Domain Generalization (DG) research has gained considerable traction as of late, since the ability to generalize to unseen data distributions is a requirement that eludes even state-of-the-art training algorithms. In this paper we observe that the initial iterations of model training play a key role in domain generalization effectiveness, since the loss landscape may be significantly different across the training and test distributions, contrary to the case of i.i.d. data. Conflicts between gradients of the loss components of each domain lead the optimization procedure to undesirable local minima that do not capture the domain-invariant features of the target classes. We propose alleviating domain conflicts in model optimization, by iteratively annealing the parameters of a model in the early stages of training and searching for points where gradients align between domains. By discovering a set of parameter values where gradients are updated towards the same direction for each data distribution present in the training set, the proposed Gradient-Guided Annealing (GGA) algorithm encourages models to seek out minima that exhibit improved robustness against domain shifts. The efficacy of GGA is evaluated on five widely accepted and challenging image classification domain generalization benchmarks, where its use alone is able to establish highly competitive or even state-of-the-art performance. Moreover, when combined with previously proposed domain-generalization algorithms it is able to consistently improve their effectiveness by significant margins.

In distributed learning, sign-based compression algorithms such as signSGD with majority vote provide a lightweight alternative to SGD with an additional advantage: fault tolerance (almost) for free. However, for signSGD with majority vote, this fault tolerance has been shown to cover only the case of weaker adversaries, i.e., ones that are not omniscient or cannot collude to base their attack on common knowledge and strategy. In this work, we close this gap and provide new insights into how signSGD with majority vote can be resilient against omniscient and colluding adversaries, which craft an attack after communicating with other adversaries, thus having better information to perform the most damaging attack based on a common optimal strategy. Our core contribution is in providing a proof that begins by defining the omniscience framework and the strongest possible damage against signSGD with majority vote without imposing any restrictions on the attacker. Thanks to the filtering effect of the sign-based method, we upper-bound the space of attacks to the optimal strategy for maximizing damage by an attacker. Hence, we derive an explicit probabilistic bound in terms of incorrect aggregation without resorting to unknown constants, providing a convergence bound on signSGD with majority vote in the presence of Byzantine attackers, along with a precise convergence rate. Our findings are supported by experiments on the MNIST dataset in a distributed learning environment with adversaries of varying strength.

In this paper, we propose a method for density-based clustering in high-dimensional spaces that combines Locality-Sensitive Hashing (LSH) with the Quick Shift algorithm. The Quick Shift algorithm, known for its hierarchical clustering capabilities, is extended by integrating approximate Kernel Density Estimation (KDE) using LSH to provide efficient density estimates. The proposed approach achieves almost linear time complexity while preserving the consistency of density-based clustering.

Network reconstruction is the task of inferring the unseen interactions between elements of a system, based only on their behavior or dynamics. This inverse problem is in general ill-posed, and admits many solutions for the same observation. Nevertheless, the vast majority of statistical methods proposed for this task -- formulated as the inference of a graphical generative model -- can only produce a ``point estimate,'' i.e. a single network considered the most likely. In general, this can give only a limited characterization of the reconstruction, since uncertainties and competing answers cannot be conveyed, even if their probabilities are comparable, while being structurally different. In this work we present an efficient MCMC algorithm for sampling from posterior distributions of reconstructed networks, which is able to reveal the full population of answers for a given reconstruction problem, weighted according to their plausibilities. Our algorithm is general, since it does not rely on specific properties of particular generative models, and is specially suited for the inference of large and sparse networks, since in this case an iteration can be performed in time $O(N\log^2 N)$ for a network of $N$ nodes, instead of $O(N^2)$, as would be the case for a more naive approach. We demonstrate the suitability of our method in providing uncertainties and consensus of solutions (which provably increases the reconstruction accuracy) in a variety of synthetic and empirical cases.

Human physiological signals tend to exhibit both global and local structures: the former are shared across a population, while the latter reflect inter-individual variability. For instance, kinetic measurements of the gait cycle during locomotion present common characteristics, although idiosyncrasies may be observed due to biomechanical disposition or pathology. To better represent datasets with local-global structure, this work extends Convolutional Dictionary Learning (CDL), a popular method for learning interpretable representations, or dictionaries, of time-series data. In particular, we propose Personalized CDL (PerCDL), in which a local dictionary models local information as a personalized spatiotemporal transformation of a global dictionary. The transformation is learnable and can combine operations such as time warping and rotation. Formal computational and statistical guarantees for PerCDL are provided and its effectiveness on synthetic and real human locomotion data is demonstrated.

