SketchySGD: Reliable Stochastic Optimization via Robust Curvature Estimates

We introduce SketchySGD, a stochastic quasi-Newton method that uses sketching to approximate the curvature of the loss function. Quasi-Newton methods are among the most effective algorithms in traditional optimization, where they converge much faster than first-order methods such as SGD. However, for contemporary deep learning, quasi-Newton methods are considered inferior to first-order methods like SGD and Adam owing to higher per-iteration complexity and fragility due to inexact gradients. SketchySGD circumvents these issues by a novel combination of subsampling, randomized low-rank approximation, and dynamic regularization. In the convex case, we show SketchySGD with a fixed stepsize converges to a small ball around the optimum at a faster rate than SGD. In the non-convex case, SketchySGD converges linearly under two additional assumptions, interpolation and the Polyak-Lojaciewicz condition, the latter of which holds with high probability for wide neural networks. Numerical experiments on image and tabular data demonstrate the improved reliability and speed of SketchySGD for deep learning, compared to standard optimizers such as SGD and Adam and existing quasi-Newton methods.

ControlBurn: Nonlinear Feature Selection with Sparse Tree Ensembles

ControlBurn is a Python package to construct feature-sparse tree ensembles that support nonlinear feature selection and interpretable machine learning. The algorithms in this package first build large tree ensembles that prioritize basis functions with few features and then select a feature-sparse subset of these basis functions using a weighted lasso optimization criterion. The package includes visualizations to analyze the features selected by the ensemble and their impact on predictions. Hence ControlBurn offers the accuracy and flexibility of tree-ensemble models and the interpretability of sparse generalized additive models. ControlBurn is scalable and flexible: for example, it can use warm-start continuation to compute the regularization path (prediction error for any number of selected features) for a dataset with tens of thousands of samples and hundreds of features in seconds. For larger datasets, the runtime scales linearly in the number of samples and features (up to a log factor), and the package support acceleration using sketching. Moreover, the ControlBurn framework accommodates feature costs, feature groupings, and $\ell_0$-based regularizers. The package is user-friendly and open-source: its documentation and source code appear on https://pypi.org/project/ControlBurn/ and https://github.com/udellgroup/controlburn/.

Resource-Constrained Neural Architecture Search on Tabular Datasets

The best neural architecture for a given machine learning problem depends on many factors: not only the complexity and structure of the dataset, but also on resource constraints including latency, compute, energy consumption, etc. Neural architecture search (NAS) for tabular datasets is an important but under-explored problem. Previous NAS algorithms designed for image search spaces incorporate resource constraints directly into the reinforcement learning rewards. In this paper, we argue that search spaces for tabular NAS pose considerable challenges for these existing reward-shaping methods, and propose a new reinforcement learning (RL) controller to address these challenges. Motivated by rejection sampling, when we sample candidate architectures during a search, we immediately discard any architecture that violates our resource constraints. We use a Monte-Carlo-based correction to our RL policy gradient update to account for this extra filtering step. Results on several tabular datasets show TabNAS, the proposed approach, efficiently finds high-quality models that satisfy the given resource constraints.

Data-Efficient and Interpretable Tabular Anomaly Detection

Anomaly detection (AD) plays an important role in numerous applications. We focus on two understudied aspects of AD that are critical for integration into real-world applications. First, most AD methods cannot incorporate labeled data that are often available in practice in small quantities and can be crucial to achieve high AD accuracy. Second, most AD methods are not interpretable, a bottleneck that prevents stakeholders from understanding the reason behind the anomalies. In this paper, we propose a novel AD framework that adapts a white-box model class, Generalized Additive Models, to detect anomalies using a partial identification objective which naturally handles noisy or heterogeneous features. In addition, the proposed framework, DIAD, can incorporate a small amount of labeled data to further boost anomaly detection performances in semi-supervised settings. We demonstrate the superiority of our framework compared to previous work in both unsupervised and semi-supervised settings using diverse tabular datasets. For example, under 5 labeled anomalies DIAD improves from 86.2\% to 89.4\% AUC by learning AD from unlabeled data. We also present insightful interpretations that explain why DIAD deems certain samples as anomalies.

Towards Group Robustness in the presence of Partial Group Labels

Learning invariant representations is an important requirement when training machine learning models that are driven by spurious correlations in the datasets. These spurious correlations, between input samples and the target labels, wrongly direct the neural network predictions resulting in poor performance on certain groups, especially the minority groups. Robust training against these spurious correlations requires the knowledge of group membership for every sample. Such a requirement is impractical in situations where the data labeling efforts for minority or rare groups are significantly laborious or where the individuals comprising the dataset choose to conceal sensitive information. On the other hand, the presence of such data collection efforts results in datasets that contain partially labeled group information. Recent works have tackled the fully unsupervised scenario where no labels for groups are available. Thus, we aim to fill the missing gap in the literature by tackling a more realistic setting that can leverage partially available sensitive or group information during training. First, we construct a constraint set and derive a high probability bound for the group assignment to belong to the set. Second, we propose an algorithm that optimizes for the worst-off group assignments from the constraint set. Through experiments on image and tabular datasets, we show improvements in the minority group's performance while preserving overall aggregate accuracy across groups.

