Albert Akhriev

Nicola Mariella, Albert Akhriev, Francesco Tacchino et al.

Optimal Transport (OT) has fueled machine learning (ML) across many domains. When paired data measurements $(\boldsymbolμ, \boldsymbolν)$ are coupled to covariates, a challenging conditional distribution learning setting arises. Existing approaches for learning a $\textit{global}$ transport map parameterized through a potentially unseen context utilize Neural OT and largely rely on Brenier's theorem. Here, we propose a first-of-its-kind quantum computing formulation for amortized optimization of contextualized transportation plans. We exploit a direct link between doubly stochastic matrices and unitary operators thus unravelling a natural connection between OT and quantum computation. We verify our method (QontOT) on synthetic and real data by predicting variations in cell type distributions conditioned on drug dosage. Importantly we conduct a 24-qubit hardware experiment on a task challenging for classical computers and report a performance that cannot be matched with our classical neural OT approach. In sum, this is a first step toward learning to predict contextualized transportation plans through quantum computing.

Albert Akhriev, Jakub Marecek

Many real-world monitoring and surveillance applications require non-trivial anomaly detection to be run in the streaming model. We consider an incremental-learning approach, wherein a deep-autoencoding (DAE) model of what is normal is trained and used to detect anomalies at the same time. In the detection of anomalies, we utilise a novel thresholding mechanism, based on value at risk (VaR). We compare the resulting convolutional neural network (CNN) against a number of subspace methods, and present results on changedetection net.

Albert Akhriev, Jakub Marecek, Andrea Simonetto

In tracking of time-varying low-rank models of time-varying matrices, we present a method robust to both uniformly-distributed measurement noise and arbitrarily-distributed ``sparse'' noise. In theory, we bound the tracking error. In practice, our use of randomised coordinate descent is scalable and allows for encouraging results on changedetection net, a benchmark.

Sergiy Zhuk, Tigran Tchrakian, Albert Akhriev et al.

This paper describes a new algorithm for solar energy forecasting from a sequence of Cloud Optical Depth (COD) images. The algorithm is based on the following simple observation: the dynamics of clouds represented by COD images resembles the motion (transport) of a density in a fluid flow. This suggests that, to forecast the motion of COD images, it is sufficient to forecast the flow. The latter, in turn, can be accomplished by fitting a parametric model of the fluid flow to the COD images observed in the past. Namely, the learning phase of the algorithm is composed of the following steps: (i) given a sequence of COD images, the snapshots of the optical flow are estimated from two consecutive COD images; (ii) these snapshots are then assimilated into a Navier-Stokes Equation (NSE), i.e. an initial velocity field for NSE is selected so that the corresponding NSE' solution is as close as possible to the optical flow snapshots. The prediction phase consists of utilizing a linear transport equation, which describes the propagation of COD images in the fluid flow predicted by NSE, to estimate the future motion of the COD images. The algorithm has been tested on COD images provided by two geostationary operational environmental satellites from NOAA serving the west-hemisphere.