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We prove an effective equidistribution theorem for orbits of certain unipotent subgroups in arithmetic quotients of perfect Lie groups with a polynomial error term. Even for semisimple quotients, our result provides the first infinite…
We study the problem of estimating the covariance matrix of a high-dimensional distribution when a small constant fraction of the samples can be arbitrarily corrupted. Recent work gave the first polynomial time algorithms for this problem…
This paper presents a novel version of the hypergraph neural network method. This method is utilized to solve the noisy label learning problem. First, we apply the PCA dimensional reduction technique to the feature matrices of the image…
Verifying uniform conditions over continuous spaces through random sampling is fundamental in machine learning and control theory, yet classical coverage analyses often yield conservative bounds, particularly at small failure probabilities.…
Deep neural networks are known to be annotation-hungry. Numerous efforts have been devoted to reducing the annotation cost when learning with deep networks. Two prominent directions include learning with noisy labels and semi-supervised…
We consider the problem of analyzing the structure of spectroscopic cubes using unsupervised machine learning techniques. We propose representing the target's signal as a homogeneous set of volumes through an iterative algorithm that…
Despite being robust to small amounts of label noise, convolutional neural networks trained with stochastic gradient methods have been shown to easily fit random labels. When there are a mixture of correct and mislabelled targets, networks…
We study the problem of high-dimensional linear regression in a robust model where an $\epsilon$-fraction of the samples can be adversarially corrupted. We focus on the fundamental setting where the covariates of the uncorrupted samples are…
Motivated by multi-task and meta-learning approaches, we consider the problem of learning structure shared by tasks or users, such as shared low-rank representations or clustered structures. While all previous works focus on well-specified…
We study the problem of semi-supervised learning on graphs in the regime where data labels are scarce or possibly corrupted. We propose an approach called $p$-conductance learning that generalizes the $p$-Laplace and Poisson learning…
Here we study the problem of learning labels for large text corpora where each text can be assigned a variable number of labels. The problem might seem trivial when the label dimensionality is small and can be easily solved using a series…
We study a general online linear optimization problem(OLO). At each round, a subset of objects from a fixed universe of $n$ objects is chosen, and a linear cost associated with the chosen subset is incurred. To measure the performance of…
We study the problem of learning in the presence of a drifting target concept. Specifically, we provide bounds on the error rate at a given time, given a learner with access to a history of independent samples labeled according to a target…
The amount of manually labeled data is limited in medical applications, so semi-supervised learning and automatic labeling strategies can be an asset for training deep neural networks. However, the quality of the automatically generated…
In traditional models of supervised learning, the goal of a learner -- given examples from an arbitrary joint distribution on $\mathbb{R}^d \times \{\pm 1\}$ -- is to output a hypothesis that is competitive (to within $\epsilon$) of the…
We consider the problem of learning a discrete distribution in the presence of an $\epsilon$ fraction of malicious data sources. Specifically, we consider the setting where there is some underlying distribution, $p$, and each data source…
Existing semi-supervised learning algorithms adopt pseudo-labeling and consistency regulation techniques to introduce supervision signals for unlabeled samples. To overcome the inherent limitation of threshold-based pseudo-labeling, prior…
Given data drawn from a mixture of multivariate Gaussians, a basic problem is to accurately estimate the mixture parameters. We give an algorithm for this problem that has a running time, and data requirement polynomial in the dimension and…
Semi-supervised learning (SSL) can reduce the need for large labelled datasets by incorporating unlabelled data into the training. This is particularly interesting for semantic segmentation, where labelling data is very costly and…
We quantify the separation between the numbers of labeled examples required to learn in two settings: Settings with and without the knowledge of the distribution of the unlabeled data. More specifically, we prove a separation by…