Personalised federated learning (FL) aims at collaboratively learning a machine learning model taylored for each client. Albeit promising advances have been made in this direction, most of existing approaches works do not allow for uncertainty quantification which is crucial in many applications. In addition, personalisation in the cross-device setting still involves important issues, especially for new clients or those having small number of observations. This paper aims at filling these gaps. To this end, we propose a novel methodology coined FedPop by recasting personalised FL into the population modeling paradigm where clients' models involve fixed common population parameters and random effects, aiming at explaining data heterogeneity. To derive convergence guarantees for our scheme, we introduce a new class of federated stochastic optimisation algorithms which relies on Markov chain Monte Carlo methods. Compared to existing personalised FL methods, the proposed methodology has important benefits: it is robust to client drift, practical for inference on new clients, and above all, enables uncertainty quantification under mild computational and memory overheads. We provide non-asymptotic convergence guarantees for the proposed algorithms and illustrate their performances on various personalised federated learning tasks.

Learning a predictive model of the mean return, or value function, plays a critical role in many reinforcement learning algorithms. Distributional reinforcement learning (DRL) methods instead model the value distribution, which has been shown to improve performance in many settings. In this paper, we model the value distribution as approximately normal using the Markov Chain central limit theorem. We analytically compute quantile bars to provide a new DRL target that is informed by the decrease in standard deviation that occurs over the course of an episode. In addition, we propose a policy update strategy based on uncertainty as measured by structural characteristics of the value distribution not present in the standard value function. The approach we outline is compatible with many DRL structures. We use two representative on-policy algorithms, PPO and TRPO, as testbeds and show that our methods produce performance improvements in continuous control tasks.

With the attention mechanism, transformers achieve significant empirical successes. Despite the intuitive understanding that transformers perform relational inference over long sequences to produce desirable representations, we lack a rigorous theory on how the attention mechanism achieves it. In particular, several intriguing questions remain open: (a) What makes a desirable representation? (b) How does the attention mechanism infer the desirable representation within the forward pass? (c) How does a pretraining procedure learn to infer the desirable representation through the backward pass? We observe that, as is the case in BERT and ViT, input tokens are often exchangeable since they already include positional encodings. The notion of exchangeability induces a latent variable model that is invariant to input sizes, which enables our theoretical analysis. - To answer (a) on representation, we establish the existence of a sufficient and minimal representation of input tokens. In particular, such a representation instantiates the posterior distribution of the latent variable given input tokens, which plays a central role in predicting output labels and solving downstream tasks. - To answer (b) on inference, we prove that attention with the desired parameter infers the latent posterior up to an approximation error, which is decreasing in input sizes. In detail, we quantify how attention approximates the conditional mean of the value given the key, which characterizes how it performs relational inference over long sequences. - To answer (c) on learning, we prove that both supervised and self-supervised objectives allow empirical risk minimization to learn the desired parameter up to a generalization error, which is independent of input sizes. Particularly, in the self-supervised setting, we identify a condition number that is pivotal to solving downstream tasks.

The intersection of social media, low-cost trading platforms, and naive investors has created an ideal situation for information-based market manipulations, especially pump&dumps. Manipulators accumulate small-cap stocks, disseminate false information on social media to inflate their price, and sell at the peak. We collect a dataset of stocks whose price and volume profiles have the characteristic shape of a pump&dump, and social media posts for those same stocks that match the timing of the initial price rises. From these we build predictive models for pump&dump events based on the language used in the social media posts. There are multiple difficulties: not every post will cause the intended market reaction, some pump&dump events may be triggered by posts in other forums, and there may be accidental confluences of post timing and market movements. Nevertheless, our best model achieves a prediction accuracy of 85% and an F1-score of 62%. Such a tool can provide early warning to investors and regulators that a pump&dump may be underway.

Proactive edge association is capable of improving wireless connectivity at the cost of increased handover (HO) frequency and energy consumption, while relying on a large amount of private information sharing required for decision making. In order to improve the connectivity-cost trade-off without privacy leakage, we investigate the privacy-preserving joint edge association and power allocation (JEAPA) problem in the face of the environmental uncertainty and the infeasibility of individual learning. Upon modelling the problem by a decentralized partially observable Markov Decision Process (Dec-POMDP), it is solved by federated multi-agent reinforcement learning (FMARL) through only sharing encrypted training data for federatively learning the policy sought. Our simulation results show that the proposed solution strikes a compelling trade-off, while preserving a higher privacy level than the state-of-the-art solutions.

