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We introduce and analyze Structured Stochastic Zeroth order Descent (S-SZD), a finite difference approach which approximates a stochastic gradient on a set of $l\leq d$ orthogonal directions, where $d$ is the dimension of the ambient space. These directions are randomly chosen, and may change at each step. For smooth convex functions we prove almost sure convergence of the iterates and a convergence rate on the function values of the form $O(d/l k^{-c})$ for every $c<1/2$, which is arbitrarily close to the one of Stochastic Gradient Descent (SGD) in terms of number of iterations. Our bound also shows the benefits of using $l$ multiple directions instead of one. For non-convex functions satisfying the Polyak-{\L}ojasiewicz condition, we establish the first convergence rates for stochastic zeroth order algorithms under such an assumption. We corroborate our theoretical findings in numerical simulations where assumptions are satisfied and on the real-world problem of hyper-parameter optimization, observing that S-SZD has very good practical performances.

Before delegating a task to an autonomous system, a human operator may want a guarantee about the behavior of the system. This paper extends previous work on conformal prediction for functional data and conformalized quantile regression to provide conformal prediction intervals over the future behavior of an autonomous system executing a fixed control policy on a Markov Decision Process (MDP). The prediction intervals are constructed by applying conformal corrections to prediction intervals computed by quantile regression. The resulting intervals guarantee that with probability $1-\delta$ the observed trajectory will lie inside the prediction interval, where the probability is computed with respect to the starting state distribution and the stochasticity of the MDP. The method is illustrated on MDPs for invasive species management and StarCraft2 battles.

Languages vary considerably in syntactic structure. About 40% of the world's languages have subject-verb-object order, and about 40% have subject-object-verb order. Extensive work has sought to explain this word order variation across languages. However, the existing approaches are not able to explain coherently the frequency distribution and evolution of word order in individual languages. We propose that variation in word order reflects different ways of balancing competing pressures of dependency locality and information locality, whereby languages favor placing elements together when they are syntactically related or contextually informative about each other. Using data from 80 languages in 17 language families and phylogenetic modeling, we demonstrate that languages evolve to balance these pressures, such that word order change is accompanied by change in the frequency distribution of the syntactic structures which speakers communicate to maintain overall efficiency. Variability in word order thus reflects different ways in which languages resolve these evolutionary pressures. We identify relevant characteristics that result from this joint optimization, particularly the frequency with which subjects and objects are expressed together for the same verb. Our findings suggest that syntactic structure and usage across languages co-adapt to support efficient communication under limited cognitive resources.

Article prediction is a task that has long defied accurate linguistic description. As such, this task is ideally suited to evaluate models on their ability to emulate native-speaker intuition. To this end, we compare the performance of native English speakers and pre-trained models on the task of article prediction set up as a three way choice (a/an, the, zero). Our experiments with BERT show that BERT outperforms humans on this task across all articles. In particular, BERT is far superior to humans at detecting the zero article, possibly because we insert them using rules that the deep neural model can easily pick up. More interestingly, we find that BERT tends to agree more with annotators than with the corpus when inter-annotator agreement is high but switches to agreeing more with the corpus as inter-annotator agreement drops. We contend that this alignment with annotators, despite being trained on the corpus, suggests that BERT is not memorising article use, but captures a high level generalisation of article use akin to human intuition.

We present a systematic refactoring of the conventional treatment of privacy analyses, basing it on mathematical concepts from the framework of Quantitative Information Flow (QIF). The approach we suggest brings three principal advantages: it is flexible, allowing for precise quantification and comparison of privacy risks for attacks both known and novel; it can be computationally tractable for very large, longitudinal datasets; and its results are explainable both to politicians and to the general public. We apply our approach to a very large case study: the Educational Censuses of Brazil, curated by the governmental agency INEP, which comprise over 90 attributes of approximately 50 million individuals released longitudinally every year since 2007. These datasets have only very recently (2018-2021) attracted legislation to regulate their privacy -- while at the same time continuing to maintain the openness that had been sought in Brazilian society. INEP's reaction to that legislation was the genesis of our project with them. In our conclusions here we share the scientific, technical, and communication lessons we learned in the process.

