相关论文: For Distinguishing Conjugate Hidden Subgroups, the…

For large classes of group testing problems, we derive lower bounds for the probability that all significant items are uniquely identified using specially constructed random designs. These bounds allow us to optimize parameters of the…

Hidden Markov Models (HMMs) can be accurately approximated using co-occurrence frequencies of pairs and triples of observations by using a fast spectral method in contrast to the usual slow methods like EM or Gibbs sampling. We provide a…

We prove that, if $G$ is a finite almost simple group and $H$ is a maximal subgroup of $G$, then the $10$th term of the derived series of $H$ is perfect. The same is true if $G$ is perfect and $H$ is core-free. The constant $10$ is best…

Given the noisy pairwise measurements among a set of unknown group elements, how to recover them efficiently and robustly? This problem, known as group synchronization, has drawn tremendous attention in the scientific community. In this…

Many real-world decision making tasks require us to choose among several expensive observations. In a sensor network, for example, it is important to select the subset of sensors that is expected to provide the strongest reduction in…

A celebrated theorem of Pippenger states that any almost regular hypergraph with small codegrees has an almost perfect matching. We show that one can find such an almost perfect matching which is `pseudorandom', meaning that, for instance,…

One of the foundational theorems of extremal graph theory is Dirac's theorem, which says that if an n-vertex graph G has minimum degree at least n/2, then G has a Hamilton cycle, and therefore a perfect matching (if n is even). Later work…

In this paper we consider the problem of constructing measurements optimized to distinguish between a collection of possibly non-orthogonal quantum states. We consider a collection of pure states and seek a positive operator-valued measure…

We discuss a graph-based approach for testing spatial point patterns. This approach falls under the category of data-random graphs, which have been introduced and used for statistical pattern recognition in recent years. Our goal is to test…

A perfect code in a graph $\Gamma$ is a subset $C$ of $V(\Gamma)$ such that no two vertices in $C$ are adjacent and every vertex in $V(\Gamma)\setminus C$ is adjacent to exactly one vertex in $C$. Let $G$ be a finite group and $C$ a subset…

We show that measuring any two quantum states by a random POVM, under a suitable definition of randomness, gives probability distributions having total variation distance at least a universal constant times the Frobenius distance between…

Combining p-values from multiple independent tests is a fundamental task in statistical inference, but presents unique challenges when the p-values are discrete. We extend a recent optimal transport-based framework for combining discrete…

Anomaly detection (AD) has attracted considerable attention in both academia and industry. Due to the lack of anomalous data in many practical cases, AD is usually solved by first modeling the normal data pattern and then determining if…

We consider the problem of a state determination for a two-level quantum system which can be in one of two nonorthogonal mixed states. It is proved that for the two independent identical systems the optimal combined measurement (which…

Probabilistic graphical models (PGMs) provide a compact representation of knowledge that can be queried in a flexible way: after learning the parameters of a graphical model once, new probabilistic queries can be answered at test time…

The study of convex optimization has historically been concerned with worst-case convergence rates. The development of the Optimized Gradient Method (OGM), due to \citet{drori2012PerformanceOF,Kim2016optimal}, marked a major milestone in…

This paper introduces the use of unbalanced optimal transport methods as a similarity measure for diffeomorphic matching of imaging data. The similarity measure is a key object in diffeomorphic registration methods that, together with the…

We investigate a state discrimination problem in operationally the most general framework to use a probability, including both classical, quantum theories, and more. In this wide framework, introducing closely related family of ensembles…

Probabilistic 3D point cloud registration methods have shown competitive performance in overcoming noise, outliers, and density variations. However, registering point cloud pairs in the case of partial overlap is still a challenge. This…

It is known that any quantum algorithm for Graph Isomorphism that works within the framework of the hidden subgroup problem (HSP) must perform highly entangled measurements across Omega(n log n) coset states. One of the only known models…