Federated Learning (FL) involves training a model over a dataset distributed among clients, with the constraint that each client's dataset is localized and possibly heterogeneous. In FL, small and noisy datasets are common, highlighting the need for well-calibrated models that represent the uncertainty of predictions. The closest FL techniques to achieving such goals are the Bayesian FL methods which collect parameter samples from local posteriors, and aggregate them to approximate the global posterior. To improve scalability for larger models, one common Bayesian approach is to approximate the global predictive posterior by multiplying local predictive posteriors. In this work, we demonstrate that this method gives systematically overconfident predictions, and we remedy this by proposing $\beta$-Predictive Bayes, a Bayesian FL algorithm that interpolates between a mixture and product of the predictive posteriors, using a tunable parameter $\beta$. This parameter is tuned to improve the global ensemble's calibration, before it is distilled to a single model. Our method is evaluated on a variety of regression and classification datasets to demonstrate its superiority in calibration to other baselines, even as data heterogeneity increases. Code available at https://github.com/hasanmohsin/betaPredBayesFL

The Stochastic Approximation (SA) algorithm introduced by Robbins and Monro in 1951 has been a standard method for solving equations of the form $\mathbf{f}({\boldsymbol {\theta}}) = \mathbf{0}$, when only noisy measurements of $\mathbf{f}(\cdot)$ are available. If $\mathbf{f}({\boldsymbol {\theta}}) = \nabla J({\boldsymbol {\theta}})$ for some function $J(\cdot)$, then SA can also be used to find a stationary point of $J(\cdot)$. At each time $t$, the current guess ${\boldsymbol {\theta}}_t$ is updated to ${\boldsymbol {\theta}}_{t+1}$ using a noisy measurement of the form $\mathbf{f}({\boldsymbol {\theta}}_t) + {\boldsymbol {\xi}}_{t+1}$. In much of the literature, it is assumed that the error term ${\boldsymbol {\xi}}_{t+1}$ has zero conditional mean, and/or that its conditional variance is bounded as a function of $t$ (though not necessarily with respect to ${\boldsymbol {\theta}}_t$). Over the years, SA has been applied to a variety of areas, out of which the focus in this paper is on convex and nonconvex optimization. As it turns out, in these applications, the above-mentioned assumptions on the measurement error do not always hold. In zero-order methods, the error neither has zero mean nor bounded conditional variance. In the present paper, we extend SA theory to encompass errors with nonzero conditional mean and/or unbounded conditional variance. In addition, we derive estimates for the rate of convergence of the algorithm, and compute the ``optimal step size sequences'' to maximize the estimated rate of convergence.

Algorithmic reproducibility measures the deviation in outputs of machine learning algorithms upon minor changes in the training process. Previous work suggests that first-order methods would need to trade-off convergence rate (gradient complexity) for better reproducibility. In this work, we challenge this perception and demonstrate that both optimal reproducibility and near-optimal convergence guarantees can be achieved for smooth convex minimization and smooth convex-concave minimax problems under various error-prone oracle settings. Particularly, given the inexact initialization oracle, our regularization-based algorithms achieve the best of both worlds - optimal reproducibility and near-optimal gradient complexity - for minimization and minimax optimization. With the inexact gradient oracle, the near-optimal guarantees also hold for minimax optimization. Additionally, with the stochastic gradient oracle, we show that stochastic gradient descent ascent is optimal in terms of both reproducibility and gradient complexity. We believe our results contribute to an enhanced understanding of the reproducibility-convergence trade-off in the context of convex optimization.

The Laplace approximation provides a closed-form model selection objective for neural networks (NN). Online variants, which optimise NN parameters jointly with hyperparameters, like weight decay strength, have seen renewed interest in the Bayesian deep learning community. However, these methods violate Laplace's method's critical assumption that the approximation is performed around a mode of the loss, calling into question their soundness. This work re-derives online Laplace methods, showing them to target a variational bound on a mode-corrected variant of the Laplace evidence which does not make stationarity assumptions. Online Laplace and its mode-corrected counterpart share stationary points where 1. the NN parameters are a maximum a posteriori, satisfying the Laplace method's assumption, and 2. the hyperparameters maximise the Laplace evidence, motivating online methods. We demonstrate that these optima are roughly attained in practise by online algorithms using full-batch gradient descent on UCI regression datasets. The optimised hyperparameters prevent overfitting and outperform validation-based early stopping.

