Federated Learning (FL) is a distributed learning scheme to train a shared model across clients. One common and fundamental challenge in FL is that the sets of dnta across clients could be non-identically distributed and have different sizes. Personalized Federated Learning (P FL) attempts to solve this challenge via locally adapted models. In this work, we present a novel framework for PFL based on hierarchical Bayesian modeling and variational inference. A global model is introduced as a latent variable to augment the joint distribution of clients' parameters and capture the common trends of different clients, optimization is derived based on the principle of maximizing the marginal likelihood and conducted using variational expectation maximization. Our algorithm gives rise to a closed-form estimation of a confidence value which comprises the uncertainty of clients' parameters and local model deviations from the global model. The confidence value is used to weigh clients' parameters in the aggregation stage and adjust the regularization effect of the global model. We evaluate our method through extensive empirical studies on multiple datasets. Experimental results show that our approach obtains competitive results under mild heterogeneous circumstances while significantly outperforming state-of-the-art PFL frameworks in highly heterogeneous settings.

In many applications, it is desirable that a classifier not only makes accurate predictions, but also outputs calibrated posterior probabilities. However, many existing classifiers, especially deep neural network classifiers, tend to be uncalibrated. Post-hoc calibration is a technique to recalibrate a model by learning a calibration map. Existing approaches mostly focus on constructing calibration maps with low calibration errors, however, this quality is inadequate for a calibrator being useful. In this paper, we introduce two constraints that are worth consideration in designing a calibration map for post-hoc calibration. Then we present Meta-Cal, which is built from a base calibrator and a ranking model. Under some mild assumptions, two high-probability bounds are given with respect to these constraints. Empirical results on CIFAR-10, CIFAR-100 and ImageNet and a range of popular network architectures show our proposed method significantly outperforms the current state of the art for post-hoc multi-class classification calibration.

Bayesian optimization (BO) is a sample-efficient global optimization algorithm for black-box functions which are expensive to evaluate. Existing literature on model based optimization in conditional parameter spaces are usually built on trees. In this work, we generalize the additive assumption to tree-structured functions and propose an additive tree-structured covariance function, showing improved sample-efficiency, wider applicability and greater flexibility. Furthermore, by incorporating the structure information of parameter spaces and the additive assumption in the BO loop, we develop a parallel algorithm to optimize the acquisition function and this optimization can be performed in a low dimensional space. We demonstrate our method on an optimization benchmark function, on a neural network compression problem and on pruning pre-trained VGG16 and ResNet50 models. Experimental results show our approach significantly outperforms the current state of the art for conditional parameter optimization including SMAC, TPE and Jenatton et al. (2017).

Bayesian optimization (BO) is a sample-efficient global optimization algorithm for black-box functions which are expensive to evaluate. Existing literature on model based optimization in conditional parameter spaces are usually built on trees. In this work, we generalize the additive assumption to tree-structured functions and propose an additive tree-structured covariance function, showing improved sample-efficiency, wider applicability and greater flexibility. Furthermore, by incorporating the structure information of parameter spaces and the additive assumption in the BO loop, we develop a parallel algorithm to optimize the acquisition function and this optimization can be performed in a low dimensional space. We demonstrate our method on an optimization benchmark function, as well as on a neural network model compression problem, and experimental results show our approach significantly outperforms the current state of the art for conditional parameter optimization including SMAC, TPE and Jenatton et al. (2017).

Neural network compression is an important step for deploying neural networks where speed is of high importance, or on devices with limited memory. It is necessary to tune compression parameters in order to achieve the desired trade-off between size and performance. This is often done by optimizing the loss on a validation set of data, which should be large enough to approximate the true risk and therefore yield sufficient generalization ability. However, using a full validation set can be computationally expensive. In this work, we develop a general Bayesian optimization framework for optimizing functions that are computed based on U-statistics. We propagate Gaussian uncertainties from the statistics through the Bayesian optimization framework yielding a method that gives a probabilistic approximation certificate of the result. We then apply this to parameter selection in neural network compression. Compression objectives that can be written as U-statistics are typically based on empirical risk and knowledge distillation for deep discriminative models. We demonstrate our method on VGG and ResNet models, and the resulting system can find optimal compression parameters for relatively high-dimensional parametrizations in a matter of minutes on a standard desktop machine, orders of magnitude faster than competing methods.