Related papers: Relative Rank and Regularization
The last decade has seen a revolution in the theory and application of machine learning and pattern recognition. Through these advancements, variable ranking has emerged as an active and growing research area and it is now beginning to be…
The characteristic feature of inverse problems is their instability with respect to data perturbations. In order to stabilize the inversion process, regularization methods have to be developed and applied. In this work we introduce and…
In this paper, we prove new relations between the bias of multilinear forms, the correlation between multilinear forms and lower degree polynomials, and the rank of tensors over $GF(2)= \{0,1\}$. We show the following results for…
Feature selection identifies subsets of informative features and reduces dimensions in the original feature space, helping provide insights into data generation or a variety of domain problems. Existing methods mainly depend on feature…
Ranking populations such as institutions based on certain characteristics is often of interest, and these ranks are typically estimated using samples drawn from the populations. Due to sample randomness, it is important to quantify the…
Graph classes of bounded tree rank were introduced recently in the context of the model checking problem for first-order logic of graphs. These graph classes are a common generalization of graph classes of bounded degree and bounded…
This paper considers the problem of recovering either a low rank matrix or a sparse vector from observations of linear combinations of the vector or matrix elements. Recent methods replace the non-convex regularization with $\ell_1$ or…
The nonnegative integer rank of a matrix is a variant of the classical nonnegative rank, introduced in the 1980s, where factorizations are required to have integer entries. While computing nonnegative integer rank is generally very hard, we…
We study a conjecture called "linear rank conjecture" recently raised in (Tsang et al., FOCS'13), which asserts that if many linear constraints are required to lower the degree of a GF(2) polynomial, then the Fourier sparsity (i.e. number…
Arthur Cohn's irreducibility criterion for polynomials with integer coefficients and its generalization connect primes to irreducibles, and integral bases to the variable $x$. As we follow this link, we find that these polynomials are ready…
We investigate border ranks of twisted powers of polynomials and smoothability of symmetric powers of algebras. We prove that the latter are smoothable. For the former, we obtain upper bounds for the border rank in general and prove that…
There are several equivalent characterizations of the valuation rank of an ordered or valued field. In this paper, we extend the theory to the case of an ordered or valued {\it difference} field (that is, ordered or valued field endowed…
Rank regression offers robustness to outliers and heavy-tailed response distributions, invariance to monotonic transformations, and improved efficiency under non-Gaussian errors, making it a versatile tool for analyzing complex data. This…
Ranking algorithms find extensive usage in diverse areas such as web search, employment, college admission, voting, etc. The related rank aggregation problem deals with combining multiple rankings into a single aggregate ranking. However,…
We consider the problem of learning over non-stationary ranking streams. The rankings can be interpreted as the preferences of a population and the non-stationarity means that the distribution of preferences changes over time. Our goal is…
We study the complexity of solving the \emph{generalized MinRank problem}, i.e. computing the set of points where the evaluation of a polynomial matrix has rank at most $r$. A natural algebraic representation of this problem gives rise to a…
Recent years have witnessed the introduction and development of extremely fast rational function algorithms. Many ideas in this realm arose from polynomial-based linear-algebraic algorithms. However, polynomial approximation is occasionally…
The problem of interpreting or aggregating multiple rankings is common to many real-world applications. Perhaps the simplest and most common approach is a weighted rank aggregation, wherein a (convex) weight is applied to each input ranking…
We investigate the new, Turing-complete class of layered systems, whose lefthand sides of rules can only be overlapped at a multiset of disjoint or equal positions. Layered systems define a natural notion of rank for terms: the maximal…
We consider the classic problem of establishing a statistical ranking of a set of n items given a set of inconsistent and incomplete pairwise comparisons between such items. Instantiations of this problem occur in numerous applications in…