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In recent work, we proposed a distributed Banach-Picard iteration (DBPI) that allows a set of agents, linked by a communication network, to find a fixed point of a locally contractive (LC) map that is the average of individual maps held by said agents. In this work, we build upon the DBPI and its local linear convergence (LLC) guarantees to make several contributions. We show that Sanger's algorithm for principal component analysis (PCA) corresponds to the iteration of an LC map that can be written as the average of local maps, each map known to each agent holding a subset of the data. Similarly, we show that a variant of the expectation-maximization (EM) algorithm for parameter estimation from noisy and faulty measurements in a sensor network can be written as the iteration of an LC map that is the average of local maps, each available at just one node. Consequently, via the DBPI, we derive two distributed algorithms - distributed EM and distributed PCA - whose LLC guarantees follow from those that we proved for the DBPI. The verification of the LC condition for EM is challenging, as the underlying operator depends on random samples, thus the LC condition is of probabilistic nature.

Cluster analysis aims at partitioning data into groups or clusters. In applications, it is common to deal with problems where the number of clusters is unknown. Bayesian mixture models employed in such applications usually specify a flexible prior that takes into account the uncertainty with respect to the number of clusters. However, a major empirical challenge involving the use of these models is in the characterisation of the induced prior on the partitions. This work introduces an approach to compute descriptive statistics of the prior on the partitions for three selected Bayesian mixture models developed in the areas of Bayesian finite mixtures and Bayesian nonparametrics. The proposed methodology involves computationally efficient enumeration of the prior on the number of clusters in-sample (termed as ``data clusters'') and determining the first two prior moments of symmetric additive statistics characterising the partitions. The accompanying reference implementation is made available in the R package 'fipp'. Finally, we illustrate the proposed methodology through comparisons and also discuss the implications for prior elicitation in applications.

Cyber-physical systems (CPSs) typically consist of a wide set of integrated, heterogeneous components; consequently, most of their critical failures relate to the interoperability of such components.Unfortunately, most CPS test automation techniques are preliminary and industry still heavily relies on manual testing. With potentially incomplete, manually-generated test suites, it is of paramount importance to assess their quality. Though mutation analysis has demonstrated to be an effective means to assess test suite quality in some specific contexts, we lack approaches for CPSs. Indeed, existing approaches do not target interoperability problems and cannot be executed in the presence of black-box or simulated components, a typical situation with CPSs. In this paper, we introduce data-driven mutation analysis, an approach that consists in assessing test suite quality by verifying if it detects interoperability faults simulated by mutating the data exchanged by software components. To this end, we describe a data-driven mutation analysis technique (DaMAT) that automatically alters the data exchanged through data buffers. Our technique is driven by fault models in tabular form where engineers specify how to mutate data items by selecting and configuring a set of mutation operators. We have evaluated DaMAT with CPSs in the space domain; specifically, the test suites for the software systems of a microsatellite and nanosatellites launched on orbit last year. Our results show that the approach effectively detects test suite shortcomings, is not affected by equivalent and redundant mutants, and entails acceptable costs.

The paper provides three results for SVARs under the assumption that the primitive shocks are mutually independent. First, a framework is proposed to accommodate a disaster-type variable with infinite variance into a VAR. We show that the least squares estimates of the VAR are consistent but have non-standard properties. Second, the disaster shock is identified as the component with the largest kurtosis and whose impact effect is negative. An estimator that is robust to infinite variance is used to recover the mutually independent components. Third, an independence test on the residuals pre-whitened by Choleski decomposition is proposed to test the restrictions imposed on a SVAR. The test can be applied whether the data have fat or thin tails, and to over as well as exactly identified models. Three applications are considered. In the first, the independence test is used to shed light on the conflicting evidence regarding the role of uncertainty in economic fluctuations. In the second, disaster shocks are shown to have short term economic impact arising mostly from feedback dynamics. The third application uses the framework to study the dynamic effects of economic shocks post-covid.

