Related papers: Existence and construction of randomization defini…
We have established the method of characterizing the unitary design generated by a symmetric local random circuit. Concretely, we have shown that the necessary and sufficient condition for the circuit asymptotically forming a t-design is…
Unreplicated two-level factorial designs are often used in screening experiments to determine which factors out of a large plausible set are active. A theorem regarding the generalized word count pattern is stated and proved for…
This paper considers a restriction to non-negative matrix factorization in which at least one matrix factor is stochastic. That is, the elements of the matrix factors are non-negative and the columns of one matrix factor sum to 1. This…
Girth-regular graphs with equal girth, regular degree and chromatic index are studied for the determination of 1-factorizations with each 1-factor intersecting every girth cycle. Applications to hamiltonian decomposability and to…
Matching mechanisms play a central role in operations management across diverse fields including education, healthcare, and online platforms. However, experimentally comparing a new matching algorithm against a status quo presents some…
We study the problem of constructing strong approximate unitary $k$-designs on $D$-dimensional grids (and more generally on Cartesian products of graphs), building on the work of Schuster et al. arXiv:2509.26310 which establishes strong…
We prove the existence of subspace designs with any given parameters, provided that the dimension of the underlying space is sufficiently large in terms of the other parameters of the design and satisfies the obvious necessary divisibility…
This paper, broadly speaking, covers the use of randomness in two main areas: low-rank approximation and kernel methods. Low-rank approximation is very important in numerical linear algebra. Many applications depend on matrix decomposition…
Split-plot designs find wide applicability in multifactor experiments with randomization restrictions. Practical considerations often warrant the use of unbalanced designs. This paper investigates randomization based causal inference in…
A design is a finite set of points in a space on which every "simple" functions averages to its global mean. Illustrative examples of simple functions are low-degree polynomials on the Euclidean sphere or on the Hamming cube. We prove lower…
Random projections offer an appealing and flexible approach to a wide range of large-scale statistical problems. They are particularly useful in high-dimensional settings, where we have many covariates recorded for each observation. In…
Interesting data often concentrate on low dimensional smooth manifolds inside a high dimensional ambient space. Random projections are a simple, powerful tool for dimensionality reduction of such data. Previous works have studied bounds on…
Random embeddings project high-dimensional spaces to low-dimensional ones; they are careful constructions which allow the approximate preservation of key properties, such as the pair-wise distances between points. Often in the field of…
We propose and analyze a regularization approach for structured prediction problems. We characterize a large class of loss functions that allows to naturally embed structured outputs in a linear space. We exploit this fact to design…
In this paper, we consider robust control using randomized algorithms. We extend the existing order statistics distribution theory to the general case in which the distribution of population is not assumed to be continuous and the order…
Estimation of structure, such as in variable selection, graphical modelling or cluster analysis is notoriously difficult, especially for high-dimensional data. We introduce stability selection. It is based on subsampling in combination with…
In this survey we describe a recently-developed technique for bounding the number (and controlling the typical structure) of finite objects with forbidden substructures. This technique exploits a subtle clustering phenomenon exhibited by…
A new probabilistic technique for establishing the existence of certain regular combinatorial structures has been recentlyintroduced by Kuperberg, Lovett, and Peled (STOC 2012). Using this technique, it can be shown that under certain…
We are concerned with the problem of designing large families of subsets over a common labeled ground set that have small pairwise intersections and the property that the maximum discrepancy of the label values within each of the sets is…
Combinatorial $t$-designs have nice applications in coding theory, finite geometries and several engineering areas. There are two major methods of constructing $t$-designs. One of them is via group actions of certain permutation groups…