Can we globally optimize cross-validation loss? Quasiconvexity in ridge regression

Models like LASSO and ridge regression are extensively used in practice due to their interpretability, ease of use, and strong theoretical guarantees. Cross-validation (CV) is widely used for hyperparameter tuning in these models, but do practical optimization methods minimize the true out-of-sample loss? A recent line of research promises to show that the optimum of the CV loss matches the optimum of the out-of-sample loss (possibly after simple corrections). It remains to show how tractable it is to minimize the CV loss. In the present paper, we show that, in the case of ridge regression, the CV loss may fail to be quasiconvex and thus may have multiple local optima. We can guarantee that the CV loss is quasiconvex in at least one case: when the spectrum of the covariate matrix is nearly flat and the noise in the observed responses is not too high. More generally, we show that quasiconvexity status is independent of many properties of the observed data (response norm, covariate-matrix right singular vectors and singular-value scaling) and has a complex dependence on the few that remain. We empirically confirm our theory using simulated experiments.

ControlBurn: Feature Selection by Sparse Forests

Tree ensembles distribute feature importance evenly amongst groups of correlated features. The average feature ranking of the correlated group is suppressed, which reduces interpretability and complicates feature selection. In this paper we present ControlBurn, a feature selection algorithm that uses a weighted LASSO-based feature selection method to prune unnecessary features from tree ensembles, just as low-intensity fire reduces overgrown vegetation. Like the linear LASSO, ControlBurn assigns all the feature importance of a correlated group of features to a single feature. Moreover, the algorithm is efficient and only requires a single training iteration to run, unlike iterative wrapper-based feature selection methods. We show that ControlBurn performs substantially better than feature selection methods with comparable computational costs on datasets with correlated features.

Privileged Zero-Shot AutoML

This work improves the quality of automated machine learning (AutoML) systems by using dataset and function descriptions while significantly decreasing computation time from minutes to milliseconds by using a zero-shot approach. Given a new dataset and a well-defined machine learning task, humans begin by reading a description of the dataset and documentation for the algorithms to be used. This work is the first to use these textual descriptions, which we call privileged information, for AutoML. We use a pre-trained Transformer model to process the privileged text and demonstrate that using this information improves AutoML performance. Thus, our approach leverages the progress of unsupervised representation learning in natural language processing to provide a significant boost to AutoML. We demonstrate that using only textual descriptions of the data and functions achieves reasonable classification performance, and adding textual descriptions to data meta-features improves classification across tabular datasets. To achieve zero-shot AutoML we train a graph neural network with these description embeddings and the data meta-features. Each node represents a training dataset, which we use to predict the best machine learning pipeline for a new test dataset in a zero-shot fashion. Our zero-shot approach rapidly predicts a high-quality pipeline for a supervised learning task and dataset. In contrast, most AutoML systems require tens or hundreds of pipeline evaluations. We show that zero-shot AutoML reduces running and prediction times from minutes to milliseconds, consistently across datasets. By speeding up AutoML by orders of magnitude this work demonstrates real-time AutoML.

How Low Can We Go: Trading Memory for Error in Low-Precision Training

Low-precision arithmetic trains deep learning models using less energy, less memory and less time. However, we pay a price for the savings: lower precision may yield larger round-off error and hence larger prediction error. As applications proliferate, users must choose which precision to use to train a new model, and chip manufacturers must decide which precisions to manufacture. We view these precision choices as a hyperparameter tuning problem, and borrow ideas from meta-learning to learn the tradeoff between memory and error. In this paper, we introduce Pareto Estimation to Pick the Perfect Precision (PEPPP). We use matrix factorization to find non-dominated configurations (the Pareto frontier) with a limited number of network evaluations. For any given memory budget, the precision that minimizes error is a point on this frontier. Practitioners can use the frontier to trade memory for error and choose the best precision for their goals.

Tensor Random Projection for Low Memory Dimension Reduction

Random projections reduce the dimension of a set of vectors while preserving structural information, such as distances between vectors in the set. This paper proposes a novel use of row-product random matrices in random projection, where we call it Tensor Random Projection (TRP). It requires substantially less memory than existing dimension reduction maps. The TRP map is formed as the Khatri-Rao product of several smaller random projections, and is compatible with any base random projection including sparse maps, which enable dimension reduction with very low query cost and no floating point operations. We also develop a reduced variance extension. We provide a theoretical analysis of the bias and variance of the TRP, and a non-asymptotic error analysis for a TRP composed of two smaller maps. Experiments on both synthetic and MNIST data show that our method performs as well as conventional methods with substantially less storage.