During the past decade, machine learning algorithms have become commonplace in large-scale real-world industrial applications. In these settings, the computation time to train and test machine learning algorithms is a key consideration. At training-time the algorithms must scale to very large data set sizes.At testing-time, the cost of feature extraction can dominate the CPU runtime. Recently, a promising method was proposed to account for the feature extraction cost at testing time, called Cost-sensitive Tree of Classifiers (CSTC). Although the CSTC problem is NP-hard, the authors suggest an approximation through a mixed-norm relaxation across many classifiers. This relaxation is slow to train and requires involved optimization hyperparameter tuning. We propose a different relaxation using approximate submodularity, called Approximately Submodular Tree of Classifiers (ASTC). ASTC is much simpler to implement, yields equivalent results but requires no optimization hyperparameter tuning and is up to two orders of magnitude faster to train.

Bayesian optimization is a powerful framework for minimizing expensive objective functions while using very few function evaluations. It has been successfully applied to a variety of problems, including hyperparameter tuning and experimental design. However, this framework has not been extended to the inequality-constrained optimization setting, particularly the setting in which evaluating feasibility is just as expensive as evaluating the objective. Here we present constrained Bayesian optimization, which places a prior distribution on both the objective and the constraint functions. We evaluate our method on simulated and real data, demonstrating that constrained Bayesian optimization can quickly find optimal and feasible points, even when small feasible regions cause standard methods to fail.

A feature selection algorithm should ideally satisfy four conditions: reliably extract relevant features; be able to identify non-linear feature interactions; scale linearly with the number of features and dimensions; allow the incorporation of known sparsity structure. In this work we propose a novel feature selection algorithm, Gradient Boosted Feature Selection (GBFS), which satisfies all four of these requirements. The algorithm is flexible, scalable, and surprisingly straight-forward to implement as it is based on a modification of Gradient Boosted Trees. We evaluate GBFS on several real world data sets and show that it matches or outperforms other state of the art feature selection algorithms. Yet it scales to larger data set sizes and naturally allows for domain-specific side information.

Evaluation cost during test-time is becoming increasingly important as many real-world applications need fast evaluation (e.g. web search engines, email spam filtering) or use expensive features (e.g. medical diagnosis). We introduce Anytime Feature Representations (AFR), a novel algorithm that explicitly addresses this trade-off in the data representation rather than in the classifier. This enables us to turn conventional classifiers, in particular Support Vector Machines, into test-time cost sensitive anytime classifiers - combining the advantages of anytime learning and large-margin classification.

Recently, machine learning algorithms have successfully entered large-scale real-world industrial applications (e.g. search engines and email spam filters). Here, the CPU cost during test-time must be budgeted and accounted for. In this paper, we address the challenge of balancing test-time cost and the classifier accuracy in a principled fashion. The test-time cost of a classifier is often dominated by the computation required for feature extraction-which can vary drastically across features. We incorporate this extraction time by constructing a tree of classifiers, through which test inputs traverse along individual paths. Each path extracts different features and is optimized for a specific sub-partition of the input space. By only computing features for inputs that benefit from them the most, our cost-sensitive tree of classifiers can match the high accuracies of the current state-of-the-art at a small fraction of the computational cost.

In text mining, information retrieval, and machine learning, text documents are commonly represented through variants of sparse Bag of Words (sBoW) vectors (e.g. TF-IDF [1]). Although simple and intuitive, sBoW style representations suffer from their inherent over-sparsity and fail to capture word-level synonymy and polysemy. Especially when labeled data is limited (e.g. in document classification), or the text documents are short (e.g. emails or abstracts), many features are rarely observed within the training corpus. This leads to overfitting and reduced generalization accuracy. In this paper we propose Dense Cohort of Terms (dCoT), an unsupervised algorithm to learn improved sBoW document features. dCoT explicitly models absent words by removing and reconstructing random sub-sets of words in the unlabeled corpus. With this approach, dCoT learns to reconstruct frequent words from co-occurring infrequent words and maps the high dimensional sparse sBoW vectors into a low-dimensional dense representation. We show that the feature removal can be marginalized out and that the reconstruction can be solved for in closed-form. We demonstrate empirically, on several benchmark datasets, that dCoT features significantly improve the classification accuracy across several document classification tasks.