In this paper, we propose an analytical method for performing tractable approximate Gaussian inference (TAGI) in Bayesian neural networks. The method enables the analytical Gaussian inference of the posterior mean vector and diagonal covariance matrix for weights and biases. The method proposed has a computational complexity of $\mathcal{O}(n)$ with respect to the number of parameters $n$, and the tests performed on regression and classification benchmarks confirm that, for a same network architecture, it matches the performance of existing methods relying on gradient backpropagation.
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Gaussian Graphical Models (GGMs) are widely used for exploratory data analysis in various fields such as genomics, ecology, psychometry. In a high-dimensional setting, when the number of variables exceeds the number of observations by several orders of magnitude, the estimation of GGM is a difficult and unstable optimization problem. Clustering of variables or variable selection is often performed prior to GGM estimation. We propose a new method allowing to simultaneously infer a hierarchical clustering structure and the graphs describing the structure of independence at each level of the hierarchy. This method is based on solving a convex optimization problem combining a graphical lasso penalty with a fused type lasso penalty. Results on real and synthetic data are presented.
Panel Vector Autoregressions (PVARs) are a popular tool for analyzing multi-country datasets. However, the number of estimated parameters can be enormous, leading to computational and statistical issues. In this paper, we develop fast Bayesian methods for estimating PVARs using integrated rotated Gaussian approximations. We exploit the fact that domestic information is often more important than international information and group the coefficients accordingly. Fast approximations are used to estimate the latter while the former are estimated with precision using Markov chain Monte Carlo techniques. We illustrate, using a huge model of the world economy, that it produces competitive forecasts quickly.
We present a novel hybrid strategy based on machine learning to improve curvature estimation in the level-set method. The proposed inference system couples enhanced neural networks with standard numerical schemes to compute curvature more accurately. The core of our hybrid framework is a switching mechanism that relies on well established numerical techniques to gauge curvature. If the curvature magnitude is larger than a resolution-dependent threshold, it uses a neural network to yield a better approximation. Our networks are multilayer perceptrons fitted to synthetic data sets composed of sinusoidal- and circular-interface samples at various configurations. To reduce data set size and training complexity, we leverage the problem's characteristic symmetry and build our models on just half of the curvature spectrum. These savings lead to a powerful inference system able to outperform any of its numerical or neural component alone. Experiments with stationary, smooth interfaces show that our hybrid solver is notably superior to conventional numerical methods in coarse grids and along steep interface regions. Compared to prior research, we have observed outstanding gains in precision after training the regression model with data pairs from more than a single interface type and transforming data with specialized input preprocessing. In particular, our findings confirm that machine learning is a promising venue for reducing or removing mass loss in the level-set method.
Unsupervised multi-object representation learning depends on inductive biases to guide the discovery of object-centric representations that generalize. However, we observe that methods for learning these representations are either impractical due to long training times and large memory consumption or forego key inductive biases. In this work, we introduce EfficientMORL, an efficient framework for the unsupervised learning of object-centric representations. We show that optimization challenges caused by requiring both symmetry and disentanglement can in fact be addressed by high-cost iterative amortized inference by designing the framework to minimize its dependence on it. We take a two-stage approach to inference: first, a hierarchical variational autoencoder extracts symmetric and disentangled representations through bottom-up inference, and second, a lightweight network refines the representations with top-down feedback. The number of refinement steps taken during training is reduced following a curriculum, so that at test time with zero steps the model achieves 99.1% of the refined decomposition performance. We demonstrate strong object decomposition and disentanglement on the standard multi-object benchmark while achieving nearly an order of magnitude faster training and test time inference over the previous state-of-the-art model.
Adder Neural Networks (ANNs) which only contain additions bring us a new way of developing deep neural networks with low energy consumption. Unfortunately, there is an accuracy drop when replacing all convolution filters by adder filters. The main reason here is the optimization difficulty of ANNs using $\ell_1$-norm, in which the estimation of gradient in back propagation is inaccurate. In this paper, we present a novel method for further improving the performance of ANNs without increasing the trainable parameters via a progressive kernel based knowledge distillation (PKKD) method. A convolutional neural network (CNN) with the same architecture is simultaneously initialized and trained as a teacher network, features and weights of ANN and CNN will be transformed to a new space to eliminate the accuracy drop. The similarity is conducted in a higher-dimensional space to disentangle the difference of their distributions using a kernel based method. Finally, the desired ANN is learned based on the information from both the ground-truth and teacher, progressively. The effectiveness of the proposed method for learning ANN with higher performance is then well-verified on several benchmarks. For instance, the ANN-50 trained using the proposed PKKD method obtains a 76.8\% top-1 accuracy on ImageNet dataset, which is 0.6\% higher than that of the ResNet-50.
