Related papers: Constructive Discrepancy Minimization with Heredit…
The combinatorial discrepancy of arithmetic progressions inside $[N] := \{1, \ldots, N\}$ is the smallest integer $D$ for which $[N]$ can be colored with two colors so that any arithmetic progression in $[N]$ contains at most $D$ more…
A common way to quantify the ,,distance'' between measures is via their discrepancy, also known as maximum mean discrepancy (MMD). Discrepancies are related to Sinkhorn divergences $S_\varepsilon$ with appropriate cost functions as…
In this paper, we study the linear separability problem for stochastic geometric objects under the well-known unipoint/multipoint uncertainty models. Let $S=S_R \cup S_B$ be a given set of stochastic bichromatic points, and define $n =…
Robust inference based on the minimization of statistical divergences has proved to be a useful alternative to the classical maximum likelihood based techniques. Recently Ghosh et al. (2013) proposed a general class of divergence measures…
Correlation Clustering is an elegant model that captures fundamental graph cut problems such as Min $s-t$ Cut, Multiway Cut, and Multicut, extensively studied in combinatorial optimization. Here, we are given a graph with edges labeled $+$…
Unpaired image-to-image translation involves learning mappings between source domain and target domain in the absence of aligned or corresponding samples. Score based diffusion models have demonstrated state-of-the-art performance in…
We introduce estimation and test procedures through divergence minimization for models satisfying linear constraints with unknown parameter. Several statistical examples and motivations are given. These procedures extend the empirical…
The recent work of \cite{CRT,DonohoPol} rigorously proved (in a large dimensional and statistical context) that if the number of equations (measurements in the compressed sensing terminology) in the system is proportional to the length of…
We consider a high dimensional binary classification problem and construct a classification procedure by minimizing the empirical misclassification risk with a penalty on the number of selected features. We derive non-asymptotic probability…
Semi-supervised learning (SSL) has been proven beneficial for mitigating the issue of limited labeled data especially on the task of volumetric medical image segmentation. Unlike previous SSL methods which focus on exploring highly…
The discrepancy of a sequence measures how quickly it approaches a uniform distribution. Given a natural number $d$, any collection of one-dimensional so-called low discrepancy sequences $\left\{S_i:1\le i \le d\right\}$ can be concatenated…
When maximum likelihood estimation is infeasible, one often turns to score matching, contrastive divergence, or minimum probability flow to obtain tractable parameter estimates. We provide a unifying perspective of these techniques as…
We prove new bounds on the distributed fractional coloring problem in the LOCAL model. Fractional $c$-colorings can be understood as multicolorings as follows. For some natural numbers $p$ and $q$ such that $p/q\leq c$, each node $v$ is…
We study a unified approach and algorithm for constructive discrepancy minimization based on a stochastic process. By varying the parameters of the process, one can recover various state-of-the-art results. We demonstrate the flexibility of…
On the basis of a model system of pillars built of unit cubes, a two-component entropic measure for the multiscale analysis of spatio-compositional inhomogeneity is proposed. It quantifies the statistical dissimilarity per cell of the…
In the Correlation Clustering problem, we are given a complete weighted graph $G$ with its edges labeled as "similar" and "dissimilar" by a noisy binary classifier. For a clustering $\mathcal{C}$ of graph $G$, a similar edge is in…
Finding a maximum independent set (MIS) of a given fam- ily of axis-parallel rectangles is a basic problem in computational geom- etry and combinatorics. This problem has attracted significant atten- tion since the sixties, when Wegner…
Given an edge-colored graph, the goal of the proportional fair matching problem is to find a maximum weight matching while ensuring proportional representation (with respect to the number of edges) of each color. The colors may correspond…
Let $\chi'_\subset(G)$ be the least number of colours necessary to properly colour the edges of a graph $G$ with minimum degree $\delta\geq 2$ so that the set of colours incident with any vertex is not contained in a set of colours incident…
With the aim of generalizing histogram statistics to higher dimensional cases, density estimation via discrepancy based sequential partition (DSP) has been proposed to learn an adaptive piecewise constant approximation defined on a binary…