We present a new dataset for learning to solve, explain, and generate university-level STEM questions from 27 courses across a dozen departments in seven universities. We scale up previous approaches to questions from courses in the departments of Mechanical Engineering, Materials Science and Engineering, Chemistry, Electrical Engineering, Computer Science, Physics, Earth Atmospheric and Planetary Sciences, Economics, Mathematics, Biological Engineering, Data Systems, and Society, and Statistics. We visualize similarities and differences between questions across courses. We demonstrate that a large foundation model is able to generate questions that are as appropriate and at the same difficulty level as human-written questions.

Modern databases support queries that perform model inference (inference queries). Although powerful and widely used, inference queries are susceptible to incorrect results if the model is biased due to training data errors. Recently, prior work Rain proposed complaint-driven data debugging which uses user-specified errors in the output of inference queries (Complaints) to rank erroneous training examples that most likely caused the complaint. This can help users better interpret results and debug training sets. Rain combined influence analysis from the ML literature with relaxed query provenance polynomials from the DB literature to approximate the derivative of complaints w.r.t. training examples. Although effective, the runtime is O(|T|d), where T and d are the training set and model sizes, due to its reliance on the model's second order derivatives (the Hessian). On a Wide Resnet Network (WRN) model with 1.5 million parameters, it takes >1 minute to debug a complaint. We observe that most complaint debugging costs are independent of the complaint, and that modern models are overparameterized. In response, Rain++ uses precomputation techniques, based on non-trivial insights unique to data debugging, to reduce debugging latencies to a constant factor independent of model size. We also develop optimizations when the queried database is known apriori, and for standing queries over streaming databases. Combining these optimizations in Rain++ ensures interactive debugging latencies (~1ms) on models with millions of parameters.

One of the most exciting applications of modern artificial intelligence is to automatically discover scientific laws from experimental data. This is not a trivial problem as it involves searching for a complex mathematical relationship over a large set of explanatory variables and operators that can be combined in an infinite number of ways. Inspired by the incredible success of deep learning in computer vision, we tackle this problem by adapting various successful network architectures into the symbolic law discovery pipeline. The novelty of our approach is in (1) encoding the input data as an image with super-resolution, (2) developing an appropriate deep network pipeline, and (3) predicting the importance of each mathematical operator from the relationship image. This allows us to prior the exponentially large search with the predicted importance of the symbolic operators, which can significantly accelerate the discovery process. We apply our model to a variety of plausible relationships---both simulated and from physics and mathematics domains---involving different dimensions and constituents. We show that our model is able to identify the underlying operators from data, achieving a high accuracy and AUC (91% and 0.96 on average resp.) for systems with as many as ten independent variables. Our method significantly outperforms the current state of the art in terms of data fitting (R^2), discovery rate (recovering the true relationship), and succinctness (output formula complexity). The discovered equations can be seen as first drafts of scientific laws that can be helpful to the scientists for (1) hypothesis building, and (2) understanding the complex underlying structure of the studied phenomena. Our approach holds a real promise to help speed up the rate of scientific discovery.

Why do biased algorithmic predictions arise, and what interventions can prevent them? We examine this topic with a field experiment about using machine learning to predict human capital. We randomly assign approximately 400 AI engineers to develop software under different experimental conditions to predict standardized test scores of OECD residents. We then assess the resulting predictive algorithms using the realized test performances, and through randomized audit-like manipulations of algorithmic inputs. We also used the diversity of our subject population to measure whether demographically non-traditional engineers were more likely to notice and reduce algorithmic bias, and whether algorithmic prediction errors are correlated within programmer demographic groups. This document describes our experimental design and motivation; the full results of our experiment are available at https://ssrn.com/abstract=3615404.

Kernel regression or classification (also referred to as weighted $\epsilon$-NN methods in Machine Learning) are appealing for their simplicity and therefore ubiquitous in data analysis. However, practical implementations of kernel regression or classification consist of quantizing or sub- sampling data for improving time efficiency, often at the cost of prediction quality. While such tradeoffs are necessary in practice, their statistical implications are generally not well understood, hence practical implementations come with few performance guarantees. In particular, it is unclear whether it is possible to maintain the statistical accuracy of kernel prediction---crucial in some applications---while improving prediction time. The present work provides guiding principles for combining kernel prediction with data- quantization so as to guarantee good tradeoffs between prediction time and accuracy, and in particular so as to approximately maintain the good accuracy of vanilla kernel prediction. Furthermore, our tradeoff guarantees are worked out explicitly in terms of a tuning parameter which acts as a knob that favors either time or accuracy depending on practical needs. On one end of the knob, prediction time is of the same order as that of single -nearest-neighbor prediction (which is statistically inconsistent) while maintaining consistency; on the other end of the knob, the prediction risk is nearly minimax-optimal (in terms of the original data size) while still reducing time complexity. The analysis thus reveals the interaction between the data- quantization approach and the kernel prediction method, and most importantly gives explicit control of the tradeoff to the practitioner rather than fixing the tradeoff in advance or leaving it opaque. The theoretical results are validated on data from a range of real-world application domains; in particular we demonstrate that the theoretical knob performs as expected.

Metric learning seeks a transformation of the feature space that enhances prediction quality for a given task. In this work we provide PAC-style sample complexity rates for supervised metric learning. We give matching lower- and upper-bounds showing that sample complexity scales with the representation dimension when no assumptions are made about the underlying data distribution. In addition, by leveraging the structure of the data distribution, we provide rates fine-tuned to a specific notion of the intrinsic complexity of a given dataset, allowing us to relax the dependence on representation dimension. We show both theoretically and empirically that augmenting the metric learning optimization criterion with a simple norm-based regularization is important and can help adapt to a dataset’s intrinsic complexity yielding better generalization, thus partly explaining the empirical success of similar regularizations reported in previous works.

A key factor in a successful sensor network deployment is finding a good balance between maximizing the number of measurements taken (to maintain a good sampling rate) and minimizing the overall energy consumption (to extend the network lifetime). In this work, we present a data-driven statistical model to optimize this tradeoff. Our approach takes advantage of the multivariate nature of the data collected by a heterogeneous sensor network to learn spatio-temporal patterns. These patterns enable us to employ an aggressive duty cycling policy on the individual sensor nodes, thereby reducing the overall energy consumption. Our experiments with the OMNeT++ network simulator using realistic wireless channel conditions, on data collected from two real-world sensor networks, show that we can sample just 20% of the data and can reconstruct the remaining 80% of the data with less than 9% mean error, outperforming similar techniques such is distributed compressive sampling. In addition, energy savings ranging up to 76%, depending on the sampling rate and the hardware configuration of the node.

Categories in multi-class data are often part of an underlying semantic taxonomy. Recent work in object classification has found interesting ways to use this taxonomy structure to develop better recognition algorithms. Here we propose a novel framework to learn similarity metrics using the class taxonomy. We show that a nearest neighbor classifier using the learned metrics gets improved performance over the best discriminative methods. Moreover, by incorporating the taxonomy, our learned metrics can also help in some taxonomy specific applications. We show that the metrics can help determine the correct placement of a new category that was not part of the original taxonomy, and can provide effective classification amongst categories local to specific subtrees of the taxonomy.

We present a simple variant of the k-d tree which automatically adapts to intrinsic low dimensional structure in data.