Related papers: Fast Witness Counting
In the framework of real Hilbert spaces we study continuous in time dynamics as well as numerical algorithms for the problem of approaching the set of zeros of a single-valued monotone and continuous operator $V$. The starting poin is a…
We consider the problem of learning a classifier from observed functional data. Here, each data-point takes the form of a single time-series and contains numerous features. Assuming that each such series comes with a binary label, the…
In conventional prediction tasks, a machine learning algorithm outputs a single best model that globally optimizes its objective function, which typically is accuracy. Therefore, users cannot access the other models explicitly. In contrast…
Kernel methods are a highly effective and widely used collection of modern machine learning algorithms. A fundamental limitation of virtually all such methods are computations involving the kernel matrix that naively scale quadratically…
Permutation patterns and pattern avoidance have been intensively studied in combinatorics and computer science, going back at least to the seminal work of Knuth on stack-sorting (1968). Perhaps the most natural algorithmic question in this…
Given vectors $v_1,\dots,v_n\in\mathbb{R}^d$ and a matroid $M=([n],I)$, we study the problem of finding a basis $S$ of $M$ such that $\det(\sum_{i \in S}v_i v_i^\top)$ is maximized. This problem appears in a diverse set of areas such as…
Crowd counting aims to count the number of instantaneous people in a crowded space, and many promising solutions have been proposed for single image crowd counting. With the ubiquitous video capture devices in public safety field, how to…
The convolution potential arises in a wide variety of application areas, and its efficient and accurate evaluation encounters three challenges: singularity, nonlocality and anisotropy. We introduce a fast algorithm based on a far-field…
In this paper we consider the Target Set Selection problem. The problem naturally arises in many fields like economy, sociology, medicine. In the Target Set Selection problem one is given a graph $G$ with a function $\operatorname{thr}:…
In the recent years, intensive research work has been dedicated to prove conditional lower bounds in order to reveal the inner structure of the class P. These conditional lower bounds are based on many popular conjectures on well-studied…
Vertex direction algorithms have been around for a few decades in the experimental design and mixture models literature. We briefly review this type of algorithm and describe a new member of the family: the support reduction algorithm. The…
We study the problem of estimating precision matrices in Gaussian distributions that are multivariate totally positive of order two ($\mathrm{MTP}_2$). The precision matrix in such a distribution is an M-matrix. This problem can be…
Among the cost metrics characterizing a quantum circuit, the $T$-count stands out as one of the most crucial as its minimization is particularly important in various areas of quantum computation such as fault-tolerant quantum computing and…
Let $\epsilon_1, \dotsc, \epsilon_n$ be i.i.d. Rademacher random variables taking values $\pm 1$ with probability $1/2$ each. Given an integer vector $\boldsymbol{a} = (a_1, \dotsc, a_n)$, its concentration probability is the quantity…
We consider the problem of Robust PCA in the fully and partially observed settings. Without corruptions, this is the well-known matrix completion problem. From a statistical standpoint this problem has been recently well-studied, and…
Approximate integer programming is the following: For a convex body $K \subseteq \mathbb{R}^n$, either determine whether $K \cap \mathbb{Z}^n$ is empty, or find an integer point in the convex body scaled by $2$ from its center of gravity…
Vision Transformers achieve impressive accuracy across a range of visual recognition tasks. Unfortunately, their accuracy frequently comes with high computational costs. This is a particular issue in video recognition, where models are…
We establish efficient approximate counting algorithms for several natural problems in local lemma regimes. In particular, we consider the probability of intersection of events and the dimension of intersection of subspaces. Our approach is…
We present efficient counting and sampling algorithms for random $k$-SAT when the clause density satisfies $\alpha \le \frac{2^k}{\mathrm{poly}(k)}.$ In particular, the exponential term $2^k$ matches the satisfiability threshold…
Finite-sum optimization has wide applications in machine learning, covering important problems such as support vector machines, regression, etc. In this paper, we initiate the study of solving finite-sum optimization problems by quantum…