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Though black-box predictors are state-of-the-art for many complex tasks, they often fail to properly quantify predictive uncertainty and may provide inappropriate predictions for unfamiliar data. Instead, we can learn more reliable models by letting them either output a prediction set or abstain when the uncertainty is high. We propose training these selective prediction-set models using an uncertainty-aware loss minimization framework, which unifies ideas from decision theory and robust maximum likelihood. Moreover, since black-box methods are not guaranteed to output well-calibrated prediction sets, we show how to calculate point estimates and confidence intervals for the true coverage of any selective prediction-set model, as well as a uniform mixture of K set models obtained from K-fold sample-splitting. When applied to predicting in-hospital mortality and length-of-stay for ICU patients, our model outperforms existing approaches on both in-sample and out-of-sample age groups, and our recalibration method provides accurate inference for prediction set coverage.
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Conformal prediction constructs a confidence set for an unobserved response of a feature vector based on previous identically distributed and exchangeable observations of responses and features. It has a coverage guarantee at any nominal level without additional assumptions on their distribution. Its computation deplorably requires a refitting procedure for all replacement candidates of the target response. In regression settings, this corresponds to an infinite number of model fit. Apart from relatively simple estimators that can be written as pieces of linear function of the response, efficiently computing such sets is difficult and is still considered as an open problem. We exploit the fact that, emph{often}, conformal prediction sets are intervals whose boundaries can be efficiently approximated by classical root-finding algorithm. We investigate how this approach can overcome many limitations of formerly used strategies and we discuss its complexity and drawbacks.
Meta-learning can successfully acquire useful inductive biases from data. Yet, its generalization properties to unseen learning tasks are poorly understood. Particularly if the number of meta-training tasks is small, this raises concerns about overfitting. We provide a theoretical analysis using the PAC-Bayesian framework and derive novel generalization bounds for meta-learning. Using these bounds, we develop a class of PAC-optimal meta-learning algorithms with performance guarantees and a principled meta-level regularization. Unlike previous PAC-Bayesian meta-learners, our method results in a standard stochastic optimization problem which can be solved efficiently and scales well. When instantiating our PAC-optimal hyper-posterior (PACOH) with Gaussian processes and Bayesian Neural Networks as base learners, the resulting methods yield state-of-the-art performance, both in terms of predictive accuracy and the quality of uncertainty estimates. Thanks to their principled treatment of uncertainty, our meta-learners can also be successfully employed for sequential decision problems.
Supervised classification techniques use training samples to find classification rules with small expected 0-1 loss. Conventional methods achieve efficient learning and out-of-sample generalization by minimizing surrogate losses over specific families of rules. This paper presents minimax risk classifiers (MRCs) that do not rely on a choice of surrogate loss and family of rules. MRCs achieve efficient learning and out-of-sample generalization by minimizing worst-case expected 0-1 loss w.r.t. uncertainty sets that are defined by linear constraints and include the true underlying distribution. In addition, MRCs learning stage provides performance guarantees as lower and upper tight bounds for expected 0-1 loss. We also present MRCs finite-sample generalization bounds in terms of training size and smallest minimax risk, and show their competitive classification performance w.r.t. state-of-the-art techniques using benchmark datasets.
We present a framework to train a structured prediction model by performing smoothing on the inference algorithm it builds upon. Smoothing overcomes the non-smoothness inherent to the maximum margin structured prediction objective, and paves the way for the use of fast primal gradient-based optimization algorithms. We illustrate the proposed framework by developing a novel primal incremental optimization algorithm for the structural support vector machine. The proposed algorithm blends an extrapolation scheme for acceleration and an adaptive smoothing scheme and builds upon the stochastic variance-reduced gradient algorithm. We establish its worst-case global complexity bound and study several practical variants, including extensions to deep structured prediction. We present experimental results on two real-world problems, namely named entity recognition and visual object localization. The experimental results show that the proposed framework allows us to build upon efficient inference algorithms to develop large-scale optimization algorithms for structured prediction which can achieve competitive performance on the two real-world problems.
We propose a practical Bayesian optimization method over sets, to minimize a black-box function that takes a set as a single input. Because set inputs are permutation-invariant, traditional Gaussian process-based Bayesian optimization strategies which assume vector inputs can fall short. To address this, we develop a Bayesian optimization method with emph{set kernel} that is used to build surrogate functions. This kernel accumulates similarity over set elements to enforce permutation-invariance, but this comes at a greater computational cost. To reduce this burden, we propose two key components: (i) a more efficient approximate set kernel which is still positive-definite and is an unbiased estimator of the true set kernel with upper-bounded variance in terms of the number of subsamples, (ii) a constrained acquisition function optimization over sets, which uses symmetry of the feasible region that defines a set input. Finally, we present several numerical experiments which demonstrate that our method outperforms other methods.
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