Related papers: Permutations Unlabeled beyond Sampling Unknown
The ``sample amplification'' problem formalizes the following question: Given $n$ i.i.d. samples drawn from an unknown distribution $P$, when is it possible to produce a larger set of $n+m$ samples which cannot be distinguished from $n+m$…
We present a symbolic decomposition of the Pearson chi-square statistic with unequal cell probabilities, by presenting Hadamard-type matrices whose columns are eigenvectors of the variance-covariance matrix of the cell counts. All of the…
We consider linear systems $Ax = b$ where $A \in \mathbb{R}^{m \times n}$ consists of normalized rows, $\|a_i\|_{\ell^2} = 1$, and where up to $\beta m$ entries of $b$ have been corrupted (possibly by arbitrarily large numbers). Haddock,…
A permutation is said to be a square if it can be obtained by shuffling two order-isomorphic patterns. The definition is intended to be the natural counterpart to the ordinary shuffle of words and languages. In this paper, we tackle the…
We improve existing results in the field of compressed sensing and matrix completion when sampled data may be grossly corrupted. We introduce three new theorems. 1) In compressed sensing, we show that if the m \times n sensing matrix has…
It is well known that any positive matrix can be scaled to have prescribed row and column sums by multiplying its rows and columns by certain positive scaling factors (which are unique up to a positive scalar). This procedure is known as…
In this paper, we study the perturbation of the extreme singular values of a matrix in the particular case where it is obtained after appending an arbitrary column vector. Such results have many applications in bifurcation theory, signal…
We show that a tessellation generated by a small number of random affine hyperplanes can be used to approximate Euclidean distances between any two points in an arbitrary bounded set $T$, where the random hyperplanes are generated by…
We study the modular representation theory of the symmetric and alternating groups. One of the most natural ways to label the irreducible representations of a given group or algebra in the modular case is to show the unitriangularity of the…
In real-world applications, as data availability increases, obtaining labeled data for machine learning (ML) projects remains challenging due to the high costs and intensive efforts required for data annotation. Many ML projects,…
The label switching problem arises in the Bayesian analysis of models containing multiple indistinguishable parameters with arbitrary ordering. Any permutation of these parameters is equivalent, therefore models with many such parameters…
Clustering is often a challenging problem because of the inherent ambiguity in what the "correct" clustering should be. Even when the number of clusters $K$ is known, this ambiguity often still exists, particularly when there is variation…
The recovery of signals that are sparse not in a basis, but rather sparse with respect to an over-complete dictionary is one of the most flexible settings in the field of compressed sensing with numerous applications. As in the standard…
We give unique recovery guarantees for matrices of bounded rank that have undergone permutations of their entries. We even do this for a more general matrix structure that we call ladder matrices. We use methods and results of commutative…
Our work studies the enumeration and random generation of unlabeled combinatorial classes of unrooted graphs. While the technique of vertex pointing provides a straightforward procedure for analyzing a labeled class of unrooted graphs by…
We provide rigorous guarantees on learning with the weighted trace-norm under arbitrary sampling distributions. We show that the standard weighted trace-norm might fail when the sampling distribution is not a product distribution (i.e. when…
We consider the problem of anomaly detection with a small set of partially labeled anomaly examples and a large-scale unlabeled dataset. This is a common scenario in many important applications. Existing related methods either exclusively…
We consider the probability of having two intervals (gaps) without eigenvalues in the bulk scaling limit of the Gaussian Unitary Ensemble of random matrices. We describe uniform asymptotics for the transition between a single large gap and…
Recovery from linear measurements under sparse adversarial corruption is typically formulated as an exact-recovery problem: one seeks structural conditions on $A$ (e.g., the restricted isometry property) that guarantee unique recovery of…
A \emph{trace} of a sequence is generated by deleting each bit of the sequence independently with a fixed probability. The well-studied \emph{trace reconstruction} problem asks how many traces are required to reconstruct an unknown binary…