Calibration can reduce overconfident predictions of deep neural networks, but can calibration also accelerate training by selecting the right samples? In this paper, we show that it can. We study the effect of popular calibration techniques in selecting better subsets of samples during training (also called sample prioritization) and observe that calibration can improve the quality of subsets, reduce the number of examples per epoch (by at least 70%), and can thereby speed up the overall training process. We further study the effect of using calibrated pre-trained models coupled with calibration during training to guide sample prioritization, which again seems to improve the quality of samples selected.
Sharpness-aware minimization (SAM) and related adversarial deep-learning methods can drastically improve generalization, but their underlying mechanisms are not yet fully understood. Here, we establish SAM as a relaxation of the Bayes objective where the expected negative-loss is replaced by the optimal convex lower bound, obtained by using the so-called Fenchel biconjugate. The connection enables a new Adam-like extension of SAM to automatically obtain reasonable uncertainty estimates, while sometimes also improving its accuracy. By connecting adversarial and Bayesian methods, our work opens a new path to robustness.
Sparse variational Gaussian process (SVGP) methods are a common choice for non-conjugate Gaussian process inference because of their computational benefits. In this paper, we improve their computational efficiency by using a dual parameterization where each data example is assigned dual parameters, similarly to site parameters used in expectation propagation. Our dual parameterization speeds-up inference using natural gradient descent, and provides a tighter evidence lower bound for hyperparameter learning. The approach has the same memory cost as the current SVGP methods, but it is faster and more accurate.
In this paper, we propose new structured second-order methods and structured adaptive-gradient methods obtained by performing natural-gradient descent on structured parameter spaces. Natural-gradient descent is an attractive approach to design new algorithms in many settings such as gradient-free, adaptive-gradient, and second-order methods. Our structured methods not only enjoy a structural invariance but also admit a simple expression. Finally, we test the efficiency of our proposed methods on both deterministic non-convex problems and deep learning problems.
Deep Gaussian Processes (DGPs) are multi-layer, flexible extensions of Gaussian processes but their training remains challenging. Sparse approximations simplify the training but often require optimization over a large number of inducing inputs and their locations across layers. In this paper, we simplify the training by setting the locations to a fixed subset of data and sampling the inducing inputs from a variational distribution. This reduces the trainable parameters and computation cost without significant performance degradations, as demonstrated by our empirical results on regression problems. Our modifications simplify and stabilize DGP training while making it amenable to sampling schemes for setting the inducing inputs.
We show that many machine-learning algorithms are specific instances of a single algorithm called the Bayesian learning rule. The rule, derived from Bayesian principles, yields a wide-range of algorithms from fields such as optimization, deep learning, and graphical models. This includes classical algorithms such as ridge regression, Newton's method, and Kalman filter, as well as modern deep-learning algorithms such as stochastic-gradient descent, RMSprop, and Dropout. The key idea in deriving such algorithms is to approximate the posterior using candidate distributions estimated by using natural gradients. Different candidate distributions result in different algorithms and further approximations to natural gradients give rise to variants of those algorithms. Our work not only unifies, generalizes, and improves existing algorithms, but also helps us design new ones.
Humans and animals have a natural ability to quickly adapt to their surroundings, but machine-learning models, when subjected to changes, often require a complete retraining from scratch. We present Knowledge-adaptation priors (K-priors) to reduce the cost of retraining by enabling quick and accurate adaptation for a wide-variety of tasks and models. This is made possible by a combination of weight and function-space priors to reconstruct the gradients of the past, which recovers and generalizes many existing, but seemingly-unrelated, adaptation strategies. Training with simple first-order gradient methods can often recover the exact retrained model to an arbitrary accuracy by choosing a sufficiently large memory of the past data. Empirical results confirm that the adaptation can be cheap and accurate, and a promising alternative to retraining.
Target networks are at the core of recent success in Reinforcement Learning. They stabilize the training by using old parameters to estimate the $Q$-values, but this also limits the propagation of newly-encountered rewards which could ultimately slow down the training. In this work, we propose an alternative training method based on functional regularization which does not have this deficiency. Unlike target networks, our method uses up-to-date parameters to estimate the target $Q$-values, thereby speeding up training while maintaining stability. Surprisingly, in some cases, we can show that target networks are a special, restricted type of functional regularizers. Using this approach, we show empirical improvements in sample efficiency and performance across a range of Atari and simulated robotics environments.
Marginal-likelihood based model-selection, even though promising, is rarely used in deep learning due to estimation difficulties. Instead, most approaches rely on validation data, which may not be readily available. In this work, we present a scalable marginal-likelihood estimation method to select both the hyperparameters and network architecture based on the training data alone. Some hyperparameters can be estimated online during training, simplifying the procedure. Our marginal-likelihood estimate is based on Laplace's method and Gauss-Newton approximations to the Hessian, and it outperforms cross-validation and manual-tuning on standard regression and image classification datasets, especially in terms of calibration and out-of-distribution detection. Our work shows that marginal likelihoods can improve generalization and be useful when validation data is unavailable (e.g., in nonstationary settings).