The reliability of a machine learning model's confidence in its predictions is critical for highrisk applications. Calibration-the idea that a model's predicted probabilities of outcomes reflect true probabilities of those outcomes-formalizes this notion. While analyzing the calibration of deep neural networks, we've identified core problems with the way calibration is currently measured. We design the Thresholded Adaptive Calibration Error (TACE) metric to resolve these pathologies and show that it outperforms other metrics, especially in settings where predictions beyond the maximum prediction that is chosen as the output class matter. There are many cases where what a practitioner cares about is the calibration of a specific prediction, and so we introduce a dynamic programming based Prediction Specific Calibration Error (PSCE) that smoothly considers the calibration of nearby predictions to give an estimate of the calibration error of a specific prediction.
Learning-to-learn or meta-learning leverages data-driven inductive bias to increase the efficiency of learning on a novel task. This approach encounters difficulty when transfer is not mutually beneficial, for instance, when tasks are sufficiently dissimilar or change over time. Here, we use the connection between gradient-based meta-learning and hierarchical Bayes (Grant et al., 2018) to propose a mixture of hierarchical Bayesian models over the parameters of an arbitrary function approximator such as a neural network. Generalizing the model-agnostic meta-learning (MAML) algorithm (Finn et al., 2017), we present a stochastic expectation maximization procedure to jointly estimate parameter initializations for gradient descent as well as a latent assignment of tasks to initializations. This approach better captures the diversity of training tasks as opposed to consolidating inductive biases into a single set of hyperparameters. Our experiments demonstrate better generalization performance on the standard miniImageNet benchmark for 1-shot classification. We further derive a novel and scalable non-parametric variant of our method that captures the evolution of a task distribution over time as demonstrated on a set of few-shot regression tasks.
Model-based collaborative filtering analyzes user-item interactions to infer latent factors that represent user preferences and item characteristics in order to predict future interactions. Most collaborative filtering algorithms assume that these latent factors are static, although it has been shown that user preferences and item perceptions drift over time. In this paper, we propose a conjugate and numerically stable dynamic matrix factorization (DCPF) based on compound Poisson matrix factorization that models the smoothly drifting latent factors using Gamma-Markov chains. We propose a numerically stable Gamma chain construction, and then present a stochastic variational inference approach to estimate the parameters of our model. We apply our model to time-stamped ratings data sets: Netflix, Yelp, and Last.fm, where DCPF achieves a higher predictive accuracy than state-of-the-art static and dynamic factorization models.