Recent studies have shown that the choice of activation function can significantly affect the performance of deep learning networks. However, the benefits of novel activation functions have been inconsistent and task dependent, and therefore the rectified linear unit (ReLU) is still the most commonly used. This paper proposes a technique for customizing activation functions automatically, resulting in reliable improvements in performance. Evolutionary search is used to discover the general form of the function, and gradient descent to optimize its parameters for different parts of the network and over the learning process. Experiments with four different neural network architectures on the CIFAR-10 and CIFAR-100 image classification datasets show that this approach is effective. It discovers both general activation functions and specialized functions for different architectures, consistently improving accuracy over ReLU and other activation functions by significant margins. The approach can therefore be used as an automated optimization step in applying deep learning to new tasks.

Continuous determinantal point processes (DPPs) are a class of repulsive point processes on $\mathbb{R}^d$ with many statistical applications. Although an explicit expression of their density is known, it is too complicated to be used directly for maximum likelihood estimation. In the stationary case, an approximation using Fourier series has been suggested, but it is limited to rectangular observation windows and no theoretical results support it. In this contribution, we investigate a different way to approximate the likelihood by looking at its asymptotic behaviour when the observation window grows towards $\mathbb{R}^d$. This new approximation is not limited to rectangular windows, is faster to compute than the previous one, does not require any tuning parameter, and some theoretical justifications are provided. It moreover provides an explicit formula for estimating the asymptotic variance of the associated estimator. The performances are assessed in a simulation study on standard parametric models on $\mathbb{R}^d$ and compare favourably to common alternative estimation methods for continuous DPPs.

Various algorithms for reinforcement learning (RL) exhibit dramatic variation in their convergence rates as a function of problem structure. Such problem-dependent behavior is not captured by worst-case analyses and has accordingly inspired a growing effort in obtaining instance-dependent guarantees and deriving instance-optimal algorithms for RL problems. This research has been carried out, however, primarily within the confines of theory, providing guarantees that explain \textit{ex post} the performance differences observed. A natural next step is to convert these theoretical guarantees into guidelines that are useful in practice. We address the problem of obtaining sharp instance-dependent confidence regions for the policy evaluation problem and the optimal value estimation problem of an MDP, given access to an instance-optimal algorithm. As a consequence, we propose a data-dependent stopping rule for instance-optimal algorithms. The proposed stopping rule adapts to the instance-specific difficulty of the problem and allows for early termination for problems with favorable structure.

Statistical inference on the explained variation of an outcome by a set of covariates is of particular interest in practice. When the covariates are of moderate to high-dimension and the effects are not sparse, several approaches have been proposed for estimation and inference. One major problem with the existing approaches is that the inference procedures are not robust to the normality assumption on the covariates and the residual errors. In this paper, we propose an estimating equation approach to the estimation and inference on the explained variation in the high-dimensional linear model. Unlike the existing approaches, the proposed approach does not rely on the restrictive normality assumptions for inference. It is shown that the proposed estimator is consistent and asymptotically normally distributed under reasonable conditions. Simulation studies demonstrate better performance of the proposed inference procedure in comparison with the existing approaches. The proposed approach is applied to studying the variation of glycohemoglobin explained by environmental pollutants in a National Health and Nutrition Examination Survey data set.

Topic models have been widely explored as probabilistic generative models of documents. Traditional inference methods have sought closed-form derivations for updating the models, however as the expressiveness of these models grows, so does the difficulty of performing fast and accurate inference over their parameters. This paper presents alternative neural approaches to topic modelling by providing parameterisable distributions over topics which permit training by backpropagation in the framework of neural variational inference. In addition, with the help of a stick-breaking construction, we propose a recurrent network that is able to discover a notionally unbounded number of topics, analogous to Bayesian non-parametric topic models. Experimental results on the MXM Song Lyrics, 20NewsGroups and Reuters News datasets demonstrate the effectiveness and efficiency of these neural topic models.

In this paper, we study the optimal convergence rate for distributed convex optimization problems in networks. We model the communication restrictions imposed by the network as a set of affine constraints and provide optimal complexity bounds for four different setups, namely: the function $F(\xb) \triangleq \sum_{i=1}^{m}f_i(\xb)$ is strongly convex and smooth, either strongly convex or smooth or just convex. Our results show that Nesterov's accelerated gradient descent on the dual problem can be executed in a distributed manner and obtains the same optimal rates as in the centralized version of the problem (up to constant or logarithmic factors) with an additional cost related to the spectral gap of the interaction matrix. Finally, we discuss some extensions to the proposed setup such as proximal friendly functions, time-varying graphs, improvement of the condition numbers.