Related papers: Asymmetric R\'enyi Problem
The distinguishing result of this paper is a $\mathbf{P}$-time enumerable partition of all the potential perfect matchings in a bipartite graph. This partition is a set of equivalence classes induced by the missing edges in the potential…
We study the problem of similarity learning and its application to image retrieval with large-scale data. The similarity between pairs of images can be measured by the distances between their high dimensional representations, and the…
We study the asymmetric binary matrix partition problem that was recently introduced by Alon et al. (WINE 2013) to model the impact of asymmetric information on the revenue of the seller in take-it-or-leave-it sales. Instances of the…
We give a polynomial-time algorithm for learning high-dimensional halfspaces with margins in $d$-dimensional space to within desired TV distance when the ambient distribution is an unknown affine transformation of the $d$-fold product of an…
We study the problem of agnostically learning halfspaces which is defined by a fixed but unknown distribution $\mathcal{D}$ on $\mathbb{Q}^n\times \{\pm 1\}$. We define $\mathrm{Err}_{\mathrm{HALF}}(\mathcal{D})$ as the least error of a…
Inspired by Stufler's recent probabilistic proof of Otter's asymptotic number of unlabeled trees, we revisit work of Palmer and Schwenk, and study unlabeled forests from a probabilistic point of view. We show that the number of trees in a…
We consider a query-based data acquisition problem for binary classification of unknown labels, which has diverse applications in communications, crowdsourcing, recommender systems and active learning. To ensure reliable recovery of unknown…
Two widely-used computational paradigms for sublinear algorithms are using linear measurements to perform computations on a high dimensional input and using structured queries to access a massive input. Typically, algorithms in the former…
For two correlated graphs which are independently sub-sampled from a common Erd\H{o}s-R\'enyi graph $\mathbf{G}(n, p)$, we wish to recover their \emph{latent} vertex matching from the observation of these two graphs \emph{without labels}.…
Graph alignment refers to the task of finding the vertex correspondence between two correlated graphs of $n$ vertices. Extensive study has been done on polynomial-time algorithms for the graph alignment problem under the Erd\H{o}s-R\'enyi…
Dropout Variational Inference, or Dropout Sampling, has been recently proposed as an approximation technique for Bayesian Deep Learning and evaluated for image classification and regression tasks. This paper investigates the utility of…
We study pool-based active learning with abstention feedbacks, where a labeler can abstain from labeling a queried example with some unknown abstention rate. This is an important problem with many useful applications. We take a Bayesian…
In the \emph{trace reconstruction problem}, an unknown source string $x \in \{0,1\}^n$ is transmitted through a probabilistic \emph{deletion channel} which independently deletes each bit with some fixed probability $\delta$ and concatenates…
We study the problem of PAC learning homogeneous halfspaces in the presence of Tsybakov noise. In the Tsybakov noise model, the label of every sample is independently flipped with an adversarially controlled probability that can be…
The problem of searching for a model-based scene interpretation is analyzed within a probabilistic framework. Object models are formulated as generative models for range data of the scene. A new statistical criterion, the truncated object…
Learning from label proportions (LLP) is a weakly supervised classification problem where data points are grouped into bags, and the label proportions within each bag are observed instead of the instance-level labels. The task is to learn a…
We investigate Learning from Label Proportions (LLP), a partial information setting where examples in a training set are grouped into bags, and only aggregate label values in each bag are available. Despite the partial observability, the…
Suppose $P_n=\{1,2,...,n\}$ is a partially ordered set with the partial order defined by divisibility, that is, for any two distinct elements $i,j\in P_n$ satisfying $i$ divides $j$, $i<_{P_n} j$. A table $A_n=\{a_i|i=1,2,...,n\}$ of…
This paper studies the problem of recovering the hidden vertex correspondence between two edge-correlated random graphs. We focus on the Gaussian model where the two graphs are complete graphs with correlated Gaussian weights and the…
We give a $2^{\tilde{O}(\sqrt{n}/\epsilon)}$-time algorithm for properly learning monotone Boolean functions under the uniform distribution over $\{0,1\}^n$. Our algorithm is robust to adversarial label noise and has a running time nearly…