Related papers: Near-Optimal Cayley Expanders for Abelian Groups

We address the computational efficiency in solving the A-optimal Bayesian design of experiments problems for which the observational map is based on partial differential equations and, consequently, is computationally expensive to evaluate.…

We propose a non-parametric anomaly detection algorithm for high dimensional data. We score each datapoint by its average $K$-NN distance, and rank them accordingly. We then train limited complexity models to imitate these scores based on…

For $N \geq 2$, we study the structure of definable abelian group extensions of the additive group $(\mathbb{R}^N,+)$ by countable abelian (Borel) groups $G$. Given an extension $H$ of $(\mathbb{R}^N,+)$ by $G$, we measure the definability…

We show that any subgroup of a finitely generated virtually abelian group $G$ grows rationally relative to $G$, that the set of right cosets of any subgroup of $G$ grows rationally, and that the set of conjugacy classes of $G$ grows…

We study the problem of optimal subset selection from a set of correlated random variables. In particular, we consider the associated combinatorial optimization problem of maximizing the determinant of a symmetric positive definite matrix…

Gaussian graphical models are widely used to infer dependence structures. Bayesian methods are appealing to quantify uncertainty associated with structural learning, i.e., the plausibility of conditional independence statements given the…

Maximal Independent Set selection is a fundamental problem in distributed computing. A novel probabilistic algorithm for this problem has recently been proposed by Afek et al, inspired by the study of the way that developing cells in the…

Likelihood-free inference for simulator-based statistical models has developed rapidly from its infancy to a useful tool for practitioners. However, models with more than a handful of parameters still generally remain a challenge for the…

We show that randomly choosing the matrices in a completely positive map from the unitary group gives a quantum expander. We consider Hermitian and non-Hermitian cases, and we provide asymptotically tight bounds in the Hermitian case on the…

Mechanistic models can provide an intuitive and interpretable explanation of network growth by specifying a set of generative rules. These rules can be defined by domain knowledge about real-world mechanisms governing network growth or may…

We study the problem of estimating the number of defective items $d$ within a pile of $n$ elements up to a multiplicative factor of $\Delta>1$, using deterministic group testing algorithms. We bring lower and upper bounds on the number of…

The dispersion of a point set $P\subset[0,1]^d$ is the volume of the largest box with sides parallel to the coordinate axes, which does not intersect $P$. Here, we show a construction of low-dispersion point sets, which can be deduced from…

The following natural question arises from Shalom's innovational work (1999, Publ. IHES): "Can we establish an intrinsic criterion to synthesize relative fixed point properties into the whole fixed point property without assuming Bounded…

The aim of this thesis is to determine classes of NP relations for which random generation and approximate counting problems admit an efficient solution. Since efficient rank implies efficient random generation, we first investigate some…

We construct $\varepsilon$-approximate unitary $k$-designs on $n$ qubits in circuit depth $O(\log k \log \log n k / \varepsilon)$. The depth is exponentially improved over all known results in all three parameters $n$, $k$, $\varepsilon$.…

We study algorithms for construction of composable coresets for the task of Determinant Maximization under partition constraint. Given a point set $V\subset \mathbb{R}^d$ that is partitioned into $s$ groups $V_1,\cdots, V_s$, and integers…

Symmetric submodular maximization is an important class of combinatorial optimization problems, including MAX-CUT on graphs and hyper-graphs. The state-of-the-art algorithm for the problem over general constraints has an approximation ratio…

We confirm the Jamneshan-Tao conjecture for finite abelian groups of rank at most a fixed integer $R$ (i.e. finite abelian groups generated by at most $R$ elements), by proving an inverse theorem for 1-bounded functions of non-trivial…

Neural Networks and Decision Trees: two popular techniques for supervised learning that are seemingly disconnected in their formulation and optimization method, have recently been combined in a single construct. The connection pivots on…

We study two-layer belief networks of binary random variables in which the conditional probabilities Pr[childlparents] depend monotonically on weighted sums of the parents. In large networks where exact probabilistic inference is…