Toward Optimal Run Racing: Application to Deep Learning Calibration

This paper aims at one-shot learning of deep neural nets, where a highly parallel setting is considered to address the algorithm calibration problem - selecting the best neural architecture and learning hyper-parameter values depending on the dataset at hand. The notoriously expensive calibration problem is optimally reduced by detecting and early stopping non-optimal runs. The theoretical contribution regards the optimality guarantees within the multiple hypothesis testing framework. Experimentations on the Cifar10, PTB and Wiki benchmarks demonstrate the relevance of the approach with a principled and consistent improvement on the state of the art with no extra hyper-parameter

Generating Compact Tree Ensembles via Annealing

Tree ensembles are flexible predictive models that can capture relevant variables and to some extent their interactions in a compact and interpretable manner. Most algorithms for obtaining tree ensembles are based on versions of boosting or Random Forest. Previous work showed that boosting algorithms exhibit a cyclic behavior of selecting the same tree again and again due to the way the loss is optimized. At the same time, Random Forest is not based on loss optimization and obtains a more complex and less interpretable model. In this paper we present a novel method for obtaining compact tree ensembles by growing a large pool of trees in parallel with many independent boosting threads and then selecting a small subset and updating their leaf weights by loss optimization. We allow for the trees in the initial pool to have different depths which further helps with generalization. Experiments on real datasets show that the obtained model has usually a smaller loss than boosting, which is also reflected in a lower misclassification error on the test set.Comment: Comparison with Random Forest included in the results sectio

Learning to predict under a budget

Prediction-time budgets in machine learning applications can arise due to monetary or computational costs associated with acquiring information; they also arise due to latency and power consumption costs in evaluating increasingly more complex models. The goal in such budgeted prediction problems is to learn decision systems that maintain high prediction accuracy while meeting average cost constraints during prediction-time. Such decision systems can potentially adapt to the input examples, predicting most of them at low cost while allocating more budget for the few "hard" examples. In this thesis, I will present several learning methods to better trade-off cost and error during prediction. The conceptual contribution of this thesis is to develop a new paradigm of bottom-up approach instead of the traditional top-down approach. A top-down approach attempts to build out the model by selectively adding the most cost-effective features to improve accuracy. In contrast, a bottom-up approach first learns a highly accurate model and then prunes or adaptively approximates it to trade-off cost and error. Training top-down models in case of feature acquisition costs leads to fundamental combinatorial issues in multi-stage search over all feature subsets. In contrast, we show that the bottom-up methods bypass many of such issues. To develop this theme, we first propose two top-down methods and then two bottom-up methods. The first top-down method uses margin information from training data in the partial feature neighborhood of a test point to either select the next best feature in a greedy fashion or to stop and make prediction. The second top-down method is a variant of random forest (RF) algorithm. We grow decision trees with low acquisition cost and high strength based on greedy mini-max cost-weighted impurity splits. Theoretically, we establish near-optimal acquisition cost guarantees for our algorithm. The first bottom-up method we propose is based on pruning RFs to optimize expected feature cost and accuracy. Given a RF as input, we pose pruning as a novel 0-1 integer program and show that it can be solved exactly via LP relaxation. We further develop a fast primal-dual algorithm that scales to large datasets. The second bottom-up method is adaptive approximation, which significantly generalizes the RF pruning to accommodate more models and other types of costs besides feature acquisition cost. We first train a high-accuracy, high-cost model. We then jointly learn a low-cost gating function together with a low-cost prediction model to adaptively approximate the high-cost model. The gating function identifies the regions of the input space where the low-cost model suffices for making highly accurate predictions. We demonstrate empirical performance of these methods and compare them to the state-of-the-arts. Finally, we study adaptive approximation in the on-line setting to obtain regret guarantees and discuss future work.2019-07-02T00:00:00