Interpretation of Deep Neural Networks (DNNs) training as an optimal control problem with nonlinear dynamical systems has received considerable attention recently, yet the algorithmic development remains relatively limited. In this work, we make an attempt along this line by reformulating the training procedure from the trajectory optimization perspective. We first show that most widely-used algorithms for training DNNs can be linked to the Differential Dynamic Programming (DDP), a celebrated second-order trajectory optimization algorithm rooted in the Approximate Dynamic Programming. In this vein, we propose a new variant of DDP that can accept batch optimization for training feedforward networks, while integrating naturally with the recent progress in curvature approximation. The resulting algorithm features layer-wise feedback policies which improve convergence rate and reduce sensitivity to hyper-parameter over existing methods. We show that the algorithm is competitive against state-ofthe-art first and second order methods. Our work opens up new avenues for principled algorithmic design built upon the optimal control theory.
Recently, adaptive inference is gaining increasing attention due to its high computational efficiency. Different from existing works, which mainly exploit architecture redundancy for adaptive network design, in this paper, we focus on spatial redundancy of input samples, and propose a novel Resolution Adaptive Network (RANet). Our motivation is that low-resolution representations can be sufficient for classifying "easy" samples containing canonical objects, while high-resolution features are curial for recognizing some "hard" ones. In RANet, input images are first routed to a lightweight sub-network that efficiently extracts coarse feature maps, and samples with high confident predictions will exit early from the sub-network. The high-resolution paths are only activated for those "hard" samples whose previous predictions are unreliable. By adaptively processing the features in varying resolutions, the proposed RANet can significantly improve its computational efficiency. Experiments on three classification benchmark tasks (CIFAR-10, CIFAR-100 and ImageNet) demonstrate the effectiveness of the proposed model in both anytime prediction setting and budgeted batch classification setting.
We propose a Bayesian convolutional neural network built upon Bayes by Backprop and elaborate how this known method can serve as the fundamental construct of our novel, reliable variational inference method for convolutional neural networks. First, we show how Bayes by Backprop can be applied to convolutional layers where weights in filters have probability distributions instead of point-estimates; and second, how our proposed framework leads with various network architectures to performances comparable to convolutional neural networks with point-estimates weights. In the past, Bayes by Backprop has been successfully utilised in feedforward and recurrent neural networks, but not in convolutional ones. This work symbolises the extension of the group of Bayesian neural networks which encompasses all three aforementioned types of network architectures now.
Owing to the recent advances in "Big Data" modeling and prediction tasks, variational Bayesian estimation has gained popularity due to their ability to provide exact solutions to approximate posteriors. One key technique for approximate inference is stochastic variational inference (SVI). SVI poses variational inference as a stochastic optimization problem and solves it iteratively using noisy gradient estimates. It aims to handle massive data for predictive and classification tasks by applying complex Bayesian models that have observed as well as latent variables. This paper aims to decentralize it allowing parallel computation, secure learning and robustness benefits. We use Alternating Direction Method of Multipliers in a top-down setting to develop a distributed SVI algorithm such that independent learners running inference algorithms only require sharing the estimated model parameters instead of their private datasets. Our work extends the distributed SVI-ADMM algorithm that we first propose, to an ADMM-based networked SVI algorithm in which not only are the learners working distributively but they share information according to rules of a graph by which they form a network. This kind of work lies under the umbrella of `deep learning over networks' and we verify our algorithm for a topic-modeling problem for corpus of Wikipedia articles. We illustrate the results on latent Dirichlet allocation (LDA) topic model in large document classification, compare performance with the centralized algorithm, and use numerical experiments to corroborate the analytical results.
Amortized inference has led to efficient approximate inference for large datasets. The quality of posterior inference is largely determined by two factors: a) the ability of the variational distribution to model the true posterior and b) the capacity of the recognition network to generalize inference over all datapoints. We analyze approximate inference in variational autoencoders in terms of these factors. We find that suboptimal inference is often due to amortizing inference rather than the limited complexity of the approximating distribution. We show that this is due partly to the generator learning to accommodate the choice of approximation. Furthermore, we show that the parameters used to increase the expressiveness of the approximation play a role in generalizing inference rather than simply improving the complexity of the approximation.
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