Large language models (LLMs) are trained on a vast amount of human-written data, but data providers often remain uncredited. In response to this issue, data valuation (or data attribution), which quantifies the contribution or value of each data to the model output, has been discussed as a potential solution. Nevertheless, applying existing data valuation methods to recent LLMs and their vast training datasets has been largely limited by prohibitive compute and memory costs. In this work, we focus on influence functions, a popular gradient-based data valuation method, and significantly improve its scalability with an efficient gradient projection strategy called LoGra that leverages the gradient structure in backpropagation. We then provide a theoretical motivation of gradient projection approaches to influence functions to promote trust in the data valuation process. Lastly, we lower the barrier to implementing data valuation systems by introducing LogIX, a software package that can transform existing training code into data valuation code with minimal effort. In our data valuation experiments, LoGra achieves competitive accuracy against more expensive baselines while showing up to 6,500x improvement in throughput and 5x reduction in GPU memory usage when applied to Llama3-8B-Instruct and the 1B-token dataset.

Calibration of probabilistic forecasts in the regression setting has been widely studied in the single dimensional case, where the output variables are assumed to be univariate. In many problem settings, however, the output variables are multi-dimensional, and in the presence of dependence across the output dimensions, measuring calibration and performing recalibration for each dimension separately can be both misleading and detrimental. In this work, we focus on representing predictive uncertainties via samples, and propose a recalibration method which accounts for the joint distribution across output dimensions to produce calibrated samples. Based on the concept of highest density regions (HDR), we define the notion of HDR calibration, and show that our recalibration method produces samples which are HDR calibrated. We demonstrate the performance of our method and the quality of the recalibrated samples on a suite of benchmark datasets in multi-dimensional regression, a real-world dataset in modeling plasma dynamics during nuclear fusion reactions, and on a decision-making application in forecasting demand.

In a sequential regression setting, a decision-maker may be primarily concerned with whether the future observation will increase or decrease compared to the current one, rather than the actual value of the future observation. In this context, we introduce the notion of parity calibration, which captures the goal of calibrated forecasting for the increase-decrease (or “parity") event in a timeseries. Parity probabilities can be extracted from a forecasted distribution for the output, but we show that such a strategy leads to theoretical unpredictability and poor practical performance. We then observe that although the original task was regression, parity calibration can be expressed as binary calibration. Drawing on this connection, we use an online binary calibration method to achieve parity calibration. We demonstrate the effectiveness of our approach on real-world case studies in epidemiology, weather forecasting, and model-based control in nuclear fusion.

Among the many ways of quantifying uncertainty in a regression setting, specifying the full quantile function is attractive, as quantiles are amenable to interpretation and evaluation. A model that predicts the true conditional quantiles for each input, at all quantile levels, presents a correct and efficient representation of the underlying uncertainty. To achieve this, many current quantile-based methods focus on optimizing the pinball loss. However, this loss restricts the scope of applicable regression models, limits the ability to target many desirable properties (e.g. calibration, sharpness, centered intervals), and may produce poor conditional quantiles. In this work, we develop new quantile methods that address these shortcomings. In particular, we propose methods that can apply to any class of regression model, select an explicit balance between calibration and sharpness, optimize for calibration of centered intervals, and produce more accurate conditional quantiles. We provide a thorough experimental evaluation of our methods, which includes a high dimensional uncertainty quantification task in nuclear fusion.

In black-box optimization, an agent repeatedly chooses a configuration to test, so as to find an optimal configuration. In many practical problems of interest, one would like to optimize several systems, or tasks'', simultaneously; however, in most of these scenarios the current task is determined by nature. In this work, we explore theoffline'' case in which one is able to bypass nature and choose the next task to evaluate (e.g. via a simulator). Because some tasks may be easier to optimize and others may be more critical, it is crucial to leverage algorithms that not only consider which configurations to try next, but also which tasks to make evaluations for. In this work, we describe a theoretically grounded Bayesian optimization method to tackle this problem. We also demonstrate that if the model of the reward structure does a poor job of capturing variation in difficulty between tasks, then algorithms that actively pick tasks for evaluation may end up doing more harm than good. Following this, we show how our approach can be used for real world applications in science and engineering, including optimizing tokamak controls for nuclear fusion.