Related papers: Bypassing orthogonalization in the quantum DPP sam…
This paper considers the projection-free sparse convex optimization problem for the vector domain and the matrix domain, which covers a large number of important applications in machine learning and data science. For the vector domain…
We describe and analyze a simple algorithm for sampling from the solution $\mathbf{x}^* := \mathbf{A}^+\mathbf{b}$ to a linear system $\mathbf{A}\mathbf{x} = \mathbf{b}$. We assume access to a sampler which allows us to draw indices…
Subset selection is central to many wireless communication problems, including link scheduling, power allocation, and spectrum management. However, these problems are often NP-complete, because of which heuristic algorithms applied to solve…
Consider a Dirichlet process mixture model (DPM) with random precision parameter $\alpha$, inducing $K_n$ clusters over $n$ observations through its latent random partition. Our goal is to specify the prior distribution…
Determinantal point processes (DPPs) have attracted substantial attention as an elegant probabilistic model that captures the balance between quality and diversity within sets. DPPs are conventionally parameterized by a positive…
Determinantal Point Processes (DPPs) are popular models for point processes with repulsion. They appear in numerous contexts, from physics to graph theory, and display appealing theoretical properties. On the more practical side of things,…
Deep neural networks have made tremendous gains in emulating human-like intelligence, and have been used increasingly as ways of understanding how the brain may solve the complex computational problems on which this relies. However, these…
We study a mini-batch diversification scheme for stochastic gradient descent (SGD). While classical SGD relies on uniformly sampling data points to form a mini-batch, we propose a non-uniform sampling scheme based on the Determinantal Point…
We study the differential privacy (DP) of the quantum recommendation algorithm of Kerenidis--Prakash and its quantum-inspired classical counterpart. Under standard low-rank and incoherence assumptions on the preference matrix, we show that…
We consider the algorithmic problem of finding a near-optimal solution for the number partitioning problem (NPP). The NPP appears in many applications, including the design of randomized controlled trials, multiprocessor scheduling, and…
In the number partitioning problem (NPP) one aims to partition a given set of $N$ real numbers into two subsets with approximately equal sum. The NPP is a well-studied optimization problem and is famous for possessing a…
Quantum machine learning (QML) aims to accelerate machine learning tasks by exploiting quantum computation. Previous work studied a QML algorithm for selecting sparse subnetworks from large shallow neural networks. Instead of directly…
Gaussian Process bandit optimization has emerged as a powerful tool for optimizing noisy black box functions. One example in machine learning is hyper-parameter optimization where each evaluation of the target function requires training a…
Rejection sampling is a well-known method to sample from a target distribution, given the ability to sample from a given distribution. The method has been first formalized by von Neumann (1951) and has many applications in classical…
We present a classical algorithm that, for any $D$-dimensional geometrically-local, quantum circuit $C$ of polylogarithmic-depth, and any bit string $x \in {0,1}^n$, can compute the quantity $|<x|C|0^{\otimes n}>|^2$ to within any…
A determinantal point process (DPP) is a random process useful for modeling the combinatorial problem of subset selection. In particular, DPPs encourage a random subset Y to contain a diverse set of items selected from a base set Y. For…
Determinantal point processes (DPPs) are specific probability distributions over clouds of points that are used as models and computational tools across physics, probability, statistics, and more recently machine learning. Sampling from…
Variational quantum circuits characterise the state of a quantum system through the use of parameters that are optimised using classical optimisation procedures that typically rely on gradient information. The circuit-execution complexity…
An algorithm for sampling exactly from the normal distribution is given. The algorithm reads some number of uniformly distributed random digits in a given base and generates an initial portion of the representation of a normal deviate in…
Translating a general quantum circuit on a specific hardware topology with a reduced set of available gates, also known as transpilation, comes with a substantial increase in the length of the equivalent circuit. Due to decoherence, the…