The advancement of distributed generation technologies in modern power systems has led to a widespread integration of renewable power generation at customer side. However, the intermittent nature of renewable energy poses new challenges to the network operational planning with underlying uncertainties. This paper proposes a novel Bayesian probabilistic technique for forecasting renewable solar generation by addressing data and model uncertainties by integrating bidirectional long short-term memory (BiLSTM) neural networks while compressing the weight parameters using variational autoencoder (VAE). Existing Bayesian deep learning methods suffer from high computational complexities as they require to draw a large number of samples from weight parameters expressed in the form of probability distributions. The proposed method can deal with uncertainty present in model and data in a more computationally efficient manner by reducing the dimensionality of model parameters. The proposed method is evaluated using quantile loss, reconstruction error, and deterministic forecasting evaluation metrics such as root-mean square error. It is inferred from the numerical results that VAE-Bayesian BiLSTM outperforms other probabilistic and deterministic deep learning methods for solar power forecasting in terms of accuracy and computational efficiency for different sizes of the dataset.

The Expectation Maximization (EM) algorithm is widely used as an iterative modification to maximum likelihood estimation when the data is incomplete. We focus on a semi-supervised case to learn the model from labeled and unlabeled samples. Existing work in the semi-supervised case has focused mainly on performance rather than convergence guarantee, however we focus on the contribution of the labeled samples to the convergence rate. The analysis clearly demonstrates how the labeled samples improve the convergence rate for the exponential family mixture model. In this case, we assume that the population EM (EM with unlimited data) is initialized within the neighborhood of global convergence for the population EM that consists solely of samples that have not been labeled. The analysis for the labeled samples provides a comprehensive description of the convergence rate for the Gaussian mixture model. In addition, we extend the findings for labeled samples and offer an alternative proof for the population EM's convergence rate with unlabeled samples for the symmetric mixture of two Gaussians.

Uncertainty estimation of the trained deep learning networks is valuable for optimizing learning efficiency and evaluating the reliability of network predictions. In this paper, we propose a method for estimating uncertainty in deep learning image classification using test-time mixup augmentation (TTMA). To improve the ability to distinguish correct and incorrect predictions in existing aleatoric uncertainty, we introduce the TTMA data uncertainty (TTMA-DU) by applying mixup augmentation to test data and measuring the entropy of the predicted label histogram. In addition to TTMA-DU, we propose the TTMA class-dependent uncertainty (TTMA-CDU), which captures aleatoric uncertainty specific to individual classes and provides insight into class confusion and class similarity within the trained network. We validate our proposed methods on the ISIC-18 skin lesion diagnosis dataset and the CIFAR-100 real-world image classification dataset. Our experiments show that (1) TTMA-DU more effectively differentiates correct and incorrect predictions compared to existing uncertainty measures due to mixup perturbation, and (2) TTMA-CDU provides information on class confusion and class similarity for both datasets.

Uncertainty in perception, actuation, and the environment often require multiple attempts for a robotic task to be successful. We study a class of problems providing (1) low-entropy indicators of terminal success / failure, and (2) unreliable (high-entropy) data to predict the final outcome of an ongoing task. Examples include a robot trying to connect with a charging station, parallel parking, or assembling a tightly-fitting part. The ability to restart after predicting failure early, versus simply running to failure, can significantly decrease the makespan, that is, the total time to completion, with the drawback of potentially short-cutting an otherwise successful operation. Assuming task running times to be Poisson distributed, and using a Markov Jump process to capture the dynamics of the underlying Markov Decision Process, we derive a closed form solution that predicts makespan based on the confusion matrix of the failure predictor. This allows the robot to learn failure prediction in a production environment, and only adopt a preemptive policy when it actually saves time. We demonstrate this approach using a robotic peg-in-hole assembly problem using a real robotic system. Failures are predicted by a dilated convolutional network based on force-torque data, showing an average makespan reduction from 101s to 81s (N=120, p<0.05). We posit that the proposed algorithm generalizes to any robotic behavior with an unambiguous terminal reward, with wide ranging applications on how robots can learn and improve their behaviors in the wild.

In text mining, topic models are a type of probabilistic generative models for inferring latent semantic topics from text corpus. One of the most popular inference approaches to topic models is perhaps collapsed Gibbs sampling (CGS), which typically samples one single topic label for each observed document-word pair. In this paper, we aim at improving the inference of CGS for topic models. We propose to leverage state augmentation technique by maximizing the number of topic samples to infinity, and then develop a new inference approach, called infinite latent state replication (ILR), to generate robust soft topic assignment for each given document-word pair. Experimental results on the publicly available datasets show that ILR outperforms CGS for inference of existing established topic models.