Related papers: A general framework for perfect simulation of long…

In this work, we consider the problem of learning nonlinear operators that correspond to discrete-time nonlinear dynamical systems with inputs. Given an initial state and a finite input trajectory, such operators yield a finite output…

We demonstrate how machine learning is able to model experiments in quantum physics. Quantum entanglement is a cornerstone for upcoming quantum technologies such as quantum computation and quantum cryptography. Of particular interest are…

Here several perfect simulation algorithms are brought under a single framework, and shown to derive from the same probabilistic result, called here the Fundamental Theorem of Perfect Simulation (FTPS). An exact simulation algorithm has…

A quantum processor is a programmable quantum circuit in which both the data and the program, which specifies the operation that is carried out on the data, are quantum states. We study the situation in which we want to use such a processor…

Gaussian process (GP) regression provides a flexible, nonparametric framework for probabilistic modeling, yet remains computationally demanding in large-scale applications. For one-dimensional data, state space (SS) models achieve…

Many inference scenarios rely on extracting relevant information from known data in order to make future predictions. When the underlying stochastic process satisfies certain assumptions, there is a direct mapping between its exact…

State-space models (SSMs) are a highly expressive model class for learning patterns in time series data and for system identification. Deterministic versions of SSMs (e.g. LSTMs) proved extremely successful in modeling complex time series…

These notes provide a self-contained introduction to kernel methods and their geometric foundations in machine learning. Starting from the construction of Hilbert spaces, we develop the theory of positive definite kernels, reproducing…

This article shows a proof of concept regarding the feasibility of ab initio molecular simulation, wherein the wavefunctions and the positions of nuclei are simultaneously determined by the quantum algorithm, as is realized by the so-called…

We propose a unified framework that extends the inference methods for classical hidden Markov models to continuous settings, where both the hidden states and observations occur in continuous time. Two different settings are analyzed: hidden…

The optimal selection of experimental conditions is essential to maximizing the value of data for inference and prediction, particularly in situations where experiments are time-consuming and expensive to conduct. We propose a general…

Conformal field theory, describing systems with scaling symmetry, plays a crucial role throughout physics. We describe a quantum algorithm to simulate the dynamics of conformal field theories, including the action of local conformal…

We examine an analytic variational inference scheme for the Gaussian Process State Space Model (GPSSM) - a probabilistic model for system identification and time-series modelling. Our approach performs variational inference over both the…

We introduce the first class of perfect sampling algorithms for the steady-state distribution of multi-server queues with general interarrival time and service time distributions. Our algorithm is built on the classical dominated coupling…

A fundamental model of quantum computation is the programmable quantum gate array. This is a quantum processor that is fed by a program state that induces a corresponding quantum operation on input states. While being programmable, any…

We present the first class of perfect sampling (also known as exact simulation) algorithms for the steady-state distribution of non-Markovian loss networks. We use a variation of Dominated Coupling From The Past for which we simulate a…

The theory of open quantum systems lays the foundations for a substantial part of modern research in quantum science and engineering. Rooted in the dimensionality of their extended Hilbert spaces, the high computational complexity of…

A construction is given for simulating any deterministic finite state machine (FSM) on a quantum computer in a space-efficient manner. By constructing a superposition of input strings of lengths K or less, questions can be asked about the…

The success of kernel-based learning methods depend on the choice of kernel. Recently, kernel learning methods have been proposed that use data to select the most appropriate kernel, usually by combining a set of base kernels. We introduce…

This paper derives error bounds for regression in continuous time over subsets of certain types of Riemannian manifolds.The regression problem is typically driven by a nonlinear evolution law taking values on the manifold, and it is cast as…