Feature bagging is a well-established ensembling method which aims to reduce prediction variance by combining predictions of many estimators trained on subsets or projections of features. Here, we develop a theory of feature-bagging in noisy least-squares ridge ensembles and simplify the resulting learning curves in the special case of equicorrelated data. Using analytical learning curves, we demonstrate that subsampling shifts the double-descent peak of a linear predictor. This leads us to introduce heterogeneous feature ensembling, with estimators built on varying numbers of feature dimensions, as a computationally efficient method to mitigate double-descent. Then, we compare the performance of a feature-subsampling ensemble to a single linear predictor, describing a trade-off between noise amplification due to subsampling and noise reduction due to ensembling. Our qualitative insights carry over to linear classifiers applied to image classification tasks with realistic datasets constructed using a state-of-the-art deep learning feature map.

Real-world data often exhibits bias, imbalance, and privacy risks. Synthetic datasets have emerged to address these issues. This paradigm relies on generative AI models to generate unbiased, privacy-preserving data while maintaining fidelity to the original data. However, assessing the trustworthiness of synthetic datasets and models is a critical challenge. We introduce a holistic auditing framework that comprehensively evaluates synthetic datasets and AI models. It focuses on preventing bias and discrimination, ensures fidelity to the source data, assesses utility, robustness, and privacy preservation. We demonstrate the framework's effectiveness by auditing various generative models across diverse use cases like education, healthcare, banking, and human resources, spanning different data modalities such as tabular, time-series, vision, and natural language. This holistic assessment is essential for compliance with regulatory safeguards. We introduce a trustworthiness index to rank synthetic datasets based on their safeguards trade-offs. Furthermore, we present a trustworthiness-driven model selection and cross-validation process during training, exemplified with "TrustFormers" across various data types. This approach allows for controllable trustworthiness trade-offs in synthetic data creation. Our auditing framework fosters collaboration among stakeholders, including data scientists, governance experts, internal reviewers, external certifiers, and regulators. This transparent reporting should become a standard practice to prevent bias, discrimination, and privacy violations, ensuring compliance with policies and providing accountability, safety, and performance guarantees.

Observational cohort studies are increasingly being used for comparative effectiveness research to assess the safety of therapeutics. Recently, various doubly robust methods have been proposed for average treatment effect estimation by combining the treatment model and the outcome model via different vehicles, such as matching, weighting, and regression. The key advantage of doubly robust estimators is that they require either the treatment model or the outcome model to be correctly specified to obtain a consistent estimator of average treatment effects, and therefore lead to a more accurate and often more precise inference. However, little work has been done to understand how doubly robust estimators differ due to their unique strategies of using the treatment and outcome models and how machine learning techniques can be combined to boost their performance. Here we examine multiple popular doubly robust methods and compare their performance using different treatment and outcome modeling via extensive simulations and a real-world application. We found that incorporating machine learning with doubly robust estimators such as the targeted maximum likelihood estimator gives the best overall performance. Practical guidance on how to apply doubly robust estimators is provided.

Numerical interactions leading to users sharing textual content published by others are naturally represented by a network where the individuals are associated with the nodes and the exchanged texts with the edges. To understand those heterogeneous and complex data structures, clustering nodes into homogeneous groups as well as rendering a comprehensible visualisation of the data is mandatory. To address both issues, we introduce Deep-LPTM, a model-based clustering strategy relying on a variational graph auto-encoder approach as well as a probabilistic model to characterise the topics of discussion. Deep-LPTM allows to build a joint representation of the nodes and of the edges in two embeddings spaces. The parameters are inferred using a variational inference algorithm. We also introduce IC2L, a model selection criterion specifically designed to choose models with relevant clustering and visualisation properties. An extensive benchmark study on synthetic data is provided. In particular, we find that Deep-LPTM better recovers the partitions of the nodes than the state-of-the art ETSBM and STBM. Eventually, the emails of the Enron company are analysed and visualisations of the results are presented, with meaningful highlights of the graph structure.

Although gradient descent with momentum is widely used in modern deep learning, a concrete understanding of its effects on the training trajectory still remains elusive. In this work, we empirically show that momentum gradient descent with a large learning rate and learning rate warmup displays large catapults, driving the iterates towards flatter minima than those found by gradient descent. We then provide empirical evidence and theoretical intuition that the large catapult is caused by momentum "amplifying" the self-stabilization effect (Damian et al., 2023).B.1

This paper examines the use of tensor networks, which can efficiently represent high-dimensional quantum states, in language modeling. It is a distillation and continuation of the work done in (van der Poel, 2023). To do so, we will abstract the problem down to modeling Motzkin spin chains, which exhibit long-range correlations reminiscent of those found in language. The Matrix Product State (MPS), also known as the tensor train, has a bond dimension which scales as the length of the sequence it models. To combat this, we use the factored core MPS, whose bond dimension scales sub-linearly. We find that the tensor models reach near perfect classifying ability, and maintain a stable level of performance as the number of valid training examples is decreased.