Estimating the predictive uncertainty of a Bayesian learning model is critical in various decision-making problems, e.g., reinforcement learning, detecting the adversarial attack, self-driving car. As the model posterior is almost always intractable, most efforts were made on finding an accurate approximation to the true posterior. Even though a decent estimation of the model posterior is obtained, another approximation is required to compute the predictive distribution over the desired output. A common accurate solution is to use Monte Carlo (MC) integration. However, it needs to maintain a large number of samples, and evaluate the model repeatedly, and average multiple model outputs. In many real-world cases, this is computationally prohibitive. In this work, assuming that the exact posterior or a decent approximation is obtained, we propose a generic framework to approximate the output probability distribution induced by the model posterior with a parameterized model and in an amortized fashion. The aim is to approximate the predictive uncertainty of a specific Bayesian model, meanwhile alleviating the heavy workload of MC integration at testing time. The proposed method is universally applicable to Bayesian classification models that allow for posterior sampling. Theoretically, we show that the idea of amortization incurs no additional costs on approximation performance. Empirical results validate the strong practical performance of our approach.

Neural network compression and quantization are important tasks for fitting state-of-the-art models into the computational, memory and power constraints of mobile devices and embedded hardware. Recent approaches to model compression/quantization are based on reinforcement learning or search methods to quantize the neural network for a specific hardware platform. However, these methods require multiple runs to compress/quantize the same base neural network to different hardware setups. In this work, we propose a fully nested neural network (FN3) that runs only once to build a nested set of compressed/quantized models, which is optimal for different resource constraints. Specifically, we exploit the additive characteristic in different levels of building blocks in neural network and propose an ordered dropout (ODO) operation that ranks the building blocks. Given a trained FN3, a fast heuristic search algorithm is run offline to find the optimal removal of components to maximize the accuracy under different constraints. Compared with the related works on adaptive neural network designed only for channels or bits, the proposed approach is applicable to different levels of building blocks (bits, neurons, channels, residual paths and layers). Empirical results validate strong practical performance of proposed approach.