This paper proposes a novel analysis for the Scaffold algorithm, a popular method for dealing with data heterogeneity in federated learning. While its convergence in deterministic settings--where local control variates mitigate client drift--is well established, the impact of stochastic gradient updates on its performance is less understood. To address this problem, we first show that its global parameters and control variates define a Markov chain that converges to a stationary distribution in the Wasserstein distance. Leveraging this result, we prove that Scaffold achieves linear speed-up in the number of clients up to higher-order terms in the step size. Nevertheless, our analysis reveals that Scaffold retains a higher-order bias, similar to FedAvg, that does not decrease as the number of clients increases. This highlights opportunities for developing improved stochastic federated learning algorithms

Massive datasets, characterized by both large sample sizes and high-dimensional features, are increasingly prevalent across diverse fields. For example, the 1000 Genomes Project Consortium et al. (2015) study amassed genomic data from 2,504 individuals spanning 26 populations, yielding approximately 12 terabytes data. Often, such datasets are distributed across multiple locations. Fusing data together for centralized statistical analysis is somehow infeasible due to concerns over data privacy, memory and storage limitations, and bandwidth constraints. The absence of fusion centers has thus fueled interest in decentralized distributed learning--a paradigm that fully exploits distributed datasets by performing computations locally. This methodology has found successful applications in fields such as personalized medicine, edge computing, smart utilities, and dimension reduction (Li et al., 2011). A fundamental task in these applications is classification. Penalized support vector machines (SVMs) have been enduringly powerful tools for high-dimensional classification tasks, building on the seminal contributions of Boser et al. (1992) and Vapnik (2000). The standard objective function for penalized SVMs combines the hinge loss with a penalty term.

Multilinear Principal Component Analysis (MPCA) is an important tool for analyzing tensor data. It performs dimension reduction similar to PCA for multivariate data. However, standard MPCA is sensitive to outliers. It is highly influenced by observations deviating from the bulk of the data, called casewise outliers, as well as by individual outlying cells in the tensors, so-called cellwise outliers. This latter type of outlier is highly likely to occur in tensor data, as tensors typically consist of many cells. This paper introduces a novel robust MPCA method that can handle both types of outliers simultaneously, and can cope with missing values as well. This method uses a single loss function to reduce the influence of both casewise and cellwise outliers. The solution that minimizes this loss function is computed using an iteratively reweighted least squares algorithm with a robust initialization. Graphical diagnostic tools are also proposed to identify the different types of outliers that have been found by the new robust MPCA method. The performance of the method and associated graphical displays is assessed through simulations and illustrated on two real datasets.

Fairness of machine learning algorithms is receiving increasing attention, as such algorithms permeate the day-to-day aspects of our lives. One way in which bias can manifest in a dataset is through missing values. If data are missing, these data are often assumed to be missing completely randomly; in reality the propensity of data being missing is often tied to the demographic characteristics of individuals. There is limited research into how missing values and the handling thereof can impact the fairness of an algorithm. Most researchers either apply listwise deletion or tend to use the simpler methods of imputation (e.g. mean or mode) compared to the more advanced ones (e.g. multiple imputation); we therefore study the impact of the simpler methods on the fairness of algorithms. The starting point of the study is the mechanism of missingness, leading into how the missing data are processed and finally how this impacts fairness. Three popular datasets in the field of fairness are amputed in a simulation study. The results show that under certain scenarios the impact on fairness can be pronounced when the missingness mechanism is missing at random. Furthermore, elementary missing data handling techniques like listwise deletion and mode imputation can lead to higher fairness compared to more complex imputation methods like k-nearest neighbour imputation, albeit often at the cost of lower accuracy.

Training an energy-based model (EBM) with maximum likelihood is challenging due to the intractable normalisation constant. Traditional methods rely on expensive Markov chain Monte Carlo (MCMC) sampling to estimate the gradient of logartihm of the normalisation constant. We propose a novel objective called self-normalised log-likelihood (SNL) that introduces a single additional learnable parameter representing the normalisation constant compared to the regular log-likelihood. SNL is a lower bound of the log-likelihood, and its optimum corresponds to both the maximum likelihood estimate of the model parameters and the normalisation constant. We show that the SNL objective is concave in the model parameters for exponential family distributions. Unlike the regular log-likelihood, the SNL can be directly optimised using stochastic gradient techniques by sampling from a crude proposal distribution. We validate the effectiveness of our proposed method on various density estimation tasks as well as EBMs for regression. Our results show that the proposed method, while simpler to implement and tune, outperforms existing techniques.