Related papers: Structured Sampling for Robust Euclidean Distance …
For an empirical signed measure $\mu = \frac{1}{N} \left(\sum_{i=1}^P \delta_{x_i} - \sum_{i=1}^M \delta_{y_i}\right)$, particle annihilation (PA) removes $N_A$ particles from both $\{x_i\}_{i=1}^P$ and $\{y_i\}_{i=1}^M$ simultaneously,…
In this paper, we study the missing sample recovery problem using methods based on sparse approximation. In this regard, we investigate the algorithms used for solving the inverse problem associated with the restoration of missed samples of…
We initiate the study of sparse recovery problems under the Earth-Mover Distance (EMD). Specifically, we design a distribution over m x n matrices A such that for any x, given Ax, we can recover a k-sparse approximation to x under the EMD…
Identifying the underlying models in a set of data points contaminated by noise and outliers, leads to a highly complex multi-model fitting problem. This problem can be posed as a clustering problem by the projection of higher order…
Deep neural networks have achieved human-level accuracy on almost all perceptual benchmarks. It is interesting that these advances were made using two ideas that are decades old: (a) an artificial neuron based on a linear summator and (b)…
This paper presents a regularized regression model with a two-level structural sparsity penalty applied to locate individual atoms in a noisy scanning transmission electron microscopy image (STEM). In crystals, the locations of atoms is…
Standard Direction of Arrival (DOA) estimation methods are typically derived based on the Gaussian noise assumption, making them highly sensitive to outliers. Therefore, in the presence of impulsive noise, the performance of these methods…
Weakly supervised learning based on scribble annotations in target extraction of remote sensing images has drawn much interest due to scribbles' flexibility in denoting winding objects and low cost of manually labeling. However, scribbles…
Consider a set $P$ of $n$ points picked uniformly and independently from $[0,1]^d$ for a constant dimension $d$ -- such a point set is extremely well behaved in many aspects. For example, for a fixed $r \in [0,1]$, we prove a new…
The reliable measurement of confidence in classifiers' predictions is very important for many applications and is, therefore, an important part of classifier design. Yet, although deep learning has received tremendous attention in recent…
The Nystr\"om methods have been popular techniques for scalable kernel based learning. They approximate explicit, low-dimensional feature mappings for kernel functions from the pairwise comparisons with the training data. However, Nystr\"om…
We consider a fundamental problem in unsupervised learning called \emph{subspace recovery}: given a collection of $m$ points in $\mathbb{R}^n$, if many but not necessarily all of these points are contained in a $d$-dimensional subspace $T$…
We study the problem of robust linear regression with response variable corruptions. We consider the oblivious adversary model, where the adversary corrupts a fraction of the responses in complete ignorance of the data. We provide a nearly…
Outlier detection algorithms typically assign an outlier score to each observation in a dataset, indicating the degree to which an observation is an outlier. However, these scores are often not comparable across algorithms and can be…
We consider the problem of robust matrix completion, which aims to recover a low rank matrix $L_*$ and a sparse matrix $S_*$ from incomplete observations of their sum $M=L_*+S_*\in\mathbb{R}^{m\times n}$. Algorithmically, the robust matrix…
Realtime shape estimation of continuum objects and manipulators is essential for developing accurate planning and control paradigms. The existing methods that create dense point clouds from camera images, and/or use distinguishable markers…
This paper proposes a boosting-based solution addressing metric learning problems for high-dimensional data. Distance measures have been used as natural measures of (dis)similarity and served as the foundation of various learning methods.…
Consider the problem of inverse scattering of time-harmonic point sources from an infinite, penetrable rough interface with bounded obstacles buried in the lower half-space, where the interface is assumed to be a local perturbation of a…
We investigate the problem of learning Bayesian networks in a robust model where an $\epsilon$-fraction of the samples are adversarially corrupted. In this work, we study the fully observable discrete case where the structure of the network…
In this paper we initiate the study of whether or not sparse estimation tasks can be performed efficiently in high dimensions, in the robust setting where an $\eps$-fraction of samples are corrupted adversarially. We study the natural…