The recent increase in yearly spacecraft launches and the high number of planned launches have raised questions about maintaining accessibility to space for all interested parties. A key to sustaining the future of space-flight is the ability to service malfunctioning - and actively remove dysfunctional spacecraft from orbit. Robotic platforms that autonomously perform these tasks are a topic of ongoing research and thus must undergo thorough testing before launch. For representative system-level testing, the European Space Agency (ESA) uses, among other things, the Orbital Robotics and GNC Lab (ORGL), a flat-floor facility where air-bearing based platforms exhibit free-floating behavior in three Degrees of Freedom (DoF). This work introduces a representative simulation of a free-floating platform in the testing environment and a software framework for controller development. Finally, this work proposes a controller within that framework for finding and following optimal trajectories between arbitrary states, which is evaluated in simulation and reality.

Over the past decade, machine learning revolutionized vision-based quality assessment for which convolutional neural networks (CNNs) have now become the standard. In this paper, we consider a potential next step in this development and describe a quanvolutional neural network (QNN) algorithm that efficiently maps classical image data to quantum states and allows for reliable image analysis. We practically demonstrate how to leverage quantum devices in computer vision and how to introduce quantum convolutions into classical CNNs. Dealing with a real world use case in industrial quality control, we implement our hybrid QNN model within the PennyLane framework and empirically observe it to achieve better predictions using much fewer training data than classical CNNs. In other words, we empirically observe a genuine quantum advantage for an industrial application where the advantage is due to superior data encoding.

We propose a co-variance corrected random batch method for interacting particle systems. By establishing a certain entropic central limit theorem, we provide entropic convergence guarantees for the law of the entire trajectories of all particles of the proposed method to the law of the trajectories of the discrete time interacting particle system whenever the batch size $B \gg (\alpha n)^{\frac{1}{3}}$ (where $n$ is the number of particles and $\alpha$ is the time discretization parameter). This in turn implies that the outputs of these methods are nearly \emph{statistically indistinguishable} when $B$ is even moderately large. Previous works mainly considered convergence in Wasserstein distance with required stringent assumptions on the potentials or the bounds had an exponential dependence on the time horizon. This work makes minimal assumptions on the interaction potentials and in particular establishes that even when the particle trajectories diverge to infinity, they do so in the same way for both the methods. Such guarantees are very useful in light of the recent advances in interacting particle based algorithms for sampling.

We commonly assume that data are a homogeneous set of observations when learning the structure of Bayesian networks. However, they often comprise different data sets that are related but not homogeneous because they have been collected in different ways or from different populations. In our previous work (Azzimonti, Corani and Scutari, 2021), we proposed a closed-form Bayesian Hierarchical Dirichlet score for discrete data that pools information across related data sets to learn a single encompassing network structure, while taking into account the differences in their probabilistic structures. In this paper, we provide an analogous solution for learning a Bayesian network from continuous data using mixed-effects models to pool information across the related data sets. We study its structural, parametric, predictive and classification accuracy and we show that it outperforms both conditional Gaussian Bayesian networks (that do not perform any pooling) and classical Gaussian Bayesian networks (that disregard the heterogeneous nature of the data). The improvement is marked for low sample sizes and for unbalanced data sets.

Landscape-aware algorithm selection approaches have so far mostly been relying on landscape feature extraction as a preprocessing step, independent of the execution of optimization algorithms in the portfolio. This introduces a significant overhead in computational cost for many practical applications, as features are extracted and computed via sampling and evaluating the problem instance at hand, similarly to what the optimization algorithm would perform anyway within its search trajectory. As suggested in Jankovic et al. (EvoAPPs 2021), trajectory-based algorithm selection circumvents the problem of costly feature extraction by computing landscape features from points that a solver sampled and evaluated during the optimization process. Features computed in this manner are used to train algorithm performance regression models, upon which a per-run algorithm selector is then built. In this work, we apply the trajectory-based approach onto a portfolio of five algorithms. We study the quality and accuracy of performance regression and algorithm selection models in the scenario of predicting different algorithm performances after a fixed budget of function evaluations. We rely on landscape features of the problem instance computed using one portion of the aforementioned budget of the same function evaluations. Moreover, we consider the possibility of switching between the solvers once, which requires them to be warm-started, i.e. when we switch, the second solver continues the optimization process already being initialized appropriately by making use of the information collected by the first solver. In this new context, we show promising performance of the trajectory-based per-run algorithm selection with warm-starting.