walk labelings of graphs. These are graph labelings that are obtainable by performing a random walk on the graph, such that the labeling occurs increasingly whenever an unlabeled vertex is…