Sampling from probability distributions is a crucial task in both statistics and machine learning. However, when the target distribution does not permit exact sampling, researchers often rely on Markov chain Monte Carlo (MCMC) methods.

Quasi-Monte Carlo (QMC) is a powerful method for evaluating high-dimensional integrals. However, its use is typically limited to distributions where direct sampling is straightforward, such as the uniform distribution on the unit hypercube or the Gaussian distribution. For general target distributions with potentially unnormalized densities, leveraging the low-discrepancy property of QMC to improve accuracy remains challenging. We propose training a transport map to push forward the uniform distribution on the unit hypercube to approximate the target distribution. Inspired by normalizing flows, the transport map is constructed as a composition of simple, invertible transformations. To ensure that RQMC achieves its superior error rate, the transport map must satisfy specific regularity conditions. We introduce a flexible parametrization for the transport map that not only meets these conditions but is also expressive enough to model complex distributions. Our theoretical analysis establishes that the proposed transport QMC estimator achieves faster convergence rates than standard Monte Carlo, under mild and easily verifiable growth conditions on the integrand. Numerical experiments confirm the theoretical results, demonstrating the effectiveness of the proposed method in Bayesian inference tasks.

Recent advances in machine learning have led to the development of new methods for enhancing Monte Carlo methods such as Markov chain Monte Carlo (MCMC) and importance sampling (IS). One such method is normalizing flows, which use a neural network to approximate a distribution by evaluating it pointwise. Normalizing flows have been shown to improve the performance of MCMC and IS. On the other side, (randomized) quasi-Monte Carlo methods are used to perform numerical integration. They replace the random sampling of Monte Carlo by a sequence which cover the hypercube more uniformly, resulting in better convergence rates for the error that plain Monte Carlo. In this work, we combine these two methods by using quasi-Monte Carlo to sample the initial distribution that is transported by the flow. We demonstrate through numerical experiments that this combination can lead to an estimator with significantly lower variance than if the flow was sampled with a classic Monte Carlo.

Langevin Monte Carlo (LMC) and its stochastic gradient versions are powerful algorithms for sampling from complex high-dimensional distributions. To sample from a distribution with density $\pi(\theta)\propto \exp(-U(\theta)) $, LMC iteratively generates the next sample by taking a step in the gradient direction $\nabla U$ with added Gaussian perturbations. Expectations w.r.t. the target distribution $\pi$ are estimated by averaging over LMC samples. In ordinary Monte Carlo, it is well known that the estimation error can be substantially reduced by replacing independent random samples by quasi-random samples like low-discrepancy sequences. In this work, we show that the estimation error of LMC can also be reduced by using quasi-random samples. Specifically, we propose to use completely uniformly distributed (CUD) sequences with certain low-discrepancy property to generate the Gaussian perturbations. Under smoothness and convexity conditions, we prove that LMC with a low-discrepancy CUD sequence achieves smaller error than standard LMC. The theoretical analysis is supported by compelling numerical experiments, which demonstrate the effectiveness of our approach.

Automated driving systems rely on 3D object detectors to recognize possible obstacles from LiDAR point clouds. However, recent works show the adversary can forge non-existent cars in the prediction results with a few fake points (i.e., appearing attack). By removing statistical outliers, existing defenses are however designed for specific attacks or biased by predefined heuristic rules. Towards more comprehensive mitigation, we first systematically inspect the mechanism of recent appearing attacks: Their common weaknesses are observed in crafting fake obstacles which (i) have obvious differences in the local parts compared with real obstacles and (ii) violate the physical relation between depth and point density. In this paper, we propose a novel plug-and-play defensive module which works by side of a trained LiDAR-based object detector to eliminate forged obstacles where a major proportion of local parts have low objectness, i.e., to what degree it belongs to a real object. At the core of our module is a local objectness predictor, which explicitly incorporates the depth information to model the relation between depth and point density, and predicts each local part of an obstacle with an objectness score. Extensive experiments show, our proposed defense eliminates at least 70% cars forged by three known appearing attacks in most cases, while, for the best previous defense, less than 30% forged cars are eliminated. Meanwhile, under the same circumstance, our defense incurs less overhead for AP/precision on cars compared with existing defenses. Furthermore, We validate the effectiveness of our proposed defense on simulation-based closed-loop control driving tests in the open-source system of Baidu's Apollo.

This is a collaborative post between Monte Carlo and Databricks. We thank Matt Sulkis, Head of Partnerships, Monte Carlo, for his contributions. As companies increasingly leverage data-driven insights to innovate and maintain their competitive edge, it's essential that this data is accurate and reliable. With Monte Carlo and Databricks' partnership, teams can trust their data through end-to-end data observability across their lakehouse environments. Has your CTO ever told you that the numbers in a report you showed her looked way off?

Amazon is reportedly installing AI-powered cameras in delivery vans to keep tabs on its drivers in the UK. The technology was first deployed, with numerous errors that reportedly denied drivers' bonuses after malfunctions, in the US. Last year, the internet giant produced a corporate video detailing how the cameras monitor drivers' driving behavior for safety reasons. The same system is now apparently being rolled out to vehicles in the UK. Multiple camera lenses are placed under the front mirror.

The Plackett-Luce (PL) model is ubiquitous in learning-to-rank (LTR) because it provides a useful and intuitive probabilistic model for sampling ranked lists. Counterfactual offline evaluation and optimization of ranking metrics are pivotal for using LTR methods in production. When adopting the PL model as a ranking policy, both tasks require the computation of expectations with respect to the model. These are usually approximated via Monte-Carlo (MC) sampling, since the combinatorial scaling in the number of items to be ranked makes their analytical computation intractable. Despite recent advances in improving the computational efficiency of the sampling process via the Gumbel top-k trick, the MC estimates can suffer from high variance. We develop a novel approach to producing more sample-efficient estimators of expectations in the PL model by combining the Gumbel top-k trick with quasi-Monte Carlo (QMC) sampling, a well-established technique for variance reduction. We illustrate our findings both theoretically and empirically using real-world recommendation data from Amazon Music and the Yahoo learning-to-rank challenge.

I have got a new doorbell. It should be; it cost £89. It's a Ring video doorbell; you'll have seen them around. There are others available, made by other companies, with other four-letter names such as Nest and Arlo. When someone rings my doorbell, I'm alerted on my smartphone. I can see who is there, and speak to them. C major first inversion chord, arpeggiated, repeated, for the musically trained – you'll recognise it if you've heard it. Amazon, as it happens; Amazon acquired Ring in 2018, reportedly for more than $1bn.