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The utilisation of large and diverse datasets for machine learning (ML) at scale is required to promote scientific insight into many meaningful problems. However, due to data governance regulations such as GDPR as well as ethical concerns, the aggregation of personal and sensitive data is problematic, which prompted the development of alternative strategies such as distributed ML (DML). Techniques such as Federated Learning (FL) allow the data owner to maintain data governance and perform model training locally without having to share their data. FL and related techniques are often described as privacy-preserving. We explain why this term is not appropriate and outline the risks associated with over-reliance on protocols that were not designed with formal definitions of privacy in mind. We further provide recommendations and examples on how such algorithms can be augmented to provide guarantees of governance, security, privacy and verifiability for a general ML audience without prior exposure to formal privacy techniques.

The cumulative distribution or probability density of a random variable, which is itself a function of a high number of independent real-valued random variables, can be formulated as high-dimensional integrals of an indicator or a Dirac $\delta$ function, respectively. To approximate the distribution or density at a point, we carry out preintegration with respect to one suitably chosen variable, then apply a Quasi-Monte Carlo method to compute the integral of the resulting smoother function. Interpolation is then used to reconstruct the distribution or density on an interval. We provide rigorous regularity and error analysis for the preintegrated function to show that our estimators achieve nearly first order convergence. Numerical results support the theory.

The noncentral Wishart distribution has become more mainstream in statistics as the prevalence of applications involving sample covariances with underlying multivariate Gaussian populations as dramatically increased since the advent of computers. Multiple sources in the literature deal with local approximations of the noncentral Wishart distribution with respect to its central counterpart. However, no source has yet developed explicit local approximations for the (central) Wishart distribution in terms of a normal analogue, which is important since Gaussian distributions are at the heart of the asymptotic theory for many statistical methods. In this paper, we prove a precise asymptotic expansion for the ratio of the Wishart density to the symmetric matrix-variate normal density with the same mean and covariances. The result is then used to derive an upper bound on the total variation between the corresponding probability measures and to find the pointwise variance of a new density estimator on the space of positive definite matrices with a Wishart asymmetric kernel. For the sake of completeness, we also find expressions for the pointwise bias of our new estimator, the pointwise variance as we move towards the boundary of its support, the mean squared error, the mean integrated squared error away from the boundary, and we prove its asymptotic normality.

In the era of big data and the Internet of Things (IoT), data owners need to share a large amount of data with the intended receivers in an insecure environment, posing a trade-off issue between user privacy and data utility. The privacy utility trade-off was facilitated through a privacy funnel based on mutual information. Nevertheless, it is challenging to characterize the mutual information accurately with small sample size or unknown distribution functions. In this article, we propose a privacy funnel based on mutual information neural estimator (MINE) to optimize the privacy utility trade-off by estimating mutual information. Instead of computing mutual information in traditional way, we estimate it using an MINE, which obtains the estimated mutual information in a trained way, ensuring that the estimation results are as precise as possible. We employ estimated mutual information as a measure of privacy and utility, and then form a problem to optimize data utility by training a neural network while the estimator's privacy discourse is less than a threshold. The simulation results also demonstrated that the estimated mutual information from MINE works very well to approximate the mutual information even with a limited number of samples to quantify privacy leakage and data utility retention, as well as optimize the privacy utility trade-off.

Classic machine learning methods are built on the $i.i.d.$ assumption that training and testing data are independent and identically distributed. However, in real scenarios, the $i.i.d.$ assumption can hardly be satisfied, rendering the sharp drop of classic machine learning algorithms' performances under distributional shifts, which indicates the significance of investigating the Out-of-Distribution generalization problem. Out-of-Distribution (OOD) generalization problem addresses the challenging setting where the testing distribution is unknown and different from the training. This paper serves as the first effort to systematically and comprehensively discuss the OOD generalization problem, from the definition, methodology, evaluation to the implications and future directions. Firstly, we provide the formal definition of the OOD generalization problem. Secondly, existing methods are categorized into three parts based on their positions in the whole learning pipeline, namely unsupervised representation learning, supervised model learning and optimization, and typical methods for each category are discussed in detail. We then demonstrate the theoretical connections of different categories, and introduce the commonly used datasets and evaluation metrics. Finally, we summarize the whole literature and raise some future directions for OOD generalization problem. The summary of OOD generalization methods reviewed in this survey can be found at //out-of-distribution-generalization.com.

Federated learning is a distributed machine learning method that aims to preserve the privacy of sample features and labels. In a federated learning system, ID-based sample alignment approaches are usually applied with few efforts made on the protection of ID privacy. In real-life applications, however, the confidentiality of sample IDs, which are the strongest row identifiers, is also drawing much attention from many participants. To relax their privacy concerns about ID privacy, this paper formally proposes the notion of asymmetrical vertical federated learning and illustrates the way to protect sample IDs. The standard private set intersection protocol is adapted to achieve the asymmetrical ID alignment phase in an asymmetrical vertical federated learning system. Correspondingly, a Pohlig-Hellman realization of the adapted protocol is provided. This paper also presents a genuine with dummy approach to achieving asymmetrical federated model training. To illustrate its application, a federated logistic regression algorithm is provided as an example. Experiments are also made for validating the feasibility of this approach.

The demand for artificial intelligence has grown significantly over the last decade and this growth has been fueled by advances in machine learning techniques and the ability to leverage hardware acceleration. However, in order to increase the quality of predictions and render machine learning solutions feasible for more complex applications, a substantial amount of training data is required. Although small machine learning models can be trained with modest amounts of data, the input for training larger models such as neural networks grows exponentially with the number of parameters. Since the demand for processing training data has outpaced the increase in computation power of computing machinery, there is a need for distributing the machine learning workload across multiple machines, and turning the centralized into a distributed system. These distributed systems present new challenges, first and foremost the efficient parallelization of the training process and the creation of a coherent model. This article provides an extensive overview of the current state-of-the-art in the field by outlining the challenges and opportunities of distributed machine learning over conventional (centralized) machine learning, discussing the techniques used for distributed machine learning, and providing an overview of the systems that are available.

Alternating Direction Method of Multipliers (ADMM) is a widely used tool for machine learning in distributed settings, where a machine learning model is trained over distributed data sources through an interactive process of local computation and message passing. Such an iterative process could cause privacy concerns of data owners. The goal of this paper is to provide differential privacy for ADMM-based distributed machine learning. Prior approaches on differentially private ADMM exhibit low utility under high privacy guarantee and often assume the objective functions of the learning problems to be smooth and strongly convex. To address these concerns, we propose a novel differentially private ADMM-based distributed learning algorithm called DP-ADMM, which combines an approximate augmented Lagrangian function with time-varying Gaussian noise addition in the iterative process to achieve higher utility for general objective functions under the same differential privacy guarantee. We also apply the moments accountant method to bound the end-to-end privacy loss. The theoretical analysis shows that DP-ADMM can be applied to a wider class of distributed learning problems, is provably convergent, and offers an explicit utility-privacy tradeoff. To our knowledge, this is the first paper to provide explicit convergence and utility properties for differentially private ADMM-based distributed learning algorithms. The evaluation results demonstrate that our approach can achieve good convergence and model accuracy under high end-to-end differential privacy guarantee.

Machine Learning is a widely-used method for prediction generation. These predictions are more accurate when the model is trained on a larger dataset. On the other hand, the data is usually divided amongst different entities. For privacy reasons, the training can be done locally and then the model can be safely aggregated amongst the participants. However, if there are only two participants in \textit{Collaborative Learning}, the safe aggregation loses its power since the output of the training already contains much information about the participants. To resolve this issue, they must employ privacy-preserving mechanisms, which inevitably affect the accuracy of the model. In this paper, we model the training process as a two-player game where each player aims to achieve a higher accuracy while preserving its privacy. We introduce the notion of \textit{Price of Privacy}, a novel approach to measure the effect of privacy protection on the accuracy of the model. We develop a theoretical model for different player types, and we either find or prove the existence of a Nash Equilibrium with some assumptions. Moreover, we confirm these assumptions via a Recommendation Systems use case: for a specific learning algorithm, we apply three privacy-preserving mechanisms on two real-world datasets. Finally, as a complementary work for the designed game, we interpolate the relationship between privacy and accuracy for this use case and present three other methods to approximate it in a real-world